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1. Suppose you are restricted to investing in a portfolio of only 2 risky securities. The expected return on security A is 5% and the expected return on security B is 7%. The market portfolio, which is a combination of security A and B, has an expected return of 6%.

a.) Show how to construct an optimal portfolio with an expected return of 9%, assuming there is no risk-free asset.

b.) Show how to construct an optimal portfolio with an expected return of 7%, assuming there is a risk-free asset returning 2%.

c.) Suppose you form a portfolio by making a $10 investment in the risk-free asset and a $60 investment in the market-portfolio. What would the risk-free rate have to be if your portfolio has an expected return of 4%?

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Patrina Schowalter
Patrina SchowalterLv2
28 Sep 2019
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Related questions

Suppose that the return on a risk-free security is 5 percent. The expected return on the market portfolio is 16 percent and the volatility of the market portfolio is 22 percent

(a) Write down the equation for CML.

(b) Consider a portfolio on CML such that the expected return on the portfolio is 14 percent. What is the volatility of this portfolio? What percentages of your portfolio you need to invest on the risk-free security and the market portfolio in order to create this portfolio (i.e., the portfolio on the CML with expected return equal to 14 percent).

c) What is the volatility of the risk-free security? What is the correlation of the return on the risk-free security and the market portfolio? Show that the beta of the risk-free security is zero.

A friend says that she expects to earn 13.00% on her portfolio with a beta of 1.50. You have two-asset portfolio including stock X and a risk-free security. The expected return on stock X is 11.00% and the beta is 1.20. The expected return on the risk-free security is 3.00%. You construct a portfolio to match your friend's return. What is the beta of your portfolio? The beta of your portfolio is.xxxx round to two decimal places.

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?

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