Question

Suppose that CAPM holds. Let Rf  denote the risk free rate, E(RM) the expected return of the market portfolio, and sigmaMthe standard deviation of the market portfolio.

Now consider some portfolio on the capital market line, with expected return E(R) and standard deviation sigma_. What is the beta of this portfolio?

Select one:

1. E(R)/sigma

2. sigmaM/sigma

3. sigma/sigmaM

4. E(RM)-Rf

Answer 1

Correct answer: 3. sigma/sigmaM

According to CAPM, Expected return of an Portfolio E(R):

E(R) = Rf + B*[E(RM) – Rf

And,

Expected return of an Portfolio on Capital Market line:

E(R) = Rf + P * [E(RM) – Rf| σM

where,

Op = sigma = Standard deviation of Portfolio

OM = sigmaM = Standard deviation of Market

Now, if CAPM holds and we compare both equation then, Beta of Portfolio on Captial market line would be:

BOM ор

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.