CFA L2 Portfolio Management

Question 1

Exchange-traded funds (ETFs)

Answer 1

Shares in an index-tracking portfolio that trade on a secondary market. While most ETFs are based on direct investments in underlying securities, ETFs can also utilize derivatives, invest via American depositary receipts (ADRs), or use leverage.

• ETFs tend to distribute far less in capital gains relative to mutual funds. This is mostly due to the fact that ETFs have historically had significantly lower turnover than mutual funds have had.
• Return-of-capital (ROC) distributions are generally not taxable.

Question 2

Market maker

Answer 2

A firm/individual who actively quotes two-sided markets in a particular security by providing bids and asks.

Question 3

Authorized participants (APs)

Answer 3

Large broker-dealers (BDs) that make the market in an ETF. APs are permitted to create additional shares, or redeem existing shares, for a service fee payable to the ETF manager. This creation/redemption process is in-kind.

Since the large BDs often have the securities inside the ETF, they will give the ETF manager the securities in exhange for shares in the ETF. This process creates tax efficiencies.

Question 4

Creation basket

Answer 4

The list of required in-kind securities that go into the ETF. The ETF manager will publicly disclose these each day.

• The creation basket is a key input in determining the net asset value (NAV).

Question 5

Redemption basket

Answer 5

The specific securities the AP receives after redeeming the ETF.

Redemption process: opposite of the creation process- the AP receives the basket of securities and gives back their shares of the ETF.

Question 6

What are the 3 purposes that the in-kind process serves?

Answer 6

1. Lower cost: eliminates transaction costs.
2. Tax efficiency: The creation/redemption process IS NOT a taxable event
3. Keeping market prices in line w/ NAV: APs will engage in arbitrage transactions if the ETFs trade at a price significantly different from their NAV. If the ETF trades at a premium, APs can sell the ETF and if it trades at a discount, they can buy.

Question 7

True or false: The APs incur any transaction costs associated w/ creating the basket as well as any service fees the ETF manager charges for redeeming the basket?

Answer 7

True

Question 8

Arbitrage gap

Answer 8

The transaction costs/service fees that APs incur creates an arbitrage gap: a range of prices that an ETF should trade at.

• Because the liquidity of the securities in the basket determines the transaction cost, the arbitrage gap tends to be wider for ETFs with illiquid holdings
• ETFs that track foreign indices may have wider gaps due to time zone differences.
• APs pass on these costs in the form of bid-ask spreads on ETFs, which means that only transacting shareholders pay these costs, unlike with mutual funds where all shareholders bear this cost. Similarly, unlike mutual funds, ETFs are tax fair because redemptions are in kind and do not affect the nontransacting shareholders.
• Even the closing price of the ETF on the exchange includes a premium or discount to the NAV, driven by supply and demand factors on the exchange and the market impact costs of executing an exchange transaction.

Question 9

National Security Clearing Corporation (NSCC)

Answer 9

The organization in the U.S. that guarantees the performance of parties to a trade on an exchange.

Question 10

The Depository Trust Company (DTC)

Answer 10

A subsidiary of NSCC that transfers the securities from the account of the seller’s broker to the account of buyer’s broker. There is a two-day settlement period for ETFs.

• Six day period for APs.

Question 11

Tracking difference

Answer 11

The difference between the return on the ETF and the index’s return.

• An ETF is most likely to underperform its benchmark by the expense ratio.

Question 12

Tracking error/rolling return assessment

Answer 12

The ANNUALIZED standard deviation of the DAILY tracking difference. There are 2 types of tracking error:
1. Ex-post tracking error (backward looking): A measure of a portfolio’s tracking error relative to a benchmark portfolio over a lookback period
2. Ex-ante tracking error (forward looking)

• Also known as a rolling return assessment.

Question 13

Sources of tracking error:

Answer 13

1. Fees and expenses that ETF holders pay to the ETF manager(s).
2. Sampling and optimization: ETFs may use statistical techniques to replicate the performance of a benchmark without investing in all the securities that the index covers.
3. Depository receipts: Any difference between the price of the DR and the price of the security.
4. Index changes: Periodically the composition of the index that the ETF tracks may be changed. Since the ETF manager and AP may have to sell/buy new securities this will cost a fee.
5. Regulatory and tax requirements
6. Fund accounting practices
7. Asset manager operations: ETF managers may try to lower their cost by lending their shares to short sellers, and by foreign dividend capture (i.e., by working with foreign governments to minimize the taxes on distributions received). These methods tend to improve ETF performance relative to their benchmark.

• ETF ownership costs are least likely to be increased by security lending.
• Changes to the underlying index is most likely to be the smallest contributor to tracking error.

Question 14

Primary determinants of bid-ask spreads

Answer 14

liquidity and market structure of underlying securities

• Spreads on fixed-income ETFs tend to require a higher spread
• Specialized ETFs that focus on one commodity, sector, etc. demand a higher spread.

Question 15

Maximum spread

Answer 15

creation/redemption fee + other trading costs + spread of the underlying securities + risk premium for carrying the trade until the end of closing + APs normal profit margin - discount based on probability of offsetting the trade in secondary market

* the bid-ask spread on an ETF cannot be higher than this

Question 16

Indicated NAVs

Answer 16

Intraday estimates of NAV

• A price of an ETF trading above its NAV is trading at a premium and vice versa at a discount

Question 17

ETF premium/discount formula:

Answer 17

(Price of ETF - NAV) ÷ NAV

Question 18

Sources of ETF premiums/discounts

Answer 18

• Timing differences: ETFs on foreign securities may experience gaps between the time the ETF is traded and the time when the underlying trades in a foreign market. Similarly, OTC bonds that do not trade on an exchange will not have a true closing price; hence, the price of an ETF that comprises such bonds may not be equal to estimated NAV.
• Stale pricing: Infrequently traded ETFs may reflect noncurrent prices and, therefore, their value may differ from NAV.

Question 19

Costs of owning an ETF

Answer 19

• Mgmt fees: Since passively managed, these tend to be lower than mutual funds
• Trading fees: Includes brokerage/commission fees and bid-ask spreads.

• Long-term investors will be more concerned w/ mgmt. fees whereas short-term investors are more concerned w/ trading fees.

Question 20

Round-trip trading cost of owning an ETF

Answer 20

Round-trip commission + spread

Question 21

Total cost of owning an ETF

Answer 21

Round-trip trading cost + mgmt. fees

Question 22

Example: Costs of owning an ETF

Z&E ETF is quoted at a bid-ask spread of 0.15%. ETF commissions are 0.10% of the trade value. Management fees are 0.08% per year

Calculate the cost of holding the ETF for 3 months, for 1 year, and for 5 years. For the 5-year holding period, also calculate the average annual total cost.

Answer 22

3 months: [ (0.10 * 2) + 0.15 ] + [ (3/12) * 0.08 ] = 0.37%

1 year: [ (0.10 * 2) + 0.15 ] + 0.08 = 0.43%

5 years: [ (0.10 * 2) + 0.15 ] + [ 5 * 0.08 ] = 0.75%

Avg. annual cost = 0.75 ÷ 5 = 0.15%

Question 23

Types of ETF risks:

Answer 23

• Counterparty risk
• Settlement risk: ETFs using OTC derivative contracts as part of their strategy expose investors to the settlement risk of such contracts.
• Security lending: Like mutual funds, ETFs may lend their securities to short sellers for a fee.
• Fund closure: ETF closures involve selling the underlying holdings and making cash distributions to the investors, potentially with adverse tax consequences for them.
• Expectation-related risk:

Question 24

True or false: Exchange-traded notes (ETNs) have low counterparty risk?

Answer 24

False, ETNs have high counterparty risk

Question 25

Exchange-traded note (ETN)

Answer 25

Unsecured debt securities that track an underlying index of securities and trade on a major exchange like a stock. If the underlying index returns 5%, the ETN will return 5% to its investors. Just like a bond, if the underwriter of the ETN goes bankrupt, the investor risks total loss. ## Footnote * Unlike ETFs, ETNs do not hold the underlying securities. * Similar to ETFs, ETNs use the creation/redemption process and trade on major exchanges.

Question 26

How do banks use ETNs?

Answer 26

If a bank wants to issue unsecured debt at a fixed rate but the market int. rate is significantly higher than the swap rate, the bank may instead issue an ETN that pays the return on an equity index. The bank then would simultaneously enter into an equity swap as the equity return receiver and the (swap) fixed rate payer. The index return received is used to service the ETF, and the bank's effective borrowing cost becomes the swap fixed rate.

Question 27

Portfolio uses of ETFs

Answer 27

1. Efficient portfolio mgmt. 2. Asset class exposure mgmt. 3. Active investing

Question 28

Efficient portfolio management

Answer 28

* Portfolio liquidity mgmt: Excess cash can quickly and easily be invested into ETFs * Portfolio rebalancing: ETFs can be used to cost-effectively rebalance portfolios to target specific asset class weights. * Portfolio completion: ETFs can be used to fill temporary gaps in portfolio allocation that can arise due to new PMs coming in or investors wanting different exposures to new asset classes * Transition manager: A new PM can temporarily invest in ETFs when winding down the allocations of the old PM, so as to maintain market exposure during the transition period.

Question 29

True or false: ETFs are often suitable for very high net worth individuals?

Answer 29

False, often these individuals will invest in separately managed accounts (SMAs) that can offer lower costs.

Question 30

Factor ETFs/Smart beta ETFs

Answer 30

An ETF that is benchmarked to an index but has pre-defined rules. These are active ETF strategies that seek to outperform the benchmark. Long-term buy-and-hold investors seeking a desired factor exposure may choose to invest in these ETFs in the expectation of outperformance of that factor.

Question 31

Alternatively weighted ETFs

Answer 31

ETFs constructed using portfolio weights that differ from standard market cap weights (ex: equally weighted, weightings based on fundamentals).

Question 32

Discretionary Active ETFs

Answer 32

Actively managed and are similar to closed-end mutual funds. The largest of these are fixed-income ETFs, which include exposures to senior bank loans, mortgage securities, and floating rate notes.

Question 33

Dynamic asset allocations and multi-asset strategies

Answer 33

Dynamic top-down asset allocation ETFs that invest in stocks and bonds based on risk/return forecasts. These are popular among global asset managers and hedge funds for their discretionary asset allocation.

Question 34

Capital asset pricing model

Answer 34

A model that is used to calculate the expected return of a security based on its systematic risk. This model says that there is only one priced risk factor- systematic risk (a.k.a. market risk). Formula: Rp = Rf + β(market risk premium) - Ri = Return on asset/portfolio i. ## Footnote * The more systematic risk, the higher the expected return, according to this model. * This model was created by William Sharpe in 1964. * Multifactor models, as opposed to CAPM, say that there are multiple risk factors priced in by the market as opposed to one.

Question 35

Arbitrage pricing theory (APT)

Answer 35

An alternative to the CAPM model that is a multifactor linear model w/ multiple systematic risk factors priced by the market. However, unlike CAPM, APT does not identify the specific risk factors (or even the number of factors). ## Footnote * This model was created by Stephen Ross in 1976. * This is an equilibrium pricing model. * APT does not require that security returns be normally distributed.

Question 36

Assumptions of APT:

Answer 36

1. Unsystematic risk can be diversified away in a portfolio. 2. Returns are generated using a k-factor model. 3. No arbitrage opportunities exist.

Question 37

Arbitrage pricing model

Answer 37

The asset pricing model developed by the APT. Formula: Rp = Rf + β1 λ1 ... + βnλn - λ = expected risk premium associated with each risk factor - β = the factor sensitivity of Portfolio P to that risk factor. ## Footnote * Unlike the CAPM, the APT does not require that one of the risk factors is the market portfolio.

Question 38

Arbitrage opportunity example: Given: Portfolio A has an expected return of 10% and a beta of 1.0 Portfolio B has an expected return of 20% and a beta of 2.0 Portfolio C has an expected return of 13% and a beta of 1.5 Construct an arbitrage opportunity

Answer 38

1. We can construct a new portfolio, portfolio X 2. If we allocate 50% of portfolio X to hold portfolio A and the other 50% to portfolio B- beta of portfolio X = 0.5(1) + 0.5(2) = 1.5 3. Expected return of portfolio X = 0.5(0.1) + 0.5(0.2) = 0.15 4. Therefore, Portfolio X has the same beta as portfolio C but a higher expected return. 5. We can short portfolio C and long portfolio X to where there's no risk and also no upfront cost. ## Footnote * Generally, we want to go long assets that have a high ratio of return-per-unit-of-factor-exposure, and short assets that have a low return-to-factor-exposure ratio

Question 39

3 classifications of multifactor models:

Answer 39

1. Macroeconomic multifactor models 2. Fundamental factor models 3. Statistical factor models

Question 40

Macroeconomic multifactor models

Answer 40

Returns on assets are a result of surprises in macroeconomic results. Ex: If GDP was expected to grow at 2% but it actaully grows at 2.5%, this difference will drive positive results. ## Footnote * Betas in these models are regression based * The error term in a macroeconomic multifactor model is company-specific risk.

Question 41

Fundamental factor models

Answer 41

Asset returns are explained by multiple firm-specific factors. Factors in these models are returns, not surprises. Ex: P/E ratio, market cap, leverage ratio ## Footnote * Betas in these models are standardized from attribute data * Returns are based on multiple regression analysis. * The intercept of a fundamental factor model with standardized sensitivities has no economic interpretation; it is simply the regression intercept necessary to make the unsystematic risk of the asset equal to zero.

Question 42

Statistical factor models

Answer 42

Use statistical models to explain asset returns. The two primary types of statistical factor models are: 1. Factor analysis 2. Principal component models ## Footnote * The main weakness w/ these models is that they do not lend themselves well to economic interpretation.

Question 42

Differences between macroeconomic multifactor models and fundamental factor models

Answer 42

**Macroeconomic multifactor models** * The regression is a time series of economic surprises * The betas are regression-based * The factors are surprises in macroeconomic variables * The intercept is the expected return **Fundamental multifactor models** * The regression is cross sectional asset returns * The betas are standardized from attribute data * The factors are computed from multiple regression * The intercept is undefined

Question 43

Factor analysis models

Answer 43

Models where factors are portfolios that explain covariance in asset returns.

Question 44

Principal component models

Answer 44

Models where factors are portfolios that explain the variance in asset returns.

Question 45

Priced risk factors

Answer 45

1/2 main features of the macroeconomic multifactor model. These are risks that are priced into the market that CANNOT be diversified away. ## Footnote * Risks that can be diversified away ARE NOT priced.

Question 46

Factor sensitivities

Answer 46

1/2 main features of the macroeconomic multifactor model. Since different assets/stocks have different magnitudes of reactions to stocks, we need to account for this w/ sensitivities. Ex: Cyclical industries will react differently to negative macroeconomic surprises compared to defensive industries.

Question 47

Beta for fundamental multifactor model calculation:

Answer 47

(value of attribute k for asset i - avg. value of attribute k) ÷ st. deviation of avg. values of attribute k

Question 48

Most common uses of multifactor models:

Answer 48

* Return attribution * Risk attribution * Portfolio construction

Question 49

Return attribution

Answer 49

Being able to pinpoint where a portfolio's returns are coming from.

Question 50

Active return

Answer 50

The difference between an actively managed portfolio's returns and its benchmark Formula: Rportfolio - Rbenchmark ## Footnote * Can be measured ex-ante (based on expectations) or can be measured ex-post (after-the-fact).

Question 51

Sources of active return

Answer 51

factor return + security selection

Question 52

Factor return

Answer 52

Return that is generated from deviations of asset class portfolio weights from benchmark weights. Ex: PMs weighting their portfolios towards more Mid-cap banks than what is in the benchmark. Formula: Σ[ (βportfolio - βbenchmark) * λk ]

Question 53

Active risk/Tracking error/Tracking risk

Answer 53

Standard deviation of active return Formula: √[ (Rportfolio - Rbenchmark) ÷ (n - 1) ]

Question 54

Information Ratio

Answer 54

Active return per unit of active risk Formula: (average return on portfolios - average return on benchmarks) OR (Rportfolio - Rbenchmark) ÷ σ(Rportfolio - Rbenchmark) ## Footnote * The higher the IR, the more active return the manager earned per unit of active risk.

Question 55

Sources of active risk

Answer 55

Active risk squared = Active factor risk + active specific risk

Question 56

Active factor risk

Answer 56

Active risk attributable to factor tilts

Question 57

Active specific risk

Answer 57

Active risk attributable to stock selection Formula: Σ(Weight of portfolio - weight of benchmark)^2 * active risk squared

Question 58

Example: Factor return Fund A generated a return of 11.2% over the past 12 months, while the benchmark portfolio returned 11.8%. Suppose we are provided a fundamental factor model with two factors as given in the following: *Factor: P/E* Portfolio beta: 1.1 Benchmark beta: 1 Factor risk premium: -5% *Factor: Size* Portfolio beta: 0.69 Benchmark beta: 1.02 Factor risk premium: 2% (1) Attribute the cause of the difference in returns. (2) Describe the manager's apparent skill in factor bets as well as in security selection.

Answer 58

(1) P/E return = (1.1 - 1) * -5% = -0.5% Size return = (0.69 - 1.02) * 2 = -0.66% -0.5% + -0.66% = -1.16% Total return = 11.2% - 11.8% = -0.6% Return from factor tilts = -1.16% Return from stock selection = -0.6% = -1.16% + x = 0.56% (2) The active manager's regrettable factor bets resulted in a return of –1.16% relative to the benchmark. However, the manager's superior security selection return of +0.56% resulted in a total active return of –0.60% relative to the benchmark.

Question 59

Example: Active Risk Investor A is analyzing the performance of three actively managed mutual funds using a two-factor model. The results of his risk decomposition are shown in the following table: *Fund A, B, C (respectively)* Size factor = 6.25, 3.20, 17.85 Style factor = 12.22, 0.80, 0.11 Total factor = 18.47, 4.00, 17.96 Active specific risk = 3.22, 12.22, 19.7 Active risk squared = 21.69, 16.22, 37.66 (1) Which fund has the highest level of active risk? (2) Which fund has the highest style factor as a % of active risk? (3) Which fund has the highest size factor as a % of active risk? (4) Which fund has the lowest level of active specific risk as a % of active risk?

Answer 59

(1) √21.69 = 4.66 √16.22 = 4.03 √37.66 = 6.14 (2) 12.22 ÷ 21.69 = 56% 0.80 ÷ 16.22 = 4.9% 0.11 ÷ 37.66 = 0.29% (3) 6.25 ÷ 21.69 = 28.8% 3.20 ÷ 16.22 = 19.7% 17.85 ÷ 37.66 = 47.4% (4) 3.22 ÷ 21.69 = 14.85% 12.22 ÷ 16.22 = 75.34% 19.7 ÷ 37.66 = 52.31%

Question 60

Tracking portfolios

Answer 60

Portfolios that attempt to have the same set of risk exposures as a benchmark index. Ex: A PM that tries to create a portfolio w/ the same risk exposures as the S&P. ## Footnote * Multifactor models can be used to determine the risk exposures

Question 61

Factor portfolio

Answer 61

A portfolio that has been constructed to where there is a sensitivity of 1 (100%) to one risk factor and sensitivities of 0 for all other factors. Ex: PM believes that GDP growth will be stronger than expected but wants to hedge against all other factors. ## Footnote * *Factor portfolios are particularly useful for speculation or hedging purposes.* * Multifactor models are used to predict alpha generated from active bets on certain factors.

Question 62

Rules-based/Algorithmic active management

Answer 62

Essentially a mean reversion model. This strategy uses rules to make factor tilts to where if something outperforms in one period of time it will regress in the next. ## Footnote * This is a low cost strategy.

Question 63

Carhart Model

Answer 63

A multifactor model that builds on the 3-part Fama and French model to include market risk, size, value, and momentum as factors. Formula: Er = Rf + β*RMRF + β*SMB + β*HML + β*WML ## Footnote * RMRF = Return on value-weighted equity index * SMB = avg. return on small cap stocks - avg. return on large cap stocks * HML = avg. return on high book-to-market stocks - avg. return on low book-to-market stocks * WML = avg. returns on past winners - avg. returns on past losers

Question 64

Value at risk (VaR)

Answer 64

Measures downside risk of a portfolio. There are 3 components to VaR: 1. the loss size 2. the probability of a loss >= the specified loss size 3. the time frame. Ex: There is a 5% probability that the company will experience a loss of $25k or more in any given month = monthly VaR of $25k. ## Footnote * VaR can also be expressed in percentage terms so that for a portfolio, we could state that the 5% monthly VaR is 3%, meaning that 5% of the time the monthly portfolio value will fall by at least 3%. * We can also state VaR as a confidence level: we are 95% (i.e., 100% – 5%) confident that the portfolio will experience a loss of no more than 3%.

Question 65

Selections that must be made when estimating VaR

Answer 65

We must either choose the size or probability of the loss. If we choose the size of the loss, we will estimate the probability of losses of that size or larger. If we choose the probability of the loss, we will estimate the minimum size of the losses that will occur w/ that probability.

Question 66

3 ways to estimate VaR:

Answer 66

1. Parametric/Variance-covariance 2. Historical simulation 3. Monte carlo simulation

Question 67

Parametric/Variance-covariance method to estimating VaR

Answer 67

The first step w/ any of the 3 approaches to estimating VaR is to identify the relevant risk factors (ex: market risk, currency risk, etc.) W/ the parametric approach, each risk factor is assigned a distribution, often assumed to be normal to avoid skewness and kurtosis. Since a normal distribution can be completely described by its variance, these are all we need w/ this method. Mean and variance is usually found through a *lookback period* where we take the avg. over history. We could also estimate future values. Then, we can estimate VAR by choosing a probability. Ex: A 5% VaR will be 1.65 standard deviations away from the mean. ## Footnote * In cases where normality cannot be assumed, the parametric approach has limited usefulness. * *An assumption of a normal distribution is invalid if options are in the portfolio.*

Question 68

Example: Estimating VaR using the parametric approach given: *Security A* σ = 0.0158 μ = 0.0004 *Security B* σ = 0.0112 μ = 0.0003 Covariance = 0.000106 Use this info to estimate the 5% annual VaR for a portfolio that is 60% invested in security A and 40% invested in security B and has a value of $10mm.

Answer 68

Weighted mean = 0.6(0.0004) + 0.4(0.0003) = 0.00036 Variance of the portfolio = (wa^2 * σa^2) + (wb^2 * σb^2) + (2 * wa * wb * covariance of a & b) = (0.6)^2(0.0158)^2 + (0.4)^2(0.0112)^2 + (2 * 0.6 * 0.4 * 0.000106) = 0.000161 σ of portfolio = √0.000161 = 0.012682 1.65 * 0.012682 = 0.020925 0.00036 - 0.020925 = -0.0206 -0.0206 * $10mm = -$206k VaR = There is a 5% chance on any given day the portfolio will lose $206k in value. There are 250 trading days in the year: 0.00036 * 250 = 0.09 √250 * 1.65 * 0.012682 = 0.330858 0.09 - 0.330858 = -0.240858 $10mm * -0.240858 = -$2,409,000 VaR = There is a 5% chance in any given year the portfolio will lose $2.409mm in value. | We use √250 because the daily returns are independent distributed.

Question 69

Variance of two asset portfolio calculation

Answer 69

wa^2σa^2 + wb^2σb^2 + (2 * wa * wb * covariance of a & b)

Question 70

Historical simulation method of estimating VaR

Answer 70

This method is based on the actual periodic changes in risk factors over a lookback period. Ex: For a period of 100 days, the 5% daily VaR is just the observation below the 5 biggest losses during that period. ## Footnote * The VaR estimate under the historical simulation approach is the smallest of the largest x% losses

Question 71

Pros and cons of historical simulation method

Answer 71

Pros: No need to assume a distribution. This method can be used to estimate the VaR for portfolios that include options. Cons: If the lookback period has abnormal observations, this will skew the VaR.

Question 72

Monte Carlo simulation method to estimating VaR

Answer 72

This method is based on an assumed probability distribution of the correlations for each risk factor. Then, software generates random values for each risk factor and computes periodic returns based on these values. Then, we will use the generated outcomes and use the same steps as the historical simulation method. ## Footnote * If asset returns are correlated, this method will assume a multivariate normal distribution. * Rolling-window backtesting (not Monte Carlo simulation) is a proxy for actual investing.

Question 73

Advantages of VaR

Answer 73

* Simple and easy concept * Risk of different portfolios, asset classes, or trading operations can be compared to known relative risk. * VaR can be used for performance evaluation. * Can be a good tool when determing asset allocation of a portfolio * Regulators accept VaR as a measure of risk. * Reliability of VaR can be verified by backtesting.

Question 74

Disadvantages of VaR

Answer 74

* Estimation of VaR requires many sensitive assumptions * The assumption of normality leads to underestimates of downside risk * VaRs that do not take into account liquidity risks when an asset price falls will understate downside risk. * VaR will not capture every risk factor. * VaR does not consider risk-return trade offs.

Question 75

Conditional VaR (CVaR)

Answer 75

The expected loss, given that the loss is >= the VaR. It's the expected loss if that worst-case threshold is ever crossed. W/ the historical simulation or monte carlo methods, we just take the average of all observations that are worse than the VaR. The only way to do this w/ the parametric method is mathematically complex.

Question 76

Incremental VaR (IVaR)

Answer 76

The change in VaR from a change in the portfolio allocation to a security. It's the amount of uncertainty added to or subtracted from a portfolio by purchasing or selling an investment. IVaR will tell you that the expected loss that will happen x% of the time will increase/decrease by the IVaR.

Question 77

Marginal VaR (MVaR)

Answer 77

The additional amount of risk that a new investment position adds to a firm or portfolio. MVaR is the slope of a curve that plots VaR as a function of a security's weight in the portfolio. IVaR and MVaR are similar; however, MVaR explains the sensitivity of VaR to an x% change in the portfolio's weight.

Question 78

Relative VaR/Ex-ante tracking VaR

Answer 78

Measures the VaR of the difference between the return on a portfolio and the return on the benchmark portfolio. Ex: A 5% monthly VaR implies that 5% of the time, the portfolio's relative underperformance will be x%.

Question 79

Other risk measures than VaR

Answer 79

1. Senstivity analysis 2. Scenario analysis 3. Historical scenario 4. Hypothotical scenario 5. Stress tests

Question 80

Sensitivity analysis

Answer 80

Examines the effect of a small change in one risk factor on the entire portfolio's value.

Question 81

Scenario analysis

Answer 81

Examines the effect of significant changes in several risk factors on the entire portfolio's value. Essentially this takes a certain scenario, usually a historical scenario, and determines how an investment strategy would hold up in that environment. ## Footnote * Stress testing is essentially extreme versions of scenario analysis.

Question 82

Historical scenario

Answer 82

Uses a set of changes in risk factors that have actually occurred in the past

Question 83

Hypothetical scenario

Answer 83

Uses a set of changes that may or may not have happened in the past.

Question 84

Most commonly used risk factors for equity securities, fixed income securities, and options:

Answer 84

Equities: beta Fixed income: duration, convexity Options: Delta, gamma, vega ## Footnote * Delta and duration are first order affects while gamma and vega are second order affects

Question 85

How to measure the % △ in value of a fixed income security/portfolio for a △ in YTM

Answer 85

△ in price = -duration + 0.5 * convexity^2 ## Footnote * If duration is Macaulay duration, change duration to change in duration ÷ (1 + duration).

Question 86

How to measure the △ in call price given delta, gamma, and vega

Answer 86

△ in call price = delta + 0.5 * gamma^2 + vega

Question 87

Sensitivity risk measures

Answer 87

Measures that can alert a PM to a portfolio's exposure to various risk factors.

Question 88

Scenario risk measure

Answer 88

A measure that estimates the portfolio return that would result from either a hypothetical market event or the recurrence of an actual historical event.

Question 89

Reverse stress testing

Answer 89

Similar to stress testing, but the first step is identifying the portfolio's largest risk exposures and then when unacceptable outcomes are determined, ananlysis is run to determine what would cause those outcomes.

Question 90

Difference between VaR, senstivity analysis, and scenario analysis:

Answer 90

VaR provides a probability of loss. Sensitivity analysis provides estimates of the relative exposures to different risk factors, but no probability is associated w/ a specific scenario. Scenario analysis provides info about exposure to simultaneous changes in several risk factors but no probability is associated w/ a speicfic scenario.

Question 91

Risk measures used by banks

Answer 91

Banks use sensitivity measures, scenario analysis, stress testing, leverage risk measures, and VaR. Banks also estimate risk from asset-liabilitiy mismatches, estimate VaR for capital, and they need to disaggregate risk by geographic location and business unit type.

Question 92

Risk measures used by long-only/traditional asset managers

Answer 92

Long-onlys typically focus on relative risk measures. **Active share** is a common risk measure used by long-onlys. Examples of risk measures include size of positions, sensitivity measures to IRR and market risk, and historical and hypothetical scenario analysis.

Question 93

Active share

Answer 93

The difference between the weight of a security in the portfolio and its weight in the benchmark.

Question 94

Risk measures used by hedge funds

Answer 94

Depends on the strategy used, but in general, they use sensitivity analysis, leverage measures, scenario analysis, and stress tests. ## Footnote * L/S funds will estimate risk measures for long and short posititons. * Hedge funds that use VaR will focus on VaR measures of < 10% for short periods.

Question 95

Maximum drawdown

Answer 95

A risk measure of downside risk used by hedge funds which is the largest decrease in value over prior periods of a specific length. ## Footnote * This is commonly used for hedge funds w/ significantly non-normal return distributions. * Beta and standard deviation are not as effective for firms w/ non-normal distributions.

Question 96

Surplus-at-risk

Answer 96

A risk measure used by pension funds which is essentially a VaR for plan assets minus liabilities.

Question 97

Glidepath

Answer 97

A multi-year plan for adjusting pension fund contributions to reverse a significant overfunded or underfunded status.

Question 98

True or false: The insurance risks of a P&C insurer are highly correlated w/ the market risk of their investment portfolios?

Answer 98

False, they ARE NOT highly correlated w/ the market risk of their investment portfolios. Insurance risks are reduced by purchasing reinsurance and by geographical dispersion.

Question 99

Risk measures used by P&C insurers

Answer 99

VaR and capital-at-risk to measure risk exposure in their investment accounts. Recall, P&C insurers take premiums and invest them. Scenario analysis will also be used (ex: What if a storm passes through and destroys insured homes AND there's a market crash).

Question 100

True or false: Life insurance is more highly correlated w/ market risk exposures of their investment portfolio than P&C?

Answer 100

True. Since discount rates are important to determine the value of long-term annuities used by life insurers, market risk can highly affect these valuations.

Question 101

Risk budgeting

Answer 101

Since too much risk mgmt. can impair profit, firms must budget how much risk they're willing to take.

Question 102

Position limits

Answer 102

Limits risk by ensuring some minimum level of diversification. Ex: Only 5% of the portfolio can be allocated to financials. ## Footnote * Position limits can be expressed a currency amounts or as a % of a portfolio's value.

Question 103

Scenario limits

Answer 103

Limits on expected loss for a given scenario

Question 104

Stop-loss limits

Answer 104

Requires that a risk exposure be reduced if losses exceed a specified amount over a certain period of time. ## Footnote * Stop loss limits specify liquidation of a portfolio or a reduction in its size if a loss of a specific magnitude occurs.

Question 105

Portfolio insurance

Answer 105

A type of stop-loss limit where a risk exposure is required to be hedged as the value of a security or index falls.

Question 106

Capital allocation

Answer 106

How the capital (debt + equity) of a firm is used to fund its various business activities. VaR and other risk measures are often used to determine how much risk firms are willing to take when allocating capital to various business lines.

Question 107

Backtesting

Answer 107

A process that uses actual historical data to emulate the investment process to determine whether a particular investment strategy would have delivered the expected excess returns. The goal of this is to assess the risk/return of an investment strategy by simulating the investment process. Backtesting also helps investors improve their investment process. Example: If I build a portfolio today, I can use past performance to see how it performed and that can give me an indication of how it will do in the future. ## Footnote * Since we cannot repeat the past, backtesting is an imperfect process. * Backtesting is used for systematic and quantitative investing. Fundamental managers also make extensive use of backtesting. * Methods such as Monte Carlo analysis can allow backtesting to take into account the randomness of the future.

Question 108

Steps to backtesting

Answer 108

1. Strategy design 2. Historical investment simulation 3. Analysis of backtesting output

Question 109

Strategy design

Answer 109

Determining assumptions and investment objectives. The investment universe and the definition of return are specified during this step. Also, determining rebalancing frequency and transaction costs must be specified. Lastly, the start and end date of the backtest must be determined. ## Footnote * When higher-frequency rebalancing is used, transaction costs will be higher. * It is important to consider transaction costs because apparent profit opportunities can be eroded by high transaction costs.

Question 110

2 types of factor portfolios

Answer 110

1. Benchmark portfolios= gives equal weights to all factors. 2. Factor portfolios= each factor contributes equally to the overall risk. ## Footnote * **Risk parity takes into account volatility of each factor and correlations between factors.**

Question 111

Data-mining trap

Answer 111

When factors in factor models perform well in a backtest but do not have any logical or economic reason to be included. Positive backtesting results don't ensure that results will be positive in the future.

Question 112

Common factors in factor models

Answer 112

1. Defensive value 2. Cyclical value 3. Growth 4. Price momentum 5. Analyst sentiment 6. Profitability 7. Leverage 8. Earnings quality

Question 113

Historical investment simulation

Answer 113

We create the portfoio to be evaluated and then rebalance according to our predetermined frequency.

Question 114

Rolling window backtesting

Answer 114

Instead of backtesting for a certain window, backtesting is performed continuously. After each period, the portfolio is rebalanced. Investors can calibrate trade signals based on the rolling window. ***This is where the out-of-sample data becomes the in-sample data for the subsequent period.***

Question 115

Analysis of backtesting output

Answer 115

Compute performance statistics such as risk and return. ## Footnote * In this step, a L/S strategy can be implementing by longing the successful assets in the backtest and shorting the unsuccesful.

Question 116

What metrics will a backtest produce?

Answer 116

Average return and risk measures, such as volatility and downside risk. Other metrics can then be calculated, such as the Sharpe and Sortino ratios. ## Footnote * Visual plots can also be generated from a backtest.

Question 117

True or false: The CVaR quantifies the weighted average of all returns that exceed the specified value of loss?

Answer 117

True

Question 118

Primary issues w/ backtesting

Answer 118

1. Survivorship bias 2. Look-ahead bias 3. Data snooping

Question 119

Surivorship bias

Answer 119

When only stocks that have remained in existance (survived) are considered. ## Footnote * This is the most common error made in backtesting. * The solution to survivorship bias is to use **point-in-time data.**

Question 120

Look-ahead bias

Answer 120

When data that was not readily available at the time is used in a simulation of that time period.

Question 121

Reporting lag

Answer 121

When data describing a period is only available after the period ends. ## Footnote * This is a cause of look-ahead bias.

Question 122

Data snooping

Answer 122

When several analyses are ran and the one with the most favorable results is used to draw conclusions. ## Footnote * A solution to data snooping is to use a higher-than-normal critical t-statistic as a benchmark for declaring a variable to be significant. * Cross-validation is another potential solution to data snooping.

Question 123

Cross-validation

Answer 123

When a model is first fitted using training data, and then its performance is assessed (often over several rounds) using separate training data.

Question 124

Historical scenario analysis/Historical stress testing

Answer 124

A form of backtesting where we investigate the risk/return of an investment strategy during various regimes.

Question 125

Two common examples of regimes:

Answer 125

1. Recessions/expansions 2. Low/high volatility periods ## Footnote * A high volatility period could be defined as a period where the VIX is above its 5 year moving average. Oppositely, a low volatility period could be when the VIX is below its 5 year average.

Question 126

Historical simulation

Answer 126

Randomly sampling from the past record of asset returns where each period is equally likely to be selected. ## Footnote * Bootstrapping is often used to generate a larger sample from a past data set.

Question 127

Steps to performing simulation analysis:

Answer 127

1. Select the target variable that we want to analyze. 2. Determine the key decision variables. 3. Select the # of simulation trials to run. 4. Specify a distribution for each key variable. 5. Draw N random numbers of each key variable. 6. Compute the values of the target variable. 7. Repeat process many times. 8. Calculate metrics

Question 128

Tail dependence

Answer 128

Measures the correlation between the tails of two random variables.

Question 129

Why does rolling-window backtesting fail to account for downside asset returns?

Answer 129

Compared w/ normal distributions, asset and factor returns often exhibit negative skewness, fat tails, and tail dependence. For these reasons, rolling-window backtesting may fail to account fully for asset return randomness, especially in terms of downside risk.

Question 130

True or false: A Monte Carlo distribution requests the estimation of more parameters than a t-distribution?

Answer 130

False

Question 131

Discount rate

Answer 131

The rate used to discount an asset into PV terms. Components of the discount rate include: * The real Rf * Expected inflation * A risk premium reflecting uncertainty about the CF. ## Footnote * As we already know, the value of an asset can be derived by taking the PV of of the asset's expected FCFs. * The value of an asset depends on FCFs and the discount rate, and then as participants receive new info, the timing and amounts of expected FCFs are revised and valuations change as a result. The impact of new info will depend on its effect on current expecations, so if new info positively surprises the value will increase and vice versa.

Question 132

Inter-termporal rate of substitution/Marginal rate of substitution

Answer 132

The trade-off between real consumption now and real consumption in the future. This drives real short-term int. rates. ***This is the rate at which a consumer is willing to substitute consumption in the present for consumption in the future.*** The covariance between a risk-averse investor's intertemporal rate of substitution and expected future price is negative. Thus, the covariance between the investor's intertemporal rate of substitution and current price is positive. Formula: mt = Marginal utility of consuming 1 unit in the future at time t ÷ marginal utility of current consumption of one unit (ut ÷ u0) ## Footnote * mt < 1 * The utility we get from consuming today is always higher than the utility we get in the future. * The higher the utility investors attach for current consumption relative to future consumption, the higher the real rate. * The utility of consumption is higher during periods of scarcity.

Question 133

Real Rf formula

Answer 133

[ 1 ÷ E(mt) ] - 1 * E(mt) = Expected marginal rate of substitution ## Footnote * This formula makes sense- when times are good and the ut < u0, this will create a lower mt and thus a higher Rf. We know that int. rates should be higher when times are good. Oppositely, during hard times or times of scarcity, ut > u0, so mt will be higher, and therefore the real Rf will be lower.

Question 134

What are the two conditions that investors increase their savings rates?

Answer 134

1. When future expected returns are higher 2. When uncertainty about future income decreases

Question 135

True or false: An investor's marginal utility of a payoff is positively related to the level of uncertainty of the payoff?

Answer 135

False, inversely related. This means that investors experience a larger loss of utility for a loss in wealth than a gain in utility from an equivalent gain in wealth. This is the concept of **risk aversion.**

Question 136

How to calculate the price of a bond w/ a risk premium

Answer 136

P0 = [ E(P1) ÷ ( 1 + R) ] + cov(P1, m1) * E(P1) = Expected price in period 1 * m1 = marginal rate of substitution Everything else constant, a lower current price (P0) increases expected return due to a higher risk premium. ## Footnote * The covariance between the expected future price and the investor's marginal rate of substitution can be viewed as a risk premium. For risk averse investors, the covariance will be negative (as prices go up, the marginal utility of future consumption relative to current consumption is low). * This concept explains why yield curves tend to be upward sloping. The risk premium is lower for shorter-term bonds but higher for long-term bonds.

Question 137

True or false: If GDP growth is forecasted to be high, the utility of consumption in the future will be high and the inter-termporal rate of substitutiton will rise?

Answer 137

False, if GDP growth is forecasted to be high, the utility of consumption in the future (when incomes will be high) will be low and the inter-temporal rate of substitution will fall. Since investors will be saving less, int. rates will rise to entice people to save.

Question 138

True or false: For longer-term bonds, there is a risk premium for actual inflation?

Answer 138

True nominal int. rate of t-bill (r) = Rf + π nominal int. rate of t-bond (r) = Rf + π + θ ## Footnote * θ = actual inflation * π = risk premium for inflation uncertainty

Question 139

Taylor Rule

Answer 139

Since the Fed's primary goals are to maintain stable inflation and to keep maximum employment, the Taylor rule incorporates this into nominal int. rate interpreations. Formula: r = Rn + π + 0.5(π - πstar) + 0.5(Y - Ystar) * Rn = netural int. rate * πstar= central bank's target inflation rate * Y = log of current level of output * Ystar = log of central bank's target output

Question 140

Term spread

Answer 140

The difference between the yield on a longer-term bond yield and the yield on a short-term bond. ## Footnote * Evidence suggests that normal term spread is positive so the yield curve is upward sloping. * Positive term spreads can be attributed to increasing θ for longer periods.

Question 141

Break-even inflation rate (BEI)

Answer 141

The difference between the yield on a fixed-rate investment and the yield on an inflation-linked investment of similar maturity and credit quality. Formula: BEI = yield on non-inflation-indexed bond – yield on inflation-indexed bond OR π + θ

Question 142

True or false: The required rate of return for bonds with credit risk includes an additional risk premium?

Answer 142

True, this is known as a credit spread Formula: Required rate of return for credit risky bonds = Rf + π + θ + y * y = credit spread

Question 143

Credit spread

Answer 143

The difference in yield between a credit risky bond and a default-free bond of the same maturity. ## Footnote * Credit spreads tend to rise during times of economic downturns and fall during expansions. * When credit spreads narrows, credit risky bonds will outperform default-free bonds. Overall, lower rated bonds tend to benefit more than higher rated bonds from a narrowing of credit spreads (their yields fall more). * Credit spreads differ by sector and by time. Spreads for issuers in the consumer cyclical sector increase significantly during economic downturns. * Credit spreads differ by sector due to differences in products/services the sector produces and leverage typically used in the sector.

Question 144

Discount rate for equities

Answer 144

Rf + π + θ + λ * λ = equity risk premium

Question 145

Discount rate for commercial real estate

Answer 145

Rf + π + θ + λ + φ * risk premium for illiquidity

Question 146

Characteristics of CRE

Answer 146

* CRE has bond-like characteristics: rental income from tenants is similar to CFs on a bond. Also, credit spreads on a bond are similar to credit quality of tenants affecting the value of CRE. * The value of commercial real estate is influenced by many factors, including the state of the economy, the demand for rental properties, and property location. * Illiquidity: It could take years to exit a CRE investment at fair value. * Very cyclical

Question 147

What are the characteristics of an appropriate benchmark portfolio

Answer 147

* Should be representative of the investment universe from which the active manager may choose. * Should be replicable at low cost. * It should have weights that are available beforehand (ex-ante), and benchmark returns that can be obtained promptly afterward (ex-post).

Question 148

Alpha (α)

Answer 148

The excess return on the actively managed portfolio over the benchmark portfolio. Alpha = (α)p = Rp - (β * Rbenchmark)

Question 149

Active weights

Answer 149

The difference between a security's weight in an actively managed portfolio and its weight in the benchmark portfolio. Overweighted (underweighted) securities have positive (negative) active weights. Active weights must sum to zero. Formula: E(Ra) = W1 * ER(1) + W2 * ER(2) ... Wn * ER(n) * W1 = weight of security 1 in the portfolio

Question 150

Sharpe ratio

Answer 150

Excess return per unit of total (absolute) risk Calculation: (Rportfolio - Rf) ÷ σportfolio OR Sharpe ratio_p = √(Sharpe ratio_benchmark^2 + IR^2) ## Footnote * The Sharpe ratio is unaffected by the addition of cash or leverage in the portfolio. A 50% allocation to the risk-free asset would reduce both the excess return and standard deviation of returns by half.

Question 151

Closet index fund

Answer 151

A fund that is alleged to be actively managed but in reality closely tracks an underlying benchmark. ## Footnote * These funds will have Sharpe ratios very similar to the benchmark, low information ratios, and little active risk. After fees, the information ratio of a closet fund is often negative.

Question 152

True or false: The information ratio will not change w/ the additional of cash or the use of leverage?

Answer 152

False, it will. Adding cash to a portfolio is likely to lower active return, while active risk (i.e., volatility of active return) should not change much, meaning that the addition of cash is most likely to decrease the information ratio.

Question 153

Example: *Fund 1* ER = 10% σ = 14% Sharpe ratio = 0.57 *Fund 2* ER = 15% σ = 20% Sharpe ratio = 0.65 Rf = 2% (1) What % of cash would an investor need to hold to reduce the risk of a portfolio invested in fund 2 to the same risk level as fund 1?

Answer 153

14% ÷ 20% = 70% → Fund 1 only has 70% of the standard deviation that We can invest 70% in fund 2 and 30% in cash → ER = 15% * (0.7) + 2% * (0.3) = 11.1 σ = 20 * (0.7) + 0 * (0.3) = 14 Sharpe ratio = (11.1 - 2) ÷ 14 = 0.65 ## Footnote * This is essentially saying that by choosing the active manager w/ the highest information ratio and then making some optimal combination, the investor will have the highest possible Sharpe ratio.

Question 154

True or false: A fund w/ zero systematic risk would have a Sharpe ratio = information ratio?

Answer 154

True, all else equal.

Question 155

Optimal active risk

Answer 155

The level of active risk that maximizes the portfolio's Sharpe ratio Formula: σa = (Information ratio ÷ Sharpe ratio) * Standard deviation of the portfolio ## Footnote This is the level of optimal risk that will lead to the highest Sharpe ratio

Question 156

Sharpe ratio of a portfolio w/ optimal level of active risk

Answer 156

Sharpe ratio_portfolio^2 = √(Sharpe ratio_benchmark^2 + Information ratio^2) ## Footnote * Implication: Choosing the PM w/ the highest information ratio (skill) will produce the highest Sharpe ratio * Sharpe ratio_portfolio^2 = optimal active risk

Question 157

Total portfolio return volatility calculation

Answer 157

Benchmark return volatility + volatility of active return

Question 158

Example: Optimal active risk Fund A has an information ratio of 0.2 and active risk of 9%. The benchmark portfolio has a Sharpe ratio of 0.4 and total risk of 12%. If a portfolio w/ an optimal level of active risk has been constructed by combining Fund A w/ a benchmark portfolio, calculate: (1) Portfolio's Sharpe ratio (2) Portfolio's excess return (3) The proportion of the benchmark and Fund A in the portfolio

Answer 158

(1) √(0.4^2 + 0.2^2) = 0.4472 (2) optimal level of active risk = σa = (Information ratio ÷ Sharpe ratio_benchmark) * σb = (0.2 ÷ 0.4) * 0.12 = 0.06 → Expected active return = ERa = Information ratio * σa = 0.2 * 0.06 = 1.2% = (Rp - Rb) → benchmark Sharpe raito = (Rb - Rf) ÷ σp → 0.4 = (Rb - Rf) ÷ 0.12 → (Rb- Rf) = 0.048 → Portfolio excess return = (Rp - Rf) + (Rb - Rf) = 0.012 + 0.048 = 0.06 (3) The optimal level of active risk = 6%. The Fund A has active risk of 9%. 6% ÷ 9% = 67% should be invested in Fund A. The rest should be invested in the benchmark. If we deviate from this weighting, it will lead to deterioration of the Sharpe ratio.

Question 159

Fundametal law of active management

Answer 159

This law states that there are three components that affect the information ratio (**assumed information coefficient (IC)**, the **transfer coefficient**, and the square root of **breadth (BR)**), which in turn provide the optimal expected active return. ## Footnote * If there are no constraints, the two components that determine the information ratio are IC and BR.

Question 160

Information coefficient (IC)

Answer 160

A measure of a manager's skill. It's the risk-weighted correlation between active returns and forecasted active returns. IC can be ex-ante or ex-post. Formula: 2(# of correct bets ÷ # of bets) - 1 ## Footnote * Don't over-complicate this, it's just the correlation between what a PM says will happen vs what actually happens or what will happen.

Question 161

Transfer coefficient (TC)

Answer 161

The correlation between actual active weights (△Wi) and optimal active weights (△Wi*). The optimal active weight for a security is postively related to its expected active return and negatively related to its expected active risk. TC has to do w/ constraints on what a PM can or cannot do. Ex: A long-only can only take long positions. TC = 1 is an uncontrained portfolio TC < 1 means there are contraints (△Wi ≠ △Wi*) ## Footnote * The lower the TC, the higher the constraints.

Question 162

Breadth (BR)

Answer 162

The # of independent active bets taken per year. Ex: If a PM takes active positions in 10 securities each month, then annual BR = 10 * 12 = 120. BR only applies if: 1. Active returns are cross-sectionally UNcorrelated 2. Active returns are UNcorrelated over time Formula: N ÷ [ 1 + (N - 1) * r ] ## Footnote * BR is most likely to be equal to the # of securities multiplied by the # of decision periods per year if the active returns are correlated w/ active weights.

Question 163

Optimal weight of an asset formula:

Answer 163

△Wi* = (μi ÷ σi^2) * [ σA ÷ √(μi^2 ÷ σi^2) ] - μi = forecasted active return of asset i - σi^2 = forecasted volatility of the active return of asset i - σA = Active portfolio risk (std. deviation of active return) ## Footnote * Optimal weights are positively related to forecasted active return and negatively related to forecasted active risk.

Question 164

Grinold rule

Answer 164

Allows us to compute the expected active return based on the information coefficient, active risk, and a standardized score. Formula: μi = IC * σi * Si - Si = score of security i

Question 165

Expected value added by management

Answer 165

ERa = Σ(△Wi * μi)

Question 166

Basic fundamental law formula

Answer 166

ERa = IC * √(BR) * σa OR IR* = IC * √(BR)

Question 167

Full fundamental law formula

Answer 167

ERa = TC * IC * √(BR) * σa OR IR* = TC * IC * √(BR) ## Footnote * Because TCs in a constrained portfolio are always < 1, IR* > IR and ERa* > ERa.

Question 168

Optimal level of active risk for a constrained portfolio

Answer 168

σa = TC * [ (IR* ÷ Sharpe ratio) * σ_p ]

Question 169

Sharpe ratio of a constrained portfolio

Answer 169

√(Sharpe ratio_benchmark^2 + TC^2 * IR*^2)

Question 170

Conditional expected active return

Answer 170

E(Ra|ICr) = TC * ICr * √(BR) * σa - ICr = realized IC (ex-post)

Question 171

Actual return calculation

Answer 171

Ra + E(Ra|ICr) + noise

Question 172

True or false: The portfolio w/ the highest information ratio will not be the portfolio w/ the highest Sharpe ratio?

Answer 172

False, it will

Question 173

Given an information ratio and target level of active risk, how can we calculate expected active return?

Answer 173

ERa = Information ratio * σa

Question 174

True or false: The information ratio is useful for quantifying an actively managed portfolio's return in excess of the Rf?

Answer 174

False, the information ratio evaluates risk-adjusted return in relation to a benchmark-investment baseline, rather than in relation to a risk-free investment.

Question 175

Sector rotation

Answer 175

Allocating more of an investor's assets into a sector that's expected to outperform from a sector that is expected to underperform.

Question 176

Active risk of a stragey using sector rotation

Answer 176

σ_c = √[ σ_a^2 - (2 * σ_a * σ_b * r_ab) + σ_b^2 ] Annualized active risk using this strategy: σ_a = σ_c * √(BR)

Question 177

Annualized active return

Answer 177

IC * √(BR) * σ_a

Question 178

What can the fundamental law of active mgmt. be used to evaluate?

Answer 178

* security selection * Market timing * Other active mgmt. strategies

Question 179

Limitations of the law of active mgmt.

Answer 179

There are generally two errors derived from estimates of inputs: * Ex-ante measurment of skill: If managers are estimating their own IC, they tend to overestimate. * Independence: BR is meant to measure independent strategies that a PM makes, however most decisions are correlated.

Question 180

True or false: The maximum spread on an ETF is positively related to the probability of the AP offsetting the trade in a secondary market?

Answer 180

False, negatively related

Question 181

True or false: Spreads tend to be narrower for fixed-income ETFs as compared to large-cap equity ETFs?

Answer 181

False

Question 182

Assuming arbitrage costs are minimal, what is most likely to occur when the share price of an ETF is trading at a premium to its intraday NAV?

Answer 182

When the share price of an ETF is trading at a premium to its intraday NAV and assuming arbitrage costs are minimal, APs will step in and take advantage of the arbitrage. Specifically, APs will step in and buy the basket of securities that the ETF tracks (the creation basket) and exchange it with the ETF provider for new ETF shares (a creation unit). These new shares received by APs can then be sold on the open market to realize arbitrage profits.

Question 183

True or false: Historical yields drive the pricing of bonds more than the price history or the current duration?

Answer 183

True

Question 184

True or false: Excess kurtosis or fat tails indicates higher (than normal) probability of extreme events?

Answer 184

True

Question 185

True or false: To conduct a sensitivity analysis, we fit return data to a distribution that accounts for skewness and excess kurtosis, such as a multivariate normal distribution and then repeat the Monte Carlo simulation?

Answer 185

False, to conduct a sensitivity analysis, we fit return data to a distribution that accounts for skewness and excess kurtosis, such as a multivariate skewed Student's t-distribution and then repeat the Monte Carlo simulation.

Question 186

True or false: The real rate of return is higher, lower the utility of current consumption relative to future consumption?

Answer 186

False, the real rate of return is higher, higher the utility of current consumption relative to future consumption. If investors expect lower incomes in the future, the utility of future consumption relative to current consumption will be higher and real rate will be lower. | The marginal utility of consumption is higher during economic downturns.

Question 187

Value stock

Answer 187

Stocks w/ low price multiples, high dividend yield and tend to be in mature industries with low earnings growth.

Question 188

What causes a discount rate to change?

Answer 188

The discount rate can change either due to changes in risk-free rate or due to changes in risk premiums.

Question 189

Difference between the information ratio and the Sharpe ratio?

Answer 189

The information ratio measures the risk-adjusted returns relative to a certain benchmark while the Sharpe ratio compares the risk-adjusted returns to the risk-free rate.

Question 190

Arbitrage portfolio

Answer 190

A portfolio with factor sensitivities of zero to all factors, positive expected net cash flow, and an initial investment of zero.

Question 191

True or false: Factor sensitivities are generally specified first in fundamental factor models, whereas factor sensitivities are estimated last in macroeconomic factor models?

Answer 191

True

Question 192

True or false: The information ratio of an unconstrained portfolio is affected by aggressiveness of the active weights?

Answer 192

False, the information ratio of an unconstrained portfolio is unaffected by aggressiveness of the active weights

Question 193

True or false: ETFs that have the highest trading volumes in their asset class category are generally preferred for tactical trading applications?

Answer 193

True

Question 194

Economic capital

Answer 194

The capital needed for a firm to survive if severe losses are experienced based on the risk the business is exposed to.

Question 195

True or false: Five percent VaR is the minimum loss 5% of the time, or maximum loss with a 95% confidence level?

Answer 195

True, it can be expressed either way

Question 196

True or false: Real risk-free rate is negatively related to real GDP growth and to GDP volatility?

Answer 196

False, real risk-free rate is positively related to real GDP growth and to GDP volatility.

Question 197

True or false: Settlement risk is a key concern for foreign equity ETFs that invest in American depository receipts (ADRs)?

Answer 197

False, settlement risk is applicable for ETFs that use OTC derivative contracts, however ADRs are exchange-traded.

Question 198

True or false: The price of a risk-free inflation-indexed bond is the expected inter-temporal rate of substitution?

Answer 198

True