Empirical evidence of the CAPM and multifactor models Flashcards
Remind me of the two pass approach again for testing CAPM?
In our regression can we add more variables?
1) First stage, we estimate betas from time series regression
2) second stage, we regress average expected returns on a constant and beta.
In our regression we can include more variables, if CAPM holds then the other variables should be insigficant.
What did fama and French (1992) find out about gamma 2 and 3 measuring beta squared and a measure of idiostratic risk?
they are insignificant but that the empirical SML is still too flat.
We could impute any type of variables such as betas, size and Book to market but what does CAPM imply?
CAPM implies only betas matter and nothing else so y2 = 0
What does Cross sectional returns mean in CAPM?
In CAPM, cross-sectional returns analyze assets’ relative performance at a specific time, using beta to identify higher or lower expected returns.
What do Fama and french in (1992) add to the linear regression and what do they find?
they added firm size and the ratio of book to market value ( B/M). They find that both are significant but that beta is not. Actually size and book-to-market dominate beta,
Fama and French(1992) methodology is based on double sorting, so firstly they consider a large sample of stocks, then they estimate beta’s of the stocks using time series regression of 5 year period at the beginning of their sample, these betas are used to make double sorted portfolios, where the 1 portfolio consists of stocks with low beta and 10th portfolio consists of stocks with highest beta
Secondly, these portfolios are further split into 10 sub portfolios which are sorted on size, such that the first portfolio consists of stocks with smallest size and the 10th portfolio consists of stocks with the biggest size. So get 100 portfolios sorted on beta and firm size ( Market equity). The table shows average monthly returns of the 10 portfolios. So now detect some problems with CAPM? ( by the way we get similar results for portfolios sorted on BM and beta,
1) returns are not increasing in beta. ( CAPM predicts stocks with higher betas so have higher expected returns)
2) Firms size seems to matter when describing stock returns ( small market value firms have higher returns than with companies with of low MV. CAPM says that other variables are irrelevant such as firm size.
What interesting finding do we find about book value to market value?
Firms with a high ratio of book value to market value ( B/M) tend to earn a higher rate of return than predicted by the CAPM.
What are High B/M firms called and what are Low B/M firms called?
1) High book to market firms are ‘value stocks ( ecause they are perceived to be undervalued by the market.) ‘ - have lots of tangible assets in place.
2) Low B/M ( e.g. tesla) firms are ‘growth stock(market values their growth prospects more than their current assets) s’- Few physical assets.
Why is it good to investors that their are other variables that effect expected return?
because you can go long of stocks with maybe low size and short firms with high size e.g. and gain positive return.
Lets look at mutifactor models now, what other potential factors can effect expected returns?
1) GDP
2) Interest rates
3) Expected inflation.
Answer this?
If asset holders were compensated for idiosyncratic risk, it could create arbitrage opportunities. Since idiosyncratic risk is diversifiable, astute investors could construct well-diversified portfolios to eliminate idiosyncratic risk while still being rewarded for it. This would allow them to earn risk-free profits by exploiting the market’s mispricing of assets, leading to potential market inefficiencies and the eventual correction of these mispricings.
We are going to now talk about Aribtrage pricing theory and later on compare to CAPM .
is a financial model used to determine the expected returns of an asset or portfolio. Unlike the Capital Asset Pricing Model (CAPM), which assumes that an asset’s return is based on its sensitivity to market risk, the APT considers a broader range of factors that may affect an asset’s return.
What are some 3 main ones assumptions for the APT?
1) Idiosyncratic risk is diversified - well-diversified portfolios held by investors, thus no compensation for this risk (only systematic risk compensated).
2) No arbitrage opportunities in APT - equilibrium return on arbitrage portfolio (zero investment and systematic risk) is zero; positive returns are eliminated through arbitrage trading.
3) returns can be explained by factors
Remind us what a arbitrage opportunity is again?
An arbitrage opportunity arises when an investor can make sure profits without making a net investment ( zero investment portfolio). Since no investment is required, an investor can create large positions to secure large profits. WEIGHTS OF PORFOLIO = 0 COMPARED TO ORDINARY PORTFOLIO WHERE WEIGHTS = 1
Now looking at the APT formula for excess returns on the stock right it out and show how its different to CAPM?
1) They are more risk factors k such as inflation, GDP, where betas are dependent on them.
2) with the second point, if they were correlated, then well diversified portfolios will not be able to eliminate risk, hence arbitrage will not be riskless.
2) another one is There is no special role for the market portfolio in the APT, whereas the CAPM requires thatthe market portfolio be efficient
Lets look at findings in APT, what is the first one. To do with single factor model.
Is epsolim = 0 then no aribtrage implies that alpha j = 0
Calculate if there is any mispricing?
If there is no artbitrage then the expected return of portfolio b should be 7& not 6%, hence mispricing. It is overpriced ( remember return is inversely related to price, and return is too low here), hence their is scope for arbitrage.
So as we have seen from this example aribtrage opportunity exists, but remember now because they don’t have the same betas then its not possible to long one and short the other, to eliminnate all risks, so what do we do?
We need some somehow equate the betas.
So lets create a portfolio C, which is a combination of portfolios A and Rf asset that has the same beta as B.
We sell the overpriced portfolio.
Key here is that we are buying 1million dollars of portfolios C and selling 1million dollars of portfolio B, In equilibrium this arbitrage opportunity will be elimanted fast.
Calculate this an outline the limitation of APT?
What are the 3 factors in fama and french 1993 3 factor model following from zero investment portfolios?
rm -rf is market premium
SMB - the next factor shows that small cap stocks have higher returns than high cap stocks.
HML - called ‘distress premium, if a firm has a BE/ME, then firm has a low price relative to book price, hence they are in distress.
How are SMB and HML portfolios constructed?
How do we test the fama french 3 factor model?
What will it mean if our condition not found?
Same as CAPM in the sense that we test if Alphas = 0.
If Alphas = 0 we see the following pricing relationship.
There could be aribitrage opportunities and well as missing factors.
What is an important take to say about the 3 factor model?
Essentially we don’t know how these variables are the one, they were just found in research.
Do the expected profit bit?
Do the standard deviation bit
