Question

A portfolio is made out of 20% Treasury bills and 80% market index. If the market risk premium is 11% and the risk-free rate is 2%, what is the expected return on this portfolio according to CAPM? Enter your answer as a percentage point without the % sign, and round it to the first decimal place (i.e., if the answer is 10.3456%, enter it as 10.3).

Answer 1

CAPM: E(Ri) = Rf + βi*MRP

where Rf = risk-free rate = 2%

& MRP = market risk premium = 11%

TREASURY BILLS:

β is the covariance of the return of an asset with the return of the benchmark divided by the variance of the return of the benchmark over a certain period.

Since the covariance of the return of T-bills with the return of the market index is zero, its β will also be zero.

βt = 0

E(Rt) = Rf + βt*MRP = 2%

MARKET INDEX

Since the returns of a market index are perfectly correlated with the returns of the market itself, the covariance of the return of market index with the return of the market is equal to the market variance.

β = Covar(Ri, Rm) / σm^2 = σm^2 / σm^2 = 1

Consequently, its β will also be 1.

E(Rmi) = Rf + βmi*MRP = 2% + 1*11% = 13%

Expected return of a portfolio are given by

E(Rp) = w1*E(R1) + w2*E(R2)

E(Rp) = 20%*2% + 80%*13% = 10.80%