FNAN 250 test 3 CHAP 11

A stock has an expected return of 10.80 percent. Based on the following information, what is the stock's return in a boom state of the economy? State of EconomyProbability of Stateof EconomyRate of Return ifState OccursRecession.23−11.1%Normal.26 12.6%Boom.51 ?

E(R) = .1080 = .23(−.111) + .26(.126) + .51XX = .1976, or 19.76%

ou have gathered the following information on your investments. What is the expected return on the portfolio? StockNumber of Shares Price per Share Expected ReturnF 420 $51 13.76%G 370 $37 10.50%H 310 $63 10.92%

Portfolio value = 420($51) + 370($37) + 310($63)Portfolio value = $54,640 Weight of F = 420($51)/$54,640 = .3920Weight of G = 370($37)/$54,640 = .2505Weight of H = 310($63)/$54,640 = .3574 Portfolio expected return = .3920(13.76%) + .2505(10.50%) + .3574(10.92%)Portfolio expected return = 11.93%

A stock has a beta of 1.23 and an expected return of 11.39 percent. If the risk-free rate is 3.8 percent, what is the stock's reward-to-risk ratio?

Reward-to-risk ratio = (.1139 − .038)/1.23Reward-to-risk ratio = .0617, or 6.17%

A stock has a beta of 1.10 and an expected return of 9.36 percent. If the stock's reward-to-risk ratio is 6.41 percent, what is the risk-free rate?

Reward-to-risk ratio = .0641 = (.0936 − Rf)/1.10Rf = .0231, or 2.31%

You have a portfolio that is invested 17 percent in Stock A, 38 percent in Stock B, and 45 percent in Stock C. The betas of the stocks are .62, 1.17, and 1.46, respectively. What is the beta of the portfolio?

βPortfolio = .17(.62) + .38(1.17) + .45(1.46)βPortfolio = 1.21

The risk-free rate is 4.3 percent and the market expected return is 11 percent. What is the expected return of a stock that has a beta of 1.28?

E(R) = .043 + 1.28(.110 − .043)E(R) = .1288, or 12.88%

There is 5 percent probability of recession, 20 percent probability of a poor economy, 48 percent probability of a normal economy, and 27 percent probability of a boom. A stock has returns of −20.7 percent, 4.3 percent, 12.1 percent and 27.8 percent in these states of the economy, respectively. What is the stock's expected return?

E(R) = .05(−.207) + .20(.043) + .48(.121) + .27(.278)E(R) = .1314, or 13.14%

You have a portfolio worth $51,000 that has an expected return of 12.8 percent. The portfolio has $16,400 invested in Stock O, $24,200 invested in Stock P, with the remainder in Stock Q. The expected return on Stock O is 17.6 percent and the expected return on Stock P is 10.8 percent. What is the expected return on Stock Q?

Value in Stock Q = $51,000 − 16,400 − 24,200Value in Stock Q = $10,400 Portfolio expected return = .128 = .176 ($16,400/$51,000) + .108 ($24,200/$51,000) + E(RQ) ($10,400/$51,000) E(RQ) = .0988, or 9.88%

A portfolio consists of $13,400 in Stock M and $18,900 invested in Stock N. The expected return on these stocks is 8.50 percent and 11.60 percent, respectively. What is the expected return on the portfolio?

Weight of M = $13,400/($13,400 + 18,900)Weight of M = .4149 Portfolio expected return = .4149(8.5%) + (1 - .4149)(11.6%)Portfolio expected return = 10.31%

You own 410 shares of Stock X at a price of $39 per share, 280 shares of Stock Y at a price of $62 per share, and 345 shares of Stock Z at a price of $85 per share. What is the portfolio weight of Stock Y?

Weight of Y = 280($62)/[410($39) + 280($62) + 345($85)]Weight of Y = .2770

You own a portfolio that has a total value of $180,000 and it is invested in Stock D with a beta of .90 and Stock E with a beta of 1.32. The beta of your portfolio is equal to the market beta. What is the dollar amount of your investment in Stock D?

βPortfolio = 1.0 = .90wD + (1 − wD)(1.32)wD = .762Dollar investment in Stock D = .761905($180,000)Dollar investment in Stock D = $137,142.86

Your portfolio has a beta of 1.66. The portfolio consists of 17 percent U.S. Treasury bills, 24 percent Stock A, and 59 percent Stock B. Stock A has a risk level equivalent to that of the overall market. What is the beta of Stock B?

βPortfolio = 1.66 = .17(0) + .24(1.0) + .59βB1.66 = .24 + .59βBβB = 2.41The beta of a risk-free asset, i.e., a U. S. Treasury bill, is zero.The beta of the market is 1.0.

You have a portfolio that is equally invested in Stock F with a beta of 1.10, Stock G with a beta of 1.47, and the market. What is the beta of your portfolio?

βPortfolio = 1/3(1.10) + 1/3(1.47) + 1/3(1)βPortfolio = 1.19

The expected return on HiLo stock is 14.80 percent while the expected return on the market is 13.8 percent. The beta of HiLo is 1.27. What is the risk-free rate of return?

E(R) = .1480 = Rf + 1.27[.138 − Rf].1480 = Rf + .1753 − 1.27Rf.27Rf = .0273Rf = .1010, or 10.10%

You recently purchased a stock that is expected to earn 18 percent in a booming economy, 13 percent in a normal economy, and lose 4 percent in a recessionary economy. There is 21 percent probability of a boom, 68 percent chance of a normal economy, and 11 percent chance of a recession. What is your expected rate of return on this stock?

E(R) = .21(.18) + .68(.13) + .11(-.04)E(R) = .1218, or 12.18%

The common stock of Flavorful Teas has an expected return of 21.42 percent. The return on the market is 15 percent and the risk-free rate of return is 4.3 percent. What is the beta of this stock?

E(R) = .2142 = .043 + β(.150 − .043).1712 = .107ββ = 1.60

A stock will have a loss of 12.2 percent in a bad economy, a return of 12 percent in a normal economy, and a return of 25.9 percent in a hot economy. There is 22 percent probability of a bad economy, 25 percent probability of a normal economy, and 53 percent probability of a hot economy. What is the variance of the stock's returns?

E(R) = .22(−0.122) + .25(0.12) + .53(0.259)E(R) = .1404, or 14.04% σ2 = .22(−0.122 − .1404)2 + .25(0.12 − .1404)2 + .53(0.259 − .1404)2σ2 = .02271

A stock will have a loss of 13.1 percent in a recession, a return of 11.8 percent in a normal economy, and a return of 26.5 percent in a boom. There is 28 percent probability of a recession, 41 percent probability of normal economy, and 31 percent probability of boom. What is the standard deviation of the stock's returns?

E(R) = .28(−.131) + .41(.118) + .31(.265)E(R) = .0939, or 9.39% σ2 = .28(−.131 − .0939)2 + .41(.118 − .0939)2 + .31(.265 − .0939)2σ2 = .02348 σ = .023481/2σ = .1532, or 15.32%

If the economy booms, Meyer&Co. stock will have a return of 20.6 percent. If the economy goes into a recession, the stock will have a loss of 12.9 percent. The probability of a boom is 65 percent while the probability of a recession is 35 percent. What is the standard deviation of the returns on the stock?

E(R) = .65(.206) + .35(-.129)E(R) = .0888, or 8.88% σ2 = .35(−.129 - .0888)2 + .65(.206 - .0888)2σ2 = .025531 σ = .0255311/2σ = .1598, or 15.98%

If the economy booms, RTF, Inc., stock is expected to return 13 percent. If the economy goes into a recessionary period, then RTF is expected to only return 2 percent. The probability of a boom is 82 percent while the probability of a recession is 18 percent. What is the variance of the returns on RTF, Inc., stock?

E(R) = .82(.13) + .18(.02)E(R) = .1102 σ2 = .82(.13 - .1102)2 + .18(.02 - .1102)2σ2 = .000321 + .001464σ2 = .001786

A portfolio consists of 185 shares of Stock C that sells for $39 and 150 shares of Stock D that sells for $41. What is the portfolio weight of Stock C?

Weight of C = 185($39)/[185($39) + 150($41)]Weight of C = .5398