Answer to Question #114364 in Financial Math for dima hajj

Question

An investor is forming a portfolio by investing $50,000 in stock A that has a beta of 1.50, and $25,000 in stock B that has a beta of 0.90. The return on the market is equal to 6 percent and Treasury bonds have a yield of 4 percent. What is the required rate of return on the investor’s portfolio?

Answer 1

According to the capital asset pricing model the expected return from a stock or an investment is estimated using the following formula:

$\text{Expected return}=\text{Risk free rate}+(\text{Market return-Risk free rate} ) \times \beta$

The beta factor will be estimate as follows:

$\text{Weight}_\text{Stock A}=\dfrac{50,000}{50,000+25,000}=\dfrac{2}{3}$

$\text{Weight}_\text{Stock B}=\dfrac{25,000}{50,000+25,000}=\dfrac{1}{3}$

The beta to be used in calculation of the expected return will therefore be:

$\beta_{\text{Portfolio} }=\dfrac{2}{3} \times 1.5+\dfrac{1}{3}\times 0.9=1.3$

$\text{Expected return}=4\%+(6\%-4\% ) \times 1.3$

$\text{Expected return}=6.6\%$

Note that the risk free rate is take to be equal to the treasury bills rate since treasury bills are said to be free from risks.

​