Asset W has an expected return of 13.2 percent and a beta of 1.29. If the risk-f

Question

Asset W has an expected return of 13.2 percent and a beta of 1.29. If the risk-free rate is 4.54 percent, complete the following table for portfolios of Asset W and a risk-free asset. (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Enter your portfolio expected return answers as a percentage and round to 2 decimal places (e.g., 32.16). Round your portfolio beta answers to 3 decimal places (e.g., 32.161).)

Percentage of Portfolio Portfolio Portfolio in Asset W Expected Return Beta 0%    % 25       % 50       % 75       % 100       % 125       % 150       %

Explanation / Answer

Answer: First, we need to find the b of the portfolio. The b of the risk-free asset is zero, and the weight of the risk-free asset is one minus the weight of the stock, so the b of the portfolio is:

= XW(1.29) + (1 - XW)(0) = 1.29XW

So, to find the b of the portfolio for any weight of the stock, we simply multiply the weight of the stock times its b.

Even though we are solving for the b and expected return of a portfolio of one stock and the risk-free asset for different portfolio weights, we are really solving for the SML. Any combination of this stock and the risk-free asset will fall on the SML. For that matter, a portfolio of any stock and the risk-free asset, or any portfolio of stocks, will fall on the SML. We know the slope of the SML line is the market risk premium, so using the CAPM and the information concerning this stock, the market risk premium is:

E(RW) = .132 = .0454 + MRP(1.29)

MRP = .0866/1.29 = .06713, or 6.71%

So, now we know the CAPM equation for any stock is:

   E(Rp) = .0454 + .0671bp

The slope of the SML is equal to the market risk premium, which is 0.0671. Using these equations to fill in the table, we get the following results:  

XW            E(Rp)          ?

Percentage of Portfolio in Asset W Portfolio expected return Portfolio Beta 0% 0.0454 0 25% 0.067 0.3225(1.29*25%) 50% 0.0887 0.645 (1.29*50%) 75% 0.11031 0.9675 (1.29*75%) 100% 0.1319 1.29 (1.29*100%) 150% 0.1752 1.935 (1.29*150%)

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