A portfolio that combines the risk-free asset and the market portfolio has an expected return of 22 percent and a standard deviation of 5 percent. The risk-free rate is 4.9 percent, and the expected return on the market portfolio is 19 percent. Assume the capital-asset-pricing model holds.
Question: What expected rate of return would a security earn if it had a 0.6 correlation with the market portfolio and a standard deviation of 3 percent?
First, we must calculate the standard deviation of the market portfolio using the Capital Market Line (CML):
The risk-free rate asset has a return of 4.9% and a standard deviation of zero and the portfolio has an expected return of 22% and a standard deviation of 5%. These two points must lie on the Capital Market Line.
The slope of the Capital Market Line is:
Slope of CML = Increase in Expected Return / Increase in Standard Deviation
= (0.22- ...
In about 350 words, this solution explains the calculation for the expected rate of return of a security given its correlation with the market. All calculations are provided.