If your portfolio is invested 40 percent each in A and B and 20 percent in C , w
ID: 2711057 • Letter: I
Question
If your portfolio is invested 40 percent each in A and B and 20 percent in C , what is the portfolio expected return? (Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))
What is the variance? (Do not round intermediate calculations and round your final answer to 5 decimal places. (e.g., 32.16161))
What is the standard deviation? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
If the expected T-bill rate is 3.80 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
If the expected inflation rate is 3.50 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations and round your answers 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 and round your answers to 2 decimal places. (e.g., 32.16))
Consider the following information about three stocks:
Explanation / Answer
State of
Economu
Probability
(p)
Stock A
Stock B
Stock C
Return (r)
r*p
Return (r)
r*p
Return (r)
r*p
Boom
0.30
0.20
0.06
0.25
0.075
0.60
0.18
Normal
0.45
0.15
0.0675
0.11
0.0495
0.05
0.0225
Bust
0.25
0.01
0.0025
-0.15
-0.0375
-0.50
-0.125
Expected return = Sum (r*p)
0.13
0.087
0.0775
Answer (a-1)
Weight of stock A in portfolio = weight of stock B in portfolio = 40% or 0.40
Weight of stock C in portfolio = 20% or 0.20
Expected return on portfolio = sum of (weight of stock in portfolio * expected return of stock)
Expected return = 0.40 * 0.13 + 0.40 * 0.087 + 0.20 * 0.0775
= 0.052 + 0.0348 + 0.0155
= 0.1023 or 10.23% (rounded off)
Answer (a-2)
Variance of Portfolio = 0.01438
Answer (a-3)
Standard Deviation of Portfolio = 11.99185% or 12.00% (rounded off)
Answer (b)
Expected T-bill rate = 3.80%
Expected return on portfolio = 10.23%
Expected risk premium on portfolio = 10.23% - 3.80% = 6.43%
Answer (c-1)
Expected inflation rate = 3.50%
Approximate real rate of return = 10.23% - 3.50% = 6.73%
Exact real rate of return = [(1+nominal rate)/(1+inflation rate)] -1
= [(1+0.1023)/(1+0.0350)] -1
= (1.1023/1.0350) – 1
= 1.065024 – 1 = 0.06502 or 6.50% (rounded off)
Answer (c-2)
Expected T-bill rate = 3.80%
Expected inflation rate = 3.50%
Approximate real market risk premium = 10.23% - 3.5% - 3.80% = 2.93%
Exact real market risk premium = 6.50% – 3.80% = 2.70%
State of
Economu
Probability
(p)
Stock A
Stock B
Stock C
Return (r)
r*p
Return (r)
r*p
Return (r)
r*p
Boom
0.30
0.20
0.06
0.25
0.075
0.60
0.18
Normal
0.45
0.15
0.0675
0.11
0.0495
0.05
0.0225
Bust
0.25
0.01
0.0025
-0.15
-0.0375
-0.50
-0.125
Expected return = Sum (r*p)
0.13
0.087
0.0775