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Unformatted text preview: 5435 And, the weight of the riskfree asset is: wRf = 1 – .5435 = .4565 c. We need to find the portfolio weights that result in a portfolio with an expected return of 9 percent. We also know the weight of the riskfree asset is one minus the weight of the stock since the portfolio weights must sum to one, or 100 percent. So: E(Rp) = .09 = .103wS + .05(1 – wS) .09 = .103wS + .05 – .05wS wS = .7547 So, the β of the portfolio will be: β p = .7547(.92) + (1 – .7547)(0) = 0.694 275 d. Solving for the β of the portfolio as we did in part a, we find: β p = 1.84 = wS(.92) + (1 – wS)(0) wS = 1.84/.92 = 2 wRf = 1 – 2 = –1 The portfolio is invested 200% in the stock and –100% in the riskfree asset. This represents borrowing at the riskfree rate to buy more of the stock. 18. First, we need to find the β of the portfolio. The β of the riskfree asset is zero, and the weight of the riskfree asset is one minus the weight of the stock, the β of the portfolio is: ßp = wW(1.3) + (1 – wW)(0) = 1.3wW So, to find the β of the portfolio for any weight of the stock, we simply multiply the weight of the stock times its β . Even though we are solving for the β and expected return of a portfolio of one stock and the riskfree asset for different portfolio weights, we are really solving for the SML. Any combination of this stock and the riskfree asset will fall on the SML. For that matter, a portfolio of any stock and the riskfree 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) = .138 = .05 + MRP(1.30) MRP = .088/1.3 = .0677 or 6.77% So, now we know the CAPM equation for any stock is: E(Rp) = .05 + .0677β p The slope of the SML is equal to the market risk premium, which is 0.0677. Using these equations to fill in the table, we get the following results: wW 0% 25 50 75 100 125 150 E(Rp) .0500 .0720 .0940 .1160 .1380 .1600 .1820 ßp 0 0.325 0.650 0.975 1.300 1.625 1.950 276 19. There are two ways to correctly answer this question. We will work through both. First, we can use the CAPM. Substituting in the value we are given for each stock, we find: E(RY) = .055 + .068(1.35) = .1468 or 14.68% It is given in the problem that the expected return of Stock Y is 14 percent, but according to the CAPM, the return of the stock based on its level of risk, the expected return should be 14.68 percent. This means the stock return is too low, given its level of risk. Stock Y plots below the SML and is overvalued. In other words, its price must decrease to increase the expected return to 14.68 percent. For Stock Z, we find: E(RZ) = .055 + .068(0.85) = .1128 or 11.28% The return given for Stock Z is 11.5 percent, but according to the CAPM the expected return of the stock should be 11.28 percent based on its level of risk. Stock Z plots above the SML and is undervalued. In other words, its price must increase to decrease the expected return to 11.28 percent. We can also answer this question using the rewardtorisk ratio. All assets must have the same rewardtorisk ratio, that is, every asset must have the same ratio of the asset risk premium to its beta. This follows from the linearity of the SML in Figure 11.11. The rewardtorisk ratio is the risk premium of the asset divided by its β . This is also know as the Treynor ratio or Treynor index. We are given the market risk premium, and we know the β of the market is one, so the rewardtorisk ratio for the market is 0.068, or 6.8 percent. Calculating the rewardtorisk ratio for Stock Y, we find: Rewardtorisk ratio Y = (.14 – .055) / 1.35 = .0630 The rewardtorisk ratio for Stock Y is too low, which means the stock plots below the SML, and the stock is overvalued. Its price must decrease until its rewardtorisk ratio is equal to the market rewardtorisk ratio. For Stock Z, we find: Rewardtorisk ratio Z = (.115 – .055) / .85 = .0706 The rewardtorisk ratio for Stock Z is too high, which means the stock plots above the SML, and the stock is undervalued. Its price must increase until its rewardtorisk ratio is equal to the market rewardtorisk ratio. 20. We need to set the rewardtorisk ratios of the two assets equal to each other (see the previous problem), which is: (.14 – Rf)/1.35 = (.115 – Rf)/0.85 We can cross multiply to get: 0.85(.14 – Rf) = 1.35(.115 – Rf) Solving for the riskfree rate, we find: 0.119 – 0.85Rf = 0.15525 – 1.35Rf 277 Rf = .0725 or 7.25% 278 Intermediate 21. For a portfolio that is equally invested in largecompany stocks and longterm bonds: Return = (11.7% + 6.1%)/2 = 8.95% For a portfolio that is equally invested in small stocks and Treasury bills: Return = (16.4% + 3.8%)/2 = 10.10% 22. We know that the rewardtorisk ratios for all assets must be equal (See Question 19). This can be expressed as: [E(RA) – Rf]/β A = [E(RB) – Rf]/ßB The numerator of each equation is the risk...
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 Spring '10
 eshmalwi
 Finance, Corporate Finance

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