The Capital Asset Pricing Model (CAPM)
the equation of the SML showing the relationship between expected return and beta
-It is an equilibrium (price for all assets and an allocation for all assets) asset pricing model (individuals in total own all asset supply)
-How the assets in the portfoli
Security risk =
systematic risk + nonsystematic risk
What does it mean for risk to be "priced"? Which type of risk should be priced? Why?
Priced if investors demand a risk premium for holding it (excess return over Rf)
-Nondiversifiable should be priced because diversifiable gets diversified away
Assumptions of CAPM
perfect competition, all investors have one identical holding period, all assets are publicly traded, unlimited access to borrowing and lending at Rf, no market frictions, homogeneous expectations, mean-variance oriented
-Imply that all investors use the
Why is this tangency portfolio also the market portfolio?
Competitive forces make it that way.
Since all risky assets owned in same proportion, aggregate market portfolio must be tangency portfolio. If not, prices adjust until it is so.
-Market portfolio is efficient
Market risk premium
variance of market * average degree of risk aversion across investors
What does CAPM relate?
relates the expected return premium on individual asset i to the expected return premium on the market portfolio, M
Suppose an asset has a variance of 50-bijillion percent, but isuncorrelated with the market. What is that asset's expected returnpremium?
Rf (beta = 0)
-doesn't matter how risky an asset is individually, only depends on its relation to the market
Sharpe Ratio of market?
It gives "maximal" return per unit of risk that financial markets can offer. It is the reward for volatility.
-Slope of the Capital Market Line
-The CAPM implies that the market risk premium is positive, and equivalently, that Sm is positive.
CML =
rF + (Sharp ratio m * SDm)
Security Market Line (SML)? slope?
a positively sloped straight line displaying the relationship between expected return and beta
-Plot of the CAPM
-Slope of the SML is the market risk premium (divided by beta which is 1 for the market)
-correctly priced securities lie on the line
If asset is correctly priced, alpha should be
0
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Alpha
The E(r) above the SML (vertical distance)
-If alpha positive (above line), underpriced and should buy it
Beta of portfolio
beta of the portfolio is the weighted average of the beta of its component stocks.
How would you test the CAPM?
Test whether the CAPM holds in historical data, Using regression analysis on a large historical dataset
-[1] αi=0 and [2] E[rMt] - rf > 0
E[rit] - rf =αi+βi(E[rMt] - rf)+eit
What do we get when we estimate this regression (one asset, i)
What do we get when we estimate this regression (multiple)
Alpha and Beta
Set the y-axis, E[Rit]=E[rit] - rf Set the x-axis, E[RMt]
Estimated market risk premium
(Set the y-axis, E[Ri]=E[ri] - rf Set the x-axis, βi)
the "joint hypothesis problem
If you reject CAPM are you using wrong market proxy or is your model wrong?
Testing the CAPM anomalies
Predictability, momentum, reversal, post-earnings announcement drift, liquidity premia, other priced factors
Fama and French
In addition to the "market factor", the "value factor" and firm "size factor" seem to be priced
What happens if we relax some of the strong assumptions of the CAPM?
risk factors other than market risk (covariance with themarket portfolio) are also "priced.
Single Factor Models
• Returns on a security come from two sources:
- Common macroeconomic or market factor
- Firm specific events
**CAPM can be thought of as a single factor model
Ri=αi+βi F+ei
(a= expected excess return on security, F= surprise in macroeconomic factor, e= firm specific events)
Multifactor Models
one macroeconomic/market factor is not the only factor (risk) driving asset prices. There could be several systematic factors.
-Unexpected GDP growth, Size, Value, Liquidity
Ri=αi+βiGDP
GDP+βiIR
IR*IR+ei
The Fama and French 3-factor model (FF3):
Rit=αi+βiM
MKTt +βiSMB
MB*SMBt +βiHML*HMLt +eit
E[Ri]=E[ri]- rf = βiM MKT + βiSMB SMB + βiHML HML
-MKT: Market risk premium, RMt=rMt-rf
-SMB: Small Minus Big. The return of a portfolio of small market cap stocks in excess of a portfolio of large ma
The Fama and French 3-factor model beta meanings
If βiSMB > 0 stock i earns a premium from its exposure to the SMB factor. I.e., it earns a small firm premium. It is likely a small market cap. stock.
If βiSMB < 0 stock i has a negative exposure to the SMB factor. I.e., it pays asmall firm premium. It
*WATCH 10/21 poll every where Qs
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If you had to allocate your wealth between 2 portfolios and put 100% of your money in one of those portfolios
What type of risk would you care about?
Total Risk (systematic and non)
M-squared measure
Create an adjusted portfolio (P*) that has
the same standard deviation as the market index.
Because the market index and P* have the same standard deviation, their returns are comparable:
M2= rP* - rM
-M2 means it is underperforming the market
Treynor measure
Ratio of portfolio excess return to beta
-Higher slope of Excess return vs beta graph, higher the treynor measure
Jensen's Alpha
measures investment performance as the raw portfolio return less the return predicted by the capital asset pricing model
Out of M2, treynor, and jensens alpha, which ones are always 0 for the market?
M2 and Jensen
Information ratio
The information ratio divides the alpha of the portfolio by the nonsystematic risk
(or "tracking error").
-Measures the abnormal return per unit of risk that would be diversified away by holding the market.
-Measures how consistent the portfolio manager i
What does Jensen's alpha assume?
Assumes CAPM, if other risk factors present, would be mis estimating returns
Style analysis
Regress portfolio returns on index returns based on style (small value, small growth, large blend, etc.)
Which Measure is Appropriate for performance?
1) If not diversified, then use the Sharpe measure as it measures reward to risk.
2) If diversified, non-systematic risk is negligible and the appropriate metric is Treynor's, measuring excess return to beta.
Interpretation of Performance Statistics
If P or Q represents the entire investment, Q preferred 2
because of its higher Sharpe measure and better M .
If P and Q are competing for a role as one of a number of sub-portfolios, Q again dominates because its Treynor measure is higher.
If we seek an
Early research on stock price
Prices seem to evolve randomly
Prices should reflect all available information and all current knowledge.
Hence prices should only react (change) because of arrival of new information.
What is an efficient market?
A market that efficiently prices information
-Prices fully reflect all info
-Prices are a correct valuation of available info
-Prices react quickly and correctly to new info
Different forms of market efficiency
Weak-form market efficiency
• Prices reflect all information contained in the history of PAST trading
Semi-strong form market efficiency
• Prices reflect all PAST trading and PUBLIC information
Strong-form market efficiency
• Prices reflect all PAST
Technical Analysis
-Technical analysis is looking into historical price series to detect price patterns that can be exploited.
-It is the search for recurrent and predictable patterns in stock prices.
If publicly known trading strategies self-destruct, then markets are
Weak form efficient
Fundamental analysis
NPV of future cash flows
-Fundamental analysis makes use of earnings information, dividend prospects, balance sheet information, expectations of interest rates in the future, etc.
Grossman-Stiglitz Paradox
If the market is already efficient, then no one would spend money on security analysis. If no one does this, then how can the market be efficient?
Why should the EMH hold?
-Competition between investors
-Many highly paid well resourced analysts looking for info
Price reactions to merger announcements
Upticks a few days before (anticipation or insider trading) and then massive jump up usually
Evidence in favor of EMH
Stock prices are close to random walks
Stock returns have low serial correlation
Stock returns are hard to predict
Portfolio managers:
Do not beat the market on average
Almost no one beats the market consistently
Mutual Fund Performance
-alphas positive before fees, negative after
-skilled managers will attract new funds until the costs of managing those extra funds drive alphas down to zero.
-inconsistent performance between quarters
Evidence against EMH
Bubbles•
Momentum•
Reversals•
Post-earnings announcement drift •
Small firm effect•
Book to market effect
Momentum v Reversal
Purely using past data to make gains
-Evidence against all EMH forms
-Good or bad recent performance continues
over short to intermediate time horizons
Reversal is returns over the long term instead of short (overshooting followed by corrections
Semi-strong Tests: Anomalies
P/E Effect•
Small Firm Effect (January Effect)•
-small firms underpriced because earn larger returns than big firms (evidence against semi-strong)
Book-to-Market Ratios•
-value stocks produce higher returns than growth
Post-EarningsAnnouncementPrice
Strong-Form Tests: Insider Information
-Insiders have traded profitably in their own stock
-can private info generate abnormal returns?
Interpreting the Anomalies and counterarguments
-Can be explained by risk premia (for undiversifiable risk)
-These effects are evidence of inefficient markets