Portfolio Management

Treynor measure

(Rp - Rf)/βp Interpreted as excess returns per unit of systematic risk

Application of CAPM / SML

1. A Stock is overvalued if its expected return is lower than its required return. - Short sell this stock. 2. B Stock is undervalued if its expected return is greater than required return. - Buy this stock. 3. C Properly valued if equal. Buy, sell, or ignore this stock.

Overall risk management framework features

1. Establishing processes and policies for risk governance. 2. Determining the organization's risk tolerance. 3. Identifying and measuring existing risks. 4. Managing and mitigating risks to achieve the optimal bundle of risks. 5. Monitoring risk exposures over time. 6. Communicating across the organization. 7. Performing strategic risk analysis.

Reversal patterns for downtrends

1. Inverse head-and-shoulders 2. double bottom 3. triple bottom

Investment constraints

1. Liquidity 2. Time horizon 3. Tax situation 4. Legal and regulatory 5. Unique circumstances

Notable trends in asset management industry

1. Market share for passive has been growing over time. Due to lower fees passive managers charge investors, and in part to questions about whether active managers are actually able to add value over time on a risk-adjusted basis, especially in developed markets that are believed to be relatively efficient. 2. Amount of data available has grown exponentially, allowing managers to invest in IT and third-party services to process these data. Helps make quick investment decisions. 3. Robo-advisors are technology that can offer advice and recommendations based on investment requirements and constraints. Appeal to younger investors and those with smaller portfolios than have typically been served by asset management firms. Lowered barriers to entry into asset management industry for firms (e.g. insurance companies).

Decennial patterns

10-years

Kondratieff wave

A 54-year long economic cycle postulated by Nikolai Kondratieff.

Tactical asset allocation

A manager who varies from strategic asset allocation weights in order to take advantage of perceived short-term opportunities

Liquidity

Ability to turn investment assets into spendable cash in a short period of time without having to make significant price concessions to do so.

Permissionless networks

All network participants can view all transactions. No central authority, which gives them advantage of having no single point of failure. Ledger becomes a permanent record visible to all, and its history cannot be altered. Removes the need for trust between parties to a transaction

Surety bond

An insurance company has agreed to make a payment if a third party failts to perform under the terms of a contract or agreement with the organization. e.g. supplier does not deliver on time.

Beta is the standard

CAPM measure of systematic risk. Gauges the tendency of the return of a security to move in parallel with the return of the stock market as a whole.

Smart contracts

Electronic contracts that could be programmed to self-execute based on terms agreed to by counterparties e.g. options contract set up to be exercised automatically.

Modern portfolio theory (MPT)

Equilibrium expected returns for securities and portfolios that are a linear function of each security's or portfolio's market risk (the risk that cannot be diversified away)

Return generating models

Estimate the expected returns on risky securities based on specific factors. Factors that explain security returns can be classified as: 1. Macroeconomic, 2. fundamental, 3. statistical Statistical factors often have no basis in finance theory and are suspect in that they may represent only relations for a specific time period which have been identified by data mining.

Fama and French

Estimated 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 Carhart suggest 4th factor to measure price momentum using prior period returns.

SML plot (Security Market Line)

Expected return vs systematic risk (beta) All properly priced securities will plot directly on the SML. All stocks should plot on the SML unless they are mispriced and then they will be "over" or "under

Initial coin offerings

Financial companies have raised capital by selling cryptocurrency for money. Reduces the cost and time frame compared to carrying out a regulated IPO, and initial coin offerings typically do not come with voting rights. Investors should note that fraud has occurred with initial coin offerings and they may become subject to securities regulations.

Endowment

Fund dedicated to providing financial support on an ongoing basis for a specific purpose

Institutions (e.g. endowments, foundations)

Have large investment portfolio

Elliott Wave theory

In a prevailing uptrend, upward moves in prices consist of five waves and downward moves occur in three waves. If prevailing trend is down, downward moves have five waves and upward moves have three waves. Each of these waves, in turn, is composed of smaller waves of the same general form. Sizes of these waves thought to correspond with Fibonacci ratios. The value 1.618 is the ratio of large consecutive Fibonacci numbers. Technical analysts who employ Elliott wave theory frequently use Fibonacci ratios to set price targets

Supervised learning

Input and output data are labelled, machine learns to model the outputs from the inputs, and the machine is given new data on which to use the model

Bond mutual funds

Invest in fixed-income securities. Differentiated by bond maturities, credit ratings, issuers, and types.

Risk vs number of portfolio assets

It's not necessary to buy the entire market to diversify sufficiently. Significantly less. Once get to ~30 securities, std dev remains constant. The remaining risk is systematic / nondiversifiable.

Least squares regression line

Line that minimizes the sum of the squared distances of the points plotted from the line. Slope of this line is our estimate bata. Line steeper than 45 degrees means slope greater than 1 and the asset's estimated beta is greater than 1. Means that returns on asset i are more variable in response to systemic risk factors than is the overall market, which has a beta of one.

Specialist asset managers

May focus on a particular investment style of asset class

Various risks are not independent

Must be considered because interactions are many and frequent. Especially important during periods of stress in financial markets.

Fidelity bonds

Pay for losses that result from employee theft or misconduct.

Global minimum-variance portfolio

Portfolio on the efficient frontier that has the least risk

Tokenization

Refers to electronic proof of ownership of physical assets, which could be maintained on a distributed ledger.

Presidential cycles

Related to US presidential elections

Difference between the Sharpe ratio and M^2 measure is that

Sharpe is a slope measure and M^2 is measured in percentage terms.

The less an investor's risk aversion

The flatter his indifference curves. More risk tolerant has flatter curves

Traditional or 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 for alternative.

Candlestick charts

Use the same data as bar charts but display a box bounded by the opening and closing prices. Box is clear if the closing price is higher than the opening price, or filled if the close is lower than the opening price.

sample variance

divide by the count minus 1

Mortality risk

risk of death addressed with life insurance

Characteristics of Different Types of Investors

see image

Two measures of portfolio performance based on systematic (beta) risk rather than total risk

1) Treynor measure 2) Jensen's alpha Analogous to the Sharpe ratio and M^2 in that the Treynor measure is a measure of slope and Jensen's alpha is a measure of percentage returns in excess of those from a portfolio that has the same risk (beta) but lies on the SML.

Risk objectives

1. Absolute risk objective - e.g. have no decrease in portfolio value during any 12-month period or not decrease in value by more than 2% at any point over any 12-month period Low absolute percentage risk objectives result in portfolios made up of securities that offer guaranteed returns. Can also be stated in terms of probability of specific results rather than strict limits on portfolio results. 2. Relative risk objectives - relate to a specific benchmark or can be strict, such as, returns will not be less than 12-month euro LIBOR over any 12-month period or stated in probability.

Derivative risks

1. Delta - Sensitivity of derivatives values to the price of the underlying asset 2. Gamma - Sensitivity of delta to changes in the price of the underlying asset 3. Vega - Sensitivity of derivatives values to the volatility of the price of the underlying asset 4. Rho - Sensitivity of derivatives values to changes in the risk-free rate

Major components of an IPS typically address the following

1. Description of Client circumstances, situation, and investment objectives. 2.Statement of the Purpose of the IPS. 3. Statement of Duties and Responsibilities of investment manager, custodian of assets, and the client. 4. Procedures to update IPS and to respond to various possible situations. 5. Investment Objectives derived from communications with the client. 6. Investment Constraints that must be considered in the plan. 7. Investment Guidelines such as how the policy will be executed, asset types permitted, and leverage to be used. 8. Evaluation of Performance, the benchmark portfolio for evaluating investment performance, and other information on evaluation of investment results. 9. Appendices containing information on strategic (baseline) asset allocation and permitted deviations from policy portfolio allocations, as well as how and when the portfolio allocations should be rebalanced.

Stock mutual funds

1. Index funds (passively managed). 2. Actively managed funds - refer to funds where the management selects individual securities with the goal of producing returns greater than those of their benchmark index. Actively managed funds cost more and have higher turnover of portfolio securities. Greater tax liabilities as a result.

Examples of alternative data sources

1. Individuals who generate usable data such as social media posts, online reviews, email, and website visits. 2. Businesses that generate potentially useful information such as bank records and retail scanner data. These kinds of data are referred to as "corporate exhaust." 3. Sensors, such as radio frequency identification chips, are embedded in numerous devices such as smart phones and smart buildings. The broad network of such devices is referred to as the "Internet of Things."

Active portfolio manager has two specific issues to consider

1. Investor may have multiple managers actively managing same benchmark for the same asset class. One may overweight an index stock while another underweight the same stock. Together there is no net active management risk, although each manager has reported active management risk. Overall, risk budget underutilized 2. When all managers are actively managing portfolios relative to an index, trading may be excessive overall. Could have negative tax consequences, specifically potentially higher capital gains taxes

Types of mutual funds

1. Money market funds - Short-term debt securities and provide interest income with very low risk of changes in share value. NAVs are set to one currency unit but in some instances NAV funds declined when securities held dropped dramatically in value. Firms differentiated by the types of money market securities they purchase and average maturities.

Non-financial risks

1. Operational risk - human error, faulty organizational processes, inadequate security, or business interruptions will result in losses. example is cyber risk, refers to disruptions of an organization's information technology. 2. Solvency risk. - the organization will be unable to continue to operate because it has run out of cash. 3. Regulatory risk - the regulatory environment will change, imposing costs on the firm or restricting its activities. 4. Governmental or political risk (including tax risk). political actions outside a specific regulatory framework, such as increases in tax rates, will impose significant costs on an organization. 5. Legal risk - uncertainty about the organization's exposure to future legal action. 6. Model risk - asset valuations based on the organization's analytical models are incorrect. 7. Tail risk - extreme events (those in the tails of the distribution of outcomes) are more likely than the organization's analysis indicates, especially from incorrectly concluding that the distribution of outcomes is normal. 8. Accounting risk - the organization's accounting policies and estimates are judged to be incorrect.

3 steps of portfolio management process

1. Planning step 2. Execution step 3. Feedback step

Assumptions of the CAPM

1. Risk aversion. To accept a greater degree of risk, investors require a higher expected return. 2. Utility maximizing investors. Investors choose the portfolio, based on their individual preferences, with the risk and return combination that maximizes their (expected) utility. 3. Frictionless markets. There are no taxes, transaction costs, or other impediments to trading. 4. One-period horizon. All investors have the same one-period time horizon. 5. Homogeneous expectations. All investors have the same expectations for assets' expected returns, standard deviation of returns, and returns correlations between assets. 6. Divisible assets. All investments are infinitely divisible. 7. Competitive markets. Investors take the market price as given and no investor can influence prices with their trades.

Measures of risk for specific asset types

1. Standard deviation 2. Beta 3. Duration

2 methods to supplement VaR and CVaR

1. Stress testing - examines effects of a specific (usually extreme) change in a key variable such as an interest or exchange rate 2. Scenario analysis - similar what-if analysis of expected loss but incorporates changes in multiple inputs (e.g. interest rate change combined with significant change in oil prices)

Applications of fintech to investment management

1. Text analytics 2. Natural language processing 3. Risk analysis 4. Algorithmic trading 5. Robo-advisory services

Geometric mean

= ((1+R1)*(1+R2)*...*(1+Rn))^(1/n) - 1 Compound annual rate. When periodic rates of return vary form period to period, geometric return will have a less value than the arithmetic mean return. Geometric mean return = (1+HPR)^(1/n) - 1 CAN be negative because have to subtract 1 at the ende

Variance of returns for a portfolio of two risky assets

= w1^2 * sig1^2 + w2^2 * sig2^2 + 2*w1*w2*Cov12 Can substitute in that Cov12 = p12 * sig1 * sig2 take sqrt of above equation to get standard deviation.

Duration

A measure of the price sensitivity of debt securities to change in interest rates

Leveraged return

A return to an investor that is a multiple of the return on the underlying asset. The gain or loss on the investment as a percentage of an investor's cash investment. Investment in derivative securities produce leveraged return, because cash deposited is only a fraction of the value of the assets underlying the futures contract. Another example is real estate paid with borrowed money.

Equilibrium

A security's expected return and its required return (by all investors) are equal. Therefore, can use CAPM to estimate a security's required return.

Pooled investments

A single portfolio that contains investment funds from multiple investors. Include mutual funds

Abnormal return

Abnormal return = Actual return - expected risk-adjusted return.

Bar charts

Add the high and low prices for each trading period and often include the opening price as well. Each period displayed as vertical line with closing price indicated as a point or dash on the right side of the line.

New equity issuance (IPOs) and secondary offerings (sales of additional shares by issuer)

Add to supply of stocks. Increases in issuance of new shares may often coincide with market peaks.

Strategic asset allocation

After completing IPS. Developed to specify percentage allocations to the included asset classes. In choosing which asset classes to consider when developing the strategic asset allocation for the account, correlations of returns within an asset class should be relatively high, indicating that the assets within the class are similar in their investment performance. On other hand, it is low correlations of returns between asset classes that leads to risk reduction through portfolio diversification. Once the universe of asset classes has been specified, the investment manager will collect data on the returns, standard deviation of returns, and correlations of returns with those of other asset classes for each asset class.

Important note 2

All portfolios that lie on the CML are well-diversified and have only sysetmatic risk. That is because the portfolios on the CML are constructed from the risk-free asset and the (well-diversified) market portfolio. Any portfolio, including single securities, will be plotted along the SML. Their unsystematic risk can be significant, but it is not measured on the SML diagram, because unsystematic risk is not related to expected return. Both the CML and SML reflect reflections that hold when prices are in equilibrium.

Margin debt

Amount of margin debt is a readily available indicator because brokers required to report this data. Increases in total margin debt outstanding suggest aggressive buying by bullish margin investors. As margin investors increase limits of margin credit, ability to continue buying decreases, which causes prices to begin declining. Increasing margin debt tends to coincide with increasing market prices and decreasing margin debt tends to coincide with decreasing prices.

Notee

An IPS does not necessarily, or even typically, require a target return because future market movements are either difficult or impossible to predict with any degree of accuracy.

asset class

An asset class should be specified by type of security (e.g., stocks, bonds, alternative assets, cash) and can then be further subdivided by region or industry classification. An asset class defined only as "emerging markets" or "consumer discretionary firms" should identify the type of securities (e.g., equities or debt).

Execution step

Analysis of risk and return characteristics of various asset classes to determine how funds will be allocated to various asset types. "Top-down" analysis - portfolio manager will examine current economic conditions and forecasts of such macroeconomic variables as GDP growth, inflation, and interest rates, in order to identify asset classes that are most attractive. Resulting portfolio is typically diversified across such asset classes as cash, fixed-income securities, publicly traded equities, hedge funds, private equity, and real estate, as well as commodities and other real assets. Bottom-up security analysis - Security analysts use model valuations for securities to identify those that appear undervalued.

Attribution analysis

Analysis of the sources of returns differences between active portfolio returns and those of a passive benchmark portfolio (part of performance evaluation).

Text analytics

Analysis of unstructured data in text or voice forms. Example is analyzing frequency of words and phrases

Relative strength analysis

Analyst calculates the ratios of an asset's closing prices to benchmark values, such as stock index or comparable asset, and draws a line chart of the ratios. Increasing trend indicates that the asset is outperforming the benchmark and a decrease shows that the asset is underperforming the benchmark.

Planning step

Analyze investor's risk tolerance, return objectives, time horizon, tax exposure, liquidity needs, income needs, and any unique circumstances. Results in an investment policy statement (IPS) that details investor's investment objectives and constraints. Should specify an objective benchmark (such as index) against which success process will be measured. IPS updated every few years at least and any time investor's objectives or constraints change significantly. Strategic asset allocation is often a part of the written IPS because it helps solidify desired initial weightings to specific asset classes. Different investors will have different applicable time horizons which must be considered and evaluated appropriately as part of the investment policy statement. Two of the major components of an IPS should be a statement of the responsibilities of the investment manager and the client, and a performance evaluation benchmark.

Risk transfer

Another party takes on the risk. E.g. purchasing insurance. Insurance companies diversify so that the premiums of some parties pay the losses of others.

Distributed ledger technology

Applicable to post-trade clearing and settlement. Could automate many of the processes currently carried out by custodians and other third-parties. Can bring about real-time trade verification and settlement, which takes one or more days for many securities. Reduces trading and counterparty risk.

Money-weighted return

Applies concept of IRR to investment portfolios. Internal rate of return on a portfolio, taking into account all cash inflows and outflows. Beginning value of the account is an inflow, as are all deposits into the account. All withdrawals are outflows, as is the ending value. [IRR][CPT]

Financial risks

Arise from exposure to financial markets 1. Credit risk - Uncertainty about whether the counterparty to a transaction will fulfill its contractual obligations 2. Liquidity risk - This is the risk of loss when selling an asset at a time when market conditions make the sales price less than the underlying fair value of the asset 3. Market risk - uncertainty about market prices of assets and interest rates

Importante note 3

As an investor diversifies away unsystematic risk, the correlation between portfolio return and that of the market approaches positive one.

Feedback step

As investor circumstances change, risk and return characteristics of asset classes will change, and the actual weights of the assets in the portfolio will change with asset prices. Portfolio manager must monitor these changes and rebalance periodically in response, adjusting allocations to various asset classes back to desired percentages. Manager also measure portfolio performance and evaluate it relative to the return on the benchmark portfolio in IPS.

Active management

Attempt to outperform a chosen benchmark through manager skill, for example through fundamental or technical analysis

Passive management

Attempts to replicate performance of a chosen benchmark index about 1/5 of industry. Smaller because lower fees too.

Relative strength index (RSI)

Based on the ratio of total price increases to total price decreases over a selected number of periods. Ratio then scaled to oscillate between 0 and 100, with high values (typically those greater than 70) indicating an overbought market and low values (typically those less than 30) indicating an oversold market.

Willingness to bear risk

Based primarily on the investor's attitudes and beliefs about investments (various asset types). Quite subjective.

Expected return and standard deviation for a combination of a risk-free asset with a portfolio of risky assets

Because a risk-free asset has zero standard deviation and zero correlation of returns with a risky portfolio, allowing Asset B to be the risk-free asset and Asset A to be the risky asset portfolio results in the following reduced equation: SigP = W_A * sig_A E(R_p) = W_A * E(R_A) + W_B * E(R_B)

Change in polarity

Belief that breached resistance levels become support levels and that breached support levels become resistance levels.

Active portfolio management

Believe that their values and not market prices are correct. These investors do 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.

Rate of change (ROC) oscillator (momentum oscillator)

Calculated as 100 times the difference between the latest closing price and the closing price n periods earlier. So oscillates around 0. Buy when oscillator changes from negative to positive during an uptrend in prices and sell when changes from positive to negative.

Stochastic oscillator

Calculated from the latest closing price and highest and lowest prices reached in a recent period, such as 14 days. In sustainable uptrend, prices tend to close nearer to the recent high, and in a sustainable downtrend, prices tend to close nearer the recent low. Use two lines that are bounded by 0 and 100. The %K line is the difference between the latest price and the recent low as a percentage of the difference between the recent high and low The %D line is a 3-period average of the %K line. Technical analysts typically use stochastic oscillators to identify overbought and oversold markets. Points where the %K line crosses the %D line can also be used as trading signals in the same way as the MACD lines.

Return objectives

Can be relative to a benchmark portfolio return, such as "exceed the return on the S&P 500 index by 2% per annum" For a bank, return objective may be relative to the bank's cost of funds. Peer performance benchmarks suffer from not being investible portfolios - there is no way to match this investment return by portfolio construction before the fact.

Sentiment indicators

Can be used to discern the views of potential buyers and sellers. Market sentiment is "bullish" when prices increasing and "bearish" when expecting decreasing prices.

Diversification

Can more efficiently bear a risk

Load funds

Charge either up-front fees, redemption fees, or both

Volatility Index (VIX)

Chicago Board Options Exchange calculates VIX, which measures the volatility of options on the S&P 500 stock index. High levels of VIX suggest investors fear declines in the stock market. Technical analysts most often interpret in contrarian way - viewing a predominantly bearish investor as a bullish sign.

Artificial intelligence

Computer systems that can be programmed to simulate human cognition. Applicable to processing and organizing data before using it

Algorithmic trading

Computerized securities trading based on a predetermined set of rules. Can be useful for executing large orders by determining the best way to divide the orders across exchanges

Miners

Computers on the network to solve a cryptographic problem in the consensus mechanism in a blockchain. Impose substantial cost on any attempt to manipulate blockchain's historical record Blockchain more likely to succeed with a large number of participants in its network

Bollinger bands

Constructed based on the standard deviation of closing prices over the last n periods. Basically upper and lower lines that act as bounds around the moving average. Bands move away from one another when volatility increases and move together when prices are less volatile. Can draw high and low bands a chosen number of standard deviations above and below the n-period moving average. Useful when prices are extreme overbought - Prices at or above the upper Bollinger. These prices are too high and likely to decrease in the near term. oversold - Prices are too low and likely to increase in the near term. Close to lower Bollinger. Possible strategy is to buy when price is at lower band and sell when at upper band.

Convergence / divergence of oscillator and market prices

Convergence - Oscillator shows the same pattern as prices (e.g. both reaching higher highs). Suggests the price trend is likely to continue Divergence - Occurs when the oscillator shows a different pattern than prices (e.g. failing to reach a higher high when the price does). Indicate a potentail change in the price trend.

Cryptocurrencies

Current example of distributed ledger technology in finance. An electronic medium of exchange that allows participants to engage in real-time transactions without a financial intermediary.

Distributed ledger

Database that is shared on a network so that each participant has an identical copy. Must have consensus mechanism to validate new entries into the ledger. Use cryptography to ensure only authorized network participants can use the data. Can be permissionless or permissioned networks

Markowitz framework

Defines risk as the variance of returns. Note that in another topic, the Capital Asset Pricing Model (CAPM) employs beta as a measure of investment's systematic risk.

Ability to bear risk

Depends on financial circumstances (longer investment horizon, greater assets vs liabilities, more insurance against unexpected occurrences, and a secure job all suggest greater ability to bear risk.

Security selection

Deviations from index weights on individual securities within an asset class. e.g. overweight energy stock and underweight financial stocks. Active strategies

Market risk premium

Difference between the expected return on the market and the risk-free rate

Volume charts

Displayed below price charts with each period's volume shown as a vertical line.

Blockchain

Distributed ledger that records transactions sequentially in blocks and links these blocks in a chain. Each block has a cryptographically secured "hash" that links it to the previous block.

No-load funds

Do not charge additional fees for purchasing shares (up front fees) or for redeeming shares (redemption fees)

Moving average convergence/divergence (MACD) Oscillators

Drawn using exponentially smoothed moving averages, which place greater weight on more recent observations. MACD line is difference between two exponentially smoothed moving averages of the price, and the "signal line" is an exponentially smoothed moving average of the MACD line. Lines oscillate around zero but are not bounded. MACD oscillator can be used to indicate overbought or oversold conditions or to identify convergence or divergence with the price trend. Points where the two lines cross can be used as trading signals, much like the use of two different moving averages discussed previously. The MACD line crossing above the smoother signal line is viewed as a buy signal and the MACD line crossing below the signal line is viewed as a sell signal.

Single-factor model

E(Ri) - Rf = Bi * [E(Rm) - Rf]

General form of a multifactor model with k factors

E(Ri) - Rf = Bi1 * E(Factor 1) + Bi2 * E(Factor 2) + ... + Bik*E(Factor k) The expected excess return (above the risk-free rate) for asset i is the sum of each factor sensitivity or facotr loading (the Bs) for asset i multiplied by the expected value of that factor for the period.

Expected return of a portfolio with weight Wa to risky asset A and Wb for asset B

E(Rportfolio) = W_A*E(R_A) + W_B*E(R_B) sig_portfolio = sqrt(W_A^2*sigA^2 + W_B^2*sigB^2 + 2*W_A*W_B*p_AB*sig_A*sig_B) Imagine asset B had no risk, so its standard deviation is zero and zero correlation of returns with those of a risky portfolio Sig_portfolio = sqrt(W_A^2*sig_A^2) = W_A*sig_A The intuition of this result is quite simple: If we put X% of our portfolio into the risky asset portfolio, the resulting portfolio will have standard deviation of returns equal to X% of the standard deviation of the risky asset portfolio. The relationship between portfolio risk and return for various portfolio allocations is linear (see image)

Mutual funds

Each investor owns shares representing ownership of a portion of the overall portfolio. Total net value of the assets in the fund (pool) divided by the number of such shares is referred to as the Net Asset Value (NAV) of each share.

Objective of a bank

Earn more on the bank's loans and investments than the bank pays for deposits of various types. Keep risk low and need adequate liquidity to meet investor withdrawals.

Market model

Estimate a security's or portfolio's beta and to estimate a security's abnormal return (above its expected return) based on the actual market return Ri = ai + Bi*Rm + ei Ri = return on Asset i Rm = market return Bi = slope coefficient ai = intercept ei = abnormal return on asset i Intercept ai and slope coefficient Bi are estimated from historical return data can require that ai is risk-free rate times (1-Bi) to be consistent with general form of a single-index model in excess returns form. The factor sensitivity (beta for asset i) is a measure how sensitive the return on asset i is to the return on the overall market portfolio (market index)

Portfolio perspective

Evaluating individual investments by their contribution to the risk and return of an overall portfolio. No portfolio perspective would be holding all of your investments in one stock. The extra risk from holding only a single security is not rewarded with higher expected returns. Diversifications allows reduced portfolio risk without necessarily reducing portfolio's expected return. Use standard deviation of returns as measure of investment risk.

Neural networks

Example of AI in that they are programmed to process information in a way similar to the human brain. Example of AI not of machine learning

Negative screning

Excluding specific companies or industries from consideration for the portfolio based on ESG factors.

CML plot (Capital Market Line)

Expected return vs total risk. Only efficient portfolios appear on cML Those that arent efficient appear inside the efficient frontier

Defined benefit pension plan

Firm promises to make periodic payments to employees after retirement Benefit based on employee's years of service and compensation at or near retirement. Employer assumes investment risk and makes contributions to a fund established to provide the promised future benefit.

Tax situation

For a fully taxable account, investors may prefer tax-free bonds to taxable bonds or prefer equities that are expected to produce capital gains, which are often taxed at a lower rate than other types of income. In retirement accounts, investors may choose to put securities that generate fully taxed income.

Rectangles

Form when trading temporarily forms a range between a support level and a resistance level. Suggest prevailing trend will resume and can be used to set a price target. Flags and pennants are rectangles and triangles that appear on short-term price charts.

Moving average lines

Frequently used to smooth the fluctuations in a price chart. Moving average is simply the mean of the last n closing prices. Larger chosen value of n, smoother the moving average line. In uptrend, price is higher than the moving average and, in a downtrend, the price is lower than the moving average. Moving average lines are often viewed as support or resistance levels. Make changes in the trend easier to see. Points where the short-term average (more volatile) crosses the long-term average (smoother) can indicate changes in the price trend. When the short-term average crosses above long-term average (a "golden cross"), this is often viewed as an indicator of an emerging uptrend or a "buy" signal by technical analysts. The short-term average crossing below the long-term average (a "dead cross") is often viewed as an indicator of an emerging downtrend or a "sell" signal.

Foundation

Fund established for charitable purposes to support specific types of activities or to fund research related to a particular disease. Typical objective is to fund the activity or research on a continuing basis without decreasing the real (inflation adjusted) value of the portfolio assets. Foundations and endowments both have long investment horizons, high risk tolerance, and little need for additional liquidity.

Technical analysis vs fundamental analysis

Fundamental analysis attempts to determine intrinsic value of an asset. Technical analysis only the firm's share price and trading volume data to project a target price. Not concerned with identifying buyers' and sellers' reasons for trading Fundamental analysis uses other information like financial statements and position. Much info is subject to assumptions or restatements, and might not be available for all assets. Both require subjective judgment. Technical analysis can be applied to prices of assets that do not produce future cash flows, such as commodities. Technical analysis useful when financial statement fraud occurs. Usefulness of technical limited in markets where price and volume data might not truly reflect supply and demand. May be case in illiquid markets and in markets subject to outside manipulation.

Point-and-figure charts

Helpful in identifying changes in the direction of price movements. Drawn on graph paper with price on vertical axis. Price increment chosen is the "box size" for the chart. Horizontal axis does not represent discrete units of time but rather number of changes in direction. Typical reversal size is three times the box size to determine when a change of direction has occurred. Start at opening price and fill in a box in first column if closing price has changed by at least the box size. X indicates an increase in box size and O indicates a decrease. If price changes by more than one box size, fill in multiple X's and O's. When price changes in opposite direction by at least reversal size, analyst begin the next column.

Correlations of returns should be

High within asset classes and low among asset classes Per definition, asset classes should perform alike.

Data science

How we extract information from big data. Processing methods include: 1. Capture - Collecting data and transforming it into usable forms 2. Curation - Assuring data quality by adjusting for bad or missing data. 3. Storage - Archiving and accessing data. 4. Search - Examining stored data to find needed information. 5. Transfer - Moving data from their source or a storage medium to where they are needed.

High-frequency trading

Identifies and takes advantage of intraday securities mispricings.

Visualization techniques

Include charts and graphs from structured data. Methods for less structured data: word clouds, mind maps (display logical relations among concepts)

Unsupervised learning

Input data are not labelled and machine learns to describe the structure of the data.

Specific risk factors that affect asset classes to various degrees

Interest rate risk equity market risk foreign exchange rate risk Estimated and aggregated to determine whether they match the overall risk tolerance.

Insurance companies

Invest customer premiums with objective of funding claims as occur. Life insurance companies have relatively long-term investment horizons, while property and casualty (P&C) insurers have a shorter investment horizon

Positive screening (or "best-in-class" approach)

Invest in companies that have positive ESG practices. Portfolios and performance benchmarks must be customized under these approaches.

Private equity and venture capital

Invest in portfolio companies, often with the intention to sell them later in public offerings.

Core-satellite approach

Invest the majority, or core, portion of the portfolio in passively managed indexes and invests a smaller, or satellite, portion in active strategies. Reduces likelihood of excessive trading and offsetting active positions.

Variance and standard deviation are measures of

Investment risk. Measure variability of a distribution of returns about its mean or expected value.

Passive investment strategy

Investors believe that market prices are informationally efficient. utilizes a market index for optimal risky asset portfolio.

Open-end fund

Investors can buy newly issued shares at the NAV. Cant deviate from NAV. Newly invested cash is invested by the mutual fund managers in additional portfolio securities Investors can redeem their shares (sell them back to the fund) at NAV as well. All mutual funds charge a fee for the ongoing management of the portfolio assets, which is expressed as a percentage of the net asset value of the fund. Do not have brokerage costs, as shares are purchased from and redeemed with the fund company.

Simplifying assumption underlying modern portfolio theory

Investors have homogeneous expectations (all have same estimates of risk, return, and correlations with other risky assets for all risky assets). With this assumption, all investors face the same efficient frontier of risky portfolios and will have the same optimal risky portfolio and CAL. Under this assumption, optimal CAL for any investor is the one that is just tangent to the efficient frontier.

Jensen's alpha note

Jensens alpha is based on systemic risk and is not appropriate for a poorly-diversified portfolio Both Sharpe ratio and M-squared measure based on total risk and are appropriate for one that is not well-diversified.

Short interest ratio

Just as an increase in margin debt suggests aggressive buying and strong positive sentiment, increases in shares sold short indicate strong negative sentiment. Short interest - number of shares investors have borrowed and sold short. Short interest margin must be reported by brokerage firms. Short interest ratio is short interest divided by average daily trading volume. While high short interest ratio means investors expect the stock prices to decrease, also implies future buying demand when short sellers must return their borrowed shares.

Capital allocation line

Line of possible portfolio risk and return combinations given the risk-free rate and the risk and return of a portfolio of risky assets CAL for individual investor is the one that offers most-preferred set of possible portfolios in terms of their risk and return. In the image, the optimal portfolio is A because it results in the most preferred set of possible portfolios by combining the risk-free asset with the risky portfolio.

Time horizon

Longer an investor's time horizon the more risk and less liquidity the investor can accept in the portfolio. For an investor who must fund a large purchase at the end of this year, government securities or a bank CD may be most appropriate because of need for low risk and high liquidity

If have high will but low ability for risk

Low ability will win out. If ability is high but willingness is low, adviser attempt to educate investor about investment risk and correct any misconceptions that may be contributing to the investor's low stated willingness to take on investment risk. Advisor's job is not to change the investor's personality characteristics. Approach will most likely conform to lower of investors ability or willingness to bear risk.

M-squared (M^2) measure

M^2 = (Rp =Rf) * (sig_M/sig_P) - (Rm - Rf) First term is the excess return on a portfolio P* constructed by taking a leveraged position in portfolio P so that P* has same total risk, sigma_M as the market portfolio Considered a measure of risk-adjusted performance. Intuition is that M^2 is the additional return that could have been earned by leveraging the active portfolio (borrowing at Rf) so that its risk is equal to that of the market portfolio.

Investment companies

Manage the pooled funds of many investors Mutual funds manage these pooled funds in particular styles (e.g. index investing, growth investing, bond investing) and restrict their investments to a particular subcategory of investments (E.g. large-firm stocks, energy stocks) or particular regions (emerging markets, international, etc.)

Unique circumstances

May have nonfinancial considerations, commonly categorized as sustainable investing. e.g. ethical practices (no tobacco producers) or human rights abuses suspected. May also be based on diversification needs when investor's income heavily depends on prospects for one company or industry.

Time-weighted rate of return

Measures compound growth. The rate at which $1 compounds over a specified performance horizon. Time-weighting is the process of averaging a set of values over time. Annual time-weighted return for an investment computed by following steps: 1. Value the portfolio immediately preceding significant additions or withdrawals. Form subperiods over the evaluation period that correspond to the dates of deposits and withdrawals. 2. Compute the holding period return (HPR) of the portfolio for each subperiod. 3. Compute the product of (1 + HPR) for each subperiod to obtain a total return for the entire measurement period [i.e., (1 + HPR1) × (1 + HPR2) ... (1 + HPRn)] - 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. So (1+time-weighted rate of return)^2 = (1+HPR1)*(1+HPR2) the time-weighted rate of return is the preferred method of performance measurement, because it is not affected by the timing of cash inflows and outflows.

Beta

Measures market risk of equity securities and portfolios of equity securities. considers the risk reduction benefits of diversification and is appropriate for securities held in a well-diversified portfolio, where standard deviation is a measure of risk on a stand-alone basis

Time Weighted Vs Money Weighted Return

More money in the account at the beginning of a period results in a larger weight to that period in the money-weighted return calculation. If funds are contributed to a portfolio just before a period of poor portfolio performance, the money-weighted rate of return will tend to be lower than the time-weighted rate of return. If funds are contributed at a favorable time, money-weighted return will be higher than the time-weighted rate of return. Time-weighted rate of return removes these distortions and provides a better measure of manager's ability to select investments over the period.

Legal and regulatory

More specific legal and regulatory constraints may apply to particular investors. Trust, corporate, and qualified investment accounts may all be restricted by law from investing in particular types of securities and assets.

Multifactor models

Most commonly use macroeconomic factors, such as GDP growth, inflation, or consumer confidence, along with fundamental factors, such as earnings, earnings growth, firm size, and research expenditure.

Challenges of using big data

Must ensure that data is of high quality, accounting for possibilities of outliers, bad or missing data, or sampling biases. Volume of data must be sufficient and appropriate

longevity risk

Need to provide for families' future needs and risk of living longer than anticipated before assets run out. Purchasing a lifetime annuity

Real return

Nominal return adjusted for inflation. E.g. inflation is 2% investor earned 7%. Real return is 7-2 = 5%. Measures the increase in an investor's purchasing power due to the increase in value of investments.

Reversal patterns

Occur when a trend approaches a range of prices but fails to continue beyond that stage. e.g. head-and-shoulders pattern - suggest that demand that has been driving the uptrend is fading, especially if each of the highs in the pattern occurs on declining volume.

Full-service asset managers

Offer a variety of investment styles and asset classes

Contrarian strategy

One that buys when most traders are selling and sells when most traders and buying.

Robo-advisors

Online platforms that provide automated investment advice based on a customer's answers to survey questions. May be fully automated or assisted by a human investment advisor. Offer passively managed investments with low fees, low minimum account sizes, traditional asset classes, and conservative recommendations. Primary advantage is low cost to customers Disadvantage is that reasoning behind recommendations not apparent so customer hesitate. Many subject to same regulations and registration requirements as any other investment advsior.

ML can overfit / underfit the data

Overfitting - Machine learns the input and output data too exactly, treating noise as true parameters, and identifies spurious patterns and relationships Underfitting - Machine fails to identify actual patterns and relationships, treating true parameters as noise. Model is not complex enough for data.

Smart beta

Part of passive management approach that focuses on exposure to a particular market risk factor.

Double top and triple top

Patterns similar to head-and-shoulders in that indicate weakening in the buying pressure that has been driving an uptrend. In both cases, price reaches a resistance level at which selling pressure appears repeatedly, preventing any further increase in price. Can be used to project a price target for next downtrend.

Holding period return (HPR)

Percentage increase in the value of an investment over a given time period HPR = (end-of-period value)/(beginning-of-period value) - 1 = (Pt + Dt)/ P0 - 1

Sovereign wealth funds

Pools of assets owned by a government

Hedge funds

Pools of investor funds that are not regulated to the extend that mutual funds are. Limited in number of investors who can invest and are often sold only to qualified investors. Type of pooled investment

Separately managed account

Portfolio owned by a single investor and managed according to that investor's needs and preferences. No shares issued, as single investor owns whole account Type of pooled investment

Assuming risk averse, investors prefer

Portfolio that has the greatest expected return when choosing among portfolios that have the same standard deviation of returns. Those with the portfolios that have the greatest expected return for each level of risk (standard deviation) make up the "efficient frontier"

Efficient frontier

Portfolios that have the greatest expected return for each level of risk. Coincides with the top portion of the minimum-variance frontier. Risk-averse investor would only choose portfolios that are on the efficient frontier, because all available portfolios that are not on the efficient frontier have lower expected returns. than efficient portfolio with the same risk. Reducing the correlation between two assets results in the efficient frontier expanding to the left and possibly slightly upward. Reflects the influence of correlation on reducing portfolio risk.

Minimum-variance portfolios

Portfolios that have the lowest standard deviation of all portfolios with a given expected return Together comprise the "Minimum-variance frontier" If stocks are perfectly correlated, no diversification benefits and simply select the stock with the loweest risk

Risk budgeting

Process of allocating firm resources to assets by considering their various risk characteristics and how they contribute to meet the organization's risk tolerance. Goal is to allocate overall amount of acceptable risk to the mix of assets or investments that have the greatest expected returns over time.

Risk management

Process seeks to: 1. Identify the risk tolerance of the organization 2. Identify and measure the risks that the organization faces 3. Modify and monitor these risks. Process does not seek to modify or eliminate all of these risks. Organization may want to increase its exposure because can manage them. Risk is not something to be avoided by an organization or in an investment portfolio. Think of risk management as determining the organizational risks, optimal bundle of risks for organization, and implementing risk mitigation strategies to achieve that bundle of risks.

Closed-end funds

Professionally managed pools of investor money that do not take new investments into the fund or redeem investor shares. The shares of a closed-end fund trade like equity shares (on exchanges or OTC). As with open-end funds, portfolio management firm charges ongoing management fees.

Put/call ratio

Put options increase in value when the price of the underlying asset decreases and calls increase while price of underlying asset increases. Volume of put and call options reflects activity by investors with negative and positive outlooks, respectively about the asset. Put/call ratio is put volume divided by call volume. Increases in ratio indicate strongly bearish investor sentiment and possibly an oversold market, while low ratios indicate strongly bullish sentiment and overbought market.

Mutual fund cash position

Ratio of mutual funds' cash to total assets. During uptrends, fund managers want to invest cash quickly because cash earns only the risk-free rate of return and thus decreases fund returns. During downtrends, fund cash balances increase overall fund returns. mutual fund cash positions increase when market is falling and decrease when rising. Viewed as a contrarian indicator by analysts

Comparing the CML and the SML

Recall CML equation: E(Rp) = Rf + sigP*{ (E(Rm)-Rf)/sigM } CML uses total risk = sigP on x-axis. Only efficient portfolios will plot on the CML. On the other hand, SML uses beta (systematic risk) on the x-axis. So in a CAPM world, all the properly priced securities and portfolios of securities will plot on the SML. Portfolios that are not well diversified (efficient) plot inside the efficient frontier and are represented by risk-return combinations. Include inefficient portfolios. According to CAPM, expected returns on all portfolios (well-diversified or not) are determined by their systematic risk. So point A in image represents a high beta portfolio, point B has beta of 1, and point-c is a low-beat. Know this since expected return at point B is equal to the expected return on the market, and the expected returns at point A and C are greater and less than the expected return on the market portfolio. Low point (C) not necessarily low-risk when total-risk considered. Can have high risk when held by itself. All that plot along line labeled ß=1 have same expected return as the market portfolio and, thus, according to CAPM have same systematic risk as the market portfolio. All points on CML represent the risk-return characteristics of portfolios formed by either combining the market portfolio with the risk-free asset or borrowing at the risk-free rate in order to invest more than 100% of the portfolio's net value in the risky market portfolio. Point D - portfolio that combines the market portfolio with the risk-free asset. Point E represents portfolios created by borrowing at the risk-free rate to invest in market portfolio. Portfolios not on CML are not efficient and have risk that will not be rewarded with higher expected returns. According to CAPM, all securities and portfolios, diversified or not, will plot on the SML in equilibrium. In fact, all stocks and portfolios along the line ß=1 will plot at the same point on SML.

Performance evaluation

Refers to analysis of risk and return of the portfolio. Cannot just compare results to the benchmark. Must also consider the risk taken to achieve returns. A portfolio with greater risk than the benchmark is expected to produce higher returns over time than the benchmark.

Intermarket analysis

Refers to analysis of the interrelationships among the market values of major asset classes, such as stocks, bonds, commodities, and currencies. Relative strength ratios are useful for determining which asset classes are outperforming others. Can be used to compare relative performance of equity market sectors or industries and of various international markets.

Natural language processing

Refers to use of computers and artificial intelligence to interpret human language. Speech recognition and language translation are among the uses of natural language processing. Check for regulatory compliance or to evaluate large volumes of research reports.

Security characteristic line

Regression line referred to this. Slope of security line is Cov_im / sig_m^2 (same formula used to calculate beta)

Utility function

Represents the investor's preferences in terms of risk and return

Goal of risk management

Retain optimal mix of risks for the organization

Defined contribution pension plan

Retirement plan in which firm contributes a sum each period to employee's retirement account. The firm contribution can be based on any number of factors (years of service, age, compensation, profitability). Firm makes no promise to the employee regarding the future value of the plan assets. Investment decisions left to the employee, who assumes all investment risk.

Net return

Return after management / administrative fees have been deducted. Note that commissions on trades and other costs are deducted in both gross and net return measures.

After-tax nominal return

Return after the tax liability is deducted

Pretax nominal return

Return prior to paying taxes. Dividend income, interest income, short-term capital gains, and long-term capital gains may all be taxed at different rates.

Systematic risk (nondiversifiable risk, market risk)

Risk that cannot be diversified away Applies to individual securities as well as to portfolios. Some securities highly correlated with overall market returns. E.g. luxury good manufacturers. These firms have high systematic risk because very responsive to market changes. Companies with very little systemic risk include like utility companies.

Individual investors

Save and invest for reasons such as purchasing a house or educating their children. Special accounts allow investment for retirement to defer taxes on investment income and gains until withdrawn.

Risk-averse investor's indifference curves

See image Expected utility is the same for all points along a single indifference curve. I1 represents the most preferred portfolios

Identifying mispriced securities

See image If the estimated return plots "over" the SML, the security is "under" valued. If the estimated return plots "under" the SML, the security is "over" valued. Remember, all stocks should plot on the SML; any stock not plotting on the SML is mispriced Note that overvalued is below the line.

Risk and return of major asset classes in the united states

See image. Asset classes with the greatest average returns also have the highest standard deviations of returns. Evaluating investments using expected returns and variance of returns is a simplification, because returns do not follow a normal distribution. Distributions are negatively skewed with greater kurtosis than a normal. Liquidity can be a major concern in emerging markets and for securities that are traded infrequently (such as low-quality corporate bonds).

Treynor Measure and Jensen's Alpha

See image. Whether risk adjustment should be based on standard deviation of returns or portfolio beta depends on whether a manager's portfolio bears unsystematic risk. If a single manager is used, total risk is the relevant measure and risk adjustment using total risk, as with the Sharpe and M^2 measures, is appropriate If a fund uses multiple managers so that the overall fund portfolio is well diversified, then performance measures based on systematic (beta) risk, such as the Treynor measure and Jensen's alpha, are appropriate.

Resistance level

Selling is expected to emerge that prevents further price increases. Support and resistance levels frequently appear at psychologically important prices such as round number prices or historical highs / lows.

Risk governance

Senior management's determination of the risk tolerance of the organization, the elements of its optimal risk exposure strategy, and the framework for oversight of the risk management function. Seeks to manage risk in a way that supports the overall goals of organization so it can achieve the best business outcome consistent with organization's overall risk tolerance. Risk management committee can provide a way for various parts of the organization to bring up issues of risk management, integration risks, and the best ways to mitigate undesirable risks

Risk budgeting

Set an overall risk limit for the portfolio and budgets a portion of the permitted risk to the systemic risk to the systematic risk of the strategic asset allocation, the risk from tactical asset allocation, and the risk from security selection.

Additional note

Several studies support the idea that approximately 90% of the variation in a single portfolio's returns can be explained by its target asset allocations, with security selection and tactical variations from the target (market timing) playing a much less significant role. In fact, for actively managed funds, actual portfolio returns are slightly less than those that would have been achieved if the manager strictly maintained the target allocation, thus illustrating the difficultly of improving returns through security selection or market timing.

Sharpe ratio

Sharpe ratio = (E[R_portfolio] - Rf) / sig_portfolio A portfolio's excess returns per unit of total portfolio risk. Higher Sharpe ratio indicates better risk-adjusted portfolio performance. Used to evaluate the performance of a portfolio with risk that differs from that of a benchmark portfolio Based on the total risk (Standard deviation of returns) rather than systematic risk (beta). For this reason, can be used to evaluate the performance of concentrated portfolios (those affected by unsystematic risk) as well as well-diversified portfolios. Value of Sharpe ratio really only useful for comparison with the Sharpe ratio of another portfolio.

Exchanged-traded funds

Similar to closed-end funds in that purchases and sales are made in the market rather than with the fund itself. Difference - ETFs are most often invested to match a particular index, so not often actively managed. With closed-end funds, market price of shares can differ significantly from their NAV due to imbalances between investor supply and demand for shares at any point in time. Special redemption provisions for ETFs designed to keep market prices very close to NAVs Can be sold short, purchased on margin, and traded at interday prices, whereas open-ended funds are typically sold and redeemed only daily, based on the share NAV calculated with closing asset prices. ETF investors pay brokerage commissions when they trade, and there is a spread between bid and ask price. Investors receive any dividend income on portfolio stocks in cash, while open-ended funds offer the alternative of reinvesting dividends in additional fund shares. ETFs may produce less capital gains liability compared to open-end index funds. Because investor sales of ETF shares do not require the fund to sell any securities. If an open-end fund has significant redemptions that cause it to sell appreciated portfolio shares, shareholders incur a capital gains tax liability. Type of pooled investment

Efficient frontier can be made once identified the investable asset classes for the portfolio and the risk, return, and correlation characteristics of each asset class

Similar to one constructed for individual securities. By combining the return and risk objectives from the IPS with actual risk and return properties of the many portfolios along the efficient frontier, manager can identify that portfolio which best meets the risk and return requirements of investor.

Arithmetic mean return

Simple average of a series of periodic returns. Unbiased estimator of the true mean of the underlying distribution of returns. = Sum of returns / n

Line charts

Simplest charts. Show closing prices for each period as a continuous line

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. Combining a risky portfolio with a risk-free asset is the process that supports this. Line representing these possible combinations on capital allocation line.

Cycle theory

Study of processes that occur in cycles. Apply to markets in order to identify cycles in prices.

Challenges of quantifying infrequent risks

Subjective rather than data-driven often. Estimates of risk can also be based on the market prices of insurance, derivatives, or other securities

Unexpected changes in tax laws or regulatory environment

Subjective since hard to predict due to political nature of such changes.

Continuation patterns

Suggest a pause in trend rather than a reversal

Arms Index (Short-term Trading Index (TRIN))

TRIN = ((number of advancing issues / number of declining issues)/(volume of advancing issues / volume of declining issues)) Index value close to 1 suggests funds are flowing about evenly to advancing and declining stocks. Index values greater than 1 mean majority of volume is in declining stocks, while an index less than 1 means more of the volume is in advancing stocks.

Advantage of technical analysis

Technical analysis avoids having to use fundamental data and adjusting for accounting problems, incorporates psychological as well as economic reasons behind price changes, and tells WHEN to buy; not WHY investors are buying. Drawbacks include subjective interpretation of charts and graphs.

Deep learning

Technique that uses layers of neural networks to identify patterns, beginning with simple patterns, and advancing to more complex ones. May employ supervised or unsupervised learning. Applications include speech and image recognition.

Covariance

The extent to which two variables move together over time. Positive covariance means that the variables tend to move together Negative means that they move in opposite directions Zero means no linear relationship. If the covariance of returns between two assets is zero, knowing the return for the next period on one of the assets tells you nothing about the return of the other asset for the period. = ( Sum{(Rt1 - R1m)*(Rt2 - R2m)}/(n-1) Rt1 = return on asset 1 in period t Rt2 = return on asset 2 in period t R1m = Mean return on asset 1 R2m = Mean return on asset 2 n = number of periods Magnitude of covariance depends on magnitude of individual stocks' standard deviations and the relationship between their co-movements. An absolute measurement and measured in return units squared

Market portfolio

The market portfolio according to Capital Market Theory consists of all risky assets because all investors that hold any risky assets hold the same portfolio of risky assets. Depending on their preferences for risk and return (their indifference curves), investors may choose different portfolio weights for the risk-free asset and the risky (tangency) portfolio. Every investor, however, will use the same risky portfolio.

Key assumption of technical analysis

The market reflects both rational and irrational behavior. Implies that efficient markets hypothesis does not hold. Technical analysts believe investor behavior is reflected in trends and patterns that tend to repeat and can be identified and used for forecasting prices.

Important note

The market risk premium is equal to Rmarket - Rf So dont have to do any subtraction if given that

Security market line

The only relevant (priced) risk for an individual asset i measured by covariance between asset's returns and the returns on the market, Cov_i,mkt. Plot the security market line as a measure of the relationship between risk and return for individual assets, using Cov_i,mkt as the measure of systematic risk. Equation of SML: E(Ri) = Rf + ( (E(Rmkt) - Rf)/sig_mkt^2)*Cov_i,mkt Rearrange to: E(Ri) = Rf + ((Cov_i,mkt)/(sig_mkt^2) * (E(Rmkt) - Rf)) the rearranged equation is presented in the Capital Asset Pricing Model (CAPM), where we let the standardized covariance term, Cov_i,mkt/sig_mkt^2 be defined as Beta ß_i Most common means of describing the SML, and this relation between beta (systematic risk) and expected return is known as the "Capital Asset Pricing Model" (CAPM)

Diversification ratio

The ratio of the risk of an equally weighted portfolio of n securities to the risk of a single security selected at random from the n securities. A lower diversification ration indicates greater risk reduction benefit from diversification. Note that an equal-weighted portfolio is not necessarily the one that provides the greatest reduction in risk. Computer optimization calculate one that will produce lowest risk. Diversification works best when markets are operating normally. Diversification provides less reduction of risk during market turmoil. During periods of crisis, correlations tend to increase, which reduces the benefits of diversification.

Beta

The sensitivity of an asset's return to the return on the market's index in the context of the market model A standardized measure of the covariance of the asset's return with the market return ßi = (Covariance of Asset i's return with the market return) / (variance of the market return) = Cov_im/(sig^2_m) p_im = Cov_im / (sig_i*sig_m) remember Cov_im = p_im * sig_i*sig_m ß_i = (p_im*sig_i*sig_m)/(sig_m^2) = p_im * (sig_i/sig_m) ß_i = Cov_im / sig_m^2

Technical analysis

The study of collective market sentiment, as expressed in buying and selling and assets. Based on the idea that prices are determined by the interaction of supply and demand. Market price equates supply and demand at any instant. Only participants who actually trade affect prices, and better-informed participants trade in greater volume. Price and volume reflect the collective behavior of buyers and sellers.

If covariance is zero

Then correlation must also be zero

Unsystematic risk (unique, diversifiable, or firm-specific risk)

This risk is reduced by diversifying across assets that are not perfectly correlated. Because market portfolio contains all risky assets, it must be a well-diversified portfolio. All risk possible to diversify has been diversified away.

Indifference curve

Tool from economics that plots combinations of risk (standard deviation) and expected return among which an investor is indifferent. We are assuming that these are the only portfolio characteristics that investors care about. Slope upward for risk averse investors because they will only take on more risk if they are compensated with greater returns. More risk averse requires more increase in expected returns to compensate for given risk. Known as a higher "risk aversion coefficient" So these represent the balance of risk and return

Oscillators

Tools to find overbought or oversold markets. Based on market prices but scaled so that oscillate around a given value such as 0 or between two values such as 0 and 100. Extreme high values are indicator overbought while extreme low are oversold.

Gross return

Total return on a security portfolio before deducting fees for management and administration of account

Total risk

Total risk = systematic risk + unsystematic risk.

trend lines

Trendlines connect the increasing low points on a price chart in an uptrend and the decreasing high points in a downtrend.

Also note that

Treynor Measure and Jensen's Alpha, we can see that portfolios that lie above the SML have Treynor measures greater than those of any security or portfolio that lies along the SML and also have positive values for Jensen's alpha.

Opinion polls

Try to measure investor sentiment directly as well as several measures that are based on market data.

Tail risk

Uncertainty about the probability of extremely negative outcomes

Capital market line (CML)

Under assumption of homogeneous expectations, optimal CAL for all investors is CML E(Rp) = Rf + ((E(R_M)-Rf)/(sigM)) * sigP y-intercept = ((E(R_M)-R_f)/(sigM)) Any investor who takes no risk will take the risk-free rate, Rf. E(Rp) = Rf + (E(R_M)-Rf)*(sigP/sigM) Plots return against total risk A portfolio to the right of a portfolio on the CML has more risk than the market portfolio. Investors seeking to take on more risk will borrow at the risk-free rate to purchase more of the market portfolio.

Trend

Uptrend - prices are consistently reaching higher highs and retracing to higher lows. Downtrend - retracting to lower lows and retracing to lower highs Uptrend means demand is increasing relative to supply. Downtrend suggests supply is increasing relative to demand. Trendline identify whether trend is continuing or reversing. Breakout - When the price crosses the trendline by what analyst considers significant. Breakdown - From an uptrend. Either breakout or breakdown can signal end of previous trend.

head-and-shoulders pattern

Use to project a price target for the ensuing downtrend. Size is the difference in price between head, the highest price reached, and the neckline, the support level to which the price retraced after the left shoulder and the head have formed. Decreasing volume on each of the high prices in a head and shoulders pattern (or each of the low prices in an inverse head and shoulders) suggests weakening in the supply and demand forces that were driving the price trend. Inverse head and shoulders patterns typically occur after downtrends and indicate that the trend is going to reverse.

Self-insurance

Used to describe a situation where an organization has decided to bear a risk Bear any associated losses from this risk factor. In some cases will establish a reserve account to cover losses

Margin debt (besides indicating investor sentiment, as previously described)

Useful flow of funds indicator. Increasing margin debt may indicate that investors want to buy more stocks. Decreasing indicates increased selling.

Flow of funds

Useful for observing changes in the supply and demand of securities

Permissioned networks

Users have different levels of access. distributed ledger that allowed regulators to view records that firms are required to make available would increase transparency and decrease compliance costs.

Engagement / active ownership investing

Using share ownership as a platform to promote improved ESG practices at a company, using share voting rights and by influencing management or board members. For investment managers with clients who wish to engage in active ownership, it is important to clarify whether the clients intend to vote their shares themselves or direct the managers to vote the shares according to specified ESG factors.

Commonly used measures of tail risk (aka downside risk)

Value at risk (VaR) - minimum loss over a period that will occur with a specific probability This is not the maximum one-month loss; it is the minimum loss that will occur x% of the time. VaR does not provide a maximum loss for a period. Commonly used by banks and used in establishing minimum capital requirements Conditional VaR (CVaR) - Expected value of a loss given that the loss exceeds a minimum amount. CVaR would be expected loss, given that the loss was at least $X. Probability-weighted average loss for all losses expected to be at least $1 million.

Operational risks difficult to quantify

Very difficult to predict and may result in a large cost to organization. Can examine a large sample of firms in order to determine overall probability of significant loss due to operational risks and the average loss of firms that have experienced such loss Subjective

Standard deviation

Volatility of asset prices and interest rates. May not be the appropriate measure of risk for non-normal probability distributions, especially those with negative skew or positive excess kurtosis.

Risk shifting

Way to change the distribution of possible outcomes and is accomplished primarily with derivatives. e.g. financial firm uses forward currency contracts. or buy put option to protect itself

Big data

Widely used expression that refers to all the potentially useful information that is generated in the economy. Not only data from traditional sources, such as financial market,s company financial reports, and government economic statistics, but also alternative data (from non-traditional sources) Characteristics of big data: 1. volume - continues to grow by orders of magnitude. 2. velocity - How quickly data are communicated. Real-tyime data such as stock market price feeds hae a low "latency." Data that are communicated only periodically or with a lag have high latency. 3. variety - Varying degrees of structure in which data may exist. Structured forms such as spreadsheets to semistructured such as photos to unstructured such as video.

Jensen's alpha

a_p = R_P - [Rf + ß_p(R_M - Rf)] Percentage portfolio return above that of a portfolio (or security) with the same beta as the portfolio that lies on the SML.

Investment policy statement

begin with the investor's goals in terms of risk and return Determined and written jointly. Investor expectations in terms of returns must be compatible with investor's tolerance for risk At a minimum contain a clear statement of client circumstances and constraints, an investment strategy based on these, and some benchmark against which to evalute the account performance

Asset management firms include

both independent managers and divisions of larger financial services companies. Referred to as "buy-side" firms, in contrast with sell-side firms, such as broker-dealers and investment banks

Support level

buying is expected to emerge that prevents further price decreases Support level to do with buying and resistance level to do with selling

Risk tolerance

determining risk tolerance involves setting the overall risk exposure the organization will take by identifying the risks the firm can effectively take and the risks that the organization should reduce or avoid. Some of factors that determine an organization's risk tolerance are its expertise in its lines of business, its skill at responding to negative outside events, its regulatory environment, and its financial strength and ability to withstand losses. Management should consider internal and external risks.

fintech

developments in technology that can be applied to the financial services industry. Primary areas where fintech is developing: 1. Increasing functionality to handle large sets of data that may come from many sources and exist in a variety of forms. 2. Tools and techniques such as artificial intelligence for analyzing very large datasets. 3. Automation of financial functions such as executing trades and providing investment advice. 4. Emerging technologies for financial recordkeeping that may reduce the need for intermediaries.

Risk budget may be constructed based on investment categories

domestic equities, domestic debt securities, international equities, and international debt securities.

Triangle Continuation Pattern

form when prices reach lower highs and higher lows over a period of time. Can be symmetrical (higher lows and lower highs), ascending (higher lows and a resistance level), or descending (lower highs and a support level). Suggest buying and selling pressure have become roughly equal temporarily, but they do not imply a change in direction of the trend. size of a triangle (difference between the two trendlines at the time when the pattern begins to form) can be used to set a price target, assuming the price breaks out of the triangle and the previous trend continues.

Multi-boutique firm

holding company that includes a number of different specialist asset managers.

Machine learning

important development of AI in which computer algorithm given inputs of source data with no assumptions about probability distributions, and may be given outputs of target data. Algorithm designed to learn, without human assistance, how to model the output data based on input data or to learn how to detect and recognize patterns. Requires vast amounts of data. Begins with a training dataset in which the algorithm looks for relationships Validation dataset is then used to refine these relationship models, which can then be applied to a test dataset to analyze predictive ability.

Note that

in Sharpe Ratios as Slopes and M-Squared for a Portfolio that portfolios that lie above the CML have Sharpe ratios greater than those of any portfolios along the CML and have positive M2 measures.

Thematic investing

in sectors or companies in order to promote specific ESG-related goals

Effective risk management would most likely attempt to

maximize expected return for a given level of risk. Risk management requires establishment of a risk tolerance (maximum acceptable level of risk) for the organization and will attempt to maximize expected returns for that level of risk. Some significant risks the firm is exposed to may be borne by the firm or even increased as a result of risk management.

risk-neutral investor

no preference regarding risk and would be indifferent between two such investments.

Conclusion from capital market theory - equilibrium security returns depend

on a stock's or portfolio's systematic risk, not its total risk as measured by standard deviations. Assumptions of model is that diversification is free. Investors will not be compensated for bearing risk that can be eliminated at no cost. Riskiest stock (std dev of returns) does not necessarily have the greatest return. The equilibrium return on a stock with high systematic risk may be less than that of a stock with much less firm-specific risk but more sensitivity to factors that drive the return of the overall market. Im summary: unsystematic risk is not compensated in equilibrium because it can be eliminated for free through diversification. Systematic risk is measured by the contribution of a security to the risk of a well-diversified portfolio, and the expected equilibrium return on an individual security will depend only on its systematic risk.

Correlation

p12 = Cov12 / s1*s2 s1,s2 = standard deviations of 1 and 2 Cov12 = p12*s1*s2 Has no units. Bound by -1 and +1. A correlation coefficient of +1 means that deviations from the mean or expected return are always proportional in the same direction. That is, they are perfectly positively correlated. A correlation coefficient of -1 means that deviations from the mean or expected return are always proportional in opposite directions. That is, they are perfectly negatively correlated. A correlation coefficient of zero means that there is no linear relationship between the two stocks' returns. They are uncorrelated. One way to interpret a correlation (or covariance) of zero is that, in any period, knowing the actual value of one variable tells you nothing about the value of the other.

Risk budget may be a single metric

portfolio beta, value at risk, portfolio duration, or returns variance

risk-seeking investor

prefers more risk to less and, given equal expected returns, will choose the more risky investment

Note on CAPM calculations

required rate is from Rf + ß*(Rmkt-Rf Return on stock is (Pf - Pi + D)/Pi Compare. If return greater than required rate it's underpriced.

The greatest portfolio risk

results when the correlation between the assets is +1. Portfolio risk is reduced as gets smaller. 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.

If two risky asset returns are perfectly correlated

sigma_portfolio = sqrt(Var_portfolio) = sqrt(w1^2*sig1^2+w2^2*sig2^2+(2*w1*w2*sig1*sig2)) = w1*sig1 + w2*sig2

risk-averse investor

simply dislikes risk. Given two investments that have equal expected returns, choose one with less risk (standard deviation) an investor may select a very risky portfolio despite being risk averse; a risk-averse investor will hold very risky assets if he feels that the extra return he expects to earn is adequate compensation for the additional risk.

Capital asset pricing model (CAPM)

the equation of the SML showing the relationship between expected return and beta (systematic risk) ß = Cov_i,mkt / sig_mkt^2 Formally, the CAPM is stated as: E(Ri) = Rf + ßi * [E(Rmkt) - Rf] Holds that inequilibrium the expected return on risky asset (E(Ri) is the risk free rate (Rf) plus a beta adjusted market risk premium (ßi[E(Rmkt)-Rf] Beta measures systematic (market or covariance) risk

variance

the sum of squared deviations from the mean, divided by the count use population mean