Finance Management Chapter 11 - FIN 780
What is the variance of a portfolio consisting of $3,500 in stock G and $6,500 in stock H. Economy | Probability | Returns, G - H Boom | 15% | 15% - 9% Normal | 85% | 8% - 6%
0.000247 E(r)Boom = [$3,500 ÷ ($3,500 + $6,500) × .15)] + [$6,500 ÷($3,500 + $6,500) × .09) = .0525 + .0585= .111 E(r)Normal = [$3,500 ÷($3,500 + $6,500) × .08)] + [$6,500 ÷($3,500 + $6,500) × .06) = .028 + .039= .067 E(r)Portfolio = (.15 × .111) + (.85 × .067) = .01665 + .05695 = .0736 VarPortfolio = [.15 × (.111 - .0736)2] + [.85 × (.067 - .0736)2] = .000209814 + .000037026 = .00024684 = .000247
What is the beta of a portfolio comprised of the following securities? Amount Security Stock | Amount Invested | Security Beta A | $2,000 | 1.2 B | $3,000 | 1.46 C | $5,000 | 0.72
1.038 ValuePortfolio = $2,000 + $3,000 + $5,000 = $10,000 BetaPortfolio = ($2,000 ÷ $10,000 × 1.20) + ($3,000 ÷ $10,000 × 1.46) + ($5,000 ÷ $10,000 × .72) = .24 + .438 + .36 = 1.038
The common stock of Flavorful Teas has an expected return of 14.4%. The return on the market is 10% and the risk-free rate of return is 2.5%. What is the beta of this stock?
1.59 E(r) = .144 = .025 + b × (.10 - .025); .119 = .075b; b 1.5866666 = 1.59
Your portfolio has a beta of 1.18. The portfolio consists of 20% U.S. Treasury bills, 30% in stock A, and 50% in stock B. Stock A has a risk-level equivalent to that of the overall market. What is the beta of stock B?
1.76 BetaPortfolio = 1.18 = (.20 × 0) + (.30 × 1.0) + (.50 × bB) = 0 + .3 + .50bB; .88 = .50bB; bB = 1.76 The beta of a risk-free asset is zero. The beta of the market is 1.0.
The risk-free rate of return is 3.5% and the market risk premium is 7.5%. What is the expected rate of return on a stock with a beta of 1.28?
13.10% E(r) = .035 + (1.28 × .075) = .1310 = 13.10%
Kurt's Adventures, Inc. stock is quite cyclical. In a boom economy, the stock is expected to return 30% in comparison to 12% in a normal economy and a negative 20% in a recessionary period. The probability of a recession is 15%. There is a 30% chance of a boom economy. The remainder of the time the economy will be at normal levels. What is the standard deviation of the returns on Kurt's Adventures, Inc. stock?
15.38% E(r) = (.30 × .30) + (.55 × .12) + (.15 × -.20) = .09 + .066 - .03 = .126 Var = .30 × (.30 - .126)2 + .55 × (.12 - .126)2 + .15 × (-.20 - .126)2 = .0090828 + .0000198 + .0159414 = .025044 Std dev = √.025044 = .15825 = 15.83%
You own the following portfolio of stocks. What is the portfolio weight of stock C? Number Price. Stock | # of shares | $ per share| A | 100 | $22 B | 600 | $17 C | 400 | $46 D | 200 | $38
47.9% Portfolio weightC = (400 × $46) ÷ [(100 × $22) + (600 × $17) + (400 × $46) + (200 × $38)] = $18,400 ÷ $38,400 = 47.9%
The Inferior Goods Co. stock is expected to earn 13% in a recession, 7% in a normal economy, and lose 6% in a booming economy. The probability of a boom is 20% while the probability of a normal economy is 55% and the chance of a recession is 25%. What is the expected rate of return on this stock?
5.90% E(r) = (0.20 x -0.06) + (0.55 x 0.07) + (0.25 x 0.13) = -0.012 + 0.0385 + 0.0325 = 0.059
What is the expected return on a portfolio which is invested 20% in stock A, 50% in stock B, and 30% in stock C? Economy | Probability | Returns, A - B - C Boom | 20% | 18% - 9% - 6% Normal | 70% | 11% - 7% - 9% Recession | 10% | -10% - 4% - 13%
8.25% E(r)Boom = (.20 × .18) + (.50 × .09) + (.30 × .06) = .036 + .045 + .018 = .099 E(r)Normal = (.20 × .11) + (.50 × .07) + (.30 × .09) = .022 + .035 + .027 = .084 E(r)Bust = (.20 × -.10) + (.50 × .04) + (.30 × .13) = -.020 + .020 + .039 = .039 E(r)Portfolio = (.20 × .099) + (.70 × .084) + (.10 × .039) = .02376 + .0588 + .0039 = .0825 = 8.25%
You have a portfolio consisting of stock A and Stock B. The portfolio has an expected return of 11.2%. Stock A has an expected return of 12% while stock B is expected to return 7%. What is the portfolio weight of stock A?
84% ".112" = [.12 × x] + [.07 × (1 - x)] = .12x + .07 - .07x; .042 =.05x; x = 84%
