Suppose a hedge fund invests in a set of very illiquid stocks (which may not even be publicly traded). Because the stocks are illiquid, their price is only observed 15 days af- ter the end of every month. But, they are pretty highly correlated with the stock market other- wise. Finally, because they are illiquid, investors demand a an average risk premium of 0.2% per month.

 

Also assume that the stock market is e????cient, so that Rm,t and Rm,t−1 are statistically indepen- dent. That is, E[Rm,t|Rm,t−1] = E[Rm,t]. Suppose E[Rm,t] = 1% and V ar(Rm,t) = σm2 = 2%, and that Rm,t is i.i.d for all t. Assume the risk free rate is 0.1%.

 

Putting all this information together (and waving our hands a little), we can infer the return to the hedge fund is given by:

Rt,HF = 0.5Rm,t + 0.5Rm,t−1 + 0.2 + εt, (1) where εt has mean zero and standard deviation σε, and cov(εt, Rm,t) = cov(εt, Rm,t−1) = 0.

 

(a) What is the CAPM beta of HF? What is it's alpha?
(b) Is your answer to part (a) a good representation of the fund's true risk exposure to the mar-

ket? If not, what could you do to calculate the true market risk exposure?