Financial management (security risk return and rate)

1- Security A has an expected return of 7 percent a standard deviation of returns of 35 percent, a correlation coefficient with the market of -0.3, and a beta coefficient of -1.5. Security B has an expected return of 12 percent, a standard deviation of returns of 10 percent, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier? Why?

First, we need to find the risk per unit return for each security by using the coefficient of variable or CV.

CV = standard deviation of returns/expected return

For security A,

CV = 35%/7%
CV = 5%

For security B,

CV = 10%/12%
CV = 0.83%

Standard deviation is generally considered a measure of risk. The expected return is a measure of return. So, CV is a measure of risk per unit return. We can see that security A has higher risk per unit of return than security B.

2-An individual has $35,000 invested in a stock which has a beta of 0.8 and $40,000 invested in stock with a beta of 1.4. If these are the only two investment in her portfolio, what is her portfolio's beta?

First, we have to find the weight for the money invested in each stock in her portfolio as follows: -

First stock 35,000/75,000 = 46.67%
Second stock 40,00 0/75,000 = 53.33%
Total 100.00%

Then, we will multiply the weight to each stock's beta: -

First stock 0.8 x 46.67% = 0.37336
Second stock 1.4 x 53.33% = 0.74662
Total portfolio's beta 1.11998

3-Assume that the risk -free rate is 5 percent and the market risk premium is 6 percent. What is the expected return for the overall stock market? What is the required rate of return on a stock that has a beta of 1.2?

market risk premium = expected return for the overall stock market - risk-free rate
6% = X - 5%
11% = X

Then, you need to find the required rate of return for the stock by using the CAPM approach formula.

rs = rf + (rm - rf)b

where rs is the required rate of return for stock
rf is the risk-free rate
rm is the market required rate of return
b is the beta of the stock

Then, you need to replace the information into the equation.

rs = 5.0% + (11% - 5%) x 1.2
rs = 12.2%

PFA