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Flashcards in BKM Chapter 9 Deck (48)
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Main uses for CAPM (2)

(BKM - 9)

1. benchmark ROR for evaluating potential investments

2. estimating the expected return on assets not yet traded in the marketplace


CAPM assumptions about individual behavior (3)

(BKM - 9)

all investors:

1. are mean-variance optimizers

2. have investment horizon = 1 period

3. use identical input lists (b/c all relevant info is publicly available)


CAPM assumptions about market structure (4)

(BKM - 9)

1. all assets are publicly held & traded on public exchanges

2. investors can borrow/lend at the risk-free rate and short positions are allowed

3. no taxes

4. no transaction costs


Categories of CAPM assumptions (2)

(BKM - 9)

1. individual behavior

2. market structure


Key results of CAPM (3)

(BKM - 9)

all investors arrive at identical efficient frontiers (based on assumptions)

>> all have identical CALs

>> all have identical optimal risky portfolios = market portfolio


Each investor's CAL under CAPM

(BKM - 9)



Reason portfolio managers hold risky portfolios <> market portfolio in reality

(BKM - 9)

b/c of differences in input lists


Which stocks are included in the market portfolio under CAPM?

(BKM - 9)

all stocks


Expected risk premium of the market portfolio under CAPM (alternative formula)

(BKM - 9)

E[R(M)] = A-bar * sigma^2(M)

where A-bar = average risk aversion of all investors and y* = 1


CAPM assumption about expected returns of individual securities

(BKM - 9)

an individual asset's risk premium is determined by it's contribution to total risk


Market price of risk

(BKM - 9)

reward-to-risk ratio for the efficient portfolio (= market portfolio)

= market risk premium / market variance


Classic CAPM formula (aka mean-beta relationship)

(BKM - 9)

E[r(i)] = risk-free rate + beta * market risk premium


What does beta measure?

(BKM - 9)

measures the contribution of the individual asset to the variance of the market portfolio


Difference between CAPM and the single-index model and optimal risky portfolios

(BKM - 9)

CAPM assumes every stock has alpha = 0

with rebalancing (so all alpha's = 0) both will end at the same optimal risky portfolios = market portfolio


Mean-beta relationship and the security market line (SML) - slope, y-intercept, and points of interest

(BKM - 9)

plots expected returns on the y-axis and beta on the x-axis

SML has slope = market risk premium

y-intercept = risk-free rate

E[r(M)] = return when beta = 1

individual stocks fall above/below the SML depending on their alphas (positive > above)



(BKM - 9)

alpha = difference b/w an individual stock's expected return and the SML (required return from CAPM)

alpha = investor forecast return - CAPM return


Interpretation of the SML

(BKM - 9)

required return under CAPM for the associated beta

(all fairly priced securities live on the SML)


Difference b/w the SML and the CML

(BKM - 9)

SML can be used for individual assets and efficient portfolios vs. CML which can only be used for efficient portfolios (b/c the x-axis is standard deviation, which isn't appropriate for individual assets)


Reasons short positions are harder to take than long positions (3)

(BKM - 9)

1. large amount of collateral needed

2. limited supply may restrict short positions

3. short positions are prohibited for some investment companies


Short position

(BKM - 9)

borrowing a stock & immediately selling it, betting the price will decrease before the debt is owed


When to use the zero-beta model of CAPM?

(BKM - 9)

with restrictions on borrowing/borrowing rate <> risk-free rate


Problem with the assumption about borrowing at the risk-free rate under CAPM and consequence

(BKM - 9)

in reality, there may be higher rates on borrowing than lending

>> means that borrowers & lenders may have different optimal risky portfolios <> market portfolio


Characteristics of efficient portfolios (3)

(BKM - 9)

1. combining efficient portfolios produces an efficient portfolio

2. the market portfolio is an aggregation of efficient portfolios, therefore it is efficient

3. every efficient portfolio (except the global min. variance portfolio) has a companion portfolio on the bottom half of the min-variance frontier with which it is uncorrelated


Zero-beta portfolios

(BKM - 9)

uncorrelated companion portfolios on the bottom half of the min-variance frontier


Zero-beta version of CAPM

(BKM - 9)

replaces risk-free rate in regular CAPM with the expected return for the zero beta portfolio


Zero-beta SML and market risk premium compared to regular CAPM

(BKM - 9)

SML is flatter than the regular SML

market risk premium < under normal CAPM (smaller reward for systematic risk)


Types of assets that are not tradeable (2)

(BKM - 9)

1. private businesses

2. human capital (e.g. individual earning power)


Mean-beta relationship considering the size of labor income

(BKM - 9)

E[R] = E[R(M)] * [Cov(excess stock return, excess market return) + P(H)/P(M) * Cov(excess stock return, excess return on HC)] / [market variance + P(H)/P(M) * Cov(excess market return, excess return on HC)]

P(H) = value of aggregate human capital
P(M) = market value of traded assets
HC = aggregate human capital

**uses excess returns


Extra-market risks

(BKM - 9)

inflation or changes in parameters describing future investment opportunities

ex: interest rates, future energy costs, volatility, market risk premium, betas


Hedge asset demand, price, and return relative to CAPM

(BKM - 9)

increase in demand

increase in price

decrease in return


When to use a multiperiod model with CAPM?

(BKM - 9)

use with future extra-market risks (consumption risks)


Additional sources of risk under ICAPM (2) vs. regular CAPM assumptions

(BKM - 9)

1. changes in investment opportunity parameters (e.g. decrease in interest rates)

2. changes in prices of consumption goods (inflation can manifest as higher future costs of living)

regular CAPM: assumes the only source of risk is return variance and investment opportunities do not change over time


Intertemporal CAPM (ICAPM)

(BKM - 9)

with K sources of risk and K associated hedge portfolios:

E[R] = beta(M) * E[R(M)] + sum of beta(k) * E[R(K)]

beta(M) = beta relative to the market index

beta(K) = beta on the kth hedge portfolio

**uses excess returns


Consumption-based CAPM (CCAPM)

(BKM - 9)

E[R] = beta(C) * risk premium(C)

where C = consumption tracking portfolio (highest correlated portfolio with consumption growth)

beta(iC) not necessarily = 1

**uses excess returns


Reason trading occurs in the market

(BKM - 9)

CAPM assumption that all investors hold he same optimal risky portfolio would mean trades are unnecessary (no transaction costs = no trades)

trading occurs because in reality investors do not actually share identical beliefs



(BKM - 9)

ease and speed an asset can be sold at market value



(BKM - 9)

discount from fair market value that a seller must accept in order to quickly sell an asset


Bid-ask spread and relative liquidity

(BKM - 9)

bid-ask spread = max buying price - min selling price

low bid-ask spread = most liquid
high bid-ask spread = least liquid


Liquidity traders

(BKM - 9)

investors with no additional information


Relationship b/w expected ROR and bid-ask spread

(BKM - 9)

as bid-ask spread increases, expected ROR increase at a decreasing rate


Conclusion about liquidity and CAPM

(BKM - 9)

expected liquidity can impact prices (and therefore ROR) which means that it may not equal CAPM required return


Liquidity beta

(BKM - 9)

measures sensitivity of a firm's returns to changes in market liquidity


Reasons CAPM is difficult to test (4)

(BKM - 9)

1. tests must use a proxy portfolio (b/c we cannot pinpoint the market portfolio/identify all tradeable assets) & it is difficult to distinguish b/w CAPM failure or failure due to use of proxy portfolio

2. estimated betas are subject to error

3. alphas and betas may vary with time but regression techniques require them to be constant

4. true betas may be conditional


Uses for a market portfolio/market index (4)

(BKM - 9)

1. diversification vehicle to mix with the active portfolio

2. benchmark performance

3. means to determine fair compensation for risky enterprises

4. means to determine proper prices in regulated industries


Support for the theory that the optimal risky portfolio is the market index (CAPM result)

(BKM - 9)

on average, professionally managed mutual funds are unable to beat a market index (e.g. passive strategy outperforms)


Mutual fund theorem

(BKM - 9)

conclusion that a passive strategy is efficient


Beta formula

(BKM - 9)

beta = Cov(R(i), R(M)) / sigma^2(M)

where R = excess returns
i = asset/secrurity
M = market portfolio


Simple CAPM arbitrage opportunity (assuming known alpha and beta values) - requirements (2) and weights

(BKM - 9)

1. beta = 0 (riskless)
2. alpha > 0 (positive abnormal return)

select a portfolio with alpha > 0, market portfolio (M), and risk-free asset portfolio (F)
w(M) = -beta(stock)
w(stock) = 1
w(F) = beta(stock) - 1

where stock = asset/portfolio with alpha > 0