If your portfolio is invested 25 percent each in A and B and 50 percent in C, wh
ID: 2764006 • Letter: I
Question
If your portfolio is invested 25 percent each in A and B and 50 percent in C, what is the portfolio expected return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
What is the variance? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)
What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
If the expected T-bill rate is 4.30 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
If the expected inflation rate is 3.90 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
What are the approximate and exact expected real risk premiums on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Consider the following information about three stocks:Explanation / Answer
This portfolio does not have an equal weight in each asset. We first need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get:
To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then sum.The result is the variance. So, the variance and standard deviation of the portfolio is:
b.If the expected T-bill rate is 4.30 percent, what is the expected risk premium on the portfolio?
= Rm - rf = 10.9%-4.3% =6.6%
c-1. The approximate expected real return is the expected nominal return minus the inflation rate, so:
Approximate expected real return = .1009– .039=0.07 7%
c-2.The approximate real risk premium is the expected return minus the risk-free rate, so:
Boom: E(Rp) = .25(.30) + .25(.42) + .50(.58) = 0.47 Normal: E(Rp) = .25(.23) + .25(.21) + .50(.19) = 0.205 Bust: E(Rp) = .25(.01) + .25(-.22) + .50(-.50) = -0.3025 And the expected return of the portfolio is: E(Rp) = .22(.47) + .46(.205) + .32(–.3025) = 0.1009 or 10.09%