Please assist with Part A and Part B. Thank you. You believe that security Z has
ID: 1123544 • Letter: P
Question
Please assist with Part A and Part B. Thank you.
You believe that security Z has an expected rate of return (r) of 15 percent. It has a beta (B) of 1.5. The risk-free rate of return (r) is 5 percent and the market expected rate of return (rm) is 9 percent. a) Is this security priced correctly according to the Capital Asset Pricing Model? Explain your answer in detail. (b) Suppose now that the market portfolio has a standard deviation equal to "1-4, and that your utility function is U = -2, where re and , are the expected rate of return and standard deviation of your portfolio, where x is the share of your portfolio invested in the market portfolio and (1-x) is the share invested in the risk-free asset. What is the optimal (utility- maximizing value forx?Explanation / Answer
1
According to CAPM, required return=risk free+beta*(market return-risk free)=5%+1.5*(9%-5%)=11%
The security is not properly priced as per CAPM model as the expected return is more than the required return. The security is underpriced or undervlaued as expected return is more than the required return
2
Standard deviaiton of portoflio=x*4%
Expected return of the portoflio=x*9%+(1-x)*5%=5%+4%*x
So, U=0.05+0.04x-2*0.0016*x^2
To maximize, differentiating U w.r.t. x, we get
dU/dx=0.04-0.0064x
Setting dU/dx to zero, we get x=100/16=6.25
d2U/dx2=-0.04
As second differentiation is negative, Utility is maximised at x=6.25
hence, x=6.25 or 625%