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Assume that two investments are combined in a portfolio.

a. In words, what is the expected rate of return on the portfolio?

b. What condition must be present for the portfolio to have lower risk
than the weighted average of the two investments?

c. Is it possible for the portfolio to have lower risk than that of either
investment?

d. Is it possible for the portfolio to be riskless? If so, what condition
is necessary to create such a portfolio?

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Elin Hessel
Elin HesselLv2
28 Sep 2019

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As part of our portfolio management chapter, we discussed diversification benefits. We said that when two stocks are combined into a portfolio, we end up with a portfolio that has a better return and better risk than the best of the two stocks. Any reasonable person would expect to have an average return and average risk when two securities are combined into a portfolio. How is it even possible to have a portfolio that has lower risk than the best of the two securities included into the portfolio?

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.

1.a) You want to create a portfolio equally as risky as the market, and you have $500,000 to invest. Information about the possible investments is given below:

Asset Investment Beta
Stock A $133,310 0.8
Stock B $141,185 1.36
Stock C -- 1.48
Risk-free asset -- --

How much must you invest in Stock C?

1.b) Your portfolio has a beta of 0.9. The portfolio consists of 15 percent U.S. Treasury bills, 30 percent stock A, and 55 percent stock B. Stock A has a risk level equivalent to that of the overall market. What is the beta of stock B?

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