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11 Jun 2019

Consider a risky portfolio that offers a rate of return of 15% per year with a standard deviation of 20% per year. Suppose an investor is indifferent between investing in the risky portfolio and investing in a risk free asset earning 8% per year.
a) What is the investor's risk aversion coefficient?
b) If allowed to invest in a combination of the risky portfolio and the risk free asset, what proportion would the investor hold in the risky portfolio?
c) What is the expected rate of return and the standard deviation of the rate of return on the optimally chosen combination?
d) What would be the investor's certainty equivalent return for the optimally chosen combination?

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Collen Von
Collen VonLv2
11 Jun 2019

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2. Suppose that you have a risky asset that provides you with an expected return of 12% per year with 20% volatility (standard deviation). Con-sider a risk-free asset that provides you with a 3% risk-free return.

(a) If you have $100,000 and invest 80% into the risky asset and 20% into the risk-free asset, what is the expected return and risk of your portfolio?

(b) How much will your portfolio be worth if the realized return on the risky asset is 15%?

(c) If you cannot borrow money, what is the maximum possible ex-pected return on your portfolio, and what is the minimum?

(d) If you are allowed to borrow money at the risk-free rate, how can you get a portfolio with an 18% expected return and what is the risk of this portfolio?

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return on 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is 0.4. The T-Bill rate of return is 5%.

A) The portion of the optimal risky portfolio that should be invested in stock B is what?

B) What is the expected return on the optimal risky portfolio?

C) Investors wants to have an expected return of 10% for a complete portfolio. What proportion of his investment is in T-Bills?

D) What proportion of the investor's complete portfolio is in stock A and in stock B?

1. Consider a portfolio P comprised of two risky assets (A andB) whose returns have a correlation of zero. Risky asset A has anexpected return of 10% and standard deviation of 15%. Risky asset Bhas an expected return of 7% and standard deviation of 11%.Assuming a risk-free rate of 2.5%, what is the standard deviationof returns on the optimal risky portfolio?

a) 9.18%

b) .918%

c) .84%

d) 8.42%

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