Question

In: Finance

Given that the risk-free rate is 5%, the expected return on the market portfolio is 20%,...

Given that the risk-free rate is 5%, the expected return on the market portfolio is 20%, and the standard deviation of returns to the market portfolio is 20%, answer the following questions:

a. You have $100,000 to invest. How should you allocate your wealth between the risk free asset and the market portfolio in order to have a 15% expected return?

b. What is the standard deviation of your portfolio in (a)?

c. Now suppose that you want to have a portfolio, which pays 25% expected return. What is the weight in the risk free asset and in the market portfolio?

d. What do these weights mean: What are you doing with the risk free asset and what are you doing with the market portfolio?

e. What is the standard deviation of the portfolio in c?

f. What is your conclusion about the effect of leverage on the risk of the portfolio?

Solutions

Expert Solution

a

Let the weight of risk free asset = x , so the weight of market portfolio = 1-x

risk free rate = 5% , return on market = 20%, expected return = 15%

Expected return = weight of risk free asset* risk free rate of return + weight of market portfolio* return from market

15% = 5x + (1 -x)20

= 5x + 20 - 20x

15 = 20 - 15x

15x = 5

x = 5/15 = 0.33

y = 1-0.33 = 0.67

Investment in risk free asset = 0.33 * 100000 = $33000

Investment in market portfolio = 0.67*100000 = $ 67000

Answer B:

This portfolio consists of a risk free asset and market portfolio.

The risk free asset has no standard deviation.

Standard deviations of the market portfolio = 20%

So standard deviation of the market portfolio = 20% * 0.67 = 13.4%

Standard deviation of portfolio = SD of risk free asset + SD of market portfolio = 0 + 13.4% = 13.4%

Answer C

Taking the same equation from part A ,

25 = 5x + (1 -x)20

25 = 5x + 20 - 20x

25 = 20 - 15x

5 = -15x

x = - 0.33

The weight of risk free asset = -0.33

The weight of market portfolio = 1.033

Answer D:

A negative asset weight indicates that we have sold the risk less asset to invest in risky asset. Here we have sold off the risk free asset. A negative 0.33 weight of risk free asset mean that we have gone short on this asset and a weight of 1.033 means that we have invested more than 100% in the market portfolio. So the proceeds from the risk free asset plus the investment fund has been invested in the market portfolio. But please note that the total weight of the portfolio assets sum up to 1

Hope this helps!!!!

jeff jeffy answered 5 months ago
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