CFA Level I: Portfolio Management
Capital Asset Pricing Model (CAPM) : Practical Considerations
1. 70% of executives use capm to calculate their cost of equity capital 2. Best model / most widely accepted for costing equity capital 3. For sure doesn't work in practice for portfolio planning, there are other better models
Financial Risks Include: (3 main)
1. Credit Risk: counterparties might not fulfill obligations 2. Liquidity Risk: may receive less than fair value at sale 3. Market Risk: uncertainty about asset prices and interest rates, etc.
5 Common Types of Investment Screening:
1. Negative Screening 2. Best-in-Class (positive screening) 3. Shareholder Engagement (voting rights structure) 4. Thematic Investing (impact investing) 5. ESG
2 reasons for asset class actual weights to deviate from policy weights:
1. Tactical asset allocation or market timing (By deliberate choice) 2. Drift (As a result of divergence of the returns of the different asset classes)
Conditional Value at Risk (CVaR)
: a tail loss measure. : weighted average of all loss outcomes in the statistical distribution that exceed the VaR loss. Conditional VaR: Expected value of loss, given that loss exceeds specific amount i.e. given that we are in the extreme tail of the distribution and an extreme outcome is occurring. ↳ example = Given that we are in one of those months where we will lose $1 Million, what is the expected loss during that month?" ↳ Note: by definition, the expected loss must be greater than $1 Million, because VaR is saying "at least a loss of $1 Million". ↳ Harder to calculate Conditional VaR
Managing Risks: Self-Insuring
: the notion of bearing a risk that is considered undesirable but too costly to eliminate by external means. In some cases, self-insuring means simply to bear the risk. In other cases, it may involve the establishment of a reserve to cover losses. Example: : setting aside money to use in event of loss or injury
Indifference Curves + Capital Allocation Line
Combine the two to select which portfolio combination provides the adequate risk/return profile for each investor. Want to choose the indifference curve with the highest possible CAL (depending on the risk aversion of each investor) : points below CAL not preferable : points above CAL not attainable
How are commissions on trades and other execution fees used when calculating Gross & Net Return?
Commissions on trades and other costs that are necessary to generate the investment returns are deducted in both gross and net return measures.
Institutional Investors: Endowment Fund
Investment Objective: - to provide financial support for a specific purpose on an ongoing basis. Common Investment Characteristics: - long investment horizons - high risk tolerance - pre-planned annual spending needs - little need for additional liquidity For example, in the United States, many universities have large endowment funds to support their programs.
Bond Mutual Funds
Mutual funds that invest primarily in bonds and occasionally preferred shares. Characteristics: - NAV = total bond value / # of shares - Differentiated by bond maturities - Differentiated by credit ratings - Differentiated by issuers - Differentiated by issuer types Examples include government bond funds, tax-exempt bond funds, high-yield (lower rated corporate) bond funds, and global bond funds.
Active Investment Strategy (Active Portfolio Management)
Many investors and portfolio managers believe their estimates of security values are correct and market prices are incorrect. Such investors will not use the weights of the market portfolio but will invest more than the market weights in securities that they believe are undervalued and less than the market weights in securities which they believe are overvalued.
Portfolio Perspective
Evaluating individual securities by their contribution to the risk and return characteristics of the whole portfolio. - Portfolios affect risk more than returns. - Adding a risky asset can actually reduce portfolio risk
Institutional Investors: Banks
Investment Objective: - invest excess reserves - to earn more on loans and investments than the bank pays for deposits of various types. Common Investment Characteristics: - very short-duration fixed-income investments - very short-duration money market securities - keep risk low - need adequate liquidity to meet investor withdrawals
Indifference Curve
plots the combinations of risk-return pairs that an investor would accept to maintain a given level of utility (i.e., the investor is indifferent about the combinations on any one curve because they would provide the same level of overall utility). Indifference curves are thus defined in terms of a trade-off between expected rate of return and variance of the rate of return. Because an infinite number of combinations of risk and return can generate the same utility for the same investor, indifference curves are continuous at all points.
Risk + Return for US Asset Classes by Decade
see attached. Major Asset Classes: 1. Stocks (large cap v. small cap) 2. Bonds (long term: gov't v. corp.) 3. Treasury Bills (short term)
Two Fund Separation Theorem
states that all investors' optimum portfolios will be made up of some combination of an optimal portfolio of risky assets and the risk-free asset.
Single + Multi Period, Holding Period Return (HPR) aka Total Return
the % increase in the value of an investment over a given time period; a synonym for total return. Single Period HPR (%) = (Pₜ - P₀ + Divₜ) / P₀ where; Pₜ = price at time t P₀ = price at time 0 Divₜ = dividend or interest payment at time t Multi-Period HPR (%) = [(1 + R₁) × (1 + R₂) × (1 + Rₙ)] - 1 where; R₁ = year 1 annual return R₂ = year 2 annual return Rₙ = year n annual return
Investment Objectives (IPS) + Capital Market Expectations =
the strategic asset allocation that is expected to allow the client to achieve his or her investment objectives (at least under normal capital market conditions).
the CAPM and the SML are functions that give an indication of...
what the return in the market should be, given a certain level of risk. The actual return may be quite different from the expected return.
Institutional Investors: Defined Benefit Pension Plan
Plans in which the company promises to pay a certain annual amount (defined benefit) to the employee after retirement. Because the employee's future benefit is defined, the employer assumes the investment risk. The employer makes contributions to a fund established to provide the promised future benefits. Poor investment performance will increase the amount of required employer contributions to the fund. Example: Plan: An employee might earn a retirement benefit of 2% of her final salary for each year of service. Employee Data: - years of service = 20 yrs. - final year salary = $100,000 Benefit Calculation: = $100,000 final salary × 2% × 20 years of service = $40,000 per year from retirement until death
Sentiment Indicators: Main US Based Opinion Polls
Polls of investment professionals: 1. Investors Intelligence Advisors Sentiment reports 2. Market Vane Bullish Consensus 3. Consensus Bullish Sentiment Index 4. Daily Sentiment Index Polls of individual investors: 1. American Association of Individual Investors (AAII) Barrons magazine publishes parts of 4 of these on a weekly basis. To gauge a survey's usefulness in predicting major market turns, the survey must have been published over several cycles, and each of the surveys mentioned here, based on US data, has been available for several decades.
Variance Formula σ² (sample + population)
Population Variance σ² = [(r₁ - μ)² + (r₂ - μ)² + (rₜ - μ)²] / n Sample Variance (most common) s² = [(r₁ - x̄ )² + (r₂ - x̄ )² + (rₜ - x̄ )²] / (n - 1) where; rₜ = return in period t μ = population mean x̄ = sample mean n = number of periods
Portfolio Diversification Works Best/Worst when...
Portfolio diversification works best when financial markets are operating normally; Portfolio diversification provides less reduction of risk during market turmoil, such as the credit contagion of 2008. During periods of financial crisis, correlations tend to increase, which reduces the benefits of diversification.
Because annual inflation rates can vary greatly, comparisons across various time periods is difficult and misleading using nominal returns. Therefore, it is more effective to rely on?
Real Returns : minus inflation
Pre-Tax Nominal Returns (impact of taxes)
Return prior to paying taxes. In general, all returns are pre-tax nominal returns unless they are otherwise designated. Pre-Tax Nominal Returns Measures Include: 1) Gross Return 2) Net Return 3) HPR 4) Average Return : Dividend income, interest income, short-term capital gains, and long-term capital gains may all be taxed at different rates, thus are considered pre-tax nominal returns.
Leveraged Return
Return to an investor that is a multiple of the return on the underlying asset. The leveraged return is calculated as the gain or loss on the investment as a percentage of an investor's cash investment.
What is generally a key reason for the differentiation between active and passive management?
Risk budgeting implies that the portfolio manager has to choose, for every asset class, whether to deploy security selection as a return generator. This choice is generally referred to as the choice between active or passive management
Fama French 3 Factor Model
Risk factors are: • Firm size • Book-to-market ratio • Excess return on the market portfolio E(Rᵢ) = Rf + βᵢ,₁E(Fs) + βᵢ,₂E(Bm) + ... βᵢ,ₖE(MRp) where; E(Rᵢ) = expected return of asset i Rf = risk-free rate of return βᵢ,₁ = betas are the factor sensitivities or factor loadings of the asset given each risk factor E(Fs) = expected value of firm size E(Bm) = expected value of book to market ratio E(MRp) = expected value of market risk premium Carhart added a 4th factor, momentum. These models explain US equity returns better than the market (single-index) model
Time Weighted vs. Money Weighted Return
The time-weighted rate of return is the preferred performance measure when analyzing investment managers as it neutralizes the effect of cash withdrawals or additions to the portfolio, which are generally outside of the control of the portfolio manager.
2. Execution Step: Security Analysis
The top-down view can be combined with the bottom-up insights to assess the expected level of cash flows and risk of the cash flows that each security will produce. - Allows analysts to assign valuations to securities - Allows analysts to identify preferred investments
Utility Formula
Utility theory allows us to quantify the rankings of investment choices using risk and return. U = E(r) - 1/2 Aσ² where; U = utility of an investment E(r) = expected return A = marginal reward an investor requires to accept additional risk σ2 = variance of the investment Note Re: "A" in Equation: More risk-averse investors require greater compensation for accepting additional risk. Thus, A is higher for more risk-averse individuals.
the returns of an investment strategy depend on which 3 factors?
1. Systematic Risk 2. Tactical Asset Allocation 3. Security Selection
Liquidity is a major concern in which 2 markets?
1. emerging markets 2. high yield corporate bonds
The Feedback Step
Consists of 2 parts: 1. Portfolio monitoring and rebalancing 2. Performance measurement and reporting
Separately Managed Account (SMA) aka "Wrap Account"
(SMA) An investment portfolio managed exclusively for the benefit of an individual or institution. - high minimum investment required : $100K - $500K required - usually institutional and high net-worth individuals
the greatest portfolio risk results when the correlation between asset returns is:
+1. For any value of correlation less than +1, portfolio variance is reduced. : when correlation = 0, the entire third term in the portfolio variance equation is zero. : For negative values of correlation ρ₁,₂, the third term becomes negative and further reduces portfolio variance and standard deviation. Generally: The lower the correlation of asset returns, the greater the risk reduction (diversification) benefit of combining assets in a portfolio. If asset returns were perfectly negatively correlated, portfolio risk could be eliminated altogether for a specific set of asset weights.
Kondratieff Cycles (waves)
- 50 (54) year economic cycles of 25 years of boom and 25 years of bust - driven by the life cycle of products - operate in a form similar to traditional business cycles - economic activity and commodity prices
Exchange Traded Funds (ETFs)
- Typically index funds - Trade like shares of closed end funds - Structured like open end funds - Can be shorted and used margin - Dividends typically paid out - market price usually closed to NAV due to in-kind purchases/redemptions by authorized participants, essentially arbitrage by market maker, broker : major difference from closed-end funds - Sometimes have tax advantage over open end funds
Geometric Mean
- a compound annual rate - When periodic rates of return vary, geo mean < mean - provides a more accurate representation of the growth in portfolio value over a given time period than does an arithmetic mean return Geo Mean = ⁿ√(1 + R₁) × (1 + R₂) × (1 + R₃) × (1 + Rₙ) - 1 where; n = # of periods R₁ = year 1 annual return R₂ = year 2 annual return Rₙ = year n annual return Example: An investor purchased $1,000 of a mutual fund's shares. The fund had the following total returns over a 3-year period: +5%, -8%, +12%. Calculate the value at the end of the 3-year period, the holding period return, the mean annual return, and the geometric mean annual return. : End Value = 1081.92 : HPR = 8.19% : Mean Annual Return = 3% : Geometric Mean Annual Return = 2.66%
Time-Weighted Return (TWR)
1 Year TWR = [(1 + HPR₁)(1 + HPR₂)...(1 + HPRₙ)] - 1 Multi-YrTWR = [(1 + HPR₁)(1 + HPR₂)...(1 + HPRₙ)]¹/ʸʳˢ - 1 If the total investment period is greater than one year, you must take the geometric mean of the measurement period return to find the annual time-weighted rate of return. Annualized TWR = [(ev₁/bv₁)(ev₂/bv₂)...(evₙ/bvₙ)]¹/ʸʳˢ - 1 where; ev = end value bv = beginning value annual TWR essentially geometric average, weighted by time. : Annual time weighted returns are effective annual compound returns : Measures the compound rate of growth of $1 initially invested in the portfolio over a stated measurement period. : Neutralizes the effect of cash withdrawals or additions : periods can be any length Major Use: For the evaluation of portfolios of publicly traded securities, the time-weighted rate of return is the preferred performance measure as it neutralizes the effect of cash withdrawals or additions to the portfolio, which are generally outside of the control of the portfolio manager.
In evaluating investments using only the mean (expected return) and variance (risk), we are implicitly making two important assumptions:
1) that the returns are normally distributed and can be fully characterized by their means and variances and 2) that markets are not only informationally efficient but that they are also operationally efficient. To the extent that these assumptions are violated, we need to consider additional investment characteristics, including: 1. Distributional Characteristics : skewness : kurtosis Using only mean and variance would be appropriate to evaluate investments if returns were distributed normally. Returns, however, are not normally distributed; deviations from normality occur both because the returns are skewed, which means they are not symmetric around the mean, and because the probability of extreme events is significantly greater than what a normal distribution would suggest.
2 General Types of Risk Objectives of Investors:
1. Absolute Risk Objectives : can be stated in nominal or real return terms : can be stated as probability of specific results : "not decrease in value by more than 2% at any point over any 12-month period." : "No greater than a 5% probability of returns below -5% in any 12-month period." : "return of 3% more than annual inflation rate per year." 2. Relative Risk Objectives : relate to a specific benchmark : may be relative to the liabilities of investor, org., etc. : relative to peers is not "investible" beforehand because you don't know the strategy of the peers beforehand. : "Returns will not be less than 12-month euro LIBOR over any 12-month period," : "Exceed return on the S&P 500 by 2% per annum." : "No greater than a 5% probability of returns more than 4% below the return on the MSCI World Index over any 12-month period."
2 Limitations of Sharpe & Treynor Ratios
1. Both do not give any economic significance in their results, meaning a Sharpe Ratio of 0.8 is better than a Sharpe Ratio of 0.5, but how much more meaningful is the result? Neither ratio provides any economic significance. 2. Both do not give any indication of performance relative to the performance of the passive portfolio. M² and Jensen's alpha, attempt to address these problems by comparing portfolios while also providing information about the extent of the over performance or under performance.
why do investors still often subdivide equities?
1. Decomposition into smaller asset classes corresponds to the way the asset allocation is structured in portfolios. 2. Many investment managers have expertise exclusively in specific areas of the market, such as emerging market equities, US small-cap equity, or international investment-grade credit. 3. Bringing the asset class definitions of the asset allocation in line with investment products actually available in the market may simplify matters from an organizational perspective.
Institutional Investors include:
1. Defined Benefit Pension Plans 2. Endowments and Foundations 3. Banks 4. Insurance Companies 5. Investment Companies 6. Sovereign Wealth Funds Each of these has unique goals, asset allocation preferences, and investment strategy needs.
"The Greeks": Risk Measures for Derivatives
1. Delta: sensitivity of derivative value to price of underlying : only captures small changes in value of underlying, large changes are better captured by gamma. : perhaps most important measure of derivatives risk : a first-order risk measure 2. Gamma: sensitivity of delta to price of underlying asset : a second-order risk : A numerical measure of how sensitive an option's delta (the sensitivity of the derivative's price) is to a change in the value of the underlying. 3. Vega: (options) sensitivity of derivative value to volatility of underlying : a first-order risk measure 4. Rho: (options) sensitivity of derivative value to risk-free rate : a first order risk measure
Objectives of Risk Management (3 parts)
1. Determine an organizations risk tolerance 2. Identify and measure an organizations risks 3. Monitor and modify risks Risk management does not seek to avoid or minimize risks but to identify which risks an organization is best able to take on
Avenues for Diversification
1. Diversify with asset classes 2. Diversify with index funds 3. Diversification among countries 4. Diversify by not owning your employer's stock 5. Evaluate each asset before adding to a portfolio 6. Buy insurance for risky portfolios
Capital Asset Pricing Model (CAPM): Applications of the CAPM
1. Estimates of Expected Return (and Required Return) MAJOR USE a. CAPM is used to establish required rate of return (i.e. discount rate), which is used for asset pricing (gordon growth model), NPV models, etc. This is a major use of CAPM, to establish the RRR. b. used for capital budgeting (NPV) c. cost of capital calculations for corporate debt 2. Performance Appraisal : comparing actual portfolio return with CAPM return 3. Security Selection Analysis : analysis of alternate return estimates and the CAPM returns as the basis for security selection.
Price Based Technical Indicators
1. Moving Average Lines : 20-day (monthly) & 60 day (quarterly) are common : used to determine support and resistance. : uptrends = price above moving average = support line : downtrend = price below moving average = resistance : moving-average crossovers as a buy or sell signal ↳ short cross long from underneath = bullish ↳ short cross long from above = bearish 2. Bollinger Bands (see bollinger band notecard)
Robo-Advisor Growth due to 3 Key Trends
1. Growing demand from "mass affluent" and younger investors. 2. Lower fees: The cost of digital investment advice provided by robo-advisers is often a fraction of traditional investment advice channels because of scalability. For example, in the United States, a typical financial adviser may charge a 1% annual advisory fee based on a client's assets, while robo-adviser fees typically average 0.20% annually. Additionally, robo-advisers often rely on lower fee underlying portfolio investment options, such as index funds or ETFs, when constructing portfolios for clients. 3. New entrants: Reflecting low barriers to entry, large wealth management firms have introduced robo-adviser solutions to service certain customer segments and appeal to a new generation of investors. In addition to these large wealth managers, other less-traditional entrants, such as insurance companies and asset managers, are developing solutions to cross-sell into their existing clients. Many market observers expect that non-financial firms (large technology leaders) will also become key players in the robo-adviser industry as they look to monetize their access to user data.
3 Key Asset Management Industry Trends
1. Growth of Passive Investing : due to lower fees passive managers charge investors : due to questions about probability of material risk-adjusted returns in increasingly efficient markets (i.e. large cap equity) 2. "Big Data" in the Investment Process : structured data (i.e. order book, returns data) : unstructured data (i.e. compiled search/scrape data) : statistical modeling - algorithms : machine learning (fundamental + quant. analysis) : social media data (sentiment + inv. trends) : imagery + sensory data (conditions + movement) 3. Emergence of Robo-Advisers : tech solutions via automation + investment algorithms : provide wealth management services—notably, investment planning, asset allocation, tax loss harvesting, and investment strategy selection. : offer investors advice and recommendations aligned with general investment goals and risk tolerance preferences (often obtained from an investor questionnaire). : range from exclusively digital investment advice platforms to hybrid offerings that offer both digital investment advice and the services of a human financial adviser.
Reversal Patterns (insights and price target formulas)
1. Head and Shoulders : once the neckline is breached, the security is expected to decline by the same amount as the change in price from the neckline to the top of the head : Price target = Neckline - (Head - Neckline) 2. Reverse Head and Shoulders : Price target = Neckline + (Neckline - Head) 3. Double Top, Double Bottom : A double top is when an uptrend reverses twice at roughly the same high price level. Typically, volume is lower on the second high than on the first high, signaling a diminishing of demand. : The longer the time is between the two tops and the deeper the sell-off is after the first top, the more significant the pattern is considered to be. : Top Price target = Neckline - (Top - Neckline) : Bottom Price target = Neckline + (Neckline - Bottom) 4. Triple Tops / Bottoms : same idea as double tops/bottoms : same formula as double tops/bottoms
Limitations of CAPM (7 main)
1. It's a Single Factor Model empirical researchers found stock returns, rather being explained by 1 factor (BETA), are better explained by 3 Factors. 2. It's a Single Period Model does not consider multi-period implications. 3. Market Portfolio is Unrealistic The true market portfolio according to the CAPM includes all assets, financial and non-financial, which means that it also includes many assets that are not investable, such as human capital and assets in closed economies. 4. Proxy for Market Portfolio Varies No true market portfolio requires proxies, which generate different return estimates for the same asset, which is impermissible in the CAPM. 5. Estimation of Beta Risk is Challenging A: long history of returns (3 to 5 years) required to estimate beta risk, conditions can change / not align B: Betas of various periods will be different, and using daily vs. monthly returns (etc.) will give different results 6. CAPM is a Poor Predictor of Returns asset returns not determined only by systematic risk. 7. Homogeneity in investor expectations: doesn't exist.
Measures for Asset Selection (forward looking)
1. Jensens Alpha & SCL: The best measure to apply is Jensen's alpha because it uses systematic risk and is meaningful even on an absolute basis. : Jensen's alpha is also the vertical distance from the SML measuring the excess return for the same risk as that of the market + αₚ = security will outperform the market (risk adj), a superior security - αₚ = security will underperformed the market (risk adj) , an inferior security : commonly used for selecting managers, funds, etc. : used to rank magnitude of expected under/over performance of security 2. Plot Securities E(r) and β against SML: : use this relationship to decide whether the security is overvalued or undervalued in the market : All securities on the SML considered properly valued : assets above the SML (Points A and C) have a low level of risk relative to the amount of expected return and would be a good choice for investment. : assets below the SML (Point B) considered overvalued. Its return does not compensate for the level of risk and should not be considered for investment. : Of course, a short position in Asset B can be taken if short selling is permitted.
5 Major Cycles
1. Kondratieff Wave: 54-year cycle 2. 18-year cycle 3. Decennial cycle (10-years) 4. Presidential Cycle (US, 4 years) : 1st and 2nd years, worst performance : 3rd and 4th years, best performance 5. Elliot Wave Theory
5 major types of constraints on portfolio selection:
1. Liquidity 2. Time Horizon 3. Tax Concerns 4. Legal and Regulatory Factors 5. Unique Circumstances
Types of Mutual Funds by Investment Objective (4 types)
1. Money Market Funds 2. Bond Funds 3. Stock Funds 4. Balanced Funds
Non-Financial Risks Include: (8 main)
1. Operational Risk: human error, faulty processes, business interruptions, IT security (cyber risk) 2. Solvency Risk: running out of cash 3. Regulatory Risk: regulations impose costs or restrict activity (i.e. Sarbanes Oxley) 4. Political / Gov't. / Tax Risk: government actions other than regulations 5. Legal Risk: exposure to lawsuits 6. Model Risk: incorrect asset value assumptions 7. Tail Risk: underestimating probability of extreme outcomes (i.e. incorrectly assuming normality, in reality very few things are "normally distributed") : in reality, very few platykurtotic distributions (thinner tails than normal distribution) : in reality, more leptokurtotic distributions (fatter tails than normal distribution) : Thus, assuming normality (normal distribution) creates tail risk in many/most cases 8. Accounting Risk: policies and estimates may be judged to be inaccurate.
4 Categories of Technical Indicators
1. Price-Based Indicators : moving averages, bollinger bands 2. Momentum Oscillators : ROC, RSI, MACD 3. Sentiment Indicators : opinion, put/call, VIX 4. Flow-of-Funds : ARMS index, mutual fund cash, equity issuance
3 Common Meanings of Risk:
1. Risk Driver: the underlying risk (i.e. +1% or -1% 2. Risk Position: quantifies the risky action taken (i.e. $1,000,000 worth of risky currency) 3. Risk Exposure: the potential valuation change that may result. (i.e. $10,000 at risk) : Risk Exposure = risk position × risk driver In practice the term "risk" is used interchangeably for all three meanings.
3 Approaches to Managing Apparent Risks:
1. Self-Insuring 2. Risk Transfer 3. Risk Shifting
3 Basic Risk Measures
1. Standard Deviation (total risk) 2. Beta (systematic risk) 3. Duration Risk goes far beyond standard deviation, beta and duration which is why we use various risk assessment methods.
Portfolio Management Process (3 steps)
1. The Planning Step a) Understanding the client's needs b) Preparation of an investment policy statement (IPS) 2. The Execution Step a) Asset allocation b) Security analysis c) Portfolio construction 3. The Feedback Step a) Portfolio monitoring and rebalancing b) Performance measurement and reporting
Continuation Patterns: (insights and price target formulas)
1. Triangle Pattern : They come in three forms ↳symmetrical triangles ↳ascending triangles ↳descending triangles : range between high/low prices narrows, : typically form over a couple weeks : Measuring Implication = height of triangle at beginning of formation, i.e. price target = same as height of triangle at beginning added to the triangle tip : Once trendline broken, price expected to move by at least amount of breakthrough above/below trendline. : breaks outs typically between half/three-quarters of the way through the pattern. : longer pattern persists, more volatile and sustained the subsequent price movement is likely to be. 2. Rectangle Pattern (small range) 3. Flags and Pennants (minor continuation patterns) : typically form over a week : flags -> trendlines form opposite of larger trend : The key difference between a triangle and pennant is that a pennant is a short-term formation whereas a triangle is a long-term formation. : The price is expected to change by at least the same amount as the price change from the start of the trend to the formation of the flag or pennant. : Target = see screenshot
2 Alternative Portfolio Organizing Principles (different from the framework of modern portfolio theory)
1. Use of ETFs and Robo-Advisors : The broad array of ETF offerings, covering the main equity and fixed income indices as well as commodities, enable retail investors to obtain fast, inexpensive, and liquid exposure to asset classes. Robo-advice has further reduced the costs for retail investors to create a well-diversified portfolio. 2. Risk-Parity Investing : Proponents of risk parity investing argue that traditionally constructed portfolios have considerable risk from equities. That is, the typically high (60% or more) weight of equities in institutional portfolios understates the risk impact: equities tend to be much more volatile than fixed income. : Opponents of risk parity argue that following the global financial crisis of 2007-2009, favorable results of risk parity portfolios were caused by the long period of decline in interest rates that benefited bond market performance.
8 Conclusions from Utility Function
1. Utility is unbounded on both sides. 2. Higher return contributes to higher utility. 3. Higher variance reduces the utility but the reduction in utility gets amplified by the risk aversion coefficient, A. Utility can always be increased, albeit marginally, by getting higher return or lower risk. 4. Utility does not indicate or measure satisfaction itself—it can be useful only in ranking various investments. 5. A > 0 for a risk-averse investor 6. A < 0 for a risk-seeking investor 7. A = 0 for a risk-neutral investor 8. Risk free asset (σ² = 0) generates same utility for all investors
Measures of Tail Risk (VaR, CVaR)
1. Value-at-Risk (VaR): minimum loss over a period with a specific probability (time frame, amount, probability) ↳ example = 1 month VaR of $1 Million with 5% probability, means "expect a loss of at least $1 Million in 5% of months". ↳ can have daily VaR, annual VaR, etc. 2. Conditional VaR: Expected value of loss, given that loss exceeds specific amount i.e. given that we are in the extreme tail of the distribution and an extreme outcome is occurring. ↳ example = Given that we are in one of those months where we will lose $1 Million, what is the expected loss during that month?" ↳ Note: by definition, the expected loss must be greater than $1 Million, because VaR is saying "at least a loss of $1 Million". ↳ Harder to calculate Conditional VaR
4 Key Principles of Strategic Asset Allocation
1. a portfolio's systematic risk accounts for most of its change in value over the long term. 2. the returns to groups of similar assets (e.g., long-term debt claims) predictably reflect exposures to certain sets of systematic factors (e.g., for the debt claims, unexpected changes in the interest rate). 3. the SAA is a means of providing the investor with exposure to the systematic risks of asset classes in proportions that meet the risk and return objectives. 4. The process of formulating a strategic asset allocation is based on the IPS + capital market expectations
Assumptions of CAPM
1. risk averse, utility maximizing investors : to accept a greater degree of risk, investors require a higher expected return : investors choose the portfolio, based on their individual preferences, with the risk and return combination that maximizes their (expected) utility 2. frictionless markets : there are no taxes, transaction costs, or other impediments to trading 3. One-period horizon : all investors have the same one-period time horizon 4. homogeneous expectations : all investors have the same expectations for assets' expected returns, standard deviation of returns, and returns correlations between assets 5. divisible assets : all investments are infinitely divisible 6. competitive markets = investors are price takers : investors take the market price as given and no investor can influence prices with their trades
4 Basic Principles of Portfolio Optimization
1. weight in each non-market security should = αᵢ / σ²ₑᵢ : where αᵢ = jensen's alpha of non-market security i : where σ²ₑᵢ = nonsystematic variance of security i 2. total weight of all non-market securities in the portfolio = Σ (wᵢαᵢ) / (wᵢ² σ²ₑᵢ) : where (wᵢαᵢ) = weighted sum of all non-market securit : where (wᵢ² σ²ₑᵢ) = weighted sum of nonsystematic var. 3. The weight in the market portfolio = E(Rₘ) / σ²ₘ 4. The information ratio = αᵢ /σₑᵢ (i.e., alpha divided by nonsystematic risk), measures the abnormal return per unit of risk added by the security to a well-diversified portfolio. : larger information ratio = more valuable the security
Returns Generating Models: 3 and 4 Factor Models
3 Factor Model Fama + French estimated the sensitivity of security returns to three factors: 1. firm size 2. firm book value to market value ratio 3. return on the market portfolio minus the risk-free rate (excess return on the market portfolio). 4 Factor Model (Carhart suggests a fourth factor) 1. firm size 2. firm book value to market value ratio 3. return on the market portfolio minus the risk-free rate (excess return on the market portfolio). 4. price momentum using prior period returns. (Together, these four factors do a relatively good job of explaining returns differences for U.S. equity securities over the period for which the model has been estimated.)
Sell-Side Firm
A broker/dealer that sells securities and provides independent investment research and recommendations to their clients (i.e., buy-side firms).
Mutual Funds (characteristics, benefits, 2 classifications)
A co-mingled investment pool in which investors in the fund each have a pro-rata claim on the income and value of the fund. Characteristics: - value = net asset value (NAV) - NAV computed daily based on closing prices of securities in the portfolio Benefits: - low investment minimums - diversified portfolios - daily liquidity (can get in and out easily) - standardized performance - tax reporting *Highly important investment vehicle for individuals and institutions Classification: 1. Open End Mutual Fund 2. Closed End Mutual Fund
Relative Strength Analysis
A comparison of the performance of one asset with the performance of another asset or a benchmark based on changes in the ratio of the securities' respective prices over time. : used to show over/under-performance to benchmark : Typically analyst prepares line chart of RS ratio RS = Asset Under Analysis / Benchmark RS > 1 = overperformance RS < 1 = underperformance Note: Do not confuse with RSI, not the same thing (RSI = relative strength index)
Ideal Correlation Levels:
A correlation above 0.90 is considered high because the assets do not provide much opportunity for diversification of risk Low correlations—generally less than 0.50—are desirable for portfolio diversification.
Flow-of-Funds Indicators: Arms (aka TRIN) Index
A flow of funds indicator applied to a broad stock market index (i.e. SP500, Dow30, etc.) to measure the relative extent to which money is moving into or out of rising and declining stocks. Arms Index = (# of advancing issues ÷ # of declining issues) ÷ (Volume advancing issues ÷ Volume declining issues) How to read: (contrarian) : index near 1.0 = the market is in balance; ↳ same amount of money is moving into rising stocks as into declining stocks. : index above 1.0 = more volume in declining stocks : index below 1.0 = most trading activity in rising stocks
Institutional Investors: Foundation Fund
A foundation is a fund established for charitable purposes to support specific types of activities or to fund research related to a particular disease. Investment Objective: - to fund the activity or research on a continuing basis without decreasing the real (inflation adjusted) value of the portfolio assets. Common Investment Characteristics: - long investment horizons - high risk tolerance - pre-planned annual spending needs - little need for additional liquidity
Momentum Oscillators (rate of change oscillators)
A graphical representation of market sentiment that is constructed from price data and calculated so that it oscillates either between a high and a low or around some number ( 0 and 100) M = (P₁ - Pₙ) × 100 where; M = momentum oscillator value P₁ = last closing price Pₙ = closing price n days ago, typically 10 days : make extremes of market sentiment more clear : extreme highs indicate overbought : extreme lows indicate oversold Convergence -> oscillator moves with price trend Divergence -> oscillator moves opposite price trend Short-term trading signal in non-trending market
Q. The following table shows data for the stock of JKU and a market index. Expected return of JKU = 15% Expected return of market index = 12% Risk-free rate = 5% Standard deviation of JKU returns = 20% Standard deviation of market index returns = 15% Correlation of JKU and market index returns = 0.75 Based on the capital asset pricing model (CAPM), JKU is most likely: A. undervalued. B. fairly valued. C. overvalued.
A is correct. βJKU = (ρJKU,M × σJKU)/σM = (0.75 × 0.2)/0.15 = 1.0 and E(RJKU) = Rf + βJKU × (RM − Rf) = 0.05 + 1 × (0.12 − 0.05) = 1.12 The required rate of return of JKU is 12%, and the expected return of JKU is 15%. Therefore, JKU is undervalued relative to the security market line (SML); the risk-return relationship lies above the SML. B is incorrect because for JKU to be properly valued it would need to have an expected return equal to 12%. C is incorrect because for JKU to be overvalued it would need to have an expected return less than 12%.
Q. Which flow-of-funds indicator is considered bearish for equities? A. A large increase in the number of IPOs. B. Higher-than-average cash balances in mutual funds. C. An upturn in margin debt but one that is still below the long-term average.
A is correct. A large increase in the number of IPOs increases the supply of equity and if overall demand remains the same, puts downward pressure on equities. Also, companies tend to issue shares of equity when the managers believe they will receive a premium price, which is also an indicator of a market top.
Q. Portfolios are most likely to provide: A. risk reduction. B. risk elimination. C. downside protection.
A is correct. Combining assets into a portfolio should reduce the portfolio's volatility. However, the portfolio approach does not necessarily provide downside protection or eliminate all risk.
Q. Which of the following may be controlled by an investor? A. Risk B. Raw returns C. Risk-adjusted returns
A is correct. Many decision makers focus on return, which is not something that is easily controlled, as opposed to risk, or exposure to risk, which may actually be managed or controlled
Q. An analyst uses a multi-factor model to estimate the expected returns of various securities. The model analyzes historical and cross-sectional return data to identify factors that explain the variance or covariance in the securities' observed returns. This model is most likely a: A. statistical factor model. B. macroeconomic factor model. C. fundamental factor model.
A is correct. Statistical factor models use historical and cross-sectional return data to identify factors that explain the variance or covariance in the observed returns of securities. B is incorrect because macroeconomic factor models use economic factors that are correlated with security returns, such as economic growth, the interest rate, the inflation rate, productivity, etc. C is incorrect because fundamental factor models use the relationships between security returns and firms' underlying fundamentals, such as earnings, earnings growth, cash flow generation, investment in research, etc.
Q. With respect to the mean-variance portfolio theory, the capital allocation line, CAL, is the combination of the risk-free asset and a portfolio of all: A. risky assets. B. equity securities. C. feasible investments.
A is correct. The CAL is the combination of the risk-free asset with zero risk and the portfolio of all risky assets that provides for the set of feasible investments. Allowing for borrowing at the risk-free rate and investing in the portfolio of all risky assets provides for attainable portfolios that dominate risky assets below the CAL.
Q. With respect to the capital asset pricing model, the primary determinant of expected return of an individual asset is the: A. asset's beta. B. market risk premium. C. asset's standard deviation.
A is correct. The CAPM shows that the primary determinant of expected return for an individual asset is its beta, or how well the asset correlates with the market.
Q. With respect to capital market theory, which of the following asset characteristics is least likely to impact the variance of an investor's equally weighted portfolio? A. Return on the asset. B. Standard deviation of the asset. C. Covariances of the asset with the other assets in the portfolio.
A is correct. The asset's returns are not used to calculate the portfolio's variance [only the assets' weights, standard deviations (or variances), and covariances (or correlations) are used].
Q. A client who is a 34-year old widow with two healthy young children (aged 5 and 7) has asked you to help her form an investment policy statement. She has been employed as an administrative assistant in a bureau of her national government for the previous 12 years. She has two primary financial goals—her retirement and providing for the college education of her children. This client's time horizon is best described as being: A. long term. B. short term. C. medium term.
A is correct. The client's financial objectives are long term. Her stable employment indicates that her immediate liquidity needs are modest. The children will not go to college until 10 or more years later. Her time horizon is best described as being long term.
Q. Which of the following institutions will on average have the greatest need for liquidity? A. Banks. B. Investment companies. C. Non-life insurance companies.
A is correct. The excess reserves invested by banks need to be relatively liquid. Although investment companies and non-life insurance companies have high liquidity needs, the liquidity need for banks is on average the greatest.
Q. As one moves to the right along an investor's efficient frontier, a set increase in risk is most likely to lead to: A. sequentially smaller increases in expected return. B. consistent increases in expected return. C. sequentially larger increases in expected return.
A is correct. The increase in return with every unit increase in risk keeps decreasing as one moves from left to right because the slope of the efficient frontier continues to decrease. Thus, investors obtain decreasing increases in returns as they assume more risk. B is incorrect because the slope of the efficient frontier continues to decrease, leading to smaller incremental returns, not consistent. C is incorrect because the slope of the efficient frontier continues to decrease, leading to smaller incremental returns, not larger.
Q. Which of the following statements most accurately defines the market portfolio in capital market theory? The market portfolio consists of all: A. risky assets. B. tradable assets. C. investable assets.
A is correct. The market includes all risky assets, or anything that has value; however, not all assets are tradable, and not all tradable assets are investable. Answer is A because in capital market theory, the benchmark index is a proxy for the entire market. This implies that, given the assumption above, the market portfolio consists of all risky assets.
Q. The dominant capital allocation line is the combination of the risk-free asset and the: A. optimal risky portfolio. B. levered portfolio of risky assets. C. global minimum-variance portfolio.
A is correct. The use of leverage and the combination of a risk-free asset and the optimal risky asset will dominate the efficient frontier of risky assets (the Markowitz efficient frontier).
Q. Which of the following performance measures is mostappropriate for an investor who is not fully diversified? A. M-squared. B. Treynor ratio. C. Jensen's alpha.
A is the correct. M² adjusts for risk using standard deviation (i.e., total risk).
Sharpe Ratio (aka reward-to-variability ratio)
A measure of the average excess return earned per unit of standard deviation of return. Sharpe Ratio = (E(Rₚ)−Rf) / σₚ where; E(Rₚ) = expected portfolio return Rf = risk free rate of return σₚ = total portfolio risk (std. dev. of returns) How to Read: : numerator must be positive to give meaningful results : higher Sharpe ratio = better risk-adjusted performance : lower Sharpe ratio = better risk-adjusted performance : If the numerator is negative, the ratio will be less negative for riskier portfolios, resulting in incorrect rankings. (i.e. higher negative numbers = worse perform) Limitations: 1. Uses total risk, not only systematic risk which is the only risk that is priced. 2. Ratio itself is not informative, requires comparison SR is also the slope of the CAL (capital allocation line). Note, however, that the ratio uses the total risk of the portfolio, not its systematic risk. The use of total risk is appropriate if the portfolio is an investor's total portfolio—that is, the investor does not own any other assets.
Beta (formula + definition)
A measure of the sensitivity of a given investment or portfolio to movements in the overall market. Beta captures an asset's systematic risk, or the portion of an asset's risk that cannot be eliminated by diversification. βᵢ = ρᵢₘ × (σᵢ / σₘ) where; βᵢ = beta of asset i ρᵢₘ = correlation coefficient of asset i to the market m σᵢ = standard deviation of asset i σₘ = standard deviation of the market m Details: : The variances and correlations required for the calculation of beta are usually based on historical returns. : + βᵢ = positive return correlation with market trends : - βᵢ = negative return correlation with market trends : 0 βᵢ = no returns correlation with the market : Risk-Free asset's β = 0 : Markets β with itself is 1, therefore average β of all stocks in the market is 1 : Most stocks in developed markets have β of 0.7
M²: Risk Adjusted Performance (RAP)
A measure of what a portfolio would have returned if it had taken on the same total risk as the market index, which is a Risk Adjusted Performance (RAP) measure, and stated in % terms. M² = (Rₚ− Rf) × (σₘ / σₚ) + Rf or M² = Sharpe Ratio × σₘ - Rf where; M² = additional return % if portfolio risk = market risk (Rₚ− Rf) = excess portfolio return (σₘ / σₚ) = portfolio specific leverage ratio Rf = risk free rate of return Sharpe Ratio = (Rₚ− Rf) / σₚ : produces same portfolio rankings as the Sharpe ratio but is stated in % terms : can be thought of as a rescaling of the Sharpe ratio that allows for easier comparisons among different portfolios. Example: If M² = 12%, and market return was 10%, then the portfolio used to calculate M² outperformed the market benchmark by 12% - 10% = 2%. Result of the M² calculation would be 12%, then you must compare to market benchmark to see if the portfolio over or under performed.
Return Generating Models (definition + types)
A model that can provide an estimate of the expected return of a security given certain parameters and estimates of the values of the independent variables in the model. Types of Return Generating Models 1. Single Factor Models : the market model 2. 3 and 4 Factor Models : 3 factor = Fama + French : 4 factor = Carhart 3. Multi-Factor Models
Relative Strength Index (RSI) (momentum oscillator)
A momentum indicator that compares the magnitude of recent gains and losses over a specified time period to measure speed and change of price movements of a security : shows how strong the move is in its current direction : 14-day period generally used in TA software. : trade time horizon must be considered and RS should be adjusted to consider appropriate investment horizon RSI = 100 - [100 / (1 + RS)] where; RS = Σ(Up changes for the period under consideration) ÷ Σ(Down changes for the period under consideration) : Can also apply trendlines to analyze RSI : solid trends can start at/above RSI of 70 and stay there for significant amount of time. RSI to lie within 0 and 100. : A value above 70 represents an overbought situation. : Values below 30 suggest the asset is oversold. ↳ BUT MUST CONSIDER CONTEXT (trends, etc. and not simply buy/sell based on above70, below30) : The 30-70 range is a good rule of thumb, but because the oscillator is a measure of volatility, less volatile stocks (such as utilities) may normally trade in a much narrower range. More volatile stocks (such as small-capitalization technology stocks) may trade in a wider range. The range also does not have to be symmetrical around 50. For example, in an uptrend, one might see a range of 40-80 but in downtrends, a range of 20-60.
Value at Risk (VaR)
A money measure of the minimum value of losses expected during a specified time period at a given level of probability. : measure of minimum (extreme) downside risk metric : measure of size of the tail of the distribution of profits : No ultimate maximum that one can state. : several ways to estimate VaR, each of which has its own advantages and disadvantages. The different measures can lead to highly diverse estimates. : same model risk as derivative pricing models. VaR is based on a particular assumption about the probability distribution of returns or profits. If that assumption is incorrect, the VaR estimate will be incorrect. VaR also requires certain inputs. If those inputs are incorrect, the VaR estimate will be incorrect. : As with any risk measure, one should supplement it with other measures. Contains 3 Elements: 1. an amount stated in units of currency 2. a time period 3. a probability Example: Assume a London bank determines that its VaR is £3 million at 5% for one day. This statement means that the bank expects to lose a minimum of £3 million in one day 5% of the time. A critical, and often overlooked word, is minimum. With a probability of 5% and a measurement period of one day, we can interpret the bank's VaR as expecting a minimum loss of £3 million once every 20 business days.
Multi-Boutique Asset Management Firm
A multi-boutique firm is a holding company that includes a number of different specialist asset managers. Allows individual asset management firms to: - retain their own unique investment cultures - equity ownership stakes in their firm - benefit from centralized, shared services of the holding company (e.g., technology, sales and marketing, operations, and legal services).
Closed End Mutual Fund
A mutual fund in which no new investment money is accepted. New investors invest by buying existing shares, and investors in the fund liquidate by selling their shares to other investors. Characteristics: - often actively managed - Fixed # of shares - Issued as IPO - trade like stock, have commission and spread, margin and shorting - Fee (%) for ongoing management - Market prices and NAV differ (at premium/discount) - Don't need to hold cash or sell shares to meet redemptions as open end funds do.
Open End Mutual Fund (most common, widely referred to)
A mutual fund that accepts new investment money and issues additional shares at NAV of the fund at the time of investment. Characteristics: - can purchase or redeem shares at NAV - # shares changes with new purchases or redemptions - fee (%) for ongoing management - Load Funds: upfront or redemption charges, or both - No-Load Funds: no upfront or redemption charges * no evidence suggesting load outperform no-load
Money Market Mutual Funds
A mutual fund that invests in money-market instruments such as treasury bills, certificates of deposit, and commercial paper. Goals: - security of principal - high levels of liquidity - returns in line with money market rates Characteristics: - invest in short-term debt securities - provide interest income - low risk of changes in share value - Fund NAVs are typically set to one currency unit - Funds differentiated by : types of money market securities they purchase : average maturities. - in US there are 2 types: taxable and tax-free : taxable invest in IG corporate and federal debt : non-taxable invest in state and local gov't debt : substitute for bank savings accounts since early 1980s
Diversifying with Asset Classes (list of 13 asset classes)
A partial list of asset classes includes: 1. domestic large caps 2. domestic small caps 3. growth stocks 4. value stocks 5. domestic corporate bonds 6. long-term domestic government bonds 7. domestic Treasury bills (cash) 8. emerging market stocks 9. emerging market bonds 10. developed market stocks (excl. domestic market) 11. developed market bonds 12. real estate 13. gold and other commodities In addition, industries and sectors are used to diversify portfolios. The exact proportions in which these assets should be included in a portfolio depend on the risk, return, and correlation characteristics of each and the home country of the investor.
The security characteristic line (SCL)
A plot of a security's expected excess return over the risk-free rate as a function of the excess return on the market y-axis = asset excess return = Ri - Rf x-axis = market excess return = Rm - Rf Slope = βᵢ = Covᵢₘ / σ²ₘ y-intercept = jensen's alpha = Rp - CAPM : Associated with the single-index mode
Treynor Ratio
A simple extension of the Sharpe ratio and resolves the Sharpe ratio's first limitation (total risk instead of systematic) by substituting beta (systematic risk) for total risk. A measure of risk-adjusted performance that relates a portfolio's excess returns to the portfolio's beta. Treynor Ratio = (E(Rₚ)−Rf) / βₚ where; E(Rₚ) = expected portfolio return Rf = risk free rate of return βₚ = systematic risk of the portfolio How to Read: : numerator must be positive to give meaningful results : does not work for negative beta assets : higher TR = better risk-adjusted performance : If the numerator is negative, the ratio will be less negative for riskier portfolios, resulting in incorrect rankings. (i.e. higher negative numbers = worse perform)
Sentiment Indicators: Put/Call Ratio
A technical analysis indicator that evaluates market sentiment based upon the volume of put options traded divided by the volume of call options traded for a particular financial instrument. Put/Call Ratio = Put Volume / Call Volume : The volume in call options is greater than the volume traded in put options over time, so the put/call ratio is normally below 1.0 : contrarian indicator ↳ higher value = bearish ↳ lower value = bullish Extremes : At extreme lows where call option volume is significantly greater than put option volume, market sentiment is said to be so overly positive that a correction is likely. At extreme highs in the put/call ratio, market sentiment is said to be so extremely negative that an increase in price is likely.
The optimal portfolio in the Markowitz framework occurs when an investor achieves the diversified portfolio with the: A. Highest utility B. Highest return C. Lowest risk
A. Highest Utility. The optimal portfolio in the Markowitz framework occurs when the investor achieves the diversified portfolio with the highest utility.
Q. With respect to the benefits of portfolios, portfolios affect: A. risk more than returns B. returns more than risk C. risk and return equally
A. This example illustrates one of the critical ideas about portfolios: Portfolios affect risk more than returns.
CAPM Alternatives: Arbitrage Pricing Theory (APT)
APT proposes a linear relationship between expected return and risk allowing for numerous specific risk factors for a particular asset: E(Rₚ) = Rf + λ₁βₚ,₁ + ... + λₖβₚ,ₖ where; E(Rₚ) = the expected return of portfolio p Rf = the risk-free rate λₖ = the risk premium for factor k : expected return in excess of the risk-free rate βₚ,ₖ = the sensitivity of the portfolio to factor k K = the number of risk factors Details: : A no-arbitrage condition in asset markets is used to determine the risk factors and estimate betas for the risk factors. : does not specify any of the risk factors : difficult to identify risk factors : difficult to estimate betas of all portfolio assets : from a practical standpoint, CAPM is preferred to APT.
Ability vs. Willingness to Bear Risk
Ability to bear risk depends on financial circumstances. : A greater ability to bear investment risk ↳Longer investment horizons (20 years vs. 2 years) ↳Greater assets versus liabilities (more wealth) ↳More insurance against unexpected occurrences ↳A secure job Willingness to bear risk is based primarily on the investor's attitudes and beliefs about investments (various asset types). : quite subjective : short questionnaire can be used to categorize the investor's risk aversion or risk tolerance. : Using the questionnaire, the responses, a), b), c), and d), are coded 1, 2, 3, and 4, respectively, and summed. : lowest score is 5, highest score is 20, : higher scores indicating greater risk tolerance. : For two random samples drawn from the faculty and staff of large US universities (n = 406), the mean score was 12.86 with a standard deviation of 3.01 and a median (i.e., most frequently observed) score of 13.
How is risk related to the number of assets in a portfolio?
Academic studies have shown that as you increase the number of stocks in a portfolio, the portfolio's risk falls toward the level of market risk. One study showed that it only took about 12 to 18 stocks in a portfolio to achieve 90% of the maximum diversification possible. Another study indicated it took 30 securities. Whatever the number, it is significantly less than all the securities. Note re: Image Attached: Once you get to 30 or so securities in a portfolio, the standard deviation remains constant. The remaining risk is systematic, or nondiversifiable, risk.
Managing Risks: Risk Shifting
Actions that change the distribution of risk outcomes. : generally involves derivatives as risk modification vehicle. : diverts some portion of the risk distribution to another market participant who either bears the risk or intermediates that risk by moving it to yet another party. : represents the bulk of hedging : most common form of risk management by financial organizations : derivatives can provide essentially the same exposure as the underlying but can do so at lower cost and capital requirements. As such, derivatives permit the efficient shifting of risk across the probability distribution and from one party to another.
Managing Risks: Risk Transfer
Actions to pass on a risk to another party, often, but not always, in the form of an insurance policy. : the concept of insurance relies on the diversification or pooling of risks
Active Vs. Passive Management
Active Managers: : fundamental research + quantitative research : specialist active attempt to outperform benchmarks : multi-asset active, combination of benchmarks Passive Managers: : attempt to replicate the returns of a market index. : This may include traditional broad market index tracking or a smart beta approach that focuses on exposure to a particular market risk factor.
Risk monitoring, mitigation, and management
Actively monitoring and managing risk requires pulling together risk governance, identification and measurement, infrastructure, and policies and processes and continually reviewing and reevaluating in the face of changing risk exposures and risk drivers. It requires recognizing when risk exposure is not aligned with risk tolerance and then taking action to bring them back into alignment.
Practical Insight of Enterprise Risk
Although there are a very high number of risks faced by every organization, most organizations are primarily affected by a small number of key risk drivers, or primary underlying factors that create risk.
Leveraged Portfolios with Different Lending and Borrowing Rates
Although we can invest (lend) at Rf, we can in reality borrow at only Rb (bank rate), a rate that is higher than the risk-free rate. With different lending and borrowing rates, the CML will no longer be a single straight line, and is kinked at point M, beyond which the slope of the CML line becomes smaller (more flat). When w₁ (risk free asset weight) >= 0: : Between points Rf & M on CML, the lending rate is Rf : Slope of CML = (E(Rₘ) - Rf) / σₘ : E(Rₚ) = Rf + [(E(Rₘ) - Rf) / σₘ] × σₚ When w₁ (risk free asset weight) < 0: : Beyond point M on CML, the lending rate is Rb: : Slope of CML = (E(Rₘ) - Rb) / σₘ : E(Rₚ) = Rb + [(E(Rb) - Rb) / σₘ] × σₚ where; Rf = risk free rate Rb = bank rate of borrowing E(Rₚ) = expected portfolio return, not including rf asset : All passive portfolios will lie on the kinked CML, although the investment in the risk-free asset may be positive (lending), zero (no lending or borrowing), or negative (borrowing). : Leverage allows less risk-averse investors to increase the amount of risk they take by borrowing money and investing more than 100 percent in the passive portfolio.
Risk View of a Portfolio
An alternative risk view of the same portfolio might be 70% driven by global equity returns, 20% by domestic equity returns, with the remaining 10% driven by interest rates. The equity component might be allocated 65% to value and 35% to growth. The portfolio might also have 45% illiquid securities and the remainder liquid. Other allocations can be stated in terms of exposures to inflation, long-term interest rates, currencies, and so on.
Risk Budgeting: Security Selection
An attempt to generate higher returns than the asset class benchmark by selecting securities with a higher expected return. Example : an investment manager may decide to add more IBM stock in his portfolio than the weight in his equity benchmark if he expects this stock to do better than the benchmark. To fund this purchase, he may sell another stock expected to do worse than either the benchmark or IBM. Obviously, deciding to deviate from policy weights or to select securities aiming to beat the benchmark creates additional uncertainty about returns. This risk is over and above the risk inherent in the policy portfolio. Hence, an investment policy should set risk limits and desired payoffs for each of these three activities.
Buy-Side Firm
An investment management company or other investor that uses the services of brokers or dealers (i.e., the client of the sell side firms). An asset manager is commonly referred to as a buy-side firm
2. Execution Step: Top-Down Approach to Asset Allocation
An investment selection approach that begins with consideration of macroeconomic conditions and then evaluates markets and industries based upon such conditions.
2. Execution Step: Bottom-Up Approach to Asset Allocation
An investment selection approach that focuses on company-specific circumstances, such as management quality and business prospects, rather than emphasizing economic cycles or industry analysis.
Risk Neutral Investor
An investor that requires the same rate of return on all investments regardless of levels and types of risk, because the investor is indifferent with regard to how much risk is borne. : higher return investments are more desirable even if they come with higher risk. : Many investors may exhibit characteristics of risk neutrality when the investment at stake is an insignificant part of their wealth. Simply put, they only care about total return, and the level of risk required to get that return is irrelevant.
Enterprise Risk Management
An overall assessment of a company's risk position. A centralized approach to risk management sometimes called firmwide risk management.
Bollinger Bands
Are drawn above/below moving average by a specific number of standard deviations. Short Term (contrarian) : sell at top band -> security overbought : buy at bottom band -> security oversold Longer Term : buy on significant breakout above top band : sell on significant breakdown below bottom band These are moving averages that are offset by a standard deviation. This means 95% of all price action will take place in between the top and bottom bands. Some traders look for stocks trading outside their Bollinger Bands as that indicates an extreme situation (5% status). The idea here is that these stocks are very extended and are due to reverse. In combination with RSI and candle stick patterns, this can help us find good stocks for reversal strategies.
Volume is used to
Assess the strength or conviction of buyers and sellers in determining a security's price. Volume ↑ + Price ↑ = more and more investors are buying the financial instrument and they are doing so at higher and higher prices. : "confirmation", together they confirm validity of growth Volume ↓ + Price ↑ = implication is that fewer and fewer market participants are willing to buy that stock at the new price. If this trend in volume continues, the price rally will soon end because demand for the security at higher prices will cease. : "divergent", rally will soon end.
Examples of ESG Screening Issues:
Attached in image Opponents of ESG: The effort and costs associated with limiting the investment universe as part of sustainable investing suggests a negative impact on investment returns. Proponents of ESG: Sustainable investing proponents argue, however, that potential improvements in governance and the avoidance of risks by companies that screen favorably improve returns. Significant empirical research has been conducted on the performance of ESG factors in equities, including the return differences of ESG equity portfolios relative to mainstream equity portfolios. Academic research remains mixed on the impact of ESG factors on portfolio returns.
Q. Risk management in the case of individuals is best described as concerned with: A. hedging risk exposures. B. maximizing utility while bearing a tolerable level of risk. C. maximizing utility while avoiding exposure to undesirable risks.
B is correct. For individuals, risk management concerns maximizing utility while taking risk consistent with individual's level of risk tolerance.
Q. With respect to return-generating models, the intercept term of the market model is the asset's estimated: A. beta. B. alpha. C. variance.
B is correct. In the market model, Ri = αi + βiRm + ei, the intercept, αi, and slope coefficient, βi, are estimated using historical security and market returns.
Q. With respect to return-generating models, the slope term of the market model is an estimate of the asset's: A. total risk. B. systematic risk. C. nonsystematic risk.
B is correct. In the market model, Ri = αi + βiRm + ei, the slope coefficient, βi, is an estimate of the asset's systematic or market risk.
Q. With respect to capital market theory, an investor's optimal portfolio is the combination of a risk-free asset and a risky asset with the highest: A. expected return. B. indifference curve. C. capital allocation line slope.
B is correct. Investors will have different optimal portfolios depending on their indifference curves. The optimal portfolio for each investor is the one with highest utility; that is, where the CAL is tangent to the individual investor's highest possible indifference curve.
Q. Which of the following institutional investors will most likelyhave the longest time horizon? A. Defined benefit plan. B. University endowment. C. Life insurance company.
B is correct. Most foundations and endowments are established with the intent of having perpetual lives. Although defined benefit plans and life insurance companies have portfolios with a long time horizon, they are not perpetual.
Q. With respect to the pricing of risk in capital market theory, which of the following statements is most accurate? A. All risk is priced. B. Systematic risk is priced. C. Nonsystematic risk is priced.
B is correct. Only systematic risk is priced. Investors do not receive any return for accepting nonsystematic or diversifiable risk.
Q. Tactical asset allocation is best described as: A. Attempts to exploit arbitrage possibilities among asset classes. B. The decision to deliberately deviate from the policy portfolio. C. Selecting asset classes with the desired exposures to sources of systematic risk in an investment portfolio.
B is correct. Tactical asset allocation allows actual asset allocation to deviate from that of the strategic asset allocation (policy portfolio) of the IPS. Tactical asset allocation attempts to take advantage of temporary dislocations from the market conditions and assumptions that drove the policy portfolio decision.
Q. Compared to the efficient frontier of risky assets, the dominant capital allocation line has higher rates of return for levels of risk greater than the optimal risky portfolio because of the investor's ability to: A. lend at the risk-free rate. B. borrow at the risk-free rate. C. purchase the risk-free asset.
B is correct. The CAL dominates the efficient frontier at all points except for the optimal risky portfolio. The ability of the investor to purchase additional amounts of the optimal risky portfolio by borrowing (i.e., buying on margin) at the risk-free rate makes higher rates of return for levels of risk greater than the optimal risky asset possible.
Stochastic Oscillator (momentum oscillator)
Based on the assumption that in an up trend, the stock price tends to close near the high of its recent range, while on a down trend it tends to close around its recent low. : Usually calculated with 14-day period ↳ lower (higher) time periods = shorter (longer) horizon : oscillates between 0 and 100 : Composed of two lines %k and %D %K = 100 ( C - L14 / H14 - L14) where %K = oscillator value (daily), ↳ means that the latest closing price (C) was in the %K percentile of the high-low range (L14 to H14). C = latest closing price L14 = lowest price in past 14 days H14 = highest price in past 14 days %D =average of last three %K values calculated daily ↳ slower moving, smoother line ↳ "the signal line" Crossings: (same as moving average cross usage) : shorter term movements ↳%K line crosses %D line from below = bullish ↳%K line crosses %D line from above = bearish Default Range (don't simply read default and decide) : above 80 = overbought = bearish : below 20 = oversold = bullish
3. The Feedback Step: Portfolio Monitoring and Rebalancing
Because of changes in security prices and fundamental factors, PM's must: 1. analyze asset allocation 2. analyze individual security selection 3. analyze current weightings vs. planned weightings as a result of market price changes
Returns from Tactical Allocation Formula
Because tactical asset allocation is the deliberate decision to deviate from policy weights, the return contribution from tactical asset allocation is equal to: Tactical Returns = Actual Return - Policy Weighted E(r) where; Tactical Returns = % returns due to tactical allocation Actual Return = % return of portfolio in period t Policy Weighted E(r) = % return of portfolio if asset class weightings were maintained per the SAA
What should the relative weight of securities in the portfolio be?
Because we are concerned with maximizing risk-adjusted return, securities with: 1. higher αi should get higher weights 2. greater nonsystematic risk = less weight
1. The Planning Step: 8 Main Considerations of Portfolio Planning
Begins with an analysis of the investor's: 1. Risk tolerance 2. Return objectives 3. Time horizon 4. Tax exposure 5. Liquidity needs 6. Income needs 7. Any unique circumstances or investor preferences. 8. Benchmark of Success This analysis results in an investment policy statement (IPS) that details the investor's investment objectives and constraints. It should also specify an objective benchmark (such as an index return) against which the success of the portfolio management process will be measured.
Beta (practical application)
Beta can be constructed given other factors as below: Two main ways are highlighted in black: βᵢ = Covᵢₘ / σ²ₘ ↳ ρᵢₘ = Covᵢₘ / (σᵢ × σₘ) ↳ Covᵢₘ = ρᵢₘ × σᵢσₘ ↳ βᵢ = (ρᵢₘ × σᵢσₘ) / σ²ₘ ↳ βᵢ = ρᵢₘ × (σᵢ / σₘ) Alternative Approach to Beta (use market model): Rᵢ = αᵢ + βᵢRₘ + eᵢ : historical asset and market returns are used for estimating the two parameters αi and βi. : estimated by using regression analysis, which is a statistical process that evaluates the relationship between a given variable (the dependent variable) and one or more other (independent) variables. Beta Levels + Types of Securities: : β > 1 = expected return is higher than market return ↳ cyclical securities ↳ use high beta securities if you believe market will rise : β < 1 = expected return is less than market return ↳ defensive securities ↳ use low beta securities if you believe market will fall : β = 0, risk-free assets : -β = required return will be less than the risk-free rate ↳ insurance is an example Beta should be calculated over a given time horizon: 12 Month β = assets current systematic risk : less accurate : short-term events significantly affect result 3-5 Year β = assets systematic risk over medium term : more accurate : less affected by short term events : may not accurately reflect structural changes of asset 5+ Year β = assets long term systematic risk : more stable or reliable : may not be best predictor of future systematic risk
Risk Assessment Methods
Both are often used to complement VaR. These are common sense approaches that ask "If this happens, then how are we affected?" 1. Stress Test : effects of change in a single variable 2. Scenario Analysis : effects of a set of changes in multiple variables : i.e. "if multiple factors move against us, what will that do to our solvency position?"
Q. When analyzing a head and shoulders pattern that represents the reversal of an upward trend, the highest trading volume is most likely on the upward side of the: A. right shoulder. B. head. C. left shoulder.
C is correct. In the classic head and shoulders pattern, the left shoulder shows a strong rally on strong volume, followed by a reversal back to the price level where it started. The head is a more pronounced version of the left shoulder but on lower volume. The right shoulder is a mirror image of the left shoulder, also on lower volume. A is incorrect because the right shoulder mirrors the left shoulder, but on lower volume. B is incorrect because the upward trend of the head typically has lower volume than the left shoulder.
Q. Which of the following performance measures is consistent with the CAPM? A. M-squared. B. Sharpe ratio. C. Jensen's alpha.
C is correct. Jensen's alpha adjusts for systematic risk, and M-squared and the Sharpe Ratio adjust for total risk.
Q. An organization choosing to accept a risk exposure may: A. buy insurance. B. enter into a derivative contract. C. establish a reserve fund to cover losses.
C is correct. Risk acceptance is similar to self-insurance. An organization choosing to self-insure may set up a reserve fund to cover losses. Buying insurance is a form of risk transfer and using derivatives is a form of risk-shifting, not risk acceptance.
Which of the following is not consistent with a risk-budgeting approach to portfolio management? A. Limiting the beta of the portfolio to 0.75 B. Allocating investments by their amount of underlying risk sources or factors C. Limiting the amount of money available to be spent on hedging strategies by each portfolio manager
C is correct. Risk budgeting is any means of allocating a portfolio by some risk characteristics of the investments. This approach could be a strict limit on beta or some other risk measure or an approach that uses risk classes or factors to allocate investments. Risk budgeting does not require nor prohibit hedging, although hedging is available as an implementation tool to support risk budgeting and overall risk governance.
Q. With respect to utility theory, the most risk-averse investor will have an indifference curve with the: A. most convexity. B. smallest intercept value. C. greatest slope coefficient.
C is correct. The most risk-averse investor has the indifference curve with the greatest slope.
Q. The sum of an asset's systematic variance and its nonsystematic variance of returns is equal to the asset's: A. beta. B. total risk. C. total variance.
C is correct. The sum of systematic variance and nonsystematic variance equals the total variance of the asset. References to total risk as the sum of systematic risk and nonsystematic risk refer to variance, not to risk.
Q. Mutual funds that hold high cash positions are most likely viewed by technical analysts as being: A. neutral. B. bearish. C. bullish.
C is correct. When mutual funds hold high cash positions, the cash represents buying power that will move prices higher when the funds are used to add positions to the portfolio. Therefore, technical analysts view mutual funds that hold high cash positions as a bullish indicator. A is incorrect because holding high cash is not a neutral indicator. Technical analysts look at mutual funds holding high cash as a bullish indicator because that money represents buying power that will move prices higher when the money is used to add positions to the portfolio. B is incorrect because although a fund manager may hold high cash when they are bearish, technical analysts look at this as a bullish indicator because that money represents buying power that will move prices higher when the money is used to add positions to the portfolio.
Characteristics of Different Types of Investors
Chart provides a summary of the risk tolerance, investment horizon, liquidity needs, and income objectives for different types of investors.
Market Cap. + Beta: Not explicitly correlated, but kind of are
Check to see if stocks with larger market caps within a given index have Beta's closer to 1 than stocks in the same index with smaller market caps. There will be exceptions, but it seems logical to think.
How to Choose Which Method for Modifying Risk
Choosing which risk mitigation method to use—risk prevention and avoidance, self-insuring, risk transfer, or risk shifting—is a critical part of the risk management process. Fortunately, the methods are not mutually exclusive, and many organizations use all methods to some extent. No single method provides a clear-cut advantage over the others. As with all decisions, the trade-off is one of costs versus benefits that are weighed in light of the risk tolerance of the organization or individual. Risk takers should identify risks that offer few rewards in light of potential costs and avoid those risks when possible. They should self-insure where it makes sense and diversify to the extent possible. They should consider insurance when risks can be pooled effectively if the cost of the insurance is less than the expected benefit. If derivatives are used, they must consider the trade-off of locking in outcomes with forward commitments versus the flexibility relative to cash cost of contingent claims, which can tailor the desired outcomes or payoffs by shifting the risk. Ultimately, the decision is always one of balancing costs against benefits while producing a risk profile that is consistent with the risk management objectives of the organization.
Returns Measures (4 Classifications, 6 Types)
Classifications: 1. Holding Period Return 2. Average Returns a) arithmetic mean = simple avg. of periodic returns b) geometric mean = compound annual rate 3. Time-Weighted Return 4. Money-Weighted Return Types: 1. gross return = return before management fees 2. net return = return after management fees 3. pre-tax nominal = return before deducting taxes 4. after-tax nominal = after deducting tax liability 5. real return = after adjusting for inflation 6. leveraged return = return on cash investment
Drew Strategy - Active Specialty in Global Real ESG, w/ Robo UI
Companies that are improving the human experience and environment in which we live. (build it slow and steady, quality light is key) Benefits - can differentiate, participate in growing segment - can use research and marketing experience - current lack of clarity provides opportunity - can use RIMM Risks - tough to find - data is expensive - transparency is low - uncertain about returns compared to traditional investments Decision: - ESG flows are booming, and while it is tough to truly deliver on the mission, that is exactly why it could be highly profitable. By being a participant in Real ESG Investing early on, you can establish yourself with quality insights and interesting stories... but most important is to be profitable.
Diversification Among Countries
Countries are different because of industry focus, economic policy, and political climate. The US economy produces many financial and technical services and invests a significant amount in innovative research. The Chinese and Indian economies, however, are focused on manufacturing. Countries in the European Union are vibrant democracies whereas East Asian countries are experimenting with democracy. Thus, financial returns in one country over time are not likely to be highly correlated with returns in another country. Country returns may also be different because of different currencies. In other words, the return on a foreign investment may be different when translated to the home country's currency. Because currency returns are uncorrelated with stock returns, they may help reduce the risk of investing in a foreign country even when that country, in isolation, is a very risky emerging market from an equity investment point of view. Investment in foreign countries is an essential part of a well-diversified portfolio.
Strategic Asset Allocation (SAA) (aka policy portfolio)
Definition The set of exposures to IPS-permissible asset classes that is expected to achieve the client's long-term objectives given the client's investment constraints. Elements used to create: : constraints and objectives articulated in the IPS : long-term capital market expectations of asset classes. : The strategic asset allocation or policy portfolio will subsequently be implemented into real portfolios. : Exhibit 7 illustrates conceptually how investment objectives and constraints and long-term capital market expectations combine into a policy portfolio. In practice this is done a bit differently because this framework: a) is single period, whereas in practice, the constraints from the IPS will make it more appropriate to use multi-period models. Multi-period problems can be more effectively addressed using simulation., b) IPS gives threshold levels for risk and expected return, combined with a number of additional constraints that cannot be captured in this model : investors indifference curve (utility curve) : efficient frontier of portfolios, specified in asset classes' expected returns, standard deviations of return, and correlations, translate into an efficient frontier of portfolios. Details : could include a policy of hedging portfolio risks not explicitly covered by asset class weights. ↳ example 1: hedge ratios for fx exposure ↳ example 2: management of interest rate risk resulting from asset-liability mismatch, and the ↳ example 3: hedging of inflation risk. ↳ "overlay" portfolios of derivatives used for this
Risk Policies and Processes (definition + elements)
Definition: : limits, requirements, constraints, and guidelines—some quantitative, some procedural—to ensure risky activities are in line with the organization's predetermined risk tolerance and regulatory requirements. Elements: 1. updating and protecting data 2. controlling cash flows 3. conducting due diligence on investments 4. handling exceptions and escalations 5. checklists to support important decisions In a good risk framework, processes would naturally evolve to consider risk at all key decision points, such as investment decisions and asset allocation.
Elements of Risk Infrastructure: (7 parts)
Definition: the people and systems required to track risk exposures and perform most of the quantitative risk analysis to allow an assessment of the organization's risk profile. Infrastructure would include: 1. risk capture (the important operational process by which a risk exposure gets populated into a risk system) 2. a database 3. data model 4. analytic models and systems 5. a stress or scenario engine 6. ability to generate reports 7. resources to build, execute risk framework
Returns Generating Models: Multi-Factor Model (general)
Determines the expected excess return (above the risk-free rate) for Asset i given a variety of factor variables. E(Rᵢ) - Rf = βᵢ,₁E(F₁) + βᵢ,₂E(F₂) + ... βᵢ,ₖE(Fₖ) where; E(Rᵢ) = expected return of asset i Rf = risk-free return βᵢ,₁ = betas are the factor sensitivities or factor loadings of the asset given each risk factor E(F₁) = expected value of risk factor 1 E(F₂) = expected value of risk factor 2 E(Fₖ) = expected value of risk factor k There are 3 types of factors (F): 1. Macroeconomic Factors (i.e. GDP growth, rates, etc.) 2. Fundamental Factors (earnings, leverage, etc.) 3. Statistical Factors (no basis in finance theory, just based on algorithmic variable groupings, not used too much)
M²Alpha
Difference between the risk-adjusted performance of the portfolio and the performance of the benchmark. M²Alpha = M² - Rₘ where; M²Alpha = % difference between RAP of Mkt v. Port. M² = RAP % of Portfolio Rₘ = benchmark market % return + M² Alpa = portfolio outperformed the market - M² Alpa = portfolio underperformed the market 0 M² Alpa = portfolio RAP equivalent to market
Diversifying with Index Funds
Diversifying among asset classes can become costly for small portfolios because of the number of securities required. For example, creating diversified exposure to a single category, such as a domestic large company asset class, may require a group of at least 30 stocks. Exposure to 10 asset classes may require 300 securities, which can be expensive to trade and track. Instead, it may be effective to use exchange-traded funds or mutual funds that track the respective indexes, which could bring down the costs associated with building a well-diversified portfolio. Therefore, many investors should consider index mutual funds as an investment vehicle as opposed to individual securities.
Portfolio Expected Return Formula
E(Rₚ) = [W₁×E(R₁)] + [W₂×E(R₂)] if given a required return, say x%, can solve using: x% = [W₁×E(R₁)] + [(1 - W₁)×E(R₂)], then consolidate the W₁'s and solve like you taught Anna lol.
Evaluate Each Asset Before Adding to your Portfolio (formula)
Every time you add a security or an asset class to the portfolio, recognize that there is a cost associated with diversification. There is a cost of trading an asset as well as the cost of tracking a larger portfolio. In some cases, the securities or assets may have different names but belong to an asset class in which you already have sufficient exposure. A general rule to evaluate whether a new asset should be included to an existing portfolio is based on the following risk-return trade-off relationship: E(Rₙ) = Rf + [(σₙ × ρₙ,ₚ) / σₚ] × [E(Rₚ) - Rf)] where; E(Rₙ) = expected return of new asset Rf = risk free rate σₙ = standard deviation (risk) of new asset ρₙ,ₚ = correlation of new asset with portfolio σₚ = standard deviation (risk) of portfolio E(Rₚ) = expected portfolio return If the new asset's risk-adjusted return benefits the portfolio, then the asset should be included. The condition can be rewritten using the Sharpe ratio on both sides of the equation as: [(E(Rₙ) - Rf) / σₙ] > [(E(Rₚ) - Rf) / σₚ) × ρₙ,ₚ] If the Sharpe ratio of the new asset is greater than the Sharpe ratio of the current portfolio times the correlation coefficient, it is beneficial to add the new asset.
Important data to gather from a client:
For Individuals: 1. family situation 2. employment situation 3. financial information 4. situation of client's spouse , family members 5. requirements of client's spouse, family members 6. The health of the client and his or her dependents In an institutional relationship: 1. key stakeholders in the organization 2. key stakeholder perspectives 3. key stakeholder requirements Notes on Info Gathering: : may be done informally or via structured interviews : may be done questionnaires or : may be done via analysis of data. : can be gathered electronically and use special systems that record data and produce customized reports. : Good record keeping is very important, and may be crucial in a case in which any aspect of the client relationship comes into dispute at a later stage.
Full Service Asset Manager
Full-service asset managers are those that offer a variety of investment styles and asset classes.
Technical vs. Fundamental Analysis Applications
Fundamental (widely used) 1. Equities 2. Fixed Income Technical (widely used) 1. Currencies 2. Commodities 3. Derivatives
Annualized Return How do you Annualize a Return?
General Formula : Annualized Return % = (1 + Rp)ᶜ With Daily Periods Given: : Ann. Ret. % = (1 + Rd)³⁶⁵/ᵈᵃʸˢ With Weekly Periods Given: : Ann. Ret. % = (1+ Rw)⁵²/ʷᵉᵉᵏˢ With Monthly Periods Given: : Ann. Ret. % = (1 + Rm)¹²/ᵐᵒⁿᵗʰˢ With Quarterly Periods Given: : Ann. Ret. % = (1 + Rq)⁴/ᑫᵘᵃʳᵗᵉʳˢ With More than 1-Year Period Given: : Ann. Ret. % = (1 + Rmos.)ʸᵉᵃʳ/ᵖᵉʳᶦᵒᵈˢ --> ex.) 18 mo. return is 4%. to annualize the return, Ann Ret. % = (1 + 0.04)²/³ = 2.65%. --> there are 2, 6 mo. periods in 1 year and 3, 6 mo. periods in 18 months, so 2/3 is the appropriate way to annualize this example.
Flow of Funds Indicators
Generally tell us what sentiment is, given asset flows. : more money flowing into low risk assets = negative : more money flowing into risky assets = positive 1. TRIN or ARMS - measures the relative extent to which money is moving into or out of rising and declining stocks. : index near 1 = market is in balance : index > 1 = more volume in declining stocks : index < 1 = more volume in rising stocks 2. Margin Debt : more margin loans = increase in purchases of stock : less margin loans = decrease in purchases of stock 3. Mutual Fund Cash Positions : low in uptrends, high in downtrends : easiest to see : tells us what "informed market participants" think : Example 1 - if cash is 2% of 100 largest mutual funds portfolio, tells us they are almost fully invested in the market (risk-on) : Example 2 - if cash is 11% of 100 largest mutual funds portfolio, tells us they are defensive (risk-off). 4. New Equity Issuance, Secondary Offerings
2. Execution Step: Asset Allocation (Goals + Considerations)
Goals are to: 1. Assess risk/return characteristics of investments 2. Form economic and capital market expectations 3. Form a proposed allocation of asset classes suitable for the client. Considerations include the distribution among: 1. Equities : sectors : trends 2. Fixed-Income Securities : corporate bonds, gov't bonds, etc. : investment grade, high yield 3. Cash : developed v. emerging, etc. : risk-on v. risk-off 4. Commodities 5. Real Estate 6. Funds 7. Private Equity 8. Geographical Weightings within asset classes.
Top Down example of practical (general) risk-management:
Good risk management ties together all steps from: 1. the highest governance decisions 2. to lower-level specifics, such as: : models : reports : operational checklists
Security Market Line (SML)
Graphical representation of the expected return-beta relationship of the CAPM. Formula for line = CAPM formula E(Rᵢ) = Rf + βᵢ(Rₘ - Rf) where; x-axis = βᵢ = systematic risk of the asset or portfolio y-axis = E(Rᵢ) = expected asset return y-intercept of SML = Rf = risk free rate of return Slope of SML = Rₘ - Rf = market risk premium Application: : Anything not on the Security Market Line is mis-priced : Asset returns above SML = underpriced : Asset returns below SML = overpriced : all securities will plot on the SML when markets are in equilibrium
Gross vs. Net Return (impact of fees)
Gross return : total portfolio return before deducting fees for the management and administration of the investment account. : Appropriate measure for evaluating and comparing the investment skill of asset managers because it does not include any fees related to the management and administration of an investment. Net return : the return after these fees have been deducted. : measures return of investment vehicle for the investor. Note: Trading + execution costs are deducted from both gross and net return.
Strategic Risk Analysis and Integration
Helps turn risk management into an offensive weapon to improve performance. Good risk management is a key to increasing the value of the overall business or portfolio. A risk management framework should provide the tools to better understand the how and why of performance and help sort out which activities are adding value, and which are not. In investing, rigorous analysis can support better investment decisions and improve strategy and risk-adjusted returns.
Stock Mutual Funds (2 types)
Historically, the largest types of mutual funds based on market value of assets under management are stock (equity) funds. 2 Types of Stock Funds: 1. Passively Managed (i.e. index funds) : buy and hold normally 2. Actively Managed (i.e. selected individual securities) : higher turnover of securities in portfolio : higher tax liability than passively managed via more frequent capital gains distribution
Margin Debt Rate of Change
How is margin debt changing in terms of volume? : % increasing or decreasing?
Hybrid / Balanced Mutual Funds
Hybrid or balanced funds are mutual funds that invest in both bonds and stocks. These types of funds represent a small fraction of the total investment in US mutual funds but are more common in Europe. Lifecycle or Target Date funds manage the asset mix based on a desired retirement date. For example, if an investor is 40 years old in 2019 and planned to retire at the age of 67, he could invest in a mutual fund with a target date of 2046 and the fund would manage the appropriate asset mix over the next 27 years. In 2019 it might be 90 percent invested in shares and 10 percent in bonds. As time passes, however, the fund would gradually change the mix of shares and bonds to reflect the appropriate mix given the time to retirement.
How are asset volatility and data frequency correlated in the context of technical analysis?
In general, the greater the volatility of the data, the greater the likelihood that an analyst can find useful information in more-frequent data sampling.
An asset's risk should be measured how?
In relation to the remaining systematic or non-diversifiable risk, which should be the only risk that affects the asset's price. This view of risk is the basis of the capital asset pricing model, or CAPM.
Defined Contribution Pension Plan
Individual accounts to which an employee and typically the employer makes contributions during their working years and expect to draw on the accumulated funds at retirement. The firm makes no promise to the employee regarding the future value of the plan assets. The investment decisions are left to the employee, who assumes all of the investment risk. The firm's contribution based factors including: 1. years of service 2. the employee's age 3. compensation 4. profitability 5. % of employee's contribution The employee bears: 1. the investment risk 2. inflation risk
Institutional Investors: Investment Companies
Investment Objective: - Manage the pooled funds of many investors Common Investment Characteristics: - Mutual funds manage funds in particular styles : index, growth, bond investing - restrict investments to subcategories of investments : large-firm stocks, energy stocks, speculative bonds - restrict investments to particular regions : emerging market stocks, international bonds, Asian-firm stocks
Institutional Investors: Insurance Companies
Investment Objective: - invest customer premiums to pay claims as they occur. Common Investment Characteristics: - General Account allocation : more conservative : IG fixed income - Surplus Account allocation (assets - liabilities) : more risky : higher return objective - Time Horizon : Life Insurance = long-term investment horizon : Property and Casualty (P&C) Insurers = shorter investment horizon because claims are expected to arise sooner than for life insurers.
Portfolio Planning Deliverables
Investment Policy Statement (IPS) 1a. General investment policy : communicates a plan for achieving investment success. : developed via fact-finding discussion with client, can include questionnaire to uncover risk tolerance, etc. : may involve asset-liability management studies, identification of liquidity needs, and a wide range of tax and legal considerations. 1b. Sustainable investment policy (esg)
Capital Market Expectations
Investor's expectations concerning the risk and return prospects of asset classes, however broadly or narrowly the investor defines those asset classes. Quantified in Terms Of: 1. asset class expected returns : E(r) = Rf + one or more asset class risk premium(s) : calculated via historical estimates, economic analysis, and various kinds of valuation models. 2. asset class standard deviation of returns : frequently based on historical data and risk models. 3. correlations among pairs of asset classes : frequently based on historical data and risk models. When associated with the client's investment objectives, the result is the strategic asset allocation that is expected to allow the client to achieve his or her investment objectives (at least under normal capital market conditions).
Main Conclusion of Modern Portfolio Theory
Investors should not only hold portfolios but should also focus on how individual securities in the portfolios are related to one another.
Passive Investment Strategy
Investors who believe market prices are informationally efficient often follow a passive investment strategy (i.e., invest in an index of risky assets that serves as a proxy for the market portfolio and allocate a portion of their investable assets to a risk-free asset, such as short-term government securities).
Passive Management: Smart Beta Asset Management Strategies
Involves the use of simple, transparent, rules-based strategies as a basis for investment decisions. Styles of "Smart Beta" include: - size - value - momentum - dividend characteristics Characteristics - higher management fees and - higher portfolio turnover relative to passive market-cap weighted strategies.
Common Diversification Strategy (use to construct portfolio)
It is not surprising that most diversified portfolios of investors contain: 1. domestic stocks 2. domestic bonds 3. foreign stocks 4. foreign bonds 5. real estate 6. cash 7. other asset classes
Buy Insurance for Risky Portfolios
It may come as a surprise, but insurance is an investment asset—just a different kind of asset. Insurance has a negative correlation with your assets and is thus very valuable. Insurance gives you a positive return when your assets lose value, but pays nothing if your assets maintain their value. Over time, insurance generates a negative average return. Many individuals, however, are willing to accept a small negative return because insurance reduces their exposure to an extreme loss. In general, it is reasonable to add an investment with a negative return if that investment significantly reduces risk (an example of a classic case of the risk-return trade-off). Alternatively, investments with negative correlations also exist. Historically, gold has a negative correlation with stocks; however, the expected return is usually small and sometimes even negative. Investors often include gold and other commodities in their portfolios as a way of reducing their overall portfolio risk, including currency risk and inflation risk. Buying put options is another way of reducing risk. Because put options pay when the underlying asset falls in value (negative correlation), they can protect an investor's portfolio against catastrophic losses. Of course, put options cost money, and the expected return is zero or marginally negative.
Lending vs. Borrowing (Leveraged) Portfolio's:
Lending portfolios : portfolios between 100% risk-free asset and 100% market portfolio on the CAL/CML : "lending" because some portion will be invested in the risk free asset, i.e. lending to the government to get the Rf rate of return. Leveraged Portfolios : portfolios to the right of the market portfolio on the CAL/CML : "leveraged" because to move beyond 100% of investable capital in the market portfolio, borrowing is required, which implies the investor is using leverage. : Implies a short position in the risk-free asset, i.e. borrowing at the risk-free rate and investing the borrowed capital in the market portfolio.
Linear vs. Logarithmic Scale
Logarithmic Scale: : Definition = A scale in which equal distances represent equal proportional changes in the underlying quantity. : Application = A logarithmic scale is appropriate when the data move through a range of values representing several orders of magnitude (e.g., from 10 to 10,000); Linear Scale: : Definition = A scale in which equal distances correspond to equal absolute amounts. Also called arithmetic scale. : Application = a linear scale is better suited for narrower ranges (e.g., prices from $35 to $50). The share price history of a particular company, for instance, is usually best suited to a linear scale because the data range is usually narrow.
Risk Governance
Managing risk to support organizations goals within it's risk tolerance. : done at enterprise level by senior management : risk management committee identifies risks that should be pursued, limited or avoided
Sentiment Indicators: Margin Debt (also a flow-of-funds indicator)
Margin debt magnifies the gains or losses resulting from the investment. Investor psychology plays an important role in the intuition behind margin debt as an indicator. : Rising margin debt = rising index level = bullish : Falling margin debt = falling index level = bearish : for the 113 months shown in Exhibit 31, the correlation coefficient between the levels of margin debt and the S&P 500 is 80.2 percent. ↳ When stock margin debt is increasing, investors are aggressively buying and stock prices will move higher because of increased demand. ↳ Eventually, the margin traders use all of their available credit, so their buying power (and, therefore, demand) decreases, which fuels a price decline. ↳ Falling prices may trigger margin calls and forced selling, thereby driving prices even lower.
Returns Generating Models: The Market Model (aka single index model, aka CAPM)
Market Model has a single risk factor, the market return. Equation is simply the equation for a straight line as in ( y = mx + b), because asset returns are a linear function of market returns. : Rᵢ = αᵢ + βᵢRₘ + eᵢ : E(Rᵢ) = αᵢ + βᵢRₘ ↳ can be re-written as CAPM: ↳ E(Rᵢ) = Rf + βᵢ(Rₘ - Rf) where; Rᵢ = realized asset return E(Rᵢ) = expected asset return αᵢ = intercept = Rf(1 - β) βᵢ = slope coefficient (i.e. sensitivity of returns to risk factor, market risk) Rₘ = market return eᵢ = abnormal return on asset i, which is a deviation from the expected return in a given period Details: : used to estimate a security's (or portfolio's) beta and to estimate a security's abnormal return (return above its expected return) based on the actual market return. : The intercept αi and slope coefficient βi are estimated from historical return data. : We can require that αi = Rf(1 − βi) to be consistent with the general form of a single-index model in excess returns form. : Regression analysis is done to plot the dots and the line based on the inputs provided (i.e. to plot the line) : Beta is the slope of the line, which tells us the sensitivity of the assets return to the market return Example: If Rᵢ = 1.5, then when then market is up 10%, the asset will be up by 15% (+50%).
Correlation Coefficient Formula (ρA,B)
Measured on an absolute scale from -1 to 1. ρ₁,₂ = cov₁,₂ / (σ₁ × σ₂) where; ρ₁,₂ = correlation of asset 1 and asset 2 cov₁,₂ = covariance of assets 1 and 2 σ₁ = standard deviation of asset 1 σ₂ = standard deviation of asset 2
Diversification Ratio
Measures the risk reduction benefits of a simple portfolio construction method, equal weighting. = equal weight portfolio σ / random security σ where; σ = standard deviation of returns : Lower diversification ratio = greater risk-reduction benefit from diversification. While the diversification ratio provides a quick measure of the potential benefits of diversification, an equal-weighted portfolio is not necessarily the portfolio that provides the greatest reduction in risk. Computer optimization can calculate the portfolio weights that will produce the lowest portfolio risk (standard deviation of returns) for a given group of securities. Example: Avg. σ of n stocks = 25% Avg. σ of equally weighted portfolio of n stocks = 18% Diversification Ratio = 18 / 25 = 0.72 or 72% , which means that the equally weighted portfolio's σ is approximately 71% of that of a in the set of n securities selected at random. - Note: If the standard deviation of returns for an equally weighted portfolio is 25%, there are no diversification benefits and the diversification ratio equals one. - Even if companies were chosen from a similar industry grouping, we see significant risk reduction. - An even greater portfolio effect (i.e., lower diversification ratio) could have been realized if we had chosen companies from completely different industries."
Money Weighted Return (or IRR -> same as YTM, CF yield -- internal return to a series of CF)
Money Weighted Return = Σ[CFₜ / (1 + r)ᵗ] = 0 where; CFₜ = cash flow to investor, not realized gain or loss : periods must have equal lengths : applies the concept of IRR to investment portfolios. : defined as the internal rate of return on a portfolio, taking into account all cash inflows and outflows. : Beginning value of account + deposits = inflow : Ending value + withdrawals from account = outflows : more weight given to periods with more money invested, and vice versa (gains/losses have more impact) Example: : investor buys a share of stock for $100 at t = 0 : at end of the year (t = 1), buys 1 more share for $120 : End of Year 2, investor sells both shares for $130 each. : each year the stock paid a $2.00 per share dividend : What is the money-weighted rate of return? Net cash flows: CF0 = -100; CF1 = -120 − 2 = -118; CF2 = +260 + 4 = +264 CPT IRR = 13.86%
Nominal vs. Real Returns (impact of inflation)
Nominal Return = (1 + Rf Rate) × (1 + Inflation rate) × (1 + Risk Premium) Real Return: removes impact of inflation = (1 + Rf Rate) × (1 + Risk Premium) or = (1 + Nominal Return) / (1 + Inflation) : Real return measures the increase in an investor's purchasing power : Real returns useful in comparing returns across time periods because inflation rates may vary over time. : Real returns useful in comparing returns among countries when returns are expressed in local currencies instead of a constant investor currency and when inflation rates vary between countries (which are usually the case). : After-tax real return is what the investor receives as compensation for postponing consumption and assuming risk after paying taxes on investment returns. : after-tax real return is a reliable benchmark for making investment decisions : not commonly calculated by asset managers because it is difficult to estimate a general tax component applicable to all investors.
Total Variance = Systematic Variance + Nonsystematic Variance
Nonsystematic Variance σ²ₑᵢ = σ²ᵢ − (β²ᵢ σ²ₘ σ²ₑᵢ) = σ²ᵢ − β²ᵢσ²ₘ
Risk Tolerance Factors + Definition
Overall level of risk exposure for that an organization will accept. Factors: 1. Expertise in specific lines of business 2. Ability to respond to external events (flexibility) 3. Financial strength 4. Regulatory environment Weigh risk exposures against their expected benefits
3 Core Performance Evaluation Questions
Performance evaluation seeks to answer the following questions: 1. Performance Measurement: analysis of return and risk. Q: What was the investment portfolio's past performance, and what may be expected in the future? 2. Performance Attribution: analysis of return drivers Q: How did the investment portfolio produce its observed performance, and what are the expected sources of expected future performance? :identifying + quantifying sources of portfolio 3. Performance Appraisal: analysis of investment skill Q: Was the observed investment portfolio's performance the result of investment skill or luck? : identifying and measuring investment skill.
CAPM Alternatives: Carhart 4 Factor Asset Pricing Model
Proposes that 3 factors seem to explain asset returns better than just systematic risk. Those 3 factors are relative size, relative book-to-market value, and beta of the asset. With Carhart's addition of relative past stock returns, the model can be written as follows: E(Rᵢₜ)= αᵢ+ βᵢ,ₘₖₜMKTₜ+ βᵢ,ₛₘSMₜ + βᵢ,ₕₘₗHMLₜ + βᵢ,ᵤₘUMₜ where; E(Rᵢ) = asset return in excess of 1-month T-bill return MKT = the excess return on the market portfolio SM = difference btwn. small-cap, large-cap ret (size) HML = the difference in returns between high-book-to-market stocks and low-book-to-market stocks (value versus growth) UM = difference in returns of prior year winners v. losers (momentum) Details: : Historical analysis shows coefficient on MKT is not significantly different from zero, which implies that stock return is unrelated to the market. : The factors that explain stock returns are ↳ size (smaller co.'s outperform larger companies) ↳ book-to-market ratio (value outperform glamour) ↳ momentum (past winners outperform past losers) The four-factor model has been found to predict asset returns much better than the CAPM and is extensively used in estimating returns for US stocks. But, there is no assurance that the model will continue to work well in the future.
Systematic Risk
Risk that affects the entire market or economy; it cannot be avoided and is inherent in the overall market. Systematic risk is also known as non-diversifiable or market risk. Systematic Risks Include: - interest rates - inflation - economic cycles - political uncertainty - widespread natural disasters : can be magnified through selection or using leverage : can be diminished by including low correlation securities to the portfolio : the expected equilibrium return (required return) on an individual security will depend only on its systematic risk.
Covariance Formula (cov₁,₂)
Sample Covariance Cov₁,₂ = (rₜ,₁ - x̄₁ )(rₜ,₂ - x̄₂ ) / (n - 1) Population Covariance Cov₁,₂ = (rₜ,₁ - μ₁ )(rₜ,₂ - μ₂ ) / n where; rₜ,₁ = observed return in period t for asset 1 rₜ,₂ = observed return in period t for asset 2 x̄₁ = sample mean of asset 1 x̄₂ = sample mean of asset 2 μ₁ = population mean of asset 1 μ₂ = population mean of asset 2 Note: It's very difficult to interpret a covariance directly, as we can only interpret if it is positive or negative and higher or lower than another covariance. Why? This is because covariance extends to infinity above and below 0, so the magnitude of the covariance is not based on an absolute scale. This is why we use correlation instead of covariance, because correlation is measured on an absolute scale (-1 to 1).
Short Interest Ratio
Sentiment Indicator Short Int. Ratio = # shares sold short / avg. daily volume : rising short interest = negative sentiment : falling short interest = positive sentiment
Put-Call Ratio
Sentiment indicator : put volume > call volume: Ratio > 1 ↳ negative sentiment : call volume > put volume: Ratio < 1 ↳ positive sentiment : also a contrarian indicator
Describe the systematic and nonsystematic risk components of the following assets: A. risk-free asset, such as a three-month Treasury bill B. The market portfolio, such as the S&P 500.
Solution to 1A: By definition, a risk-free asset has no risk. Therefore, a risk-free asset has zero systematic risk and zero nonsystematic risk. Solution to 1B: As we mentioned earlier, a market portfolio is a diversified portfolio, one in which no more risk can be diversified away. We have also described it as an efficient portfolio. Therefore, a market portfolio does not contain any nonsystematic risk.
Risk and Return of a Leveraged Portfolio with Equal Lending and Borrowing Rates Mr. Miles decides to set aside a small part of his wealth for investment in a portfolio that has greater risk than his previous investments because he anticipates that the overall market will generate attractive returns in the future. He assumes that he can borrow money at 5 percent and achieve the same return on the S&P 500 as before: an expected return of 15 percent with a standard deviation of 20 percent. Calculate his expected risk and return if he borrows 25 percent, 50 percent, and 100 percent of his initial investment amount.
Solution: The leveraged portfolio's standard deviation and return can be calculated with the following equations: E(Rₚ) = w₁Rf + (1 - w₁)E(Rₘ) , σₚ = (1 - w₁)σₘ Note: The proportion invested in T-bills becomes negative instead of positive because Mr. Miles is borrowing money. 1. 25% of initial investment is borrowed: w₁ = -0.25, and (1 - w₁) = 1.25, etc. : E(Rₚ) if w₁ = -0.25 = (-0.25 × 5%) + (1.25 × 15%) = 17.5%. : σ if w₁ = -0.25 = 1.25 × 20% = 25%. 2. 50% of initial investment is borrowed: : E(Rₚ) if w₁ = -0.50 = (-0.50 × 5%) + (1.50 × 15%) = 20.0%. : σ if w₁ = -0.50 = 1.50 × 20% = 30%. 3. 100% of initial investment is borrowed: : E(Rₚ) if w₁ = -1.00 = (-1.00 × 5%) + (2.00 × 15%) = 25.0%. : σ if w₁ = -1.00 = 2.00 × 20% = 40%. Note that negative investment (borrowing) in the risk-free asset provides a higher expected return for the portfolio but that higher return is also associated with higher risk.
Institutional Investors: Sovereign Wealth Funds
Sovereign wealth funds refer to pools of assets owned by a government. For example, the Abu Dhabi Investment Authority, a sovereign wealth fund in the United Arab Emirates funded by Abu Dhabi government surpluses, has approximately USD 700 billion in assets. Investment Objective: - varying investment horizons and objectives based on funding the government's goals Common Investment Characteristics: - manage fx reserves - manage government assets (pensions, etc.) - varying investment horizons and objectives based on funding the government's goals - The largest SWFs tend to be concentrated in Asia and in natural resource-rich places. Examples: - Singapore, Temasek Holdings: $375 Billion - Norway, Government Pension Fund: $1.058 Trillion
Specialist Asset Manager
Specialist asset managers may focus on a particular investment style or a particular asset class.
Steps Toward an Actual Portfolio
Step 1: Strategic Asset Allocation Step 2: Risk Budgeting
2. Execution Step: Portfolio Construction
Steps: 1. Asset Allocation 2. Risk Management 3. Trade Execution Key Objectives: - achieve optimal diversification - What is important is not the risk of any single investment, but rather how all the investments perform as a portfolio. Considerations: - asset class weightings - asset class sector weightings - individual security weightings Greatest Impact: - the asset allocation decision is commonly viewed as having the greatest impact.
Sentiment Indicators: VIX + overbought/sold Indicator
Technicians use the VIX in conjunction with trend, pattern, or oscillator tools, and it is interpreted from a contrarian perspective. When other indicators suggest that the market is oversold and the VIX is at an extreme high, this combination is considered bullish.
18-year Cycle
The 18-year cycle is interesting because three 18-year cycles make up the longer 54-year Kondratieff Wave. The 18-year cycle is most often mentioned in connection with real estate prices, but it can also be found in equities and other markets.
Moving Average Convergence/Divergence Oscillator (MACD) (momentum oscillator)
The MACD is the difference between a short-term and a long-term moving average of the security's price. Constructed via two lines, the MACD line and the signal line. Elements: : MACD line = difference between two exponentially smoothed moving averages, generally 12 and 26 days. : Signal line = exponentially smoothed average of MACD line, generally 9 days. : indicator oscillates around 0, no upper or lower limit. Overbought vs. Oversold: : analyst compares the current level with the historical performance of the oscillator for a particular security to determine when a security is out of its normal sentiment range. 3 Uses of MACD: 1. Crossovers of MACD & Signal Line ↳ MACD cross Signal Line from below = bullish ↳ MACD cross Signal Line from above = bullish 2. MACD outside normal range ↳ can set max to +1, min to -1 for a given security ↳ if MACD is outside normal range, then measure 3. Trend Lines on MACD itself ↳ MACD trending w/ direction of price = convergence ↳ MACD trending against price direction = divergence
Risk Tolerance
The amount of risk an investor is willing and able to bear to achieve an investment goal. : higher risk tolerance = greater willingness to take risks : risk tolerance is negatively related to risk aversion
Risk Budgeting: Tactical Asset Allocation
The decision to deliberately deviate from the policy exposures to systematic risk factors (i.e., the policy weights of asset classes stated in the strategic asset allocation) with the intent to add value based on forecasts of the near-term relative performance returns of those asset classes. Example: : an investor may decide to temporarily invest more of the portfolio in equities than the SAA prescribes if the investor anticipates that equities will deliver a higher return over the short term than other asset classes.
Jensen's Alpha
The difference between the actual portfolio return and the calculated risk-adjusted return is a measure of the portfolio's performance relative to the market portfolio. αₚ = Rₚ - {Rf + βₚ[E(Rₘ)- Rf]} remember, the second term in brackets is CAPM where; αₚ = portfolio alpha % based on systematic risk only Rₚ = portfolio return {Rf + βₚ[E(Rₘ)- Rf]} = CAPM Notes: : stated as % return : returns in the equation are all realized, actual returns. : based on systematic risk : portfolio risk (beta) equal but lies on the SML : By definition, αₘ of the market is zero. : If period contains multiple Rf, then avg. Rf is used. : Jensen's alpha is also the vertical distance from the SML measuring the excess return for the same risk as that of the market + αₚ = portfolio outperformed the market - αₚ = portfolio underperformed the market 0 αₚ = portfolio RAP equivalent to market : commonly used for ranking managers, funds, etc. : used to rank magnitude of under/over performance
2. The Execution Step: 3 Steps of Execution Phase
The execution step involves an analysis of the risk and return characteristics of various asset classes to determine how funds will be allocated to the various asset types. 1. Asset Allocation Target 2. Security Analysis 3. Portfolio Construction
1. The Planning Step: Investment Policy Statement
The first step in the investment process is to understand the client's needs (objectives and constraints) and develop an investment policy statement (IPS). (IPS) A written planning document that describes a client's investment objectives and risk tolerance over a relevant time horizon, along with constraints that apply to the client's portfolio. The IPS should be updated at least every few years and any time the investor's objectives or constraints change significantly.
7 Key Points of an Investment Policy Statement: (R-R-T-T-L-L-U)
The important points to cover in an IPS are: 1. Risk 2. Return 3. Time horizon 4. Tax situation 5. Liquidity 6. Legal restrictions 7. Unique constraints of a specific investor
Risk Management Framework (7 steps)
The infrastructure, process, and analytics needed to support effective risk management in an organization. This process should fully integrate the "risk" and "return" aspects of the enterprise into decisions in support of best achieving its goals within its tolerance for risk. 1. Identify risk governance policies and processes 2. Determine an organizations risk tolerance 3. Identify and measure risks ↳ unidentified risk can cause the biggest problems 4. Manage or mitigate risks 5. Monitor risk exposures 6. Communicate across organization 7. Perform Strategic Risk Analysis
Capital Asset Pricing Model (CAPM) same as single factor, single index model - used as the "required rate of return (RRR)" - used in context of asset selection
The model shows that the primary determinant of expected return for a security is its beta, or how well the security correlates with the market. The higher the beta of an asset, the higher its expected return will be. It is also the equation of the SML showing the relationship between expected return and beta: E(Rᵢ) = Rf + βᵢ(Rₘ - Rf) remember, CAPM is used as RRR, so E(Rᵢ) = RRR only when the markets are in equilibrium where; E(Rᵢ) = expected asset return βᵢ = slope coefficient (i.e. sensitivity of returns to risk factor, market risk) Rₘ = market return Rf = risk free return (rate) Implications: : CAPM is used as RRR, so E(Rᵢ) = RRR only when the markets are in equilibrium. ↳ forecast HPR = expected holding period return, calculated as expected cash flows over period, defined as HPR = (P1 - P0 + CF1) / P0 ↳ forecast HPR % > CAPM = underpriced asset ↳ forecast HPR % < CAPM = overpriced asset ↳ forecast HPR % = CAPM = equilibrium : β > 1 = expected return is higher than market return : β < 1 = expected return is less than market return : -β = required return will be less than the risk-free rate ↳ When combined with the market, the asset reduces the risk of the overall portfolio, which makes the asset very valuable. ↳Insurance is one such asset.
3. The Feedback Step: Performance Evaluation and Reporting
The performance of the portfolio must be evaluated, which will include assessing whether: 1. Return requirement has been achieved 2. Portfolio performance relative to any benchmark Analysis of performance may suggest that the client's objectives need to be reviewed and perhaps changes made to the IPS.
Global Minimum Variance Portfolio
The portfolio on the efficient frontier that has the least risk.
Risk Budgeting
The process of deciding on the amount of risk to assume in a portfolio (the overall risk budget), and subdividing that risk over the sources of investment return (e.g., strategic asset allocation, tactical asset allocation, and security selection). Based on: 1. Organizational goals and risk tolerance 2. Risk characteristics of assets or investments Measures: : VaR: Value at Risk : Portfolio Beta : Portfolio Duration Because the decision about the total amount of risk to be taken is made in constructing the IPS, at this stage we are concerned about the subdivision of that risk.
Risk Management Definition
The process of identifying the level of risk an organization wants, measuring the level of risk the organization currently has, taking actions that bring the actual level of risk to the desired level of risk, and monitoring the new actual level of risk so that it continues to be aligned with the desired level of risk.
After-Tax Nominal Return (impact of taxes)
The return after tax liability is deducted. The after-tax nominal return is computed as total return minus any allowance for taxes on dividends, interest and realized gains. ATNR % = Total Return - Tax Liability where; Total Return = Holding Period Return Tax Liability = any taxes on dividends, interest, short/long term cap. gains Taxable investors evaluate investment managers based on the after-tax nominal return.
Rebalancing Policy
The set of rules that guide the process of restoring a portfolio's asset class weights to those specified in the strategic asset allocation. As the portfolio is constructed and its value changes with the returns of the asset classes and securities in which it is invested, the weights of the asset classes will gradually deviate from the policy weights in the strategic asset allocation. This process is referred to as drift. Periodically, or when a certain threshold deviation from the policy weight (the bandwidth) has been breached, the portfolio should be rebalanced back to the policy weights. The set of rules that guide the process of restoring the portfolio's original exposures to systematic risk factors is known as the rebalancing policy. Even absent a formal risk budget, formulating a rebalancing policy is an important element of risk management, as the following example illustrates.
Returns Generating Models: Single Factor Model (general)
The simplest factor model is a single-factor model. A single-factor model with the return on the market, Rm, as its only risk factor. E(Rᵢ) - Rf = βᵢ × [E(Rₘ) - Rf] where; E(Rᵢ) = expected asset return βᵢ = slope coefficient (i.e. sensitivity of returns to risk factor, market risk) Rₘ = market return Rf = risk free return (rate) Note: Although the single-index model is simple, it fits nicely with the capital market line. As the capital market line equation is E(Rₚ) = Rf + [(E(Rₘ) - Rf) / σₘ] × σₚ, which when rearranged is equal to the single factor model or single index model formula. Thus, the CML, which holds only for well-diversified portfolios, is fully consistent with a single-index model.
9 Sections of the Investment Policy Statement
There is no single standard format for an IPS. Many IPS and investment governance documents with a similar purpose (as noted previously), however, include the following sections: 1. Introduction: describes the client. 2. Statement of Purpose: states the purpose of the IPS. 3. Statement of Duties and Responsibilities: details the duties and responsibilities of the client, the custodian of the client's assets, and the investment managers. 4. Procedures: explains steps to keep IPS current and the procedures to follow to respond to contingencies. 5. Investment Objectives: explains client objectives 6. Investment Constraints: presents constraint factors 7. Investment Guidelines: provides information about how policy should be executed (i.e., permitted use of leverage and derivatives) and on specific types of assets excluded from investment, if any. 8. Evaluation and Review: provides guidance on obtaining feedback on investment results, the benchmark portfolio, etc. 9. Appendices: (A) Strategic Asset Allocation (B) Rebalancing Policy. (C) Many investors specify a strategic asset allocation (SAA), also known as the policy portfolio, which is the baseline allocation of portfolio assets to asset classes in view of the investor's investment objectives and the investor's policy with respect to rebalancing asset class weights. This SAA may include a statement of policy concerning hedging risks (i.e. currency, interest rate risk)
Minimum Variance Portfolio (MVP) + Minimum Variance Frontier
These portfolios that have the lowest standard deviation of all portfolios with a given expected return are known as minimum-variance portfolios. How it works: For each level of expected portfolio return, we can vary portfolio weights on the individual assets to determine the portfolio that has the least risk. ↳ components = E(r), W₁, σₚ Together they make up the minimum-variance frontier.
Efficient Frontier
Those portfolios that have the greatest expected return for each level of risk (standard deviation) make up the efficient frontier. : coincides with top portion of minimum-var. frontier : portfolios that are not on the efficient frontier have lower expected returns than an efficient portfolio with the same risk : A risk-averse investor would only choose portfolios that are on the efficient frontier
Total Risk
Total risk = systematic risk + unsystematic risk (measured as standard deviation) : σ of returns is a measure of total risk : Well-diversified portfolios have low unsystematic risk : Total risk for a diversified portfolio is essentially equivalent to the systematic risk
Traditional vs. Alternative Asset Management
Traditional: : focus on equities and fixed-income securities. Alternative: : focus on asset classes such as private equity, hedge funds, real estate, or commodities : Profit margins tend to be higher : many traditional asset managers have been moving into this area, somewhat blurring the distinction between these types of firms.
Nonsystematic Risk
Unique risk that is local or limited to a particular asset or industry that need not affect assets outside of that asset class, can be diversified away from / avoided. Nonsystematic Risks Include: - failure of a drug trial - airliner crash - company scandal - resignation of key employee (ceo, etc.) : can avoid nonsystematic risk through diversification by forming a portfolio of assets that are not highly correlated with one another. : Therefore, according to theory, in an efficient market no incremental reward is earned for taking on diversifiable risk. : investors who have nonsystematic risk must diversify it away by investing in many industries, many countries, and many asset classes. : the expected equilibrium return (required return) on an individual security will depend only on its systematic risk.
Several assumptions about individual behavior that we make in the definition of utility: U = E(r) - 1/2 Aσ² where; U = utility of an investment E(r) = expected return A = marginal reward an investor requires to accept additional risk σ2 = variance of the investment
We assume that investors: 1. risk averse 2. prefer more to less (greater return to lesser) 3. rank different portfolios in a preferred order 4. rankings are internally consistent 5. If investor prefers X to Y and Y to Z, then must prefer X to Z. This property implies that the indifference curves for the same individual can never touch or intersect.
Portfolio Beta
Weighted average of portfolio stocks' betas. βₚ = ΣWᵢβᵢ or βₚ = W₁β₁ + W₂β₂ .... + Wᵢβᵢ where; Wᵢ = weight of asset i βᵢ = beta of asset i
Risk Seeking Investor
When investor prefers more risk to less (more risky) : if 2 investments have same return, higher risk is chosen : Thus, an investor choosing the riskier investment means that the investor gets extra "utility" from the uncertainty associated with the gamble. The value of the extra "utility" provided by uncertainty will ultimately determine if the investment is worthwhile for them.
Risk Averse Investor
When investors prefer less risk to more risk. (less risky) : if 2 investments have same return, lower risk is chosen : if 2 investments have same risk, higher return is chosen : if risky investment offers sufficient return, risk averse investors may still invest because the expected return is adequate compensation for the additional risk. Note: investors do not minimize risk, it's a trade off between risk and return.
Regression Analysis for Beta
While regression is a Level II concept, for our purposes, you can think of it as a mathematical estimation procedure that fits a line to a data plot. OLS Regression is what is used. Details: Y-Axis = Excess Asset Returns (Ri - Rf) X-Axis = Excess Market Returns (Rm - Rf) Y-Intercept = αᵢ Slope Coefficient = βᵢ = Covᵢₘ / σ²ₘ Line = Security Characteristic Line, which summarizes a particular security's systematic risk and rate of return The least squares regression line is the line that minimizes the sum of the squared distances of the points plotted from the line (this is what is meant by the line of best fit). The slope of this line is our estimate of beta. In Regression of Asset Excess Returns Against Market Asset Returns, the line is steeper than 45 degrees, the slope is greater than one, and the asset's estimated beta is greater than one. Our interpretation is that the returns on Asset i are more variable in response to systematic risk factors than is the overall market, which has a beta of one.
Extreme Value Theory (need to find these benchmarks online)
a branch of study that focuses primarily on extreme outcomes, which is called extreme value theory, and leads to measures of the statistical characteristics of outcomes that occur in the tails of the distribution. There are mathematical rules that define the statistical properties of such large outcomes, and these rules have been widely used for years in the insurance business. In the past 20 years or so, risk managers have taken to using them to help gauge the likelihood of outcomes that exceed those that would normally be expected.
Capital Allocation Line (CAL)
line chart plot of risk-return combinations available by varying portfolio allocation between a risk-free asset and a risky portfolio. : move up and down the line by allocating more/less capital to either the risk-free asset or risky portfolio (i.e. changing the weights). : The capital allocation line represents the portfolios available to an investor. Formula for CAL: E(Rₚ) = Rf + [(E(Rᵢ) - Rf) / σᵢ] × σₚ where; E(Rₚ) = expected return of portfolio Rf = risk free asset return E(Rᵢ) = expected return of risky asset σᵢ = standard deviation of risky asset σₚ = standard deviation of portfolio : Intercept of y-axis = Rf : slope of CAL = (E(Rᵢ) - Rf) / σᵢ which is the additional required return for every increment in risk, and is sometimes referred to as the market price of risk.
Which return measure does an investor actually receive?
net-of-expenses after-tax real return
Capital Market Line (CML)
the capital allocation line using the market index portfolio (i.e. S&P500, etc.) as/instead of the risky asset. Formula for CML: E(Rₚ) = Rf + [(E(Rₘ) - Rf) / σₘ] × σₚ where; E(Rₚ) = expected portfolio return, not including Rf asset Rf = risk free asset return E(Rₘ) = expected return of the market (risky asset) σₘ = standard deviation of the market (risky asset) σₚ = standard deviation of portfolio : Intercept of y-axis = Rf : slope of CAL = (E(Rᵢ) - Rf) / σᵢ which is the additional required return for every increment in risk, and is sometimes referred to as the market price of risk. : CML is tangent to the efficient frontier of risky assets : the market portfolio is the point on the Markowitz efficient frontier where a line from the risk-free asset is tangent to the Markowitz efficient frontier. : The combinations of the risk-free asset and the market portfolio, which may be achieved by the points between these two limits, are termed "lending" portfolios. In effect, the investor is lending part of his or her wealth at the risk-free rate. : All points on the interior of the Markowitz efficient frontier are inefficient portfolios in that they provide the same level of return with a higher level of risk or a lower level of return with the same amount of risk. : When plotted together, the point at which the CML is tangent to the Markowitz efficient frontier is the optimal combination of risky assets, on the basis of market prices and market capitalizations. The optimal risky portfolio is the market portfolio.
CML vs. SML Capital Market Line vs. Security Market Line
the capital market line (CML) does not apply to all securities or assets but only to portfolios on the efficient frontier. ↳Efficient frontier gives optimal combinations of expected return and total risk. ↳ only assets that plot on the CML are market (i.e. sp500) and risk free assets. ↳ slope of CML is sharpe ratio the security market line applies to any security, efficient or not. ↳Total risk and systematic risk are equal only for efficient portfolios because those portfolios have no remaining diversifiable risk.
The larger the bid-ask spread,
the higher the cost of trading.
Risk Identification and Measurement Process (5 steps)
the main quantitative core of risk management; : must include qualitative assessment and evaluation of all potential sources of risk and the organization's risk exposures. This ongoing work involves: 1. analyzing environment for relevant risk drivers (fundamental underlying factors) 2. analyzing business / portfolio to see risk exposures 3. tracking changes in risk exposures 4. calculating risk metrics 5. sizing risks under various scenarios and stresses
The point where the efficient frontier intersects with the indifference curve with the highest utility attainable (i.e., the point of tangency) represents what?
the optimal asset allocation for the client/investor, i.e. the point of tangency represents the strategic asset allocation.
Performance Measures: σ v. β
σ : standard deviation measures total risk : better to use for non-fully diversified portfolios β : beta measures systematic risk only : better to use for fully diversified portfolios (i.e. market)
Portfolio Standard Deviation (given variance, converting to σₚ)
σ²ₚ = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov₁,₂ ↳ we can substitute Cov₁,₂ = ρ₁,₂σ₁σ₂ to get portfolio standard deviation formula ↳σₚ = √w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρ₁,₂σ₁σ₂ where; w₁ = weight of investment 1 σ₁² = variance of investment 1 ρ₁,₂ = correlation coefficient of investment 1 and 2 Cov₁,₂ = covariance of investment 1 and 2
