Authorized participants

(APs) A special group of institutional investors

who are authorized by the ETF issuer to

participate in the creation/redemption process.

APs are large broker/dealers, often market

makers.

Creation basket

The list of securities (and share amounts) the

authorized participant (AP) must deliver to the

ETF manager in exchange for ETF shares.

The creation basket is published each

business day.

Creation/redemption

The process in which ETF shares are

created or redeemed by authorized

participants transacting with the ETF

issuer.

Creation units

Large blocks of ETF shares transacted

between the authorized participant (AP) and

the ETF manager that are usually but not

always equal to 50,000 shares of the ETF.

iNAVs

ndicatedÓ net asset values are

intraday Öfair value estimates of an

ETF share based on its creation

basket.

Redemption basket

The list of securities (and share amounts) the

authorized participant (AP) receives when it

redeems ETF shares back to the ETF manager.

The redemption basket is published each

business day.

Describe factors affecting ETF bid–ask spreads.

ETF spreads are positively related to the cost of creation/redemption, the spread on the underlying securities, the risk premium for carrying trades until close of trade, and the APs’ normal profit margin. ETF spreads are negatively related to the probability of completing an offsetting trade on the secondary market. Creation/redemption fees and other trading costs can influence spreads as well.

Describe sources of ETF premiums and discounts to NAV.

ETF premium (discount) % = (ETF price – NAV) / NAV

Sources of premium or discount include timing difference for ETFs with foreign securities traded in different time zones and stale pricing for infrequently traded ETFs.

Describe types of ETF risk.

Risks of investing in ETFs include counterparty risk (common for ETNs), fund closures, and expectation-related risk.

Describe costs of owning an ETF.

ETF costs include trading cost and management fees. Short-term investors focus on lower trading costs while longer-term, buy-and-hold investors seek lower management fees. Trading costs tend to be lower for more-liquid ETFs. Liquidity is evaluated using the ratio of average dollar volume to average assets (higher is better).

Explain the creation/redemption process of ETFs and the function of authorized participants.

Authorized participants (APs) can create additional shares by delivering the creation basket to the ETF manager. Redemption is similarly conducted by tendering ETF shares and receiving a redemption basket. These primary market transactions are in kind and require a service fee payable to the ETF issuer, shielding the nontransacting shareholders from the costs and tax consequences of creation/redemption. The creation/redemption process ensures that market prices of ETFs stay within a narrow band of the NAV.

Describe sources of tracking error for ETFs.

Tracking error is the annualized standard deviation of the daily tracking difference. Sources of tracking error include fees and expenses of the fund, sampling, and optimization used by the fund, the fund’s investment in depository receipts (DRs) (as opposed to the underlying shares directly), changes in the index, regulatory and tax requirements, fund accounting practices, and asset manager operations.

Identify and describe portfolio uses of ETFs.

Portfolio uses of ETFs include the following:

- Efficient portfolio management, including liquidity management, portfolio rebalancing, portfolio completion, and transition management.
- Asset class exposure management, including core exposure to an asset class or sub-asset class as well as tactical strategies.
- Active investing, including smart beta, risk management, alternatively weighted ETFs, discretionary active ETFs, and dynamic asset allocation.

Describe how ETFs are traded in secondary markets.

ETFs are traded just like other shares on the secondary markets. Market fragmentation may widen the quoted spreads for European ETFs.

Active factor risk

The contribution to active risk squared

resulting from the portfolio different-than

benchmark exposures relative to factors

specified in the risk model.

Active return

The return on a portfolio minus

the return on the portfolio

benchmark.

Active risk

The standard deviation of

active returns.

Active risk squared

The variance of active returns;

active risk raised to the second

power.

Active specific risk

The contribution to active risk squared

resulting from the portfolio active weights on

individual assets as those weights interact

with assetsÖ residual risk.

Arbitrage

(1) The simultaneous purchase of an undervalued asset or portfolio and sale of an overvalued but equivalent asset or portfolio in order to obtain a riskless profit on the price differential. Taking advantage of a market inefficiency in a

risk-free manner.

(2) The condition in a financial market in which equivalent

assets or combinations of assets sell for two different prices, creating an opportunity to profit at no risk with no commitment of money. In a well functioning financial market, few arbitrage opportunities are possible.

(3) Arisk-free operation that earns an expected positive net profit but requires no net investment of money.

Arbitrage opportunity

An opportunity to conduct an arbitrage; an

opportunity to earn an expected positive net

profit without risk and with no net

investment of money.

Arbitrage portfolio

The portfolio that exploits an

arbitrage opportunity.

Company fundamental factors

Factors related to the company internal performance, such as factors relating to earnings growth, earnings variability, earnings momentum, and financial leverage.

Company share-related factors

Valuation measures and other factors related to share price or the trading characteristics of the shares, such as earnings yield, dividend yield, and book-to market value.

Factor

A common or underlying element

with which several variables are

correlated.

Factor portfolio

Pure factor portfolio portfolio with

sensitivity of 1 to the factor in

question and a sensitivity of 0 to all

other factors.

Factor price

The expected return in excess of the risk

free rate for a portfolio with a sensitivity of 1

to one factor and a sensitivity of 0 to all

other factors.

Factor risk premium

The expected return in excess of the risk

free rate for a portfolio with a sensitivity of

to one factor and a sensitivity of 0 to all

other factors. Also called factor price.

Fundamental factor models

A multifactor model in which the factors are

attributes of stocks or companies that are

important in explaining cross-sectional

differences in stock prices.

Information ratio

(IR) Mean active return divided by

active risk; or alpha divided by the

standard deviation of diversifiable

risk.

Macroeconomic factor model

A multifactor model in which the factors

are surprises in macroeconomic

variables that significantly explain equity

returns.

Macroeconomic factors

Factors related to the economy, such

as the inflation rate, industrial

production, or economic sector

membership.

Priced risk

Risk for which investors demand

compensation for bearing (e.g., equity risk,

company-specific factors, macroeconomic

factors).

Pure factor portfolio

A portfolio with sensitivity of 1 to

the factor in question and a

sensitivity of 0 to all other factors.

Security selection risk

Active specific riskThe contribution to active

risk squared resulting from the portfolio

active weights on individual assets as those

weights interact with assetsÖ residual risk.

Standardized beta

With reference to fundamental factor models, the

value of the attribute for an asset minus the average

value of the attribute across all stocks, divided by

the standard deviation of the attribute across all

stocks.

Statistical factor model

A multifactor model in which statistical

methods are applied to a set of historical

returns to determine portfolios that best

explain either historical return covariances or

variances.

Systematic risk

Risk that affects the entire market or

economy; it cannot be avoided and is

inherent in the overall market. Systematic

risk is also known as non-diversifiable or

market risk.

Tracking error

The standard deviation of the differences

between a portfolio returns and its

benchmarkÖs returns; a synonym of active

risk. Also called tracking risk.

Tracking risk

The standard deviation of the differences

between a portfolio returns and its

benchmarkÖs returns; a synonym of active

risk. Also called tracking error.

Define arbitrage opportunity and determine whether an arbitrage opportunity exists.

An arbitrage opportunity is defined as an investment opportunity that bears no risk and has no cost, but provides a profit. Arbitrage is conducted by forming long and short portfolios; the proceeds of the short sale are used to purchase the long portfolio. Additionally, the factor sensitivities (betas) of the long and short portfolios are identical and, hence, our net exposure to systematic risk is zero. The difference in returns on the long and short portfolios is the arbitrage return.

Describe uses of multifactor models and interpret the output of analyses based on multifactor models.

Multifactor models can be useful for risk and return attribution and for portfolio composition. In return attribution, the difference between an active portfolio’s return and the benchmark return is allocated between factor return and security selection return.

In risk attribution, the sum of the active factor risk and active specific risk is equal to active risk squared (which is the variance of active returns):

active risk squared = active factor risk + active specific risk

active factor risk = active risk squared − active specific risk

Multifactor models can also be useful for portfolio construction. Passive managers can invest in a tracking portfolio, while active managers can go long or short factor portfolios.

A factor portfolio is a portfolio with a factor sensitivity of 1 to a particular factor and zero to all other factors. It represents a pure bet on a single factor and can be used for speculation or hedging purposes. A tracking portfolio is a portfolio with a specific set of factor sensitivities. Tracking portfolios are often designed to replicate the factor exposures of a benchmark index like the S&P 500.

Describe the potential benefits for investors in considering multiple risk dimensions when modeling asset returns.

Multifactor models enable investors to take on risks that the investor has a comparative advantage in bearing and avoid the risks that the investor is unable to absorb.

Models that incorporate multiple sources of systematic risk have been found to explain asset returns more effectively than single-factor CAPM.

Explain sources of active risk and interpret tracking risk and the information ratio.

Active return is the difference between portfolio and benchmark returns (RP − RB), and active risk is the standard deviation of active return over time. Active risk is determined by the manager’s active factor tilt and active asset selection decisions:

active risk squared = active factor risk + active specific risk

The information ratio is active return divided by active risk

Calculate the expected return on an asset given an asset’s factor sensitivities and the factor risk premiums.

Expected return = risk-free rate + ∑(factor sensitivity) × (factor risk premium)

Describe and compare macroeconomic factor models, fundamental factor models, and statistical factor models.

A multifactor model is an extension of the one-factor market model; in a multifactor model, asset returns are a function of more than one factor. There are three types of multifactor models:

Macroeconomic factor models assume that asset returns are explained by surprises (or shocks) in macroeconomic risk factors (e.g., GDP, interest rates, and inflation). Factor surprises are defined as the difference between the realized value of the factor and its consensus expected value.

Fundamental factor models assume asset returns are explained by the returns from multiple firm-specific factors (e.g., P/E ratio, market cap, leverage ratio, and earnings growth rate).

Statistical factor models use multivariate statistics (factor analysis or principal components) to identify statistical factors that explain the covariation among asset returns. The major weakness is that the statistical factors may not lend themselves well to economic interpretation.

Describe arbitrage pricing theory (APT), including its underlying assumptions and its relation to multifactor models.

The arbitrage pricing theory (APT) describes the equilibrium relationship between expected returns for well-diversified portfolios and their multiple sources of systematic risk. The APT makes only three key assumptions: (1) unsystematic risk can be diversified away in a portfolio, (2) returns are generated using a factor model, and (3) no arbitrage opportunities exist.

Active share

A measure of how similar a portfolio is to its

benchmark. A manager who precisely replicates the

benchmark will have an active share of zero; a

manager with no holdings in common with the

benchmark will have an active share of one.

Conditional VaR (CVaR)

The weighted average of all loss outcomes in the

statistical (i.e., return) distribution that exceed the VaR

loss. Thus, CVaR is a more comprehensive measure

of tail loss than VaR is. Sometimes referred to as the

expected tail loss or expected shortfall.

Convexity

A measure of how interest rate

sensitivity changes with a change

in interest rates.

Delta

The relationship between the option price and the

underlying price, which reflects the sensitivity of the

price of the option to changes in the price of the

underlying. Delta is a good approximation of how an

option price will change for a small change in the

stock.

Duration

A measure of the approximate

sensitivity of a security to a change in

interest rates (i.e., a measure of interest

rate risk).

Ex ante tracking error

A measure of the degree to which the

performance of a given investment portfolio

might be expected to deviate from its

benchmark; also known as relative VaR.

Expected shortfall

A measure of the degree to which the

performance of a given investment portfolio

might be expected to deviate from its

benchmark; also known as relative VaR.

Expected tail loss

Conditional VaR

Gamma

A measure of how sensitive an option delta is to a

change in the underlying. The change in a given

instrumentÖs delta for a given small change in the

underlyingOs value, holding everything else

constant.

Historical simulation method

The application of historical

price changes to the current

portfolio.

Incremental VaR (IVaR)

A measure of the incremental effect of an asset on the

VaR of a portfolio by measuring the difference

between the portfolio VaR while including a specified

asset and the portfolios VaR with that asset

eliminated.

Lookback period

The time period used to

gather a historical data set.

Marginal VaR (MVaR)

A measure of the effect of a small change in a position size on portfolio VaR.

Maximum drawdown

The worst cumulative loss ever sustained by an asset

or portfolio. More specifically, maximum drawdown is

the difference between an asset or a portfolioÔs

maximum cumulative return and its subsequent

lowest cumulative return.

Monte Carlo simulation

A technique that uses the inverse transformation method for converting a randomly generated uniformly distributed number into a simulated value of a random variable of a desired distribution.

Each key decision variable in a Monte Carlo simulation requires an assumed statistical distribution; this assumption facilitates incorporating non-normality, fat tails, and tail dependence as well as solving high-dimensionality problems.

Parametric method

A method of estimating VaR that uses the historical mean,

standard deviation, and correlation of security price movements to estimate the portfolio VaR. Generally assumes a normal distribution but can be adapted to non-normal distributions with the addition of skewness and kurtosis. Sometimes called thevarianceovariance method or the analytical method.

Relative VaR

Ex ante tracking error A measure of the degree

to which the performance of a given

investment portfolio might be expected to

deviate from its benchmark; also known as

relative VaR.

Reverse stress testing

A risk management approach in which the

user identifies key risk exposures in the

portfolio and subjects those exposures to

extreme market movements.

Risk budgeting

The allocation of an asset owner total risk

appetite among groups or divisions (in the case

of a trading organization) or among strategies

and managers (in the case of an institutional or

individual investor).

Risk decomposition

The process of converting a set

of holdings in a portfolio into a

set of exposures to risk factors.

Risk factors

Variables or characteristics with which

individual asset returns are correlated.

Sometimes referred to simply as

factors.

Stop-loss limit

Constraint used in risk management that

requires a reduction in the size of a

portfolio, or its complete liquidation, when a

loss of a particular size occurs in a specified

period.

Stress tests

A risk management technique that assesses the portfolio

response to extreme market movements.

Tail risk

The risk that losses in extreme events

could be greater than would be expected

for a portfolio of assets with a normal

distribution.

Value at risk (VaR)

The minimum loss that would be expected a

certain percentage of the time over a

certain period of time given the assumed

market conditions.

Vega

The change in a given derivative instrument for a given small change in volatility, holding everything else constant. A sensitivity measure for options that reflects the effect of volatility.

Demonstrate how equity, fixed-income, and options exposure measures may be used in measuring and managing market risk and volatility risk.

Equity risk is measured by beta (sensitivity to overall market returns).

The interest rate risk of fixed-income securities is measured by duration (sensitivity to change in yield) and convexity (second-order effect, change in duration).

Options risk is measured by delta (sensitivity to asset price changes), gamma (second-order effect, change in delta), and vega (sensitivity to asset price volatility).

Market risk can be managed by adjusting portfolio holdings to control the exposures to these various risk factors.

Describe sensitivity risk measures and scenario risk measures and compare these measures to VaR.

Sensitivity analysis is used to estimate the change in a security or portfolio value to an incremental change in a risk factor.

Scenario analysis refers to estimation of the effect on portfolio value of a specific set of changes in relevant risk factors.

A scenario of changes in risk factors can be historical, based on a past set of risk factors changes that actually occurred, or hypothetical (based on a selected set of significant changes in the risk factors of interest).

Describe advantages and limitations of VaR.

Advantages of VaR: Widely accepted by regulators. Simple to understand. Expresses risk as a single number. Useful for comparing the risk of portfolios, portfolio components, and business units.

Disadvantages of VaR:

Subjective in that the time period and the probability are chosen by the user.

Very sensitive to the estimation method and assumptions employed by the user.

Focused only on left-tail outcomes.

Vulnerable to misspecification by the user.

Describe advantages and limitations of sensitivity risk measures and scenario risk measures.

VaR, sensitivity analysis, and scenario analysis complement each other, and a risk manager should not rely on only one of these measures.

VaR provides a probability of loss.

Sensitivity analysis provides estimates of the relative exposures to different risk factors, but does not provide estimates of the probability of any specific movement in risk factors.

Scenario analysis provides information about exposure to simultaneous changes in several risk factors or changes in risk correlations, but there is no probability associated with a specific scenario.

Explain constraints used in managing market risks, including risk budgeting, position limits, scenario limits, and stop-loss limits.

Risk budgeting begins with determination of an acceptable amount of risk and then allocates this risk among investment positions to generate maximum returns for the risk taken.

Position limits are maximum currency amounts or portfolio percentages allowed for individual securities, securities of a single issuer, or classes of securities, based on their risk factor exposures.

A stop-loss limit requires that an investment position be reduced (by sale or hedging) or closed out when losses exceed a given amount over a specified time period.

A scenario limit requires adjustment of the portfolio so that the expected loss from a given scenario will not exceed a specified amount.

Compare the parametric (variance–covariance), historical simulation, and Monte Carlo simulation methods for estimating VaR.

Value at risk estimation methods:

Parametric method—uses the estimated variances and covariances of portfolio securities to estimate the distribution of possible portfolio values, often assuming a normal distribution.

Historical simulation—uses historical values for risk factors over some prior lookback period to get a distribution of possible values.

Monte Carlo simulation—draws each risk factor change from an assumed distribution and calculates portfolio values based on a set of changes in risk factors; repeated thousands of times to get a distribution of possible portfolio values.

Describe extensions of VaR.

Conditional VaR (CVaR) is the expected loss given that the loss exceeds the VaR.

Incremental VaR (IVaR) is the estimated change in VaR from a specific change in the size of a portfolio position.

Marginal VaR (MVaR) is the estimate of the change in VaR for a small change in a portfolio position and is used as an estimate of the position’s contribution to overall VaR.

Ex ante tracking error, also referred to as relative VaR, measures the VaR of the difference between the return on a portfolio and the return on the manager’s benchmark portfolio.

Estimate and interpret VaR under the parametric, historical simulation, and Monte Carlo simulation methods.

The x% VaR is calculated as the minimum loss for the current portfolio, x% of the time, based on an estimated distribution of portfolio values.

Describe risk measures used by banks, asset managers, pension funds, and insurers.

Banks are concerned with many risks including asset-liability mismatches, market risk for their investment portfolio, their leverage, the duration and convexity of their portfolio of fixed-income securities, and the overall risk to their economic capital.

Asset managers are most concerned with returns volatility and the probability distribution of either absolute losses or losses relative to a benchmark portfolio.

Pension fund managers are concerned with any mismatch between assets and liabilities as well as with the volatility of the surplus (assets minus liabilities).

P&C companies are concerned with the sensitivity of their investment portfolio to risk factors, the VaR of their economic capital, and scenarios that incorporate both market and insurance risks as stress tests of the firm.

Life insurers are concerned with market risks to their investment portfolio assets and liabilities (to make annuity payments), any mismatch between assets and liabilities, and scenarios that would lead to large decreases in their surplus.

Explain the use of value at risk (VaR) in measuring portfolio risk.

Value at risk (VaR) is an estimate of the minimum loss that will occur with a given probability over a specified period expressed as a currency amount or as percentage of portfolio value.

Describe the use of sensitivity risk measures and scenario risk measures.

A stress test based on either sensitivity or scenario analysis uses extreme changes to examine the expected effects on a portfolio or organization, often to determine the effects on a firm’s equity or solvency. A reverse stress test is designed to identify scenarios that would result in business failure.

Sensitivity analysis can give a risk manager a more complete view of the vulnerability of a portfolio to a variety of risk factors. Sensitivity and scenario risk measures provide additional information about portfolio risk but do not necessarily provide probabilities or, in the case of sensitivity measures, the sizes of expected changes in risk factors and portfolio value.

Sensitivity and scenario analysis provide information that VaR does not and are not necessarily based on historical results. A historical scenario will not necessarily be repeated. Hypothetical scenarios may be misspecified, and the probability that a scenario will occur is unknown.

Explain how risk measures may be used in capital allocation decisions.

Firms use risk measures by adjusting expected returns for risk when making capital allocation decisions.

Backtesting

The process that approximates the real-life

investment process, using historical data, to

assess whether an investment strategy

would have produced desirable results.

Bootstrapping

The use of a forward substitution process to

determine zero-coupon rates by using the par

yields and solving for the zero-coupon rates

one by one, from the shortest to longest

maturities.

Data snooping

The subconscious or conscious manipulation of data in a

way that produces a statistically significant result (i.e., the

p-value is sufficiently small or the t-statistic sufficiently

large to indicate statistical significance), such as by

running multiple simulations and naively accepting the

best result. Also known as p-hacking.

Historical scenario analysis

A technique for exploring the performance and risk of investment strategies in different structural regimes.

Historical simulation

A simulation method that uses past return

data and a random number generator that

picks observations from the historical series

to simulate an asset future returns.

Historical stress testing

The process that tests how investment

strategies would perform under some of the

most negative (i.e., adverse) combinations

of events and scenarios.

Look-ahead bias

The bias created by using information that was

unknown or unavailable in the time periods over

which backtesting is conducted, such as

company earnings and macroeconomic indicator

values.

Point-in-time data

Data consisting of the exact information

available to market participants as of a

given point in time. Point-in-time data is

used to address look-ahead bias.

Risk parity

A portfolio allocation scheme that

weights stocks or factors based

on an equal risk contribution.

Rolling windows

A backtesting method that uses a rolling-window (or walk

forward) framework, rebalances the portfolio after each

period, and then tracks performance over time. As new

information arrives each period, the investment manager

optimizes (revises and tunes) the model and readjusts

stock positions.

Sensitivity analysis

A technique for exploring how a target

variable (e.g., portfolio returns) and risk

profiles are affected by changes in input

variables (e.g., the distribution of asset or

factor returns).

Simulation

A technique for exploring how a target variable (e.g. portfolio returns) would perform in a hypothetical environment specified by the user, rather than a

historical setting.

Survivorship bias

The bias that results when data as of a given date

reflects only those entities that have survived to that

date. Entities can include any element of an index or

list that is constituted through time: stocks, investment

funds, etc. Survivorship bias is a form of look-ahead

bias.

Identify problems in a backtest of an investment strategy.

Problems in a backtest of an investment strategy include the following:

Survivorship bias—When using data that only includes entities that have persisted until today.

Look-ahead bias—When using information that would have been unavailable at the time of the investment decision.

Data snooping—When a model is chosen based on backtesting performance. (i.e., a large t-statistic or a small p-value).

Cross-validation is when a model is first fitted using training data, and then its performance is assessed (often over several rounds) using separate testing data. An investment strategy can also be cross-validated using data from different geographic regions: performance from other global markets can help determine whether a strategy is robust.

Contrast Monte Carlo and historical simulation approaches.

Monte Carlo and historical simulation approaches are methods used to account for skewness, excess kurtosis, and tail dependence.

In historical simulation, observations are randomly chosen from the historical dataset so that each observation has an equal probability of being selected.

Simulations (both historical and Monte Carlo) are nondeterministic and random.

In a Monte Carlo simulation, a statistical distribution is specified and calibrated using historical return data. When the assets or factors are correlated, a multivariate distribution should be used rather than modeling each asset or factor on a standalone basis.

Demonstrate the use of sensitivity analysis.

Sensitivity analysis is a method for evaluating how a target variable (such as portfolio return) varies due to changes in the input variables (such as asset or factor returns).

Sensitivity analysis can overcome the shortcomings of a traditional Monte Carlo simulation, because it is not limited to multivariate normal distributions (which do not take into account fat tails or negative skewness).

To conduct a sensitivity analysis, we fit factor return data to a distribution that accounts for skewness and excess kurtosis (e.g., a multivariate skewed Student’s t-distribution), and then repeat the Monte Carlo simulation.

While use of a skewed multivariate t-distribution helps to take fat tails and skewness into account, this also increases the possibility of estimation error, because a multivariate skewed t-distribution requires estimates of more parameters.

Interpret metrics and visuals reported in a backtest of an investment strategy.

The backtest of an investment strategy will produce return metrics, such as average return, and risk measures, such as volatility and downside risk. Other measures that can be calculated include the Sharpe ratio, the Sortino ratio, and maximum drawdown (the maximum loss from a peak to a trough).

Visuals used in a backtest of an investment strategy often include return distribution plots.

Describe objectives in backtesting an investment strategy.

The primary goal of backtesting is to assess the risk and return of an investment strategy by simulating the investment process.

Backtesting uses past data to evaluate whether a particular investment strategy would have produced excess returns historically. This assessment allows an investor to optimize their investment process and strategy.

Describe and contrast steps and procedures in backtesting an investment strategy.

The three steps in backtesting an investment strategy are:

- Strategy design:

Specify the investment hypothesis and goals.

Determine the investment process and rules of the investment strategy.

Select key parameters.

2.Historical investment simulation:

For each period, assemble a portfolio according to the previously determined rules.

Rebalance the portfolio over time based on those investment rules.

- Analysis of output:

Compute performance statistics, such as risk and return for the portfolio.

Calculate other relevant metrics, such as turnover.

In rolling-window backtesting, an investor makes use of a walk-forward (rollingwindow) process, calibrates or fits trade signals or factors based on this rolling window, periodically rebalances the portfolio, and then evaluates portfolio performance over time. In this way, rolling-window backtesting simulates real-world investing.

Explain inputs and decisions in simulation and interpret a simulation.

Historical simulation is relatively simple and shares many of the advantages and disadvantages of rolling-window backtesting: both historical simulation and rollingwindow backtesting depend on the assumption that randomness in the future can be predicted using return distributions from the past.

Historical simulation sometimes makes use of bootstrapping, whereby random samples are drawn with replacement. Bootstrapping is useful when the number of simulations needed is large relative to the size of (historical) dataset.

Evaluate and interpret a historical scenario analysis.

Scenario analysis is a method for investigating the performance and risk of investment strategies under different structural regimes (such as recession versus nonrecession, or high volatility versus low volatility). Stress testing examines the performance of a strategy under the most adverse combinations of events and scenarios.

If asset returns do not follow a multivariate normal distribution, scenario analysis and simulation can provide a more complete picture of investment strategy performance. Scenario analysis can be used to analyze the performance and risk of investment strategies in different structural regimes.

Asset return distributions often exhibit skewness and excess kurtosis (i.e., fat tails). Also, conventional rolling-window backtesting may not fully account for the dynamic nature of financial markets or possible extreme downside risk. Scenario analysis and simulation can provide a more thorough portrayal of investment strategy performance.

Inter-temporal rate of substitution

The ratio of the marginal utility of consumptions periods in the future (the numerator) to the marginal utility of consumption today (the denominator).

Explain the relationship between the consumption hedging properties of equity and the equity risk premium.

Equities are generally cyclical; they have higher values during good times and have poor consumption hedging properties. Therefore, the risk premium on equities should be positive.

Explain how the phase of the business cycle affects credit spreads and the performance of credit-sensitive fixed-income instruments.

Credit spreads tend to rise during times of economic downturns and shrink during expansions. When spreads narrow, lower-rated bonds tend to outperform higher-rated bonds.

Explain the role of expectations and changes in expectations in market valuation.

Market prices reflect current expectations. Only changes in expectations cause a change in market price.

Explain the relationship between the long-term growth rate of the economy, the volatility of the growth rate, and the average level of real short-term interest rates.

Interest rates are positively related to GDP growth rate and to the expected volatility in GDP growth due to a higher risk premium.

Explain how the characteristics of the markets for a company’s products affect the company’s credit quality.

Spreads for issuers in consumer cyclical sector widen considerably during economic downturns compared to spreads for issuers in the consumer non-cyclical sector.

Explain the notion that to affect market values, economic factors must affect one or more of the following: 1) default-free interest rates across maturities, 2) the timing and/or magnitude of expected cash flows, and 3) risk premiums.

The value of any asset can be computed as present value of its expected future cash flows discounted at an appropriate risk-adjusted discount rate. Risky cash flows require the discount rate to be higher due to inclusion of a risk premium.

Describe the factors that affect yield spreads between non-inflation-adjusted and inflation-indexed bonds.

Break-even inflation rate (BEI) = yield on non-inflation indexed bonds − yield on inflation indexed bonds

BEI is comprised of two elements: expected inflation (π) and risk premium for uncertainty in inflation (θ).

Describe how economic analysis is used in sector rotation strategies.

Relative outperformance of sectors can be discerned ex post. Ex ante forecasting of this outperformance is the objective of active managers.

Describe cyclical effects on valuation multiples.

Price multiples tend to follow the business cycle: multiples rise during economic expansions (as analysts revise growth estimates upward) and fall during contractions (as growth estimates are revised downward).

Explain how the phase of the business cycle affects short-term and long-term earnings growth expectations.

Cyclical industries (e.g., durable goods manufacturers and consumer discretionary) tend to be extremely sensitive to the business cycle; their earnings rise during economic expansions and fall during contractions. Non-cyclical or defensive industries tend to have relatively stable earnings.

Explain how the phase of the business cycle affects policy and short-term interest rates, the slope of the term structure of interest rates, and the relative performance of bonds of differing maturities.

When the economy is in recession, short-term policy rates tend to be low. Investor expectations about higher future GDP growth and inflation as the economy comes out of recession lead to higher longer-term rates. This leads to positive slope of the yield curve. Conversely, an inversely sloping yield curve is often considered a predictor of future recessions.

Describe the economic factors affecting investment in commercial real estate.

Commercial real estate has equity-like and bond-like characteristics. The valuation depends on the rental income stream, the quality of tenants, and the terminal value at the end of the lease term. The discount rate for commercial real estate includes a risk premium for uncertainty in terminal value and also for illiquidity.

Describe how value added by active management is measured

value-added = active return = active portfolio return − benchmark return

portfolio active return = Σ(active weight of security i × return of security i).

Active return is composed of two parts: asset allocation return plus security selection return:

Describe the practical strengths and limitations of the fundamental law of active management

While the fundamental law can be used for evaluating market timing, security selection, and sector rotation strategies, one has to be aware of its practical limitations. The limitations of the fundamental law include bias in measurement of the ex-ante information coefficient and lack of true independence while measuring breadth of an active strategy.

Explain how the information ratio may be useful in investment manager selection and choosing the level of active portfolio risk.

An investor will always choose the active manager with the highest information ratio regardless of her risk aversion. The investor will combine this optimal active portfolio with the benchmark to create a portfolio with a suitable level of optimal risk based on her risk preferences.

Describe and interpret the fundamental law of active portfolio management, including its component terms—transfer coefficient, information coefficient, breadth, and active risk (aggressiveness).

The three components of the information ratio are the information coefficient (measure of manager’s skill), the breadth (number of independent active bets), and the transfer coefficient (the degree of constraints on manager’s active management).

For an unconstrained portfolio, TC = 1.

Compare active management strategies, including market timing and security selection, and evaluate strategy changes in terms of the fundamental law of active management.

The information coefficient of a market timer = IC = 2(% correct) − 1

The fundamental law can also be used to evaluate active sector rotation strategies.

Ask price

The price at which a trader will sell a specified quantity of a security. Also called ask, offer price, or offer.

Best ask

The offer to sell with the lowest ask price. Also called best offer or inside ask.

Best bid

The offer to buy with the highest bid price. Also called the inside bid.

Best offer

Best askThe offer to sell with the lowest ask price. Also called best offer or inside ask.

Bid-ask spread

The ask price minus the bid price.

Bid price

The price at which a trader will buy a specified quantity of a security. Also called bid.

Delay costs

Implicit trading costs that arise from the inability to complete desired trades immediately. Also called

slippage.

Effective spread

Two times the difference between the

execution price and the midpoint of the

market quote at the time an order is

entered.

Implementation shortfall

The difference between the money

return (or value) on a notional or paper

portfolio and the actual portfolio return

(or value).

Inside ask

Best ask The offer to sell with the lowest ask price. Also called best offer or inside ask.

Inside bid

Best bid The offer to buy with the highest bid price. Also called the inside bid.

Inside spread

The spread between the best bid price and the best ask price. Also called the market bid-ask spread, inside bid-ask spread, or market spread.

Latency

The elapsed time between the occurrence of an event and a subsequent action that depends on that event.

Limit order book

The book or list of limit orders to buy and sell that pertains to a security.

Market fragmentation

Trading the same instrument in multiple venues.

Market impact

The effect of the trade on transaction prices. Also called

price impact.

Midquote price

The average, or midpoint, of the prevailing bid and ask

prices.

Opportunity cost

The value that investors forgo by choosing a particular course of action; the value of something in its best

alternative use.

Price improvement

When trade execution prices are better than quoted

prices.

Describe abusive trading practices that real-time surveillance of markets may detect.

Real-time surveillance and monitoring of electronic markets seek to detect market abuses and potential crises as they unfold, allowing for a faster response. Abusive trading practices include front running and market manipulation. Market manipulation activities include trading for price impact, rumormongering, wash trading, spoofing, bluffing, gunning the market, and squeezing and cornering.

Describe comparative advantages of low-latency traders.

Electronic market traders employ advanced orders, trading tactics, and trading algorithms. Electronic markets enable hidden orders, leapfrogging algorithms, flickering quotes, electronic arbitrage, and machine learning.

Explain the components of execution costs, including explicit and implicit costs.

Explicit trading costs include brokerage, taxes, and fees; implicit costs include the bid-ask spread, price impact, slippage, and opportunity cost.

Calculate and interpret effective spreads and VWAP transaction cost estimates.

Effective spread = 2 × (per-share effective spread transaction cost)

VWAP transaction cost = trade size × (side) × (trade VWAP – benchmark VWAP)

where:

side = + 1 for buy orders and –1 for sell orders

Describe characteristics and uses of electronic trading systems.

Latency is defined as the time lapse between the occurrence of an event and execution of a trade based on that event. Electronic trading systems allow low-latency traders a competitive advantage by jumping the order queue.

Describe the risks associated with electronic trading and how regulators mitigate them.

Risks of electronic trading include HFT arms races at a disadvantage to small traders, as well as increases in systemic risk due to runaway algorithms, fat finger errors, overcharge orders, and malevolent orders.

Describe factors driving the development of electronic trading systems.

The factors driving the development of electronic trading systems include lower cost, higher accuracy, provision for audit trails, fraud prevention, and a continuous market during trading hours.

Identify and contrast the types of electronic traders.

Electronic traders include news traders, dealers, arbitrageurs, front runners, quote matchers, and buy-side traders.

Describe market fragmentation.

Market fragmentation results when a security trades in multiple markets. Trading algorithms such as liquidity aggregation (i.e., creation of a super book) and smart order routing seek to overcome the challenges posed by market fragmentation.

Describe the implementation shortfall approach to transaction cost measurement.

Implementation shortfall is the difference in value between a hypothetical (or paper) portfolio in which the trade is fully executed with no cost, and the value of the actual portfolio.