Chapter 7. Capital Asset Pricing and Arbitrage Pricing Theory. CAPM: Simplifying Assumptions. Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets No taxes and no transaction costs
Capital Asset Pricing and Arbitrage Pricing Theory
Individual investors are price takers
Single-period investment horizon
Investments are limited to traded financial assets
No taxes and no transaction costs
Information is costless and available to all investors
Investors are rational mean-variance optimizers
Required return = rf + βS [E(rM) – rf]
If you believe the stock will actually provide a return of ____, what is the implied alpha?
Portfolio Beta is the weighted average of underlying Betas
5 + 1.5 [14 – 5] = 18.5%
17% - 18.5% = -1.5%
Adjusted β =
Calculated betas are adjusted to account for the empirical finding that betas different from _ tend to move toward _ over time.
A firm with a beta __ will tend to have a ___________________ in the future. A firm with a beta ___ will tend to have a ____________________ in the future.
lower beta (closer to 1)
higher beta (closer to 1)
2/3 (Calculated β) + 1/3 (1)
2/3 (1.276) + 1/3 (1)
The CAPM is “false” based on the ____________________________.
validity of its assumptions
The CAPM could still be a useful predictor of expected returns. That is an empirical question.
Huge measurability problems because the market portfolio is unobservable.
Conclusion: As a theory the CAPM is untestable.
However, the __________ of the CAPM is testable.
Betas are ___________ at predicting returns as other measurable factors may be.
More advanced versions of the CAPM that do a better job at ___________________________ are useful at predicting stock returns.
not as useful
estimating the market portfolio
Still widely used and well understood.
Fama and French noted that stocks of ____________ and stocks of firms with a _________________ have had higher stock returns than predicted by single factor models.
high book to market
Problem: Empirical model without a theory
Will the variables continue to have predictive power?
FF proposed a 3 factor model of stock returns as follows:
rM – rf = Market index excess return
Ratio of ______________________________________ measured with a variable called ____:
HML: High minus low or difference in returns between firms with a high versus a low book to market ratio.
_______________ measured by the ____ variable
SMB: Small minus big or the difference in returns between small and large firms.
book value of equity to market value of equity
Firm size variable
Arises if an investor can construct a zero investment portfolio with a
sure profit, e.g. Credit Card B/T
Since no net investment outlay is required, an investor can create arbitrarily large positions to secure large levels of profit
With efficient markets, profitable arbitrage opportunities will quickly disappear
Suppose Rf = ___ and a well diversified portfolio P has a beta of ___ and an alpha of ___ when regressed against a systematic factor S. Another well diversified portfolio Q has a beta of ___ and an alpha of ___.
If we construct a portfolio of P and Q with the following weights:
What should αp = ___
Note: Σ W = 1
WP = and WQ = ;
Then βp =
(-2.25 x 1.3) + (3.25 x 0.9) = 0
(-2.25 x 2%) + (3.25 x 1%) = - 1.25%
αp = -1.25% means an investor will earn rf – 1.25% or 4.75% on portfolio PQ.
In theory one could short this portfolio and pay 4.75%, and invest in the riskless asset and earn 6%, netting the 1.25% difference.
Arbitrage should eliminate the negative portfolio alpha quickly.
The result: For a well diversified portfolio
Rp = βpRS (Excess returns)
(rp,i – rf) = βp(rS,i – rf)
and for an individual security
(rp,i – rf) = βp(rS,i – rf) + ei
Advantage of the APT over the CAPM:
RS is the excess return on a portfolio with a beta of 1 relative to systematic factor “S”