CAPM testing Flashcards
What are the Lintner’s findings of test of CAPM?
CAPM assumes your portfolio is perfectly diversified that is Market. What Lintner’s findings suggests that high beta stock are not contributing to the portfolio as theory suggests, but actually low beta stocks were giving higher return then theoretically.
Problems of his study: he used average historic return instead of expected return, and he didn’t have actual beta- s instead he used estimates which can cause all sort of econometrics issue.
What are the first and second pas regressions?
First pass regression - Running n time series regression to estimate n different beta-s for n different companies in your sample over t time period. For each company you will get error term for over t period, so the variance of it would be your idiosyncratic risk that is not explained by market, in other words no rewards for this.
Second pass regression - regress average return of i-th company over t period against estimated beta-s R(avg)i = gamma0 + gamma1 x Beta(i) + u(i)
what CAPM would suggest is that gamma0 = risk free rate, and gamma1 = Market risk premium
What are the CAPM test result?
Lintner, Milner and Scholes, Black Jensen =>
Empirically CAPM underestimating low beta return and overestimating high beta return.
The cause might be the assumptions we make: may be there no such thing as risk free return if we consider
•INFLATION and UNCERTAINTY
•UNLIMITED lending and borrowing
What is zero-Beta CAPM?
Look at the and note
Practical evidence for CAPM?
Fama and Mcbet 1974
Estimated betas against mean return
Their second pass regression
Ri=g0 + g1xb + g2b(sq) + g3xSe + ui
They estimated betas for 60months and used that for second pass reg
they found lots of gamma0, gamma1, gamma2 and gamma3 => theyr calculated average of gamms and found gamma2 and gamma3 to be statistically insignificant or 0. (Practical evidence in favour for CAPM)
What is Roll’s argument why CAPM is not working?
if Market protfolio is on the efficient frontier => beta would explain everything or R.sq is 100 = CAPM is perfect
but we use estimate of Market portfolio ( why do we use only US stock market what about the rest of the world, bond, property etc) => this is the reason why we found CAPM was not working
ie CAPM is not testable because you cant define what is MARKET PORTFOLIO
EPS/P (price earnings) and MV(size) effect on stock return
By Jaffa Keim and Westerfield
They looked Price Earning effect and Size (market value)effect. Why are they anomalies?
Question is are they distinct anomalies? Or manifestation of same anomaly?
On the surface they almost related because size or market value is price by number of shares.
Existing evidences are contradictory
Improvement by JKW
•Looked much longer period
•Mitigated survivorship bias
Findings - EP and Size are effects are significant and seem separate effect. Jan is particularly special for both effects hence making whole year look like effected by EP and Size Both effects are related to Price Bringing Price variable eliminates EP effect in Jan but does not eliminate Size effect in Jan
Anomaly Question remains!
Chan & Lakonishok – response to FF, to rescue beta
They conducted tests in usefulness of beta (Veracity=truthfulness)
Q: OK, say CAPM has no issue, but does high beta really outperform low beta?
Is compensation on beta risk really is equal (Rm-rf)?
Assume everybody interests in M portfolio (draw the efficient frontier graph) => if this tangent line is same for every body it is called CML and we derive our SML for any stock.
SML equation is our CAPM model
SML: E(R)= rf + β (Rm – rf)
Now consider Market model: where return is positively related to market
MM:R= a +βRm+e
Stock return and its variation is derived from its fundamentals ie risk and information. If any variation that is unrelated to risk and info then that is caused by NOISE. (i.e. rumours, sentiment, …)
Chan and Lakon estimated (Rm-rf) = 5,5% and st.deviation=16,5% for last 20 years.
Check whether it is significant or not (Rm-rf)/(st.dev/sq root of n) = 5,5%/(16%/sqroot20) = 1.36
T stat is not significant, but it is actual premium economically significant with precision, why is that? Here is they making argument about NOISE is messing up the CAPM. It would need 69 years of data to make it significant. So therefore FF study result could be due to high st.error
They did test on R= y0 + y1 β + e and found y1 to be not significant, which explains noise effect.
2nd reason why CAPM does not work
People use CAPM, Markowitz ides of ultimate diversification, to trying track S&P500 index and this action in return messes p the CAPM. Suggesting institutional factor not risk and return. Because they buy any stock included in S&P regardless of risk and return profile.
3rd reason why CAPM might not work
Chan & Lakon did a test for down market months and for up market months
We use realised returns, but in the CAPM expected return is what we are looking for and it is given by CAPM equation. NO one will invest unless they expect positive return this is why CAPM doesn’t work, because they found
Market risk premium is positive during market up months
Market risk premium is negative during down months
For this reason β is useful for market timing ie when market is up buy in with high β
Conclusion: rejecting β is premature, though they found more debate than just a CAPM 1. Market model and its usefulness for market timing
- noted about NOISE in the market, which makes it hard to capture true measure
- Institutional factors that alter CAPM’s fundamental
Bhardwaj and Brooks
Is the size realy a price effect?
Is the size realy a price effect? What about January anomaly?
Typical explanation for small firms effect:
1. Small shares are neglected
2. Market has miss assessment risk
3. Small firms are volatile
4. Transaction costs – higher bid ask spread, which means higher return required Basically small firm and low price stock are highly correlated by definition
BB study found that small firms effect is really a price effect. Given the high transaction cost and low liquidity, gains on low stocks are an illusion. Performance on low stock worsens as the holding period lengthens, and their good return in January is due to bid-ask bias, as most trade occur at bid in December and most occur at ask in January. Though if transaction costs are considered investing in small stock does not profit at all.
On the other hand J. Berk claims small firms effect is not an anomaly, because MV is negatively correlated with expected return.
Fama and French 1992
Q: Does beta really explain return when all the anomalies taken account? (according to CAPM beta is sufficient on its own)
Q: Does beta really explain return when all the anomalies taken account? (according to CAPM beta is sufficient on its own)
They evaluate effects of beta, size, BV/MV, E/P, leverage
They estimated betas in a way such that size effects (ie price effects) were taken out from it. Furthermore they used these betas in conjunction of potential other anomalies.
Results from these regressions were not good for CAPM
1. betas even on its own doesn’t explain cross returns (when size effect was purged) ie CAPM doesn’t work
2. E/P related to average return but subsumed by size and BE/ME, but do they represent risk?
May be why not? – we know that small firms are riskier than large firms, and BE/ME is a leverage ratio, if firm is highly leveraged potential financial distress drags down the ME.
3. Size and BE/ME give best parsimonious model to explain cross returns – this is a huge contradiction against CAPM and Finance
