Fin 380 - Ch 13 Test practice

99. You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 13 percent and Stock Y with an expected return of 8 percent. Your goal is to create a portfolio with an expected return of 12.4 percent. All money must be invested. How much will you invest in stock X?

$8,800 E(Rp) = 0.124 = .13x + .08(1 - x); x = 88 percent Investment in Stock X = 0.88($10,000) = $8,800

75. What is the variance of the returns on a portfolio that is invested 60 percent in stock S and 40 percent in stock T? state probability return S T boom 20% 17% 7% normal 80% 13% 10%

.000023 E(r)Boom = (0.60 0.17) + (0.40 0.07) = 0.13 E(r)Normal = (0.60 0.13) + (0.40 0.10) = 0.118 E(r)Portfolio = (0.20 0.13) + (0.80 0.118) = 0.1204 VarPortfolio = 0.20 (0.13 - 0.1204)2] + 0.80 (0.118 - 0.1204)2 = .000023

76. What is the variance of the returns on a portfolio comprised of $5,400 of stock G and $6,600 of stock H? state probability return G H boom 36% 21% 13% normal 64% 13% 7%

.001097 E(r)Boom = [$5,400/($5,400 + $6,600)][0.21] + [($6,600/($5,400 + $6,600)][0 .13] = 0.166 E(r)Normal = [$5,400/($5,400 + $6,600)][0.13] + [$6,600/($5,400 + $6,600)][0.07] = 0.097 E(r)Portfolio = (0.36 0.166) + (0.64 0.097) = 0.12184 VarPortfolio = [0.36 (0.166 - 0.12184)2] + [0.64 (0.097 - 0.12184)2] = 0.001097

65. The rate of return on the common stock of Lancaster Woolens is expected to be 21 percent in a boom economy, 11 percent in a normal economy, and only 3 percent in a recessionary economy. The probabilities of these economic states are 10 percent for a boom, 70 percent for a normal economy, and 20 percent for a recession. What is the variance of the returns on this common stock?

0.002244 E(r) = (0.10 0.21) + (0.70 0.11) + (0.20 0.03) = 0.104 Var = 0.10 (0.21 - 0.104)2 + 0.70 (0.11 - 0.104)2 + 0.20 (0.03 - 0.104)2 = 0.002244

64. If the economy is normal, Charleston Freight stock is expected to return 15.7 percent. If the economy falls into a recession, the stock's return is projected at a negative 11.6 percent. The probability of a normal economy is 80 percent while the probability of a recession is 20 percent. What is the variance of the returns on this stock?

0.011925 Var = 0.80 (0.157 - 0.1024)2 + 0.20 (-0.116 - 0.1024)2 = 0.011925

78. What is the standard deviation of the returns on a $30,000 portfolio which consists of stocks S and T? Stock S is valued at $12,000. state probability return S T boom 5% 11% 5% normal 85% 8% 6% recession 10% -5% 8%

1.22 percent E(r)Boom = [$12,000/$30,000] [0.11] + [($30,000 - $12,000)/$30,000] [0.05] = 0.074 E(r)Normal = [$12,000/$30,000] [0.08] + [($30,000 - $12,000)/$30,000] [0.06] = 0.068 E(r)Bust = [$12,000/$30,000] [-0.05] + [($30,000 - $12,000)/$30,000] [0.08] = 0.028 E(r)Portfolio = (0.05 0.074) + (0.85 0.068) + (0.10 0.028) = 0.0643 VarPortfolio = [0.05 (0.074 - 0.0643)2] + [0.85 (0.068 - 0.0643)2] + [0.10 (0.028 - 0.0643)2] = .000148111 Std dev = 0.000148111 = 1.22 percent

77. What is the standard deviation of the returns on a portfolio that is invested 52 percent in stock Q and 48 percent in stock R? state probability return Q R boom 10% 14% 16% normal 90% 8% 11%

1.66 percent E. 3.41 percent E(r)Boom = (0.52 0.14) + (.0.48 0.16) = 0.1496 E(r)Normal = (0.52 0.08) + (0.48 0.11) = 0.0944 E(r)Portfolio = (0.10 .0.1496) + (0.90 0.0944) = 0.09992 VarPortfolio = [0.10 (0.1496 - 0.09992)2] + [0.90 (0.0944 - 0.09992)2] = 0.000274 Std dev = 0.000274 = 1.66 percent

62. You are comparing stock A to stock B. Given the following information, what is the difference in the expected returns of these two securities? state of economy probability of state Rate o Return A / B normal 45% 14% / 17% recession 55% -22% / -28%

1.95 percent E(r)A = (0.45 0.14) + (0.55 -0.22) = -5.80 percent E(r)B = (0.45 0.17) + (0.55 -0.28) = -7.75 percent Difference = -5.80 percent - (-7.75 percent) = 1.95 percent

73. What is the expected return on a portfolio that is equally weighted between stocks K and L given the following information? state of economy probality returns K L boom 25% 16% 13% normal 75% 12% 8%

11.13 percent E(r) = 0.25[(0.16 + 0.13)/2] + 0.75[(0.12 + 0.08)/2] = 11.13 percent

72. What is the expected return on this portfolio? stock return # shares $/stock A 12% 300 $28 B 7% 500 10 C 15% 600 13

11.92 percent Portfolio value = (300 $28) + (500 $10) + (600 $13) = $8,400 + $5,000 + $7,800 = $21,200; E(r) = ($8,400/$21,200) (0.12) + ($5,000/$21,200) (0.07) + ($7,800/$21,200) (0.15) = 11.92 percent

98. You own a portfolio that has $2,000 invested in Stock A and $1,400 invested in Stock B. The expected returns on these stocks are 14 percent and 9 percent, respectively. What is the expected return on the portfolio?

11.94 percent E(Rp) = [$2,000/($2,000 + $1,400)] [0.14] + [$1,400/($2,000 + $1,400)] [0.09] = 11.94 percent

102. Your portfolio is invested 26 percent each in Stocks A and C, and 48 percent in Stock B. What is the standard deviation of your portfolio given the following information? state probability rate A B C boom .25 .25 .25 .45 good .25 .10 .13 .11 poor .25 .03 .05 .05 bust .25 -.04 -.09 -.09

13.73 percent E(Rp)Boom = 0.26(0.25) + 0.48(0.25) + 0.26(0.45) = 0.302 E(Rp)Good = 0.26(0.10) + 0.48(0.13) + 0.26(0.11) = 0.117 E(Rp)Poor = 0.26(0.03) + 0.48(0.05) + 0.26(0.05) = 0.0448 E(Rp)Bust = 0.26(-0.04) + 0.48(-0.09) + 0.26(-0.09) = -0.077 E(Rp) = 0.25(0.302) + 0.25(0.117) + 0.25(0.0448) + 0.25(-0.077) = 0.0967 p2 = 0.25(0.302 - 0.0967)2 + 0.25(0.117 - 0.0967)2 + 0.25(0.0448 - 0.0967)2 + 0.25(-0.077 - 0.0967)2 = 0.018856 p = 0.018856 = 13.73 percent

74. What is the expected return on a portfolio comprised of $6,200 of stock M and $4,500 of stock N if the economy enjoys a boom period? state probability return M N boom 14% 23% 5% normal 80% 13% 9% recession 6% -31% 18%

15.43 percent E(r)Boom = [$6,200/($6,200 + $4,500)][0.23] + [$4,500/($6,200 + $4,500)] [0.05] = 15.43 percent

100. What is the expected return and standard deviation for the following stock? state probability rate recession .10 -.19 normal .60 .14 boom .30 .35

17.00 percent; 15.24 percent E(R) = 0.10(-0.19) + 0.60(0.14) + 0.30(0.35) = 17.00 percent 2 = 0.10(-0.19 - 0.17)2 + 0.60(0.14 - 0.17)2 + 0.30(0.35 - 0.17)2 = 0.02322 = 0.02322 = 15.24 percent

101. What is the expected return of an equally weighted portfolio comprised of the following three stocks? state probability rate A B C boom .64 .19 .13 .31 bust .36 .15 .11 .17

18.60 percent E(Rp)Boom = (0.19 + 0.13 + 0.31)/3 = 0.21 E(Rp)Bust = (0.15 + 0.11 + 0.17)/3 = 0.1433 E(Rp) = 0.64(0.21) + 0.36(0.1433) = 18.60 percent

66. The returns on the common stock of New Image Products are quite cyclical. In a boom economy, the stock is expected to return 32 percent in comparison to 14 percent in a normal economy and a negative 28 percent in a recessionary period. The probability of a recession is 25 percent while the probability of a boom is 10 percent. What is the standard deviation of the returns on this stock?

19.94 percent E(r) = (0.10 0.32) + (0.65 0.14) + (0.25 -0.28) = 0.053 Var = 0.10 (0.32 - 0.053)2 + 0.65 (0.14 - 0.053)2 + 0.25 (-0.28 - 0.053)2 = 0.039771 Std dev = 0.039771 = 19.94 percent

67. What is the standard deviation of the returns on a stock given the following information? state of economy probability rate o return boom 30% 15% normal 65% 12% recession 5% 6%

2.03 percent E(r) = (0.30 0.15) + (0.65 0.12) + (0.05 0.06) = 0.126 Var = 0.30 (0.15 - 0.126)2 + 0.65 (0.12 - 0.126)2 + 0.05 (0.06 - 0.126)2 = 0.000414 Std dev = 0.000414 = 2.03 percent

40. How many diverse securities are required to eliminate the majority of the diversifiable risk from a portfolio?

25

106. Consider the following information on three stocks: state probability rate A B C boom .45 .55 .25 .65 normal .50 .44 .18 .04 bust .05 .37 -.17 -.64

29.99 percent E(Rp)Boom = 0.35(0.55) + 0.35(0.35) + 0.30(0.65) = 0.51 E(Rp)Normal = 0.35(0.44) + 0.35(0.18) + 0.30(0.04) = 0.229 E(Rp)Bust = 0.35(0.37) + 0.35(-0.17) + 0.30(-0.64) = -0.122 E(Rp) = 0.45(0.51) + 0.50(0.229) + 0.05(-0.122) = 0.3379 RPi = 0.3379 - 0.038 = 29.99 percent

69. You own the following portfolio of stocks. What is the portfolio weight of stock C? stock # shares $/share A 500 $14 B 200 23 C 600 18 D 100 47

39.85 percent Portfolio weightC = (600 $18)/[(500 $14) + (200 $23) + (600 $18) + (100 $47)] = $10,800/$27,100 = 39.85 percent

68. You have a portfolio consisting solely of stock A and stock B. The portfolio has an expected return of 8.7 percent. Stock A has an expected return of 11.4 percent while stock B is expected to return 6.4 percent. What is the portfolio weight of stock A?

46 percent 0.087 = [0.114 x] + [0.064 (1 - x)]; x = 46 percent

71. What is the expected return on a portfolio which is invested 25 percent in stock A, 55 percent in stock B, and the remainder in stock C? state of economy probability return of state A B C boom 5% 19% 9% 6% normal 45% 11% 8% 13% recession 50% -23% 5% 25%

5.93 percent E(r)Boom = (0.25 0.19) + (0.55 0.09) + (0.20 0.06) = 0.109 E(r)Normal = (0.25 0.11) + (0.55 0.08) + (0.20 0.13) = .0975 E(r)Bust = (0.25 - 0.23) + (0.55 0.05) + (0.20 0.25) = 0.02 E(r)Portfolio = (0.05 0.109) + (0.45 0.0975) + (0.50 0.02) = 5.93 percent

60. You recently purchased a stock that is expected to earn 22 percent in a booming economy, 9 percent in a normal economy, and lose 33 percent in a recessionary economy. There is a 5 percent probability of a boom and a 75 percent chance of a normal economy. What is your expected rate of return on this stock?

E(r) = (0.05 0.22) + (0.75 0.09) + (0.20 -0.33) = 1.25 percent

61. The common stock of Manchester & Moore is expected to earn 13 percent in a recession, 6 percent in a normal economy, and lose 4 percent in a booming economy. The probability of a boom is 5 percent while the probability of a recession is 45 percent. What is the expected rate of return on this stock?

E(r) = (0.45 0.13) + (0.50 0.06) + (0.05 -0.04) = 8.65 percent

23. Which one of the following statements is correct concerning a portfolio of 20 securities with multiple states of the economy when both the securities and the economic states have unequal weights?

Given both the unequal weights of the securities and the economic states, an investor might be able to create a portfolio that has an expected standard deviation of zero.

37. Which of the following statements concerning risk are correct? I. Nondiversifiable risk is measured by beta. II. The risk premium increases as diversifiable risk increases. III. Systematic risk is another name for nondiversifiable risk. IV. Diversifiable risks are market risks you cannot avoid.

I and III only

34. Which of the following are examples of diversifiable risk? I. earthquake damages an entire town II. federal government imposes a $100 fee on all business entities III. employment taxes increase nationally IV. toymakers are required to improve their safety standards

I and IV only

18. the exected return on a portfolio considers which of the following factors I. percentage of the portfolio invested in each individual security II. projected states of the economy III. the performance of each security given various economic states IV. probability of occurrence for each state of the economy

I, II, III, and IV

19. The expected return on a portfolio: I. can never exceed the expected return of the best performing security in the portfolio. II. must be equal to or greater than the expected return of the worst performing security in the portfolio. III. is independent of the unsystematic risks of the individual securities held in the portfolio. IV. is independent of the allocation of the portfolio amongst individual securities.

I, II, and III only

25. Which one of the following statements is correct?

Over time, the average return is equal to the unexpected return.

32. Which one of the following statements related to risk is correct?

The systematic risk of a portfolio can be effectively lowered by adding T-bills to the portfolio. (treasure-bills)

24. Which one of the following events would be included in the expected return on Sussex stock?

This morning, Sussex confirmed that its CEO is retiring at the end of the year as was anticipated.

26. Which one of the following statements related to unexpected returns is correct?

Unexpected returns can be either positive or negative in the short term but tend to be zero over the long-term.

39. Which one of the following indicates a portfolio is being effectively diversified?

a decrease in the portfolio standard deviation

36. Which one of the following is the best example of a diversifiable risk?

a firm's sales decrease

14. The expected return on a stock computed using economic probabilities is:

a mathematical expectation based on a weighted average and not an actual anticipated outcome

28. Unsystematic risk:

can be effectively eliminated by portfolio diversification.

22. The standard deviation of a portfolio:

can be less than the weighted average of the standard deviations of the individual securities held in that portfolio.

29. Which one of the following is an example of unsystematic risk?

consumer spending on entertainment decreased nationally

38. The primary purpose of portfolio diversification is to:

eliminate asset-specific risk.

1. You own a stock that you think will produce a return of 11 percent in a good economy and 3 percent in a poor economy. Given the probabilities of each state of the economy occurring, you anticipate that your stock will earn 6.5 percent next year. Which one of the following terms applies to this 6.5 percent?

expected return

27. Which one of the following is an example of systematic risk?

investors panic causing security prices around the globe to fall precipitously

17. The expected rate of return on a stock portfolio is a weighted average where the weights are based on the:

market value of the investment in each stock

20. If a stock portfolio is well diversified, then the portfolio variance:

may be less than the variance of the least risky stock in the portfolio. -E. can be less than the standard deviation of the least risky security in the portfolio.

2. Suzie owns five different bonds valued at $36,000 and twelve different stocks valued at $82,500 total. Which one of the following terms most applies to Suzie's investments?

portfolio

3. Steve has invested in twelve different stocks that have a combined value today of $121,300. Fifteen percent of that total is invested in Wise Man Foods. The 15 percent is a measure of which one of the following?

portfolio weight

30. Which one of the following is least apt to reduce the unsystematic risk of a portfolio?

reducing the number of stocks held in the portfolio

15. The expected risk premium on a stock is equal to the expected return on the stock minus the:

risk free rate Risk premium = Expected return - Risk free rate

6. The principle of diversification tells us that:

spreading an investment across many diverse assets will eliminate some of the total risk

4. Which one of the following is a risk that applies to most securities?

systematic

16. Standard deviation measures which type of risk?

total

5. A news flash just appeared that caused about a dozen stocks to suddenly drop in value by about 20 percent. What type of risk does this news flash represent?

unsystematic

33. Which one of the following risks is irrelevant to a well-diversified investor?

unsystematic risk

13. The expected return on a stock given various states of the economy is equal to the:

weighted average of the returns of each economic state