The market portfolio has an expected return of 12.8 percent and a standard devia
ID: 2740875 • Letter: T
Question
The market portfolio has an expected return of 12.8 percent and a standard deviation of 22.8 percent. The risk-free rate is 5.8 percent.
What is the expected return on a well-diversified portfolio with a standard deviation of 9.8 percent? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
What is the standard deviation of a well-diversified portfolio with an expected return of 20.8 percent? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
a.
What is the expected return on a well-diversified portfolio with a standard deviation of 9.8 percent? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Explanation / Answer
SD of market portfolio = 22.80%
SD implies with total risk of a portfolio i.e., it gives a sum of Systematic risk as well as Unsystematic risk.
Unsystematic risk of market portfolio = 0
Hence systematic risk of market portfolio = 22.80%
Also, it is well known that systematic risk implies Beta of portfolio
Now, using the equation of expected return,
Expected return of market portfolio = Rf + Beta x (Rm-Rf)
12.80 = 5.80 + [22.80 x (Rm-5.80)]
7 = 22.80Rm - 132.24
Rm = 6.1070....%
a. Now, since we have a well diversified portfolio, the unsystematic risk of this portfolio will be 0 as well.
Therefore, we have the Beta of this portfolio as = 9.80%
Expected return on well diversified portfolio = Rf + Beta (Rm-Rf)
= 5.80 + 9.80 x (6.1070-5.80)
= 8.81%
b. Standard deviation of well diversified portfolio will be Beta of that portfolio
Expected return = Rf + Beta x (Rm - Rf)
20.80 = 5.80 + Beta x (6.1070-5.80)
Beta = 48.86%
Standard deviation of well diversified portfolio = 48.86%
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