Investments - 11% - 14 questions

CBOE Volatility Index (VIX)

"investor fear gauge". 1. Primary use of the VIX volatility index is as an indicator to options traders as to when they should buy or sell options. When the VIX is low, it's a good time to buy options as they are now relatively cheap. 2. After the VIX has established its peak, one should sell options as they have become more expensive. 3. Negative correlation to the S&P 500, measures market expectation of 30-day volatility 4. It trades within a given range of between 10 and 50. The VIX bottoms out at around 10. 5. It can never reach zero as that would mean that the market expects no daily movement of the underlying S&P 500 index - which is an impossibility. 6. For the VIX to stay above 50 requires large changes over an extended period of time - another near impossibility.

Tactical Asset Allocation

- Allows the advisor to make changes to a portfolio allocation based on their convictions about various asset classes looking forward. Strategy that actively adjusts asset allocation based on what can be numerous factors including valuation, momentum, risk metrics, etc. - At its simplest level, an advisor using tactical asset allocation may overweight or underweight stocks or bonds in an investment portfolio. -Some tactical asset allocation strategies may just move from stocks to cash and back depending on the advisor's expectations -Begin with a core model allocation and then use various methods such as market timing, technical analysis, economic overlay, momentum, and other strategies to make changes within the portfolio.

After tax performance Analysis

- Analysis of after-tax returns is not uniform across reporting services, in part because there is currently no consensus on which metrics are most efficient in most cases. The two main approaches used by evaluation services are: I. Net out all taxes when paid II. Assume the fund was fully liquidated at the end of the reporting period.

Standard Deviation

- Standard deviation (SD) is represented by Greek letter sigma (σ). - Measure of volatility (i.e., risk). - Measures amount of variation or dispersion from an average. - SD is considered a measure of "total risk." - The SD of a random variable is the square root of its variance. -SD is used in the Capital Allocation Line (CAL). -SD is used in the Sharpe Ratio, M2, information -The Treynor Ratio uses beta to measure risk.

Components of tax efficiency

- Tax rates - Tax rules - Turnover - Tax lot identification and management - Tax gain/loss harvesting - Wash sale-rules - Asset location - Measurements

High water mark

- The fee structure can give incentives to shut down a poorly performing fund • If a fund experiences losses, it may not be able to charge an incentive unless it recovers to its previous higher value • With deep losses, this may be too difficult so the fund closes

Utility function

-A formula for calculating the total utility that a particular person derives from consuming a combination of goods and services -Your utility function determines how happy you are with your portfolio -You are happier with a higher expected return and lower variance

After tax returns

-After-tax return can be equal to or less than the before-tax return. Remember also that the after-tax return can be greater than the before-tax return (e.g., losses in the fund have been realized but not yet recognized for tax purposes).

Low Volatility Funds

-Low-vol (and "min-vol") funds use different strategies in the name of providing portfolios that are more stable than the broader market. -They help mitigate losses during downturns, but the reduction in volatility can give you a little peace of mind and let you participate in an eventual bounce-back Low Volatility ETFs invest in securities with low volatility characteristics. These funds tend to have relatively stable share prices, and higher than average yields

Covariance

-Measures how much two random variables move or change together -Negative covariance means that variables move inversely -Assets possessing a high covariance with each other do not offer much diversification -Covariance matrixes are used to show the correlation between multiple assets -Sometimes it is desirable to determine how a return varies from other returns instead of its own return. This variability is measured by the covariance. -Can be difficult to interpret. It is often converted into the correlation coefficient, which is easier than covariance to interpret.

Coefficient of Determination (R-squared)

-R2 (also known as the coefficient of determination) •gives the proportion of variation in one variable that can be explained by another variable •this metric indicates the "closeness of fit" or "accuracy of fit" •keep in mind that no causality is claimed by the coefficient of determination Applications: • the higher the number the more meaningful the relationship • measurements below 0.8 would indicate a weak relationship between variables (i.e., the benchmark is not as helpful as a comparative tool) • R-squared gives us an indication of the level of diversification in a portfolio • assuming the benchmark/index is diversified, a portfolio is well diversified if it has a high R-squared relative to that index • R-squared on a portfolio also gauges the reliability of alpha as an indicator of the manager's return and beta as an indicator of risk

Utility Function

-The stock index has a higher expected return but a higher standard deviation (more risk) -We use a utility function to decide U(E[r],σ )=E[ y σ 2 -Your utility function determines how happy you are with your portfolio -You are happier with a higher expected return and lower variance

Describe liability-driven investment (LDI) platforms

-Underfunded plans not able to simply match interest rate exposure of liabilities to interest-rate exposure of assets. -The gap in interest rate risk between liabilities and assets is often difficult to address. -The emphasis should be on total returns, and consistent returns with low volatility.

Core principle of goals-based investing

-matching assets with liabilities -identifying risk capacity, not risk tolerance -allocating a specific amount to cash to meet immediate needs

Master Limited Partnership (MLP)

1. A partnership that looks much like a corporation (in that it acts like a corporation and is traded on a stock exchange) but is taxed like a partnership and thus avoids the corporate income tax. 2. Investment structures require 90% of cash flow to come from real estate, commodities, or natural resources, although their are exceptions. 3. The potential for unrelated business taxable income may make these inappropriate for retirement accounts. 4. Traded on a public exchange 5. UBTI, illiquidity and leverage are all potential reasons why LPs and/or MLPs may not be suitable for these types of accounts.

Beta Coefficient

1. Beta coefficient is a measure of systematic risk and should be used for a diversified portfolio. In the construction of a well-diversified portfolio, all unsystematic risk is removed. 2. The beta coefficient is a measure of volatility for a diversified portfolio—that is, the volatility of some return relative to a benchmark. 3. portfolio's historical beta coefficient can be used as an indicator of future portfolio volatility 4. beta has little meaning if the returns between the fund and the market are weak. 5. the coefficient of determination is used to determine if beta is meaningful.

Core Principles of Goals Based Investing

1. identifying risk capacity, not risk tolerance 2. matching assets with liabilities 3. allocating a specific amount to cash to meet immediate needs

Criticism's of MPT

1. taxes and transactions costs are real 2. investors are not exclusively risk-averse 3. inputs are measured with error

Buy-Write Strategy

1. Buy-write is an option trading strategy where an investor buys a security, usually a stock, with options available on it and simultaneously writes (sells) a call option on that security. 2. The purpose is to generate income from option premiums. 3. The option position only decreases in value if the price of the underlying security increases, the downside risk of writing the option is minimized. 4. This strategy can be periodically repeated to increase returns during a time when the movement of the security is lackluster. BuyWrite ETFs invest by utilizing the covered call strategy. These funds are attractive to investors who want some aggressive exposure but don't want to get involved with complicated strategies Most common example of this strategy is the use of a covered call on a stock already owned by an investor.

Correlations of most alternative investments

1. Despite high levels of individual, idiosyncratic risk, historically alternative investments ("alts") have reduced portfolio risk over long-periods of time. 2. Correlations of "alts" to most traditional investments did rise significantly during financial crises. 3. History shows that in the short-run correlations of most assets do indeed increase in times of higher volatility. 4.Correlations of most alternative investments with traditional asset classes increased in the bear market of 2007-2009. In other words, diversification using most alternative investments did not significantly reduce short-term downside risk during financial crises.

Macroeconomic Factor Investing

1. Economic growth - exposure to the business cycle 2. Real Rates - Risk of interest-rate movement 3. Inflation - Exposure to change in prices 4. Credit - Default risk from lending to companies 5. Emerging Markets- Political and sovereign risks 6. Liquidity - Holding illiquid assets

Information Ratio

1. IR equals the average excess portfolio return above a benchmark, divided by risk (measured by standard deviation). 2. Ratio provides guidance regarding a manager's ability to persistently produce returns above the benchmark. 3. Captures the size (amount) of excess return and the ability to do so consistently. IR = excess return/standard deviation IR = portfolio return - benchmark return/tracking error

Liability Driven Investing (LDI)

1. Liability-driven investments are commonly used in defined-benefit pension plans or other fixed-income plans to cover current and future liabilities through asset acquisitions. 2. The general approach to liability-driven investment plans consists of minimizing and managing liability risk followed by generating asset returns. 3. It is important to acknowledge that one's skill in managing assets via asset allocation, security selection, and/or timing should not be considered the exclusive remedy for improving funding ratios. Also technical analysis is not an appropriate. 4. Underfunded plans not able to simply match interest rate exposure of liabilities to interest-rate exposure of assets. 5. The gap in interest rate risk between liabilities and assets is often difficult to address.

Collar Option

1. Options-based hedge involves selling (writing) an out of the money call and buying an out of the money put with the same expiration date on an underlying asset that has embedded gains. 2. This strategy intends to lock in profits by buying downside protection while calls are sold to generate income to help pay for this downside protection. 3. Properly executed, these strategies preserve capital and the holding period of low cost basis stock.

Risk Parity Approach

1. Portfolio approach to asset allocation that focuses on the amount of risk units allocated to each investment or asset class as opposed to percentage allocations to asset classes based on MPT and MVO 2. Asset allocation that should be designed to balance risk (although not perfectly) 3. Common risk components include equities, credit, interest rates and commodities 4. Many portfolios leverage lower risk assets by employing debt to achieve an acceptable expected return.

Sortino Ratio vs Sharpe Ratio

1. The Sortino Ratio is identical to the Sharpe Ratio except that it uses downside semi-standard deviation (the standard deviation of the negative asset returns) instead of standard deviation (which includes the deviations of both positive and negative returns) 2. Sortino Ratio is better used when analyzing portfolios with high volatility.

Correlation Coefficient

1. The correlation coefficient is a measure of how different returns vary for different stocks. The numerical values of the correlation coefficient range from +1 to −1. If two variables move exactly together, the value of the correlation coefficient is 1. 2. Correlation coefficient is the engine that drives the whole theory of portfolio diversification. 3. There is an inverse relationship between correlation and diversification. The lower the correlation, the greater the diversification

Gains-titled Strategy

1. This strategy increases total portfolio volatility 2. Overweight value stocks in tax-deferred accounts 3. Overweight growth stocks and invest in tax-free bonds

Style Factor Investing

1. Value -Stocks discounted relative to their fundamentals 2. Minimum Volatility - Stable, lower-risk stocks 3. Momentum - Stocks with upward price trends 4. Quality - financially healthy company 5. Size - smaller, high-growth companies 6. Carry - income incentive to hold risker securities

Straddle Option

1. a strategy in which an investor purchases both a put and call on the same security with the same strike price and expiration; 2. Used when an investor believes the stock price will move significantly but does not know which way the stock will go (up or down)

Inputs need to calculate the optimal investment portfolio according to Modern Portfolio Theory include

1. expected returns 2. standard deviation 3. covariance

Coefficient of Variation (CV)

1.) To compare a series of very different values, the coefficient of variation is preferred to using only standard deviation. 2.) Where standard deviation is a measure of absolute dispersions, the coefficient of variation is a measure of relative dispersions. 3.) The coefficient of variation is defined as the ratio of the standard deviation divided by the mean. 4.) The larger value indicates greater dispersion relative to the arithmetic mean of the return.

3 Step Asset Allocation Problem

1.Make forecasts about the assets 2.Decide the feasible set of investments available to us (i.e., by varying our fraction of wealth w we invest in each) 3. From the set of all feasible options, choose the one that maximizes our utility (makes us happiest) 1. For each of the securities, forecast the quantities we need: -Expected returns, E[r] -Standard deviations, σ -co variances

Geometric Averages

A geometric mean is found by multiplying the different stock prices and then taking the nth root, where n equals the number of stocks. The geometric mean tends to produce a downward bias in the index when compared to the arithmetic mean. This is illustrated by taking two stocks priced at $10 and $20: We find that the geometric average is lower than the arithmetic average. Most annual returns are calculated using the geometric average because n represents the number of compounding periods. Compounding allows for the true yearly return to be determined.

Modern Portfolio Theory (MPT)

A method of choosing investments that focuses on the importance of the relationships among all of the investments in a portfolio rather than the individual merits of each investment. The method allows investors to quantify and control the amount of risk they accept and return they achieve.

Horizontal Spread Option - Calendar Spread

A strategy where an investor buys and sells two options, on the same underlying asset, that have the same strike price but different expiration dates. Profits are made from changes in the price difference as securities move closer to expiration dates. Also called "calendar spreads" and "time spreads."

Spread Option

A type of option or strategy in which the option derives its value from the price difference between two or more underlying assets. •A spread is a combination of two or more calls (or two or more puts) on the same stock with differing exercise prices or times to maturity. •Some options are bought, whereas others are sold, or written. •A bullish spread is a way to profit from stock price increases.

Equity Premium

Additional return investors must receive in order to invest in equities rather than treasury bills. The average return of stocks minus the average return on T Bills

Alpha

Alpha is the expected risk-adjusted return on the asset. If α is positive, that means we think the asset will outperform after adjusting for market risks.

Arithmetic mean

An average that is calculated by adding up a set of quantities and dividing the sum by the total number of quantities in the set.

The Sharpe Ratio for Company A is 0.34, while the Sharpe ratio for Company B is 0.39. What can be said about Company B?

As measured by the Sharpe ratio, Company B's risk adjusted return is superior. Sharpe ratio measures units of return experienced based on units of risk taken (i.e., it measures risk-adjusted returns). It is useful for comparing to other investments.

AI Categories

Broad AI Categories (by "inclusion") Real Assets Hedge Funds Commodities Private Equity Structured Products

A long call option allows the buyer to:

Buy the underlying asset at the exercise price on or before the expiration date or sell the option in the open market prior to expiration.

Unrelated Business Taxable Income (UBTI)

Can create current tax liability (and possible re-characterization) for tax-deferred accounts due to gains realized from investment activities such as leveraged trading strategies and other gain producing activities not considered directly related to the main function of the entity. Subject to federal and state income tax.

AI Characteristics

Concentrated or diversified Often illiquid High fees and expenses Lowly or uncorrelated to traditional investments Low to high risk spectrum Not very transparent Not highly regulated Constraints for investments and withdrawals Reporting inaccuracies and biases

Correlation

Correlation, which is covariance standardized by the product of the standard deviations of the two securities, may assume values only between +1 and -1; thus, both the sign and the magnitude may be interpreted regarding the movement of one security's return relative to that of another security.

"Vintage Year" Concept

Defined: vintage year refers to the first (initial) year of investment Application: vintage year analysis is common for venture capital projects and other private equity investments as well as real estate investment

Dollar-Weighted Return (DWR)

Dollar-weighted returns = Investor's return = Considers cash flows = IRR The dollar-weighted rate of return applies the concept of IRR to investment portfolios. The dollar-weighted rate of return is defined as the IRR of a portfolio, taking into account all cash inflows and outflows.

Dynamic Asset Allocation

Dynamic asset allocation (DAA) is a method of changing the allocation of the portfolio based on market conditions. -Strategy that provides exposure to an underlying asset(s) or allocation while guaranteeing principle at some level -Dynamic rebalancing may be difficult for private investors or institutions. -Most investors are more worried about downside risk then their gains. Because of this a dynamic asset allocation approach may be preferred. -If the risky part of the portfolio underperforms the safer part, the investor would take less risk by changing the allocation in favor of the safer assets. -valuation levels, the profitability of corporations, credit spreads, the direction and level of interest rates are some of the variables that may be used to make DAA decisions. DAA can smooth volatility and reduce the frequency of large tail losses (extreme event losses).

Pair-wise Trades

Example: sell asset at a loss (to harvest tax losses) and buy a comparable, but not identical, asset to maintain risk exposure while avoiding wash sale rules

Efficient Frontier

Graph representing a set of portfolios that maximizes expected return at each level of portfolio risk Investors seek investments that are in the northwest quadrant of the return/risk grid. When investments are not tax-efficient, they tend to move south.

Efficient Frontier

Graph representing a set of portfolios that maximizes expected return at each level of portfolio risk The more assets we add, the more the efficient frontier extends in the north westerly direction, offering more diversification

Covariance

Measures whether security returns move together or in opposition; however, only the sign, not the magnitude, of covariance may be interpreted.

Factor Analysis / Factor Investing (smart Beta)

Method for analyzing risk and performance characteristics beyond the traditional asset classes Often based on "macroeconomic" themes and "style" factors Can be used in conjunction with mean variance optimization models Common macroeconomic factors include: growth, real rates, inflation, credit quality and spreads, liquidity Common style factors include: value, momentum, volatility, quality, size and carry The intention is to identify and profit from investment factor strategies that outperform the market as a whole through timing and/or benefiting from a lack of correlation between these investments

Risk Parity Investment Approach

Portfolio approach to asset allocation that focuses on the amount of risk units allocated to each investment or asset class as opposed to percentage allocations to asset classes based on MPT and MVO •asset allocation should be designed to balance risk (although not perfectly) •common risk components include equities, credit, interest rates and commodities •many risk parity portfolios leverage lower risk assets to achieve an acceptable expected return

AI Benefits and Risk

Potential Benefits: diversification, hedging, performance, innovation, leverage, etc. Risks/Disadvantages: lock-up periods, high fees, taxes, lack of transparency, reporting standards, less regulation, risk of total loss, leverage, volatility, illiquidity, etc.

Mean-Variance Optimization ("MVO")

Process or method that measures the efficiency of various mixes of assets or investments that seeks the optimal combination of choices through diversification that minimizes risk per unit of return gained Advantages 1. Helps quantify risk and return to build optimal portfolios; 2. Can help manage risk; 3. Aligns an investor's attitude and aptitude for taking risk with an appropriate mix of assets Disadvantages 1. Assumes investors are rational; 2. Assumes history of risk and return characteristics are reasonable predictors of future performance; 3. Assumes fundamental characteristics of capital markets will remain the same 4. Does not incorporate the potential for major shocks to economies or financial markets

CAPM Example Calculation

Required rate of return using the following data: Risk-free rate = 3% Market return = 10% Fund's beta = 1.15 Use the CAPM formula to solve this problem. r = rf + (rm − rf) beta r = 3% + [(10% - 3%)x1.15] r = 3% + (7% x 1.15) r = 3% + 8.05% r = 11.05%

Risk Budgeting Investment Strategies

Risk Budgeting involves analyzing specific risk characteristics of individual assets or investments and considering how the additional of individual assets or investments impacts the risk profile of the entire portfolio. 1. There are many ways to incorporate risk budgeting into investment portfolio management. 2. VaR can be used to budget portfolio risk.

Jensen CAPM Example

Risk Free = 3% Beta= 1.75 Alpha = 0 Average Return = 16% Use Jensen's metric that incorporates the CAPM. Alpha = Ra - [Rf + Beta(Rm - Rf)] Ra = Rf + Beta (Rm - Rf) 16 = 3 + 1.75 (x - 3) 13 = 1.75x - 5.25 1.75x = 18.25 x = 10.4286

Fama French 3 Factor Model

Risk factors are: • Firm size • Book-to-market ratio • Excess return on the market portfolio market, size and value Carhart added a 4th factor, momentum. These models explain US equity returns better than the market (single-index) model

Socially Responsible Investing

Socially Responsible Investing (SRI) Environmental, Social and Governance (ESG) Inclusionary and Non-inclusionary strategies and funds 1. There are no clear conclusions on whether these types of funds deliver outperformance (data is conflicting at best) compared to the market as a whole . 2.Data cannot prove with certainty outperformance or underperformance over time (without data mining). 3. Popularity of investment companies engaging in ESG/SRI investing continues to rise in a significant way. 4. Performance attribution due to size and style are more significant than screening for social responsibility. Morningstar Sustainability Rating Measures how well the companies held in a portfolio are managing their ESG risks and opportunities relative to portfolios within their same category.

Sharpe Ratio

Sp = rp - rf / SD Reward-to-volatility ratio; ratio of portfolio excess return to standard deviation. • A risk-adjusted performance metric measuring how much return is achieved per unit of risk taken. • Measures total risk (using standard deviation). • MPT serves as the foundation for the Sharpe ratio (i.e., the higher the Sharpe ratio, the closer the portfolio is to the mean variance portfolio). • The higher the Sharpe ratio the better. • The Sharpe ratio is better used when analyzing portfolios with low volatility (vs. Sortino Ratio).

Market Timing Theory

Strategy that buys and sells assets in an attempt to predict market prices through fundamental, technical, or macro-factor analysis

Strategic Asset Allocation

Strategy that implements an asset allocation with target asset weightings and seeks to maintain these allocations. The objective of strategic allocation is to maintain these mixes. -Strategic asset allocation may be easier to implement and manage. -Usually this mix will not be changed over time unless there are significant changes in the investor's objectives or tolerance for risk. -simply rebalance the portfolio to bring it back to the original allocation over time -balancing should be based on economic decisions rather than strictly tax decisions. The advisor should attempt to be tax aware not tax efficient.

Dynamic Asset Allocation

Strategy that provides exposure to an underlying asset(s) or allocation while guaranteeing principle at some level

Strangle Option

Strategy where an investor holds a put and a call on the same asset, with the same maturity, but with different strike prices; Used when there is an expectation of large price swings in the underlying asset.

Systematic Risk (a.k.a. market risk) - Beta

Systematic risk is a broad category or composite of risk that affects the entire market rather than unique to a particular security. In effect, all securities tend to move together in a systematic manner in response to these risks. As a result, systematic risk is non-diversifiable, as it effects the entire market, regardless of which stocks an investor owns. Examples include market risk, interest rate risk, purchasing power risk, foreign currency risk, and reinvestment risk. Systematic risk cannot be eliminated through diversification or minimized because it affects the entire market. Beta is a measure by which systematic risk is determined. Beta is only an accurate measure of systematic risk when calculated for a diversified portfolio.

Taxable Equivalent Yield (TEY)

TEY = Tax-Exempt Yield / (1 - Marginal Tax Rate) = 3.25% / (1 - 40%) = 3.25% / .60 = 5.4167% You use the income tax rate, not the capital gains rate, as income from bonds is normally taxed as ordinary income.

Specific lot method

Tax accounting system in which the investor keeps track of all assets by transaction (e.g., purchase info, additional inflows and outflows, and sale) and through which the investor may subsequently choose to allocate individual shares or lots when determining basis at the time of sale or disposition.

Portfolio Turnover Rate

Tax-efficiency Ratios a simple measure of potential taxation, but not usually the best measure of tax-efficiency measures how often assets or investments in a fund or portfolio are bought and/or sold within a specific time period (usually measured annually) calculated by dividing the net assets or investments bought and sold by the portfolio value (e.g., NAV)

Consultant Capture Ratio

Tax-efficiency Ratios captures the percentage of return that taxable investors retain CCR = after-tax return / before-tax return works well in smooth, upward-trending markets

Relative Wealth Measure

Tax-efficiency Ratios the higher the better; zero indicates little tax impact RWM = [(Rat - Rbt) / (1 + Rbt)] x 1,000 RWM works in all kinds of markets RWM is particularly helpful when analyzing separately managed accounts

Capital Gains Realization Rate

Tax-efficiency Ratios the percentage of the fund's net unrealized capital gains that the manager chose to realize CGRR = CGDIST/GAINSTOCK

J-Curve Concept

The "j-curve" concept relates to the expectation that for some investments, such as private equity, there are negative cash flows for several years before leading to positive cash flows in later years.

Before-tax Alpha Hurdle

The before tax alpha hurdle for a traditional equity manager is 3.0% needed to outperform a passive or indexed alternative.

Real Return (inflation adjusted)

The inflation premium is an adjustment to the real risk-free rate to compensate investors for expected inflation and tightening or easing of monetary policy due to inflationary expectations. Nominal rate of return investors require is: Nominal risk-free rate = (1 + real risk-free rate) (1 + inflation rate) − 1 The nominal risk-free rate is the real risk-free rate adjusted for expected inflation and the relative tightening or easing in capital markets: Real risk-free rate = [(1 + nominal risk-free rate) / (1 + inflation rate)] − 1

Diversification

The process of investing in numerous securities or asset classes in order to reduce (non systematic, diversifiable) risk; diversification relies on less than perfect correlation among assets Benefits 1. Smoothes out volatility and increases the consistency of performance by reducing standard deviation; reduces risk 2. Reduces risk of loss of capital Limitations 1. it may be hard to identify lowly and negatively correlated assets; 2. Correlations usually rise in bear markets 3. Diversification may add very little benefit when it's actually needed most

Disposition Effect

The tendency to hold on to stocks that have lost value and sell stocks that have risen in value since the time of purchase Disproportionately hold on to losers and sell winners. The price you happened to pay in the past (even the fact that you ever purchased that stock) is irrelevant, except for •Tax purposes •Minimize trading costs You should not care what price you paid for it ....but people do care. This is known as the disposition effect

Time-Weighted Return (TWR)

Time-weighted returns = Manager's return = Does not consider cash flows Time-weighted rate of return method does not weigh the amount of all dollar flows during each time period. It computes the return for each period and takes the average of the results by finding the holding period for each period and averaging the returns. If the investment is for more than one year, the geometric mean of the annual returns should be computed to find the time-weighted rate of return for the measurement period. In the investment management industry, the time-weighted return is the preferred method of performance measurement because it is not affected by the timing of cash flows.

Treynor Ratio

Tp = rp - rf / Bp (beta) rp = Return rf= risk free rate -The Treynor Ratio calculates risk-adjusted return using market risk (beta) to quantify risk. - Metric to measure performance relative to risk taken as measured by beta. - Same formula as Sharpe Ratio except that it uses beta - AKA reward / volatility ratio (fluctuations around the market mean or average) - Higher is better - Use is R2 is greater than .70 - Uses beta (systematic risk only) - Treynor Ratio is useful if the portfolios being measured are part of a broader, more fully diversified portfolio. -Best for comparing two funds or investments within the same category -"reward-to-volatility ratio"

Unsystematic Risk (idiosyncratic, diversifiable)

Unsystematic risk is unique to a single business or industry, such as operations and methods of financing. These risks include business risk and financial risk. Unlike systematic risk, since this risk is not a risk of the entire market, unsystematic risk can be eliminated through diversification. Examples of unsystematic risk include business risk, financial risk, default risk, and regulatory risk.

Value at Risk

VaR can be used to budget portfolio risk. For example, an investment portfolio with two managers wants to understand and control the amount of dollars that are at risk. An investment advisor or consultant could use one of the methods such as delta-normal to determine the VaR of the portfolio. To determine the value of the diversification, the advisor could take the sum of each manager's VaR and subtract the VaR of the whole portfolio. This would give the VaR benefit from diversification keeping in mind that a variance/covariance matrix must be used. RiskMetrics developed a VaR methodology looking at exponentially weighted moving averages.

Expected utility theory

Value = Final Wealth 1. Risk (tolerance) is symmetric in gains and losses and in magnitude 2. Probabilities are weighted correctly 3. Framing does not influence decisions

Prospect Theory

Value = gain/loss vs. a reference point 1. Risk is different in the domain of losses vs. gains 2.Small probabilities overweighed Large probabilities underweighted 3.Framing Influences decisions

Gross vs Net Return

We typically work with net returns. Rt+1 = Pt+1 +CFt+1 / Pt • Example: Suppose you buy a stock at P=$100, tomorrow's price is $101 and it pays a $3 dividend • Gross return = (101+3)/100=1.04 • Net return =1.04-1=0.04 or 4% • 4%, the net return, is often a more convenient number to think about than 1.04

Backwardation

When a futures price is below the spot price; Caused by hedgers to insure against price declines in the future; Some markets are described as having normal backwardation - backwardation is desirable for investors who are "net long" - backwardation occurs when futures prices are lower than spot price -backwardation indicates short supply

After-tax Returns and Efficiency

a. asset classes and categories b. strategies (active vs. passive) c. structures (mutual funds, hedge funds ETFs, p-ships) For additional information and research you might visit Parametric Portfolio. Click on Content Type and then White Papers.

Asset Location

an exercise in which investors place certain assets and investments, based on tax status and preferences, into different accounts (e.g., taxable, tax-deferred, or tax-exempt) in order to minimize taxes during the growth and distribution phases of each account. Note - on your exam... they will have to give you a fair amount of information/detail regarding any investment for which they are asking you to place in different (taxable or tax-deferred accounts) in order to build the optimal tax-efficient portfolio.

Accountant's Ratio

equals the ratio of short-term capital gains realized to total capital gains realized "Yet another tax efficiency measure based on capital gain realizations is sometimes known as the "accountant's ratio". It equals the ratio of short-term capital gains realized during the measurement period to total capital gains realized during the period. The logic behind this measure is that if a manager is realizing many short-term gains, the manager may not be considering the tax consequences of trading decisions. While there may be some information in this measure, it does not consider the broader question of the level of capital gain realizations. It therefore provides only a partial perspective on the portfolio manager's sensitivity to tax management issues." from CFA Institute (linked above)

Contango

holds that the natural hedgers are the purchasers of a commodity, not the suppliers and is a hypothesis polar to backwardation. -contango occurs when futures prices are higher than spot prices -contango indicates immediate supply

Growth rate of your purchasing pow

r = (1+R)/(1+I) -1

Hedge Fund Performance and Survivorship Bias

• Backfill bias: - Hedge funds report returns only if they choose to, and they may do so only when their prior performance is good • Survivorship bias: - Failed funds drop out of the database - Hedge fund attrition rates are more than double those for mutual funds

Systematic Risk (a.k.a. market risk) = measured by beta

• Beta is used in Capital Asset Pricing Model (CAPM) • Measures systematic (market) risk • Represented by the Greek letter ß • Beta is calculated using regression analysis • Beta indicates an asset's likelihood of moving up or down with the market -A beta of 1.00 indicates that an asset will move directly in proportion to the market as a whole -A low beta (e.g., .40) indicates that an asset has been less volatile than the market while a high beta (e.g., 1.20) indicates that an asset has been more volatile than the market

Goal-driven Investing Management

• Investment strategy that focuses on achieving specific life goals • separate accounts (sometimes called "investment pools") for distinct goals may be established • success is measured by whether or not the client is moving positively toward his or her goal (i.e., focus on absolute return) • traditional indexes and benchmarks are not so heavily emphasized (i.e., less focus on relative return) •Many professionals support this type of investing, arguing that it helps clients understand the merits of using different funds and strategies to accomplish different goals and hopefully helps them maintain discipline during periods of under-performance

Jensen's Alpha (CAPM)

• Measurement of investment manager's risk-adjusted performance based on security selection and market timing. • Michael Jensen created this formula to measure alpha. • This metric is designed to show if the manager outperformed what should have been the result per the • Measures the value-added by manager. • Alpha = Ra - [Rf + Beta(Rm - Rf)] CAPM = r = rf + (rm − rf) beta

Asset Location

• Taxable accounts - Index and other passive funds - Growth funds with low turnover - Tax-managed funds - REITs (could be better for either type of account) - Municipal bonds • Tax-deferred accounts - Dividend stocks - Most taxable bonds - Actively management, high turnover funds - Partnerships "IF" they avoid UBTI

Sharpe Ratio Cont.

• The Sharpe ratio measures the total risk of the portfolio by including standard deviation instead of only the systematic risk (i.e., beta). • It does not implicitly assume that a portfolio is well diversified. • The foundation of the Sharpe ratio is Modern Portfolio Theory (MPT), and the idea is the higher the Sharpe ratio, the closer the portfolio is to the mean variance portfolio. • This means that The Sharpe index standardizes the return in excess of the risk-free rate by the variability of the returns.

Real vs Nominal Rate of Return

• To convert a nominal return to a real return we divide by the rate of inflation

Vertical Spread

• a strategy where an investor buys and sells two options on the same underlying asset that have the same expiration date but different strike prices • gains and losses are a result of the widening or narrowing of the difference between option premiums on the two positions

Diagonal Spread Option

• a strategy where an investor simultaneously enters into a long and a short position in the same type of option (call options or put options) and where the contracts have different strike prices and expiration dates • combines a horizontal spread (different expiration dates) and a vertical spread (different strike prices)

Systematic Risk - Beta

•Beta is used in Capital Asset Pricing Model (CAPM) •Measures systematic (market) risk •Represented by the Greek letter ß •Beta is calculated using regression analysis •Beta indicates an asset's likelihood of moving up or down with the market A beta of 1.00 indicates that an asset will move directly in proportion to the market as a whole A low beta (e.g., .40) indicates that an asset has been less volatile than the market while a high beta (e.g., 1.20) indicates that an asset has been more volatile than the market

Sortino Ratio

•The Sortino Ratio is a risk-adjusted performance metric that measures return in relation to downside risk using downside semi-standard deviation. •The Sortino Ratio is identical to the Sharpe Ratio except that is uses downside semi-standard deviation (the standard deviation of the negative asset returns) instead of standard deviation (which includes the deviations of both positive and negative returns). •The Sortino Ratio is better used when analyzing portfolios with high volatility (vs. Sharpe Ratio).

Liability-driven Strategies and Modeling

•strategies where the primary objective is matching asset returns and availability with known current and future liabilities •common in pension and retirement funds such as defined benefit plans

Measure Risk-adjusted Returns

▪ Information Ratio ▪ Sortino Ratio ▪ Treynor Ratio* ▪ Sharpe Ratio* ▪ Jensen's Alpha*

Other Risk Management Strategies

▪ Low volatility funds ▪ Buy-write strategies ▪ Factor-analysis models (smart beta) ▪ Volatility index (VIX)

Measuring Risk

▪ Systematic Risk - market risk - Beta ▪ Unsystematic Risk - diversifiable risk ▪ Standard Deviation ▪ Coefficient of Variation ▪ Covariance ▪ Correlation Coefficient ▪ Beta Coefficient ▪ Coefficient of Determination (R-squared)