FIN301 chapter 11
For a risky security to have a positive expected return but less risk than the overall market, the security must have a beta:
that is > 0 but < 1.
The beta of a risky portfolio cannot be less than _____ nor greater than ____.
the lowest individual beta in the portfolio; the highest individual beta in the portfolio
Which statement is correct?
A security with a beta of 1.54 will plot on the security market line if it is correctly priced.
Which one of the following is the best example of unsystematic risk?
A warehouse fire
Which one of the following is the vertical intercept of the security market line?
Risk-free rate
The systematic risk principle states that the expected return on a risky asset depends only on the asset's ___ risk.
market
The slope of the security market line represents the:
market risk premium.
Unsystematic risk can be defined by all of the following except:
market risk.
The addition of a risky security to a fully diversified portfolio:
may or may not affect the portfolio beta.
If a security plots to the right and below the security market line, then the security has ____ systematic risk than the market and is ____.
more; overpriced
Assume you own a portfolio of diverse securities which are each correctly priced. Given this, the reward-to-risk ratio:
of each security must equal the slope of the security market line.
A $36,000 portfolio is invested in a risk-free security and two stocks. The beta of Stock A is 1.29 while the beta of Stock B is .90. One-half of the portfolio is invested in the risk-free security. How much is invested in Stock A if the beta of the portfolio is .58?
$12,000 βP = .58 = [(A/$36,000) ×1.29] + [($36,000 - A -18,000)/$36,000)×.90] + [.50×0] A = $12,000
You want to create a $72,000 portfolio comprised of two stocks plus a risk-free security. Stock A has an expected return of 13.6 percent and Stock B has an expected return of 14.7 percent. You want to own $25,000 of Stock B. The risk-free rate is 3.6 percent and the expected return on the market is 12.1 percent. If you want the portfolio to have an expected return equal to that of the market, how much should you invest in the risk-free security?
$13,550 E(r)p = .121 = [(x / $72,000) ×.036] + {[($72,000 - x - 25,000) / $72,000 ] ×.136} + [($25,000 / $72,000) ×.147] x = $13,550
You own a $36,800 portfolio that is invested in Stocks A and B. The portfolio beta is equal to the market beta. Stock A has an expected return of 22.6 percent and has a beta of 1.48. Stock B has a beta of .72. What is the value of your investment in Stock A?
$13,558 βP = 1.0 = 1.48A+ [.72 × (1-A)] A = .368421 Investment in Stock A = $36,800 × .368421 = $13,558
A portfolio has an expected return of 13.4 percent. This portfolio contains two stocks and one risk-free security. The expected return on Stock X is 12.2 percent and on Stock Y it is 19.3 percent. The risk-free rate is 4.1 percent. The portfolio value is $48,000 of which $10,000 is the risk-free security. How much is invested in Stock X?
$18,478.87 E(r)p = .134 = [($10,000 / $48,000) × .041] + [(x / $48,000) × .122]+ {[($48,000 - 10,000 - x) / $48,000] × .193} x = $18,478.87
A stock has an expected return of 14.3 percent, the risk-free rate is 3.9 percent, and the market risk premium is 7.8 percent. What must the beta of this stock be?
1.33 E(R) = .143 = .039 + β(.078) β = 1.33
Currently, you own a portfolio comprised of the following three securities. How much of the riskiest security should you sell and replace with risk-free securities if you want your portfolio beta to equal 90 percent of the market beta?
$7,753.51 Portfolio value = $13,640 + 15,980 + 23,260 = $52,880 βP = (.90)(1.00) = [$13,640/$52,880][1.13] + [($15,980-x)/$52,880)(1.48) + [$23,260/$52,880)(.86) + ($x/$52,880)(0) x = $7,753.51
You would like to invest $24,000 and have a portfolio expected return of 11.5 percent. You are considering two securities, A and B. Stock A has an expected return of 18.6 percent and B has an expected return of 7.4 percent. Approximately how much should you invest in Stock A if you invest the balance in Stock B?
$8,786 E(RP) = .115 = .186x+ .074(1 -x) x =.3661 InvestmentA = .3661 × $24,000 = $8,786
Beasley Enterprises stock has an expected return of 8.86 percent. The stock is expected to return 12.5 percent in a normal economy and 16 percent in a boom. The probabilities of a recession, normal economy, and a boom are 11 percent, 88 percent, and 1 percent, respectively. What is the expected return if the economy is in a recession?
-20.91 percent E(R) = .0886 = (.11 ×x) + (.88 ×.125) + (.01 ×.16) x = -.2091, or -20.91 percent
A stock has a beta of 1.48 and an expected return of 17.3 percent. A risk-free asset currently earns 4.6 percent. If a portfolio of the two assets has a beta of .98, then the weight of the stock must be ___ and the risk-free weight must be___.
.66; .34 βP = .98 = x(1.48) + (1 -x)(0) x = .66 Stock weight is .66 and the risk-free weight is .34
What is the beta of the following portfolio?
.76 Portfolio value = $32,960 + 15,780 + 8,645 + 19,920 = $77,305 βP = ($32,960 /$77,305)(.76) + ($15,780/$77,305)(1.31) + ($8,645/$77,305)(1.49) + ($19,920 /$77,305)(0) = .76
You currently own a portfolio valued at $76,000 that is equally as risky as the market. Given the information below, what is the beta of Stock C?
.81 Value of risk-free asset = $76,000 -13,800-48,600-8,400 = $5,200 βP = 1 = ($13,800/$76,000)(1.21) + ($48,600/$76,000)(1.08) + ($8,400/$76,000)(βC) + ($5,200/$76,000)(0) βC = .81
What is the beta of the following portfolio?
1.08 Portfolio value = $18,400 + 6,320 + 32,900 + 11,850 = $69,470 βP = ($18,400/$69,470)(.97) + ($6,320/$69,470)(1.04) + ($32,900/$69,470)(1.23) + ($11,850/$69,470)(.88) = 1.08
You currently own a portfolio valued at $52,000 that has a beta of 1.16. You have another $10,000 to invest and would like to invest it in a manner such that the portfolio beta decreases to 1.15. What does the beta of the new investment have to be?
1.098 βP = 1.15 = ($52,000/$62,000)(1.16) + ($10,000/$62,000)x x = 1.098
You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.86 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?
1.14 βP = 1 = (1/3)(0) + (1/3)(1.86) + (1/3)(x) x = 1.14
Currently, the risk-free rate is 3.2 percent. Stock A has an expected return of 11.4 percent and a beta of 1.11. Stock B has an expected return of 13.7 percent. The stocks have equal reward-to-risk ratios. What is the beta of Stock B?
1.42 (.114 -.032)/1.11 = (.137 -.032)/βB βB = 1.42
You would like to create a portfolio that is equally invested in a risk-free asset and two stocks. One stock has a beta of 1.39. What does the beta of the second stock have to be if you want the portfolio to be equally as risky as the overall market?
1.61 1/3(0) + 1/3(1.39) + 1/3(x) = 1.0 x = 1.61
BJB stock has an expected return of 17.82 percent. The risk-free rate is 4.6 percent and the market risk premium is 8.2 percent. What is the stock's beta?
1.61 E(R) = .1782 = .046 + β(.082) β = 1.61
You own a portfolio of two stocks, A and B. Stock A is valued at $84,650 and has an expected return of 10.6 percent. Stock B has an expected return of 6.4 percent. What is the expected return on the portfolio if the portfolio value is $97,500?
10.05 percent ValueB = $97,500-84,650 = $12,850 Expected return = [($84,650/$97,500) × .106] + [($12,850/$97,500) × .064] = .1005 or 10.05 percent
You have compiled the following information on your investments. What rate of return should you expect to earn on this portfolio?
10.09 percent ValueA = 400 × $24 = $9,600 ValueB = 300 × $13 = $3,900 ValueC = 100 × $33 = $3,300 ValueD = 100 × $54 = $5,400 ValuePort = $9,600 + 3,900 + 3,300 + 5,400 = $22,200 Expected return = [($9,600/$22,200) × .136] + [($3,900/$22,200) × .148] + [($3,300/$22,200) × .074] + [($5,400 /$22,200) × .021] = .1009, or 10.09 percent
You own a portfolio that is invested as follows: $13,700 of Stock A, $4,800 of Stock B, $16,200 of Stock C, and $9,100 of Stock D. What is the portfolio weight of Stock B?
10.96 percent WeightC = $4,800/($13,700 + 4,800 + 16,200 + 9,100) = .1096, or 10.96 percent
Given the following information, what is the expected return on a portfolio that is invested 30 percent in both Stocks A and C, and 40 percent in Stock B?
11.08 percent E(RBoom) = (.30 ×.184) + (.40 ×.114) + (.30 ×.261) = .1791 E(RNormal) = (.30 ×.096) + (.40 ×.079) + (.30 ×.176) = .1132 E(RRecession) = (.30 ×.038) + (.40 ×.046) + [.30 ×(-.287)] = -.0563 E(RPortfolio) = (.04 ×.1791) + (.93 ×.1132) + [.03 ×(-.0563)] = .1108, or 11.08 percent
Stock J has a beta of 1.06 and an expected return of 12.3 percent, while Stock K has a beta of .74 and an expected return of 6.7 percent. If you create portfolio with the same risk as the market, what rate of return should you expect to earn?
11.25 percent βP = 1.0 = 1.06x+ .74(1 -x) x = .8125 E(RP) = .8125(.123) + (1 -.8125)(.067) = .1125, or 11.25 percent
You own a portfolio that is invested 43 percent in Stock A, 16 percent in Stock B, and the remainder in Stock C. The expected returns on stocks A, B, and C are 9.1 percent, 16.7 percent, and 11.4 percent, respectively. What is the expected return on the portfolio?
11.26 percent Expected return = [.43 ×.091] + [.16 ×.167] + [(1 -.43 -.16) ×.114] = .1126, or 11.26 percent
You own a portfolio consisting of the securities listed below. The expected return for each security is as shown. What is the expected return on the portfolio?
11.41 percent ValueA = 250 × $15 = $3,750 ValueB = 300 × $27 = $8,100 ValueC = 500 × $38 = $19,000 ValueD = 100 × $9 = $900 ValuePort = $3,750 + 8,100 + 19,000 + 900 = $31,750 Expected return = [($3,750 /$31,750) × .112] + [($8,100 /$31,750) × .164] + [($19,000/$31,750) × .087] + [($900/$31,750) × .245] = .1141, or 11.41 percent
S&S stock is expected to return 17.5 percent in a booming economy, 12.4 percent in a normal economy, and 1.2 percent in a recession. The probabilities of an economic boom, normal state, or recession are 2 percent, 90 percent, and 8 percent, respectively. What is the expected rate of return on this stock?
11.61 percent Expected return = (.02 ×.175) + (.90 ×.124) + (.08 ×.012) = .1161, or 11.61 percent
Fiddler's Music Stores' stock has a risk premium of 8.3 percent while the inflation rate is 3.1 percent and the risk-free rate is 3.8 percent. What is the expected return on this stock?
12.1 percent Expected return = .038 + .083 = .121, or 12.1 percent
Given the following information, what is the expected return on a portfolio that is invested 35 percent in Stock A, 45 percent in Stock B, and the balance in Stock C?
12.16 percent E(RBoom)= (.35 ×.167) + (.45 ×.189) + (.20 ×.064) = .1563 E(RNormal) = (.35 ×.142) + (.45 ×.114) + (.20 ×.095) = .1200 E(RRecession) = (.35 ×.064) + [.45 ×(-.038)] + (.20 ×.112) = .0277 E(RPortfolio) = (.12 ×.1563) + (.85 ×.1200) + (.03 ×.0277) = .1216 or 12.16 percent
You want to create a $50,000 portfolio that consists of three stocks and has an expected return of 12.6 percent. Currently, you own $14,200 of Stock A and $21,700 of Stock B. The expected return for Stock A is 16.2 percent, and for Stock B it is 10.4 percent. What is the expected rate of return for Stock C?
12.36 percent Value Stock C = $50,000 -14,200 -21,700 = $14,100 E(RP) = .126 = [($14,200/$50,000) ×.162] + [($21,700/$50,000) ×.104] + [($14,100/$50,000) ×E(RC)] E(RC) = .1236, or 12.36 percent
You own a stock that has an expected return of 15.72 percent and a beta of 1.33. The U.S. Treasury bill is yielding 3.82 percent and the inflation rate is 2.95 percent. What is the expected rate of return on the market?
12.77 percent E(R) = .1572 = .0382+ 1.33(Rm-.0382) Rm = .1277, or 12.77 percent
Assume the economy has a 12 percent chance of booming, a 4 percent chance of being recessionary, and being normal the remainder of the time. A stock is expected to return 18.7 percent in a boom, 14.4 percent in a normal economy, and lose 12 percent in a recession. What is the expected rate of return on this stock?
13.86 percent Expected return = (.12 ×.187) + (.84 ×.144) + [.04 ×(-.12)] = .1386, or 13.86 percent
You own a portfolio that has $2,200 invested in Stock A and $1,300 invested in Stock B. If the expected returns on these stocks are 11 percent and 17 percent, respectively, what is the expected return on the portfolio?
13.23 percent E(R) = [$2,200 / ($2,200 + 1,300)]×.11 + [$1,300/($2,200 + 1,300)]×.17 = .1323, or 13.23 percent
Bama Entertainment has common stock with a beta of 1.22. The market risk premium is 8.1 percent and the risk-free rate is 3.9 percent. What is the expected return on this stock?
13.78 percent E(R) = .039 + 1.22(.081) = .1378, or 13.78 percent
Which term best refers to the practice of investing in a variety of diverse assets as a means of reducing risk?
Diversification
PL Lumber stock is expected to return 22 percent in a booming economy, 15 percent in a normal economy, and lose 2 percent in a recession. The probabilities of an economic boom, normal state, or recession are 5 percent, 92 percent, and 3 percent, respectively. What is the expected rate of return on this stock?
14.84 percent Expected return = (.05 ×.22) + (.92 ×.15) + [.03 ×(-.02)] = .01484, or 14.84 percent
Southern Wear stock has an expected return of 15.1 percent. The stock is expected to lose 8 percent in a recession and earn 18 percent in a boom. The probabilities of a recession, a normal economy, and a boom are 2 percent, 87 percent, and 11 percent, respectively. What is the expected return on this stock if the economy is normal?
15.26 percent E(R) = .151 = (.02 ×-.08) + (.87 ×x) + (.11 ×.18) x = .1526, or 15.26 percent
A stock has a beta of 1.32, the expected return on the market is 12.72, and the risk-free rate is 4.05. What must the expected return on this stock be?
15.49 percent E(R) = .0405 + 1.32(.1272 -.0405) = .1549, or 15.49 percent
You own a $58,600 portfolio comprised of four stocks. The values of Stocks A, B, and C are $11,200, $17,400, and $20,400, respectively. What is the portfolio weight of Stock D?
16.38 percent WeightD = ($58,600-11,200 -17,400 -20,400) / $58,600 = .1638, or 16.38 percent
Stock A has an expected return of 14.4 percent and a beta of 1.21. Stock B has an expected return of 12.87 percent and a beta of 1.06. Both stocks have the same reward-to-risk ratio. What is the risk-free rate?
2.06 percent (.144-Rf)/1.21 = (.1287-Rf)/1.06 Rf = .0206, or 2.06 percent
Stock Y has a beta of 1.28 and an expected return of 13.7 percent. Stock Z has a beta of 1.02 and an expected return of 11.4 percent. What would the risk-free rate have to be for the two stocks to be correctly priced relative to each other?
2.38 percent (.137 -Rf)/1.28 = (.114 -Rf)/1.02 Rf = .0238, or 2.38 percent
Stock J has a beta of 1.52 and an expected return of 15.76percent. Stock K has a beta of .98 and an expected return of 11.44 percent. What is the risk-free rate if these securities both plot on the security market line?
3.60 percent (.1576-Rf)/1.52 = (.1144 -Rf)/.98 Rf = .0360, or 3.60 percent
A stock has a beta of 1.32 and an expected return of 12.8 percent. The risk-free rate is 3.6 percent. What is the slope of the security market line?
6.97 percent Slope = (.128 -.036)/1.32 = .0697, or 6.97 percent
A stock has a beta of 1.10, an expected return of 12.11 percent, and lies on the security market line. A risk-free asset is yielding 3.2 percent. You want to create a portfolio valued at $12,000 consisting of Stock A and the risk-free security such that the portfolio beta is .80. What rate of return should you expect to earn on your portfolio?
9.68 percent E(R) = .1211= .032 + 1.10(MRP) MRP = .0810 E(RP) = .032 + .80(.0810) = .0968, or 9.68 percent
Stock A has a beta of 1.09 while Stock B has a beta of .76 and an expected return of 8.2 percent. What is the expected return on Stock A if the risk-free rate is 4.6 percent and both stocks have equal reward-to-risk premiums?
9.76 percent (RA-.046)/1.09 = (.082 -.046)/.76 RA = .0976, or 9.76 percent
A stock is expected to return 13 percent in an economic boom, 10 percent in a normal economy, and 3 percent in a recessionary economy. Which one of the following will lower the overall expected rate of return on this stock?
A decrease in the probability of an economic boom
Which statement is correct?
An underpriced security will plot above the security market line.
Which one of the following is the minimum required rate of return on a new investment that makes that investment attractive?
Cost of capital
Which one of these is the best example of systematic risk?
Decrease in gross domestic product
Mary owns a risky stock and anticipates earning 16.5 percent on her investment in that stock. Which one of the following best describes the 16.5 percent rate?
Expected return
Which one of the following statements is correct?
If a risky security is correctly priced, its expected risk premium will be positive.
Which one of these represents systematic risk?
Increase in consumption created by a reduction in personal tax rates
World United stock currently plots on the security market line and has a beta of 1.04. Which one of the following will increase that stock's rate of return without affecting the risk level of the stock, all else constant?
Increase in the market risk-to-reward ratio
Julie wants to create a $5,000 portfolio. She also wants to invest as much as possible in a high risk stock with the hope of earning a high rate of return. However, she wants her portfolio to have no more risk than the overall market. Which one of the following portfolios is most apt to meet all of her objectives?
Invest $2,500 in a risk-free asset and $2,500 in a stock with a beta of 2.0
Stock A comprises 28 percent of Susan's portfolio. Which one of the following terms applies to the 28 percent?
Portfolio weight
Diversifying a portfolio across various sectors and industries might do more than one of the following. However, this diversification must do which one of the following?
Reduce the portfolio's unique risks
Which one of the following is the best example of an announcement that is most apt to result in an unexpected return?
Statement by a firm that it has just discovered a manufacturing defect and is recalling its product
The risk premium for an individual security is based on which one of the following types of risk?
Systematic
Which statement is true?
The weights of the securities held in any portfolio must equal 1.0.
Which one of the following best exemplifies unsystematic risk?
Unexpected increase in the variable costs for a firm
Which one of the following represents the amount of compensation an investor should expect to receive for accepting the unsystematic risk associated with an individual security?
Zero
Systematic risk is defined as:
any risk that affects a large number of assets.
The amount of systematic risk present in a particular risky asset relative to that in an average risky asset is measured by the:
beta coefficient.
The capital asset pricing model:
considers the relationship between the fluctuations in a security's returns versus the market's returns.
The security market line is defined as a positively sloped straight line that displays the relationship between the:
expected return and beta of either a security or a portfolio.
The security market line is a linear function that is graphed by plotting data points based on the relationship between the:
expected return and beta.
According to the capital asset pricing model, the expected return on a security will be affected by all of the following except the:
security's standard deviation.
The expected return on a security is not affected by the:
security's unique risks.
Standard deviation measures _____ risk while beta measures _____ risk.
total; systematic
Portfolio diversification eliminates:
unsystematic risk.
A portfolio is comprised of 35 securities with varying betas. The lowest beta for an individual security is .74 and the highest of the security betas of 1.51. Given this information, you know that the portfolio beta:
will be greater than or equal to .74 but less than or equal to 1.51.
Which one of the following is the computation of the risk premium for an individual security? E(R) is the expected return on the security, Rf is the risk-free rate, β is the security's beta, and E(RM) is the expected rate of return on the market.
β[E(RM) -Rf]