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

Question

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.Suppose that the market pays either 40% or 0% each with probability one half. You alter your portfolio to a more risky level by borrowing $50,000 at the risk free rate and investing it and your own $100,000 in the market portfolio. Give the probability distribution of your wealth (in dollars) next period.

Explanation / Answer

a. Let the percentage of amount to be invest in market portfolio x, then the percentage of amount to be invest in risk-free asset is 1-x. Thus,

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

x = 0.67

Thus, $66,667 should be invested in market portfolio and $33,333 in risk-free security.

b. Standard deviation of the portfolio = 0.67 x 20% = 13.33%

c. Probability distribution of wealth

50%: (150,000 x 140%) - (50,000 x 105%) = $157,500
50%: (150,000 x 100%) - (50,000 x 105%) = $97,500

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