Question

Suppose the risk-free rate is 5.2 percent and the market portfolio has an expected return of 11.9 percent. The market portfolio has a variance of .0482. Portfolio Z has a correlation coefficient with the market of .38 and a variance of .3385

According to the capital asset pricing model, what is the expected return on Portfolio Z? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

  

Expected return

????? %

Answer 1

The capital asset pricing model (CAPM) can be used to calculate the required rate of return for any risky asset

The CAPM formula is:

r_z = r_rf+ B_z (r_m-r_rf)

where:

r_rf= the rate of return for a risk-free security ; 5%

r_m = the broad market's expected rate of return ; 11.9%

B_z = beta of the asset

First we need to calculate beta of the asset using the below formula:

Since we do not know the covariance of the stock with respect to the market, we can calculate covariance using the formula:
Correlation coefficient = Covariance (stock, market) / [standard deviation (stock) * Standard deviation (market)]

we have,

0.38 = Covariance (Stock, market) / (0.0482)^0.5 * (0.3385)^0.5 (raised to the power 0.5 to covert variance to standard deviation)

Covariance = 0.38 *  (0.0482)^0.5 * (0.3385)^0.5.

Covariance = 0.048539

Now we can calculate beta

beta = 0.048539 / 0.0482

beta = 1.007023

Now calculating expected returns using CAPM formula

expected return = 5.2% + 1.007023 * (11.9 - 5.2)

= 11.94705%

answer 11.95%