If your portfolio is invested 35 percent each in A and B and 30 percent in C, wh
ID: 2715151 • Letter: I
Question
If your portfolio is invested 35 percent each in A and B and 30 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 4.10 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 3.70 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
Answer:a-1
We 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:
Boom: E(Rp) = .26(.26) + .50(.38) + .24(.55) = .3896 or 38.96%
Normal: E(Rp) = .26(.21) + .50(.19) + .24(.17) = .1904 or 19.04%
Bust: E(Rp) = .26(.05) + .50(-.38) + .24(-.46) = -.2874 or -28.74%
And the expected return of the portfolio is:
E(Rp) = .35(.3896) + .35(.1904) + .3(–.2874) = .11678 or 11.678%
Answer:a-2 Variance:To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, than add all of these up. The result is the variance. So, the variance and standard deviation of the portfolio is:
s2p = .35(.3896 – .11678)2 + .35(.1904 – .11678)2 + .3(–.2874 – .11678)2
s2p = .076956
Answer:a-3 sp = (.076956)1/2 = .2774 or 27.74%
Answer:b
The risk premium is the return of a risky asset, minus the risk-free rate. T-bills are often used as the risk-free rate, so:
RPi = E(Rp) – Rf = .11678 – .0410 = .07578 or 7.578%
Answer:c-1
The approximate expected real return is the expected nominal return minus the inflation rate, so:
Approximate expected real return = .11678 – .037 = .07978 or 7.978%
To find the exact real return, we will use the Fisher equation. Doing so, we get:
1 + E(Ri) = (1 + h)[1 + e(ri)]
1.11678 = (1.0370)[1 + e(ri)]
e(ri) = (1.11678/1.037) – 1 = .07693 or 7.693%
Answer:c-2
The approximate real risk premium is the expected return minus the risk-free rate, so:
Approximate expected real risk premium = .11678 – .0410 = .07578 or 7.578%
The exact expected real risk premium is the approximate expected real risk premium, divided by one plus the inflation rate, so:
Exact expected real risk premium = .07578/1.037 = .073076 or 7.31%