Suppose that the return on a risk-free security is 5 percent. The expected retur

Question

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.

Explanation / Answer

(a) Write down the equation for CML.

Expected Return = Rf + ( Rm- Rf)/Sd of Market * SD of Portfolio

(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).

Expected Return = Rf + ( Rm- Rf)/Sd of Market * SD of Portfolio

14 = 5 + (16-5)/22 * SD of Portfolio

SD of Portfolio = (14-5)*2

SD of Portfolio = 18%

Volatility of this portfolio = 8.47%

Percentage of Investment in  market portfolio in order to create this portfolio  be x

Percentage of Investment in  risk free asset in order to create this portfolio  be (1-x)

14 = 5*(1-x) + 16*x

14 = 5 - 5x + 16x

x = 9/11

x = 81.82%

Percentage of Investment in  market portfolio in order to create this portfolio = 81.82%

Percentage of Investment in  risk free assets in order to create this portfolio = 1-81.82%

Percentage of Investment in  risk free assets in order to create this portfolio = 18.18%

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.

Volatility of the risk-free security = 0

Correlation of the return on the risk-free security and the market portfolio = 0

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