Asset Pricing Chap 7 MPT: CAPM • A Pricing Model requires an estimate of a risk premium for a security to use in a present value- type price formula. • The Capital Asset Pricing Model • We discount using a rate “k” which is composed • Fama and French: Is Beta Dead? of the RFR and a risk premium. • We often rely on an estimate of risk based on • Oct. 2003 by William Pugh past variability (I.e., historical data, as in Chap 6) • One approach is too assign higher risk premiums to stocks with higher standard deviations. However, since MPT, using sigma this way is considered an error. Recall What MPT Tells Us What MPT Tells Us • Diversification is good, and since(?) you “can’t • The Capital Asset Pricing Model (CAPM) has beat the market” you should fully diversify. but one purpose: to estimate a risk premium for a • Investors have differing levels of risk aversion, security to use in a present value-type price but they should all hold the same fully diversified formula. The CAPM uses Beta. (not sigma) portfolio of risky assets. • Beta tells us how much risk a security adds to a • 1. Those who are more risk averse should hold diversified portfolio. Beta only measures non- some of their wealth in the risk-free asset and diversifiable risk - or market risk some in the risky portfolio. • If we use Beta in our discount rate to estimate a • 2. Those who can stand more risk may borrow, so security’s present value, is there any evidence as to own more than 100% of the risky portfolio. we are rewarded by taking on greater risk? CAPM CAPM • The Capital Asset Pricing Model (CAPM) has • The CAPM uses Beta to measure risk. Beta but one purpose: to estimate a risk premium for a tells us how much risk a security adds to a security to use in a present value-type price diversified portfolio. Beta measures risk only formula. after diversification (non-diversifiable risk). • We discount using a rate “k” which is composed • Beta is usually estimated using ex post data, in a of the RFR and a risk premium. regression least-squares estimate. (See figures • Theory tends to base any estimate of risk on past 7.6, 7.7 and 7.8). variability. • The CAPM is based on the fact that measured variability is diversifiable (avoidable) risk and thus should not be part of the risk premium 1 Security Characteristic Line CAPM (Excess) Returns for security(i) • Often use simpler Ri = a i + ßI Rm + ei SCL . • Beta is simply the slope of the regression line . (rise over run) and is the ratio of the stock’s . return over the markets return. .. .. • Beta is measuring a stock’s tendency to move . more (or less) than the market on a given day. (Excess) returns • Alpha , the y-intercept, is used by some analysts . .. on market index . to represent a tendency to outperform or . underperform the market. Ri = a i + ßiRm + ei CAPM CAPM 2 b = [COV(ri,rm)] / sm = ri,msi / sm • The “typical stock would move about the same as the market: that is, if the market rose one Beta is a function of the security’s correlation with percent, the typical security would rise one the “market” and the security’s overall variability percent. The rise over run (slope) would be one. • India Fund has a Sigma of 40%, and the SP500 • The “market’s” Beta is also one. has a sigma of 20%. Correlation is 0.15. • “Safer” securities like electric utilities and food • Thus Beta of .3 stock, even bonds, would move less than the market and their Betas would be less than one. • b = rus,ind(sIndia/ sUSsks) Insight: Beta is the product of correlation and relative risk. • “Riskier” securities like tech stocks, small cap stocks, airlines, financial weak companies, would have Betas more than one. CAPM Beta and CAPM • A security’s appropriate rate of discount “k” • Beta can also be applied to using margin: would be based on the RFR and the risk of the • Suppose you decide to leverage your portfolio 2 overall market, adjusted by the security’s to 1 (maximum initial margin). You invest in a individual Beta. ‘market’ index fund. • For example: Kellogg has a Beta of 0.6, the • Your s risk would be twice that of the market market risk premium from page 145, is about 7% (40% instead of 20%) and your leveraged over the T-bill. If the T-bill is currently 5%, the portfolio would be perfectly correlated with the “k” for Kellogg’s is 5% + 0.6(7%) = 9.2% market r =1. • b = r(s /s ) = 2. • Apple has a Beta of 1.5, it’s k would be 15.5% leveraged mkt • Suppose the risk-free rate is 3%. • Pakistan Fund has a Beta of 0, its k would be 5% • Then k = 3% + 2* 7% = 17%. 2 CAPM CAPM • History of CAPM on page 251: • Fama and French find, instead, other ways to • The CAPM has long been controversial. earn “market-beating” returns. • Fama and French did an enormous study • Buy small cap stocks showing that Beta does not predict stock • Buy stock with high dividend yields performance: high Beta stocks do not produce • Buy stocks at prices close to book value higher returns than low Betas stocks. • Buy stock with low price earnings ratios • Even putting back diversifiable risk, to get • What do these four recommendations have in Sigma , Fama & French do not any reward for common? Look at formula definition of each. taking on risk. • Maybe Beta is “dead” (the CAPM is worthless.) APT APT • An attempt to improve a single index model by • These “Quant” models have led to to some estimating a number of variables. spectacular debacles: • Often ends up as “kitchen-sink” regression • Synthetic Puts in 1987 Crash. Thought they modeling. Variables often not even named. could get free ‘portfolio insurance’ • Fama and French results are sometimes used in a • APT type model used by Long-term Capital three or four index model (P/E, price to book, Management. Went long Russian Bonds and Beta etc.) hedged by shorting U.S. Treasury Bonds. • Not at all clear these models work better in • These models tend to assume markets follow a the real world than the CAPM (which doesn’t probability distribution and are not impacted by work well but makes some sense). human behavior. 3.