Question

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 7.9 percent and a standard deviation of 10.9 percent. The risk-free rate is 4.9 percent, and the expected return on the market portfolio is 12.9 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a .54 correlation with the market portfolio and a standard deviation of 55.9 percent? (Do not round Intermedlate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

To calculate the expected rate of return for the security in question, we derive its beta using the provided correlation and standard deviation, then apply the CAPM formula, which includes the risk-free rate and the premium for taking on additional risk as compared to the market.

Step-by-step explanation:

The student's question involves calculating the expected rate of return for a security with a known correlation with the market portfolio, given the risk-free rate, the return of the market portfolio, and the standard deviation of the security. Using the Capital Asset Pricing Model (CAPM), we can establish the relationship between risk and return, which shows that the return of a security is a function of the risk-free rate plus a premium based on the systematic risk of the security (represented by beta) compared to the market. In this case, we use the provided correlation coefficient to derive beta, which then allows us to compute the expected rate of return for the security.

To solve this, we first need to find the beta of the security using the formula:

Beta = (Correlation with market portfolio × Security's standard deviation) / Market's standard deviation

Once we have beta, we can plug it into the CAPM formula:

Expected rate of return = Risk-free rate + (Beta × (Market return - Risk-free rate))

With the calculated beta, risk-free rate, and market return, we will be able to find the expected rate of return for the security.