Given that the risk-free rate is 10%, the expected return on the market portfoli

Question

Given that the risk-free rate is 10%, 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.) What is the slope of the capital market line?

B.) You have $100,000 to invest. How should you allocate your wealth among risk free assets and the market portfolio in order to have a 25% expected return?

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

D.) What is the correlation between the portfolio in b) and the market portfolio?

E.) 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 and investing it and your own $100,000 in M. Give the probability distribution of your wealth (in dollars) next period.

Explanation / Answer

A) Slope of Capital Market line = Expected return on the market portfolio - Risk Free rate / Standard deviation

   = 20 - 10 / 20

   = 10 / 20

   = 0.50

Conclusion:- The Slope of Capital market line = 0.50

B) Let A denotes allocation of wealth among risk free asset and (100000 - A) denotes allocation of wealth among market portfolio.

   A * 0. 10 + (100000 - A) * 0. 20 = 0.25 * 100000

0.10 A + 20000 - 0.20 A = 25000

(-) 0.10 A = 5000

A = (-) 50000 [Borrowing]

Conclusion:- $ 50000 is to be borrowed @ 10% and Using this borrowing, total $ 150000 (100000 + 50000) be invested in market portfolio to have a 25% expected return.

C) The standard deviation of your portfolio = 20 %   

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