BKM Chapter 9 Flashcards
Main uses for CAPM (2)
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- 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)
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all investors:
- are mean-variance optimizers
- have investment horizon = 1 period
- use identical input lists (b/c all relevant info is publicly available)
CAPM assumptions about market structure (4)
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- all assets are publicly held & traded on public exchanges
- investors can borrow/lend at the risk-free rate and short positions are allowed
- no taxes
- no transaction costs
Categories of CAPM assumptions (2)
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- individual behavior
2. market structure
Key results of CAPM (3)
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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
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CAL = CML
Reason portfolio managers hold risky portfolios <> market portfolio in reality
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b/c of differences in input lists
Which stocks are included in the market portfolio under CAPM?
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all stocks
Expected risk premium of the market portfolio under CAPM (alternative formula)
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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
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an individual asset’s risk premium is determined by it’s contribution to total risk
Market price of risk
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reward-to-risk ratio for the efficient portfolio (= market portfolio)
= market risk premium / market variance
Classic CAPM formula (aka mean-beta relationship)
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E[r(i)] = risk-free rate + beta * market risk premium
What does beta measure?
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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
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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
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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)
Alpha
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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
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required return under CAPM for the associated beta
all fairly priced securities live on the SML
Difference b/w the SML and the CML
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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)
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- large amount of collateral needed
- limited supply may restrict short positions
- short positions are prohibited for some investment companies
Short position
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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?
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with restrictions on borrowing/borrowing rate <> risk-free rate
Problem with the assumption about borrowing at the risk-free rate under CAPM and consequence
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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)
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- combining efficient portfolios produces an efficient portfolio
- the market portfolio is an aggregation of efficient portfolios, therefore it is efficient
- 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
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uncorrelated companion portfolios on the bottom half of the min-variance frontier
Zero-beta version of CAPM
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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
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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)
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- private businesses
2. human capital (e.g. individual earning power)
Mean-beta relationship considering the size of labor income
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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
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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
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increase in demand
increase in price
decrease in return
When to use a multiperiod model with CAPM?
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use with future extra-market risks (consumption risks)
Additional sources of risk under ICAPM (2) vs. regular CAPM assumptions
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- changes in investment opportunity parameters (e.g. decrease in interest rates)
- 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)
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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)
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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
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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
Liquidity
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ease and speed an asset can be sold at market value
Illiquidity
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discount from fair market value that a seller must accept in order to quickly sell an asset
Bid-ask spread and relative liquidity
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bid-ask spread = max buying price - min selling price
low bid-ask spread = most liquid
high bid-ask spread = least liquid
Liquidity traders
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investors with no additional information
Relationship b/w expected ROR and bid-ask spread
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as bid-ask spread increases, expected ROR increase at a decreasing rate
Conclusion about liquidity and CAPM
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expected liquidity can impact prices (and therefore ROR) which means that it may not equal CAPM required return
Liquidity beta
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measures sensitivity of a firm’s returns to changes in market liquidity
Reasons CAPM is difficult to test (4)
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- 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
- estimated betas are subject to error
- alphas and betas may vary with time but regression techniques require them to be constant
- true betas may be conditional
Uses for a market portfolio/market index (4)
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- diversification vehicle to mix with the active portfolio
- benchmark performance
- means to determine fair compensation for risky enterprises
- means to determine proper prices in regulated industries
Support for the theory that the optimal risky portfolio is the market index (CAPM result)
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on average, professionally managed mutual funds are unable to beat a market index (e.g. passive strategy outperforms)
Mutual fund theorem
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conclusion that a passive strategy is efficient
Beta formula
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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
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requires:
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
