Alternative CAPM Specifications

Abstract

Weak early empirical evidence with respect to the CAPM inspired a variety of alternative forms proposed by researchers to take into account realistic aspects of capital markets not considered in its original form. In the last chapter we covered Black’s (1972) zero-beta CAPM allowing short sales and borrowing at rates greater than the riskless rate. Here we review further extensions of the CAPM, including the foundational and more general intertemporal CAPM (ICAPM) which spawned a number of new models such as the international asset pricing model (IAPM), consumption CAPM (CCAPM), production CAPM (PCAPM), and conditional CAPM.

Appendices

Questions

• 1. Merton (1973) developed the intertemporal CAPM (ICAPM). What is different about the ICAPM compared to the CAPM? What new assumption does it make?

• 2. In the ICAPM, how do investors respond to unfavorable shifts in future investment opportunities? What are state variables?

• 3. In the ICAPM, what is the three-fund theorem? In view of this theorem, write the equation for the ICAPM.

• 4. In the ICAPM, if correlations $\rho _{iN} = 0$ for all securities i, which also implies that $\rho _{NM} = 0$ (where M is the market portfolio), but $r_N$ is perfectly negatively correlated with $R_f$ (which is true by definition), the correlations of stocks with the future riskless rate would be zero. What happens to the ICAPM is this special case? What is the beta of security N in this case? Is N related to the zero-beta portfolio of Black in this case? If the market beta $\beta _{i,M} = 0$ but $\beta _{i,N}>0$, is the expected return on the i asset equal to the riskless rate?

• 5. Solnik (1974) proposed an international asset pricing model (IAPM) based on an international three-fund theorem. What is this theorem and how does it change the CAPM? Write the equation for the IAPM and discuss Solnik’s model.

• 6. How did Adler and Dumas (1984) define currency risk? How is currency risk different than exchange rate risk? How did they propose to measure the exchange risk exposure of a security? Write an equation that can be used to measure this exposure.

• 7. Jorion (1990) investigated the exchange risk exposure of U.S. stocks. He modified the total exchange risk exposure equation of Adler and Dumas (1984) in what way? What did he find?

• 8. Lucas (1978) and Breeden (1979) proposed the consumption CAPM (CCAPM) using the ICAPM framework of Merton (1973). In this model, consumers buy and sell financial assets over time to smooth consumption and maximize lifetime expected utility. What assets will consumers seek? Why? How does it affect the risk premiums on these assets? What happens to other assets?

• 9. Breeden (1979) specified a CCAPM that collapses the multi-beta Merton (1973) ICAPM into a single-beta equation. Write this model and define its variables and parameters. Why did he believe that the CCAPM was a better model than the CAPM from a theoretical perspective as well as in terms of empirical testing? Later work by Breeden et al. (1989) conducted empirical tests of the CCAPM. What did they find?

• 10. Cochrane (1991, 1996) created a production CAPM (PCAPM). How is the PCAPM different from the consumption CAPM (CCAPM)? He tested it using a single factor model. Write the equation for this model and discuss his results. What did he conclude?

• 11. Assume that we scale the market factor with an instrumental lagged variable denoted as $I_{t-1}$. Write a conditional (time-varying) linear function for beta and define its terms. Assuming that the alpha term is conditional also, incorporate this instrument into the market model and discuss the parameters in this conditional form of the market model.

• 12. Does time-variation in beta explain the weak evidence for the CAPM? Discuss empirical results of studies testing conditional CAPMs.

Problems

• 1. Write the ICAPM as a multifactor model with state variables. What could be used to proxy for the state variables?

• 2. Write the market model form of Solnik’s IAPM. Solnik ran this model on 10 major industrialized countries from 1966 to 1971. What did he find? What did cross-sectional regression tests find? What did later authors find in testing the IAPM?

• 3. Assume that you are a U.S. investor buying a European stock:

  • 1. You exchange 100 dollars for 90 euros at the exchange rate 1 USD = 0.90 EUR or 1 EUR = 1.11 USD.

  • 2. You buy 10 shares of a European stock for 90 euros.

  • 3. One year later you sell the European stock for 100 euros. You exchange the 100 euros for 120 dollars at the exchange rate 1 USD = 0.83 EUR or 1 EUR = 1.20 USD.

  What is your stock rate of return? What is your euro rate of return? What is your total return?