Question

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 6.5 percent and a standard deviation of 9.5 percent. The risk-free rate is 3.5 percent, and the expected return on the market portfolio is 11.5 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a .40 correlation with the market portfolio and a standard deviation of 54.5 percent?

Answer 1

Due to insufficient data provided, we cannot accurately determine the expected rate of return for a security based on its correlation to the market portfolio and its standard deviation, as the calculation requires additional information, such as the market's standard deviation.

Step-by-step explanation:

The student has asked about the expected rate of return for a security with a given correlation to the market portfolio and its own standard deviation, under the assumptions of the Capital Asset Pricing Model (CAPM). According to CAPM, the expected rate of return for any investment is determined by the risk-free rate, the expected return on the market portfolio, and the investment's beta coefficient, which measures its relative volatility compared to the market. The correlation and standard deviation provided for this security doesn't directly give us the beta, but in theory, we could calculate it by using these values if we also had the standard deviation of the market portfolio. However, without more information, we cannot accurately calculate the beta to determine the expected rate of return for this particular security.

Answer 2

Answer: Step 1) Find share of market in the Portfolio

(11.5-3.5)x+3.5=6.5

8x=3

x=3/8

x=0.375

=37.5%

SD of market portfolio= 0.375x+0=9.5

x=9.5/0.375

=25.33%

correl = cov / (std 1 * std2)

0.4=COV/0.2533*0.545

COV= 0.2533*0.545*0.4=0.05

cov of 2 assets = b1 * b2 * variance of market

0.05=B1*1*0.2533^2

B of security=0.0032

Capm Model

3.5+0.0032(11.5-3.5)=3.5256% expected return

Step-by-step explanation:

Step 1) Find the share of market in the portfolio in order to find market SD

Step 2) Find Covariance betweens security and market by using both SDS and correlation

Step 3) Find Beta of Security using Co variance

Step 4) Use the Beta in CAPM model in order to find expected return