FIN 3826 final
You have the following rates of return for a risky portfolio for several recent years: 2005. 35.23% 2006. 18.67% 2007. -9.87% 2008. 23.45% 66. If you invested $1,000 at the beginning of 2005 your investment at the end of 2008 would be worth ___________.
$1,785.56 $1(1.3523)(1.1867)(1 + -.0987)(1.2345) = $1.7856
The holding period return on a stock was 25%. Its ending price was $18 and its beginning price was $16. Its cash dividend must have been _________.
$2.00 DIV = 16.00(.25)-(18.00-16.00) = 2
If you decide to hold 25% of your complete portfolio in the risky portfolio and 75% in the treasury bills then the dollar values of your positions in X and Y respectively would be __________ and _________.
$300, $450B. $150, $100 X = 1,000(.25)(.6) = 150 Y = 1,000(.25)(.4) = 100
The holding period return on a stock was 32%. Its beginning price was $25 and its cash dividend was $1.50. Its ending price must have been _________.
$31.50 P1+1.50-25/25 = .32 ; P1= $31.50
You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 15% and a standard deviation of 21% and a treasury bill with a rate of return of 5%. How much money should be invested in the risky asset to form a portfolio with an expected return of 11%?
$6,000 15x + 5(1 - x) = 11; x = 60%; 0.60(10,000) = $6,000
Consider the following two investment alternatives. First, a risky portfolio that pays 20% rate of return with a probability of 60% or 5% with a probability of 40%. Second, a treasury bill that pays 6%. If you invest $50,000 in the risky portfolio, your expected profit would be _________.
$7,000 Expected profit = 50,000(.6(.20)+.4(.05)) = 7,000
Annual percentage rates can be converted to effective annual rates by means of the following formula:
(1 + (APR/n))n - 1
The standard deviation of return on investment A is .10 while the standard deviation of return on investment B is .04. If the correlation coefficient between the returns on A and B is -.50, the covariance of returns on A and B is _________.
-.0020 covariance = -.50(.10)(.04) = -.0020
Which of the following correlation coefficients will produce the most diversification benefits?
-0.9
In order to construct a riskless portfolio using two risky stocks, one would need to find two stocks with a correlation coefficient of ________.
-1.0
The price of a stock is $55 at the beginning of the year and $50 at the end of the year. If the stock paid a $3 dividend and inflation was 3%, what is the real holding period return for the year?
-6.44% nominal return on stock 50+3/55 -1 = -3.64% real return -3.64-3/1.03 = -6.44%
As you lengthen the time horizon of your investment period and decide to invest for multiple years you will find that ________. I. the average risk per year may be smaller over longer investment horizons II. the overall risk of your investment will compound over time III. your overall risk on the investment will fall
. I and II only
Asset A has an expected return of 20% and a standard deviation of 25%. The risk free rate is 10%. What is the reward-to-variability ratio?
.40 20%-10%/25% = .40
The standard deviation of return on investment A is .10 while the standard deviation of return on investment B is .05. If the covariance of returns on A and B is .0030, the correlation coefficient between the returns on A and B is _________.
.60 correlation = .0030/(.10(.05)) = .60
An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of return of 20%. Stock B has an expected return of 14% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is 0.50. The risk-free rate of return is 10%. 34. The proportion of the optimal risky portfolio that should be invested in stock A is _________.
0% ((.18-.10)(.05)^2-(.14-.10)(.05)(.20)(.50))/((.18-.10)(.05)^2+(.14-.10)(.20)^2-(.18-.10+.14-.10)(.05)(.20)(.5) = 0
What is the alpha of a portfolio with a beta of 2 and actual return of 15%?
0% alpha = actual return - expected return = 15% - 15% = 0%A portfolio with a return of 15% and a beta of 2 lies on the SML and therefore has an alpha of zero.
The risk premium for exposure to exchange rates is 5% and the firm has a beta relative to exchanges rates of 0.4. The risk premium for exposure to the consumer price index is -6% and the firm has a beta relative to the CPI of 0.8. If the risk free rate is 3.0%, what is the expected return on this stock?
0.2% Return = .03 + 0.4(0.05) + 0.8(-.06) = .002
A portfolio with a 25% standard deviation generated a return of 15% last year when T-bills were paying 4.5%. This portfolio had a Sharpe measure of ____.
0.42 (15-4.5)/25 = 0.42
The expected return of portfolio is 8.9% and the risk free rate is 3.5%. If the portfolio standard deviation is 12.0%, what is the reward to variability ratio of the portfolio?
0.45 Reward to variability ratio = (.089 - .035)/.12 = 0.45
This stock has greater systematic risk than a stock with a beta of ___.
0.50 0.50 < 1.32
A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 24% while stock B has a standard deviation of return of 18%. Stock A comprises 60% of the portfolio while stock B comprises 40% of the portfolio. If the variance of return on the portfolio is .0380, the correlation coefficient between the returns on A and B is _________.
0.583 0.0380 = (.62)(.242) + (.42)(.182) + 2(.6)(.4)(.24)(.18) r; r = 0.583
The Manhawkin Fund has an expected return of 16% and a standard deviation of 20%. The risk free rate is 4%. What is the reward-to-volatility ratio for the Manhawkin Fund?
0.6 (16-4)/20 = .06
What is the dollar weighted return over the entire time period?
0.74%
A stock has a correlation with the market of 0.45. The standard deviation of the market is 21% and the standard deviation of the stock is 35%. What is the stock's beta?
0.75 (.45)(.35)(.21)/.21^2 = .75
Which of the following correlations coefficients will produce the least diversification benefit?
0.8
Research has revealed that regardless of what the current estimate of a firm's beta is, it will tend to move closer to ______ over time.
1
The market value weighted average beta of firms included in the market index will always be _____________.
1
You consider buying a share of stock at a price of $25. The stock is expected to pay a dividend of $1.50 next year and your advisory service tells you that you can expect to sell the stock in one year for $28. The stock's beta is 1.1, rf is 6% and E[rm] = 16%. What is the stock's abnormal return?
1% E(r) = ((28-25+1.50)-1)(100%) = 18% required return = 6%+(16%-6%)(1.1) = 17% abnormal return = 18%-17% = 1%
The market portfolio has a beta of _________.
1.0
What is the most likely correlation coefficient between a stock index mutual fund and the S&P 500?
1.0
If the beta of the market index is 1.0 and the standard deviation of the market index increases from 12% to 18%, what is the new beta of the market index?
1.0 Market beta always equals to 1 regardless of market volatility.
Using the index model, the alpha of a stock is 3.0%, the beta if 1.1 and the market return is 10%. What is the residual given an actual return of 15%?
1.0% Residual = 15 - (3 + 1.1 x 10) = 1%
You have a $50,000 portfolio consisting of Intel, GE and Con Edison. You put $20,000 in Intel, $12,000 in GE and the rest in Con Edison. Intel, GE and Con Edison have betas of 1.3, 1.0 and 0.8 respectively. What is your portfolio beta?
1.048 (20/50)(1.3) + (12/50)(1.0) + (18/50)(0.8) = 1.048
Consider the CAPM. The risk-free rate is 5% and the expected return on the market is 15%. What is the beta on a stock with an expected return of 17%?
1.2 17% = 5% + [15% - 5%]bs; bs = 1.2
You invest $600 in security A with a beta of 1.5 and $400 in security B with a beta of .90. The beta of this portfolio is _________.
1.26 (600/1000)(1.5)+(400/1000)(.90) = 1.26
The beta of this stock is ____. Beta equals slope coefficient
1.32 Beta equals slope coefficient = 1.32
What is the beta for a portfolio with an expected return of 12.5%?
1.5 Since 10% return corresponds to beta = 1, and 15% corresponds to beta = 2, 12.5% return will equal to beta (1 + 2)/2 = 1.5
Consider the one-factor APT. The standard deviation of return on a well-diversified portfolio is 20%. The standard deviation on the factor portfolio is 12%. The beta of the well-diversified portfolio is approximately _________.
1.67 Bp = .20/.12 = 1.67
What is the expected return on the market?
10%
A loan for a new car costs the borrower 0.8% per month. What is the EAR?
10.03% 1.008^12 - 1 = 10.03%
Consider the capital asset pricing model. The market degree of risk aversion, A, is 3. The variance of return on the market portfolio is .0225. If the risk-free rate of return is 4%, the expected return on the market portfolio is _________.
10.75% E(rm) = .04+3(.0225) = 10.75
What is the standard deviation of a portfolio of two stocks given the following data? Stock A has a standard deviation of 30%. Stock B has a standard deviation of 18%. The portfolio contains 60% of stock A and the correlation coefficient between the two stocks is -1.0.
10.8% o = square root of (.60)^2(.30)^2+(.40)^2(.18)^2+2(-1)(.30)(.18)(.60)(.40) = .108
You put up $50 at the beginning of the year for an investment. The value of the investment grows 4% and you earn a dividend of $3.50. Your HPR was ____.
11.00% 4%+$3.50/%50 = 11%
If you require a real growth in the purchasing power of your investment of 8%, and you expect the rate of inflation over the next year to be 3%, what is the lowest nominal return that you would be satisfied with?
11.24% nominal rate = (1.08)(1.03) - 1 = 11.24%
An investment earns 10% the first year, 15% the second year and loses 12% the third year. Your total compound return over the three years was ______.
11.32% (1.10)(1.15)(1-.12) = 11.32%
During the 1926 to 2008 period the geometric mean return on small firm stocks was ______.
11.43%
Consider the one-factor APT. The variance of the return on the factor portfolio is .08. The beta of a well-diversified portfolio on the factor is 1.2. The variance of the return on the well-diversified portfolio is approximately _________.
1152 (.08)(1.2)^2 = 0.1152
____ percent of the variance is explained by this regression.
12 R2 = 12 means 12% of the variance is explained by the regression.
An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 20% while the standard deviation on stock B is 15%. The correlation coefficient between the return on A and B is 0%. The standard deviation of return on the minimum variance portfolio is _________.
12% o = square root of (.36)^2(.20)^2+(.64)^2(.15)^2 = .12
An investor invests 70% of her wealth in a risky asset with an expected rate of return of 15% and a variance of 5% and she puts 30% in a Treasury bill that pays 5%. Her portfolio's expected rate of return and standard deviation are __________ and __________ respectively.
12.0%, 15.7% E(rp) = .70(15%)+.30(5%) = 12% op = .70(.05)^1/2 = 15.7%
Suppose you pay $9,800 for a $10,000 par Treasury bill maturing in two months. What is the annual percentage rate of return for this investment?
12.24% (10,000-9,800/9,800)(12/2) = 12.24%
Treasury bills are paying a 4% rate of return. A risk averse investor with a risk aversion of A = 3 should invest in a risky portfolio with a standard deviation of 24% only if the risky portfolio's expected return is at least ______.
12.64% 0.4 + (1/2(3)(.24)^2) = 12.64%
Research has identified two systematic factors that affect U.S. stock returns. The factors are growth in industrial production and changes in long term interest rates. Industrial production growth is expected to be 3% and long term interest rates are expected to increase by 1%. You are analyzing a stock is that has a beta of 1.2 on the industrial production factor and 0.5 on the interest rate factor. It currently has an expected return of 12%. However, if industrial production actually grows 5% and interest rates drop 2% what is your best guess of the stock's return?
12.9% E[rnew] = 12% + (5% - 3%)(1.2) + (-2% - 1%)(0.5) = 12.9%
What is the expected return on a stock with a beta of 0.8, given a risk free rate of 3.5% and an expected market return of 15.5%?
13.1% Expected return = 3.5 + (0.8)(15.5 - 3.5) = 13.1%
Suppose you pay $9,400 for a $10,000 par Treasury bill maturing in six months. What is the effective annual rate of return for this investment?
13.17% (10,000/9,400)^(12/6) - 1 = 13.17%
The risk premium for exposure to aluminum commodity prices is 4% and the firm has a beta relative to aluminum commodity prices of 0.6. The risk premium for exposure to GDP changes is 6% and the firm has a beta relative to GDP of 1.2. If the risk free rate is 4.0%, what is the expected return on this stock?
13.6% Return = .04 + 0.6(0.04) + 1.2(.06) = .136
An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 20% while the standard deviation on stock B is 15%. The expected return on stock A is 20% while on stock B it is 10%. The correlation coefficient between the return on A and B is 0%. The expected return on the minimum variance portfolio is approximately _________.
13.60% WA = 0.36 WB = 0.64 E(rp) = (.36)(.20)+(.64)(.10) = 1.36
The expected return on the optimal risky portfolio is _________.
14% E(rp) = 1.00(.14) = .1400
According to the CAPM, what is the expected market return given an expected return on a security of 15.8%, a stock beta of 1.2, and a risk free interest rate of 5.0%?
14.0% 15.8 = 5.0 + 1.2 x (MRP), MRP = 9.0%, Expected market return = 5.0 + 9.0 = 14.0%
The price of a stock is $38 at the beginning of the year and $41 at the end of the year. If the stock paid a $2.50 dividend what is the holding period return for the year?
14.47% HPR = (41 - 38 + 2.50)/38 = 0.1447
The annualized average return on this investment is
15.60% (1.17856)^1/4 - 1 = 15.60%
The expected return on the optimal risky portfolio is _________.
16% E[rp] = (.29)(.21) + (.71)(.14) = 16%
The slope of the capital allocation line formed with the risky asset and the risk-free asset is _________.
16-6/20 = .50
Consider the multi-factor APT with two factors. Portfolio A has a beta of 0.5 on factor 1 and a beta of 1.25 on factor 2. The risk premiums on the factors 1 and 2 portfolios are 1% and 7% respectively. The risk-free rate of return is 7%. The expected return on portfolio A is __________ if no arbitrage opportunities exist.
16.25% E(rA) = 7 + .5(1)+1.25(7) = 16.25%
The return on the risky portfolio is 15%. The risk-free rate as well as the investor's borrowing rate is 10%. The standard deviation of return on the risky portfolio is 20%. If the standard deviation on the complete portfolio is 25%, the expected return on the complete portfolio is _________.
16.25% Wrp (20) = 25 ; Wrp = 25/20 = 1.25 E(rP) = .25(10) + 1.25(15) = 16.25%
The risk-free rate and the expected market rate of return are 6% and 16% respectively. According to the capital asset pricing model, the expected rate of return on security X with a beta of 1.2 is equal to _________.
18% E(rx) = .06+1.2(.16-.06) = .18
You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of treasury bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14% and Y has an expected rate of return of 10%. 62. To form a complete portfolio with an expected rate of return of 11%, you should invest __________ of your complete portfolio in treasury bills.
19% .11 = Wf(.05)+(1-Wf)((.6)(.14)+(.4)(.10)) Wf = .19
The two factor model on a stock provides a risk premium for exposure to market risk of 12%, a risk premium for exposure to silver commodity prices of 3.5% and a risk free rate of 4.0%. What is the expected return on the stock?
19.5% Return = 3.5 + 4 + 12 = 19.5%
A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 35% while stock B has a standard deviation of return of 15%. The correlation coefficient between the returns on A and B is 0.45. Stock A comprises 40% of the portfolio while stock B comprises 60% of the portfolio. The standard deviation of the return on this portfolio is _________.
19.76% s2p = (.402)(.352) + (.602)(.15)2 + (2)(.4)(.6)(.35)(.15)(.45)s2p = .039046sp = 19.76%
Most studies indicate that investors' risk aversion is in the range _____.
2-4
The variance of the return on the market portfolio is .0400 and the expected return on the market portfolio is 20%. If the risk-free rate of return is 10%, the market degree of risk aversion, A, is _________.
2.5 A = (.20 - .10)/.04 = 2.5
You have the following rates of return for a risky portfolio for several recent years. Assume that the stock pays no dividends year. beg year price # of shares bought or sold 2005. $50. 100 bought 2006. $55 50 bought 2007. $51 75 sold 2008. $54 75 sold 83. What is the geometric average return for the period?
2.60% yr 1 55-50/50 = 10% yr 2 51-55/55 = -7.27 yr 3 54-51/51 = 5.88% ((1.10)(1+-.0727)(1.0588))^1/3 - 1 = 2.60%
Stock A has a beta of 1.2 and Stock B has a beta of 1. The returns of Stock A are ______ sensitive to changes in the market as the returns of Stock B.
20% more
The standard deviation of the returns on the optimal risky portfolio is _________.
21.4% s2rp = (.292)(.392) + (.712)(.202) + 2(.29)(.71)(.39)(.20).4 s2rp = .045804 srp = 21.4%
Consider the CAPM. The risk-free rate is 6% and the expected return on the market is 18%. What is the expected return on a stock with a beta of 1.3?
21.6% E[rs] = 6% + [18% - 6%](1.3) = 21.6%
The dollar values of your positions in X, Y, and treasury bills would be _________, __________ and __________ respectively if you decide to hold a complete portfolio that has an expected return of 8%.
243, $162, $595 .08(1000) = F(.05)+(1000-F)(.6(.14)+.4(.10)) F - 595 X = (1000-595)(.6) = 243 Y = (1000-595)(.4) = 162
A project has a 50% chance of doubling your investment in one year and a 50% chance of losing half your money. What is the expected return on this investment project?
25% E[rp] = (.5)(100) + (.5)(-50) = 25%
Consider the following two investment alternatives. First, a risky portfolio that pays 15% rate of return with a probability of 40% or 5% with a probability of 60%. Second, a treasury bill that pays 6%. The risk premium on the risky investment is _________.
3% Risk premium = (.4(.15)+.6(.05))-.06 = 0.3
Suppose you pay $9,700 for a $10,000 par Treasury bill maturing in three months. What is the holding period return for this investment?
3.09% (10,000-9,700)/9,700 = 3.09%
Security A has an expected rate of return of 12% and a beta of 1.10. The market expected rate of return is 8% and the risk-free rate is 5%. The alpha of the stock is _________.
3.7% a = .12-(.05+1.1(.08-.05)) = 0.037
If nominal rate of return on investment is 6% and inflation is 2% over a holding period, what is the real rate of return on this investment?
3.92% 6-2/1.02 = 3.92%
The stock is ______ riskier than the typical stock.
32% Beta of 1.32 means that this stock is 32% riskier than the market.
The characteristic line for this stock is Rstock = ___ + ___ Rmarket.
4.05, 1.32 intercept equals 4.05 and slope equals 1.32
You purchased a share of stock for $29. One year later you received $2.25 as dividend and sold the share for $28. Your holding-period return was _________.
4.31% 28+2.25-29?29 = 4.31%
What is the geometric average return of the following quarterly returns: 3%, 5%, 4%, and 7%, respectively?
4.74% Return = (1.03 x 1.04 x 1.05 x 1.07).25 - 1 = .0474
Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. B has an expected rate of return of 10% and a standard deviation of return of 30%. The weight of security B in the minimum variance portfolio is _________.
40% Ws = (.20)^2-(.30)(.20)(-1)/(.30)^2+(.20)^2-2(.30)(.20)(-1)
To form a complete portfolio with an expected rate of return of 8%, you should invest approximately __________ in the risky portfolio. This will mean you will also invest approximately __________ and __________ of your complete portfolio in security X and Y respectively.
40%, 24%, 16%
You find that the annual standard deviation of a stock's returns is equal to 25%. For a 3 year holding period the standard deviation of your total return would equal _______.
43% o yr 3 = (.25) (square root 3) = 0.43
You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a treasury bill with a rate of return of 6%. 57. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 9%.
45% Wrp (20) = 9 ; Wrp = 45%
The standard deviation of return on the optimal risky portfolio is _________.
5% o = square root of 0+(1.00)^2(.05)^2+0 = .05
Your investment has a 40% chance of earning a 15% rate of return, a 50% chance of earning a 10% rate of return and a 10% chance of losing 3%. What is the standard deviation of this investment?
5.14%
During the 1926 to 2008 period the geometric mean return on Treasury bills was _________.
5.31%
The buyer of a new home is quoted a mortgage rate of 0.5% per month. What is the APR on the loan?
6.0% APR = .5% x 12 = 6.0%
What is the expected return for a portfolio with a beta of 0.5?
7.5% Rp = Rr + .5 (Rm + Rr) = 5% + .5(10%-5%) = 7.5%
You have an APR of 7.5% with continuous compounding. The EAR is _____.
7.79 % e^.075 - 1 = 7.79%
An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is 0.4. The risk-free rate of return is 5%. 37. The proportion of the optimal risky portfolio that should be invested in stock B is approximately _________.
71% ((.14-.05)(.39^2)-(.21-.05)(.20)(.39)(.4))/((.14-.05)(.39^2)+(.21-.05)(.20^2)-(.14-.05+.21-.05)(.20)(.39)(.4)) = 71%
A project has a 60% chance of doubling your investment in one year and a 40% chance of losing half your money. What is the standard deviation of this investment?
73% E[rp] = (.60)(1) + (.40)(-.5) = .40 s2rp = (.60)(1 - .40)2 + (.40)(-.5 - .40)2 = .54 srp = .73
Consider the CAPM. The expected return on the market is 18%. The expected return on a stock with a beta of 1.2 is 20%. What is the risk-free rate?
8% 20% = rF + (18 - rF)(1.2); rF = 8%
According to the CAPM, what is the market risk premium given an expected return on a security of 13.6%, a stock beta of 1.2, and a risk free interest rate of 4.0%?
8.0% 13.6 = 4.0 + 1.2 x (MRP), MRP = 8.0%
The arithmetic average of -11%, 15% and 20% is ________.
8.00% (-11%+15%+20%)/3 = 8%
What is the geometric average return over one year if the quarterly returns are 8%, 9%, 5%, and 12%, respectively?
8.47% Return = (1.05 x 1.08 x 1.09 x 1.12).25 - 1 = .0847
You have an EAR of 9%. The equivalent APR with continuous compounding is _____.
8.62% LN[1 + .09] = 8.62%
The two factor model on a stock provides a risk premium for exposure to market risk of 9%, a risk premium for exposure to interest rate of (-1.3%), and a risk free rate of 3.5%. What is the expected return on the stock?
8.7% Return = 3.5 + 9 - 1.3 = 11.2%
If you are promised a nominal return of 12% on a one year investment, and you expect the rate of inflation to be 3%, what real rate do you expect to earn?
8.74% (1.12/1.03) - 1 = 8.74%
Semitool Corp has an expected excess return of 6% for next year. However for every unexpected 1% change in the market, Semitool's return responds by a factor of 1.2. Suppose it turns out the economy and the stock market do better than expected by 1.5% and Semitool's products experience more rapid growth than anticipated, pushing up the stock price by another 1%. Based on this information what was Semitool's actual excess return?
8.80% 6% + (1.5%)(1.2) + 1% = 8.8%
An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 24% while the standard deviation on stock B is 14%. The correlation coefficient between the return on A and B is 0.35. The expected return on stock A is 25% while on stock B it is 11%. The proportion of the minimum variance portfolio that would be invested in stock B is approximately _________.
85% COVAB = (.35)(.24)(.14) = .01176 WB = (.24^2 - 0.01176)/(.14^2+.24^2 - (2)(.01176)) = 85%
Your investment has a 20% chance of earning a 30% rate of return, a 50% chance of earning a 10% rate of return and a 30% chance of losing 6%. What is your expected return on this investment?
9.2% (0.2)(30%) + (0.5)(10%) + (0.3)(-6%) = 9.2%
What is the standard deviation of a portfolio of two stocks given the following data? Stock A has a standard deviation of 18%. Stock B has a standard deviation of 14%. The portfolio contains 40% of stock A and the correlation coefficient between the two stocks is -.23.
9.7% o = square root of (.40)^2(.18)^2+(.60)^2(.14)^2+2(-.23)(.18)(.14)(.40)(.60) = .097
The geometric average of -12%, 20% and 25% is _________.
9.70% ((1+-.12)(1+.20)(1+.25))^(1/3) = 9.70%
A security with normally distributed returns has an annual expected return of 18% and standard deviation of 23%. The probability of getting a return between -28% and 64% in any one year is
95.44% probability of a return within +- 2 o = 95.44%
Consider the single factor APT. Portfolio A has a beta of 1.3 and an expected return of 21%. Portfolio B has a beta of 0.7 and an expected return of 17%. The risk-free rate of return is 8%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio _________.
A, B 21-8/1.3 < 17-8/0.7 short A; Buy B
Two investment advisors are comparing performance. Advisor A averaged a 20% return with a portfolio beta of 1.5 and Advisor B averaged a 15% return with a portfolio beta of 1.2. If the T-bill rate was 5% and the market return during the period was 13%, which advisor was the better stock picker?
Advisor A was better because he generated a larger alpha Required return A = 5% + (13% - 5%)(1.5) = 17%Required return B = 5% + (13% - 5%)(1.2) = 14.6%aA = Actual return A - required return A = 20% - 17% = 3%aB = Actual return B - required return B = 15% - 14.6% = 0.4%
Which one of the following stock return statistics fluctuates the most over time?
Average return
Consider the single factor APT. Portfolio A has a beta of 0.2 and an expected return of 13%. Portfolio B has a beta of 0.4 and an expected return of 15%. The risk-free rate of return is 10%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio _________.
B, A 13-10/.2 > 15-10/.4 short B; Buy A
Consider the following two stocks, A and B. Stock A has an expected return of 10% and a beta of 1.20. Stock B has an expected return of 14% and a beta of 1.80. The expected market rate of return is 9% and the risk-free rate is 5%. Security __________ would be considered a good buy because _________.
B, it offers an expected excess return of 1.8% aA = .10 - (.05+1.20(.09-.05)) = .002 aB = .14 - (.05+1.80(.09-.05)) = .018
The CAL provided by combinations of one month T-bills and a broad index of common stocks is called the ______.
CML
According to historical data, over the long run which of the following assets has the best chance to provide the best after inflation, after tax rate of return?
Common stocks
Your timing was good last year. You invested more in your portfolio right before prices went up and you sold right before prices went down. In calculating historical performance measures which one of the following will be the largest?
Dollar weighted return
There are two independent economic factors M1 and M2. The risk-free rate is 5% and all stocks have independent firm-specific components with a standard deviation of 25%. Portfolios A and B are well diversified. Given the data below which equation provides the correct pricing model? Portfolio Beta on M1. Beta on M2 E(rp) A. 1.5. 1.75 35% B 1.0 0.65 20%
E(rP) = 5 + 8.71bP1 + 9.68bP2 35 = 5 + 1.5 g1 + 1.75 g2; Solve for g1g1 = 20 - 1.1667g220 = 5 + g1 + 0.65g2; Sub in g120 = 5 + 20 - 1.1667 g2 + 0.65 g2g2 = 9.68% g1 = 8.71%
During the 1985 to 2008 period the Sharpe ratio was greatest for which of the following asset classes?
Equity world portfolio in U.S. dollars
You have calculated the historical dollar weighted return, annual geometric average return and annual arithmetic average return. You always reinvest your dividends and interest earned on the portfolio. Which method provides the best measure of the actual average historical performance of the investments you have chosen?
Geometric average return
. Based on the outcomes in the table below choose which of the statements is/are correct: I. The covariance of Security A and Security B is zero II. The correlation coefficient between Security A and C is negative III. The correlation coefficient between Security B and C is positive
I and II only
The part of a stock's return that is systematic is a function of which of the following variables? I. Volatility in excess returns of the stock market II. The sensitivity of the stock's returns to changes in the stock market III. The variance in the stock's returns that is unrelated to the overall stock market
I and II only
When calculating the variance of a portfolio's returns squaring the deviations from the mean results in ________. I. preventing the sum of the deviations from always equaling zero II. exaggerating the effects of large positive and negative deviations III. a number in units of percentage of returns
I and II only
Which of the following are correct arguments supporting passive investment strategies? I. Active trading strategies may not guarantee higher returns but guarantee higher costs II. Passive investors can free ride on the activity of knowledge investors whose trades force prices to reflect currently available information III. Passive investors are guaranteed to earn higher rates of return than active investors over sufficiently long time horizons
I and II only
Which one of the following measure time weighted returns? I. Geometric average return II. Arithmetic average return III. Dollar weighted return
I and II only
ecurity A has a higher standard deviation of returns than Security B. We would expect that ______. I. Security A would have a higher risk premium than Security B II. the likely range of returns for Security A in any given year would be higher than the likely range of returns for Security B III. the Sharpe measure of A will be higher than the Sharpe measure of B.
I and II only
Which risk can be diversified away as additional securities are added to a portfolio? I. Total risk II. Systematic risk III. Firm specific risk
I and III
Which of the following variables do Fama and French claim do a better job explaining stock returns than beta? I. Book to market ratio II. Unexpected change in industrial production III. Firm size
I and III only
You invest all of your money in one year T-bills. Which of the following statements is/are correct? I. Your nominal return on the T-bills is riskless. II. Your real return on the T-bills is riskless .III. Your nominal Sharpe measure is zero.
I and III only
Which of the following statements is true regarding time diversification? I. The standard deviation of the average annual rate of return over severalyears will be smaller than the one-year standard deviation. II. For a longer time horizon, uncertainty compounds over a greater numberof years. III. Time diversification does not reduce risk.
I, II and III
You are considering adding a new security to your portfolio. In order to decide whether you should add the security you need to know the security's _______. I. expected return II. standard deviation III. correlation with your portfolio
I, II and III
Which of the following are assumptions of the simple CAPM model? I. Individual trades of investors do not affect a stock's price II. All investors plan for one identical holding period III. All investors analyze securities in the same way and share the same economic view of the world IV. All investors have the same level of risk aversion
I, II and III only
In a simple CAPM world which of the following statements is/are correct? I. All investors will choose to hold the market portfolio, which includes all risky assets in the world II. Investors' complete portfolio will vary depending on their risk aversion III. The return per unit of risk will be identical for all individual assets IV. The market portfolio will be on the efficient frontier and it will be the optimal risky portfolio
I, II, III and IV
Rank the following from highest average historical return to lowest average historical return from 1926-2008. I. Small stocks II. Long term bonds III. Large stocks IV. T-bills
I, III, II, IV
Rank the following from highest average historical standard deviation to lowest average historical standard deviation from 1926-2008. I. Small stocks II. Long term bonds III. Large stocks IV. T-bills
I, III, II, IV
In a study conducted by Jagannathan and Wang, it was found that the performance of beta in explaining security returns could be considerably enhanced by _____________. I. including the unsystematic risk of a stock II. including human capital in the market portfolio III. allowing for changes in beta over time
II and III only
Fama and French claim that after controlling for firm size and the ratio of firm's book value to market value, beta is ______________. I. highly significant in predicting future stock returns II. relatively useless in predicting future stock returns III. a good predictor of firm's specific risk
II only
The optimal risky portfolio can be identified by finding ____________. I. the minimum variance point on the efficient frontier II. the maximum return point on the efficient frontier the minimum variance point on the efficient frontier III. the tangency point of the capital market line and the efficient frontier IV. the line with the steepest slope that connects the risk free rate to the efficient frontier
III and IV only
According to the CAPM which of the following is not a true statement regarding the market portfolio.
It is always the minimum variance portfolio on the efficient frontier
During the 1926 to 2008 period the Sharpe ratio was greatest for which of the following asset classes?
Large U.S. stocks
During the 1926 to 2008 period which one of the following asset classes provided the lowest real return?
Long-Term U.S. Treasury Bonds
If the simple CAPM is valid and all portfolios are priced correctly, which of the situations below are possible? Consider each situation independently and assume the risk free rate is 5%.
Opiton D
A portfolio that has an expected value in one year of $1,100 could be formed if you _________.
Place 40% of your money in the risky portfolio and the rest in the risk free asset $1100 = x(1000)(1.16) + (1 - x)1000(1.06) ; x=40%=wrp
According to the CAPM, investors are compensated for all but which of the following?
Residual risk
The expected return on the market portfolio is 15%. The risk-free rate is 8%. The expected return on SDA Corp. common stock is 16%. The beta of SDA Corp. common stock is 1.25. Within the context of the capital asset pricing model, _________.
SDA Corp. stock's alpha is -0.75% a = .16-(.08+1.25(.15-.08)) = -.0075
The graph of the relationship between expected return and beta in the CAPM context is called the _________.
SML
The formula E(rp)-rf/op is used to calculate the _____________.
Sharpe measure
The arbitrage pricing theory was developed by _________.
Stephen Ross
Which stock is riskier to a non-diversified investor who puts all his money in only one of these stocks?
Stock A is riskier stock a dots are all over the graph, not in straight line
Which stock is likely to further reduce risk for an investor currently holding his portfolio in a well diversified portfolio of common stock?
Stock B stock b line looks more consistent
Which of the following provides the best example of a systematic risk event?
The Federal Reserve increases interest rates 50 basis points.
In a world where the CAPM holds which one of the following is not a true statement regarding the capital market line?
The capital market line is also called the security market line
The expected return of the risky asset portfolio with minimum variance is _________.
There is not enough information to answer this question
The rate of return on _____ is known at the beginning of the holding period while the rate of return on ____ is not known until the end of the holding period.
Treasury bills, risky assets
Which one of the following would be considered a risk-free asset in real terms as opposed to nominal?
U.S. T-bill whose return was indexed to inflation
Investing in two assets with a correlation coefficient of -0.5 will reduce what kind of risk?
Unique risk
. The capital asset pricing model was developed by _________.
William Sharpe
Investing in two assets with a correlation coefficient of 1.0 will reduce which kind of risk?
With a correlation of 1.0, no risk will be reduced
A stock's alpha measures the stock's ____________________.
abnormal return
You are constructing a scatter plot of excess returns for Stock A versus the market index. If the correlation coefficient between Stock A and the index is -1 you will find that the points of the scatter diagram ______________________ and the line of best fit has a ______________.
all fall on the line of best fit; negative slope
Risk that can be eliminated through diversification is called ______ risk.
all of the above - unique - firm specific - diversifiable
According to the capital asset pricing model, _________.
all securities' returns must lie on the security market line
According to the capital asset pricing model, a fairly priced security will plot _________.
along the security market line
Assume that both X and Y are well-diversified portfolios and the risk-free rate is 8%. Portfolio X has an expected return of 14% and a beta of 1.00. Portfolio Y has an expected return of 9.5% and a beta of 0.25. In this situation, you would conclude that portfolios X and Y _________.
are in equilibrium prem x = 14-8/1 = 6 prem y = 9.5-8/0.25 = 6 thus there are no arbitrage opportunities, and x and y are in eliqibrium
The ______ measure of returns ignores compounding.
arithmetic average
You have calculated the historical dollar weighted return, annual geometric average return and annual arithmetic average return. If you desire to forecast performance for next year, the best forecast will be given by the ________.
arithmetic average return
Asset A has an expected return of 15% and a reward-to-variability ratio of .4. Asset B has an expected return of 20% and a reward-to-variability ratio of .3. A risk-averse investor would prefer a portfolio using the risk-free asset and ______.
asset A
The _______ decision should take precedence over the _____ decision.
asset allocation, stock selection
Arbitrage is based on the idea that _________.
assets with identical risks must have the same expected rate of return
One method to forecast the risk premium is to use the _______.
average historical excess returns for the asset under consideration
The measure of risk used in the Capital Asset Pricing Model is ___________.
beta
in the context of the capital asset pricing model, the systematic measure of risk is captured by _________.
beta
You have $500,000 available to invest. The risk-free rate as well as your borrowing rate is 8%. The return on the risky portfolio is 16%. If you wish to earn a 22% return, you should _________.
borrow $375,000 y = (.22-.08)/(.16-.08) = 1.75 borrowing = 500,000(1.75-1) = 375,000
The SML is valid for _______________ and the CML is valid for ______________.
both well diversified portfolios and individual assets; well diversified portfolios only
The risk-free rate is 4%. The expected market rate of return is 11%. If you expect stock X with a beta of .8 to offer a rate of return of 12 percent, then you should _________.
buy stock X because it is underpriced E(rx) would normally be .04 + .8(.11-.04) = .096
If you want to know the portfolio standard deviation for a three stock portfolio you will have to
calculate three covariances
An adjusted beta will be ______ than the unadjusted beta.
closer to 1
The ________ is equal to the square root of the systematic variance divided by the total variance
correlation coefficient
You are recalculating the risk of ACE stock in relation to the market index and you find the ratio of the systematic variance to the total variance has risen. You must also find that the ____________.
correlation coefficient between ACE and the market has risen
According to the CAPM, the risk premium an investor expects to receive on any stock or portfolio is _______________.
directly related to the beta of the stock
If you want to measure the performance of your investment in a fund, including the timing of your purchases and redemptions you should calculate the __________.
dollar weighted return
Building a zero-investment portfolio will always involve _____________.
equal investments in a short and a long position
Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The global minimum variance portfolio has a standard deviation that is always _________.
equal to 0
The expected return on the market is the risk free rate plus the _____________.
equilibrium risk premium
If enough investors decide to purchase stocks they are likely to drive up stock prices thereby causing _____________ and ___________.
expected returns to fall; risk premiums to fall
The risk that can be diversified away is __________.
firm specific risk
Published data on past returns earned by mutual funds are required to be ______.
geometric returns
You run a regression of a stock's returns versus a market index and find the following: coefficients. lower 95%. upper 95% intercept 0.789 -1.556 3.457 slope 0.890 0.6541 1.465 Based on the data you know that the stock
has a beta that could be anything between 0.6541 and 1.465 inclusive
Liquidity is a risk factor that __________.
has yet to be accurately measured and incorporated into portfolio management
If all investors become more risk averse the SML will _______________ and stock prices will _______________.
have the same intercept with a steeper slope; fall
Historical returns have generally been __________ for stocks of small firms as/than for stocks of large firms.
higher
A stock has a beta of 1.3. The unsystematic risk of this stock is ____________ the stock market as a whole.
higher than
When all investors analyze securities in the same way and share the same economic view of the world we say they have ____________________.
homogeneous expectations
According to Tobin's separation property, portfolio choice can be separated into two independent tasks consisting of __________ and __________.
identifying the optimal risky portfolio; constructing a complete portfolio from T-bills and the optimal risky portfolio based on the investor's degree of risk aversion
Decreasing the number of stocks in a portfolio from 50 to 10 would likely _________________________.
increase the unsystematic risk of the portfolio
The dollar weighted return is the _________.
internal rate of return
In his famous critique of the CAPM, Roll argued that the CAPM ______________.
is not testable because the true market portfolio can never be observed
A security's beta coefficient will be negative if ____________.
its returns are negatively correlated with market index returns
On a standard expected return vs. standard deviation graph investors will prefer portfolios that lie to the _____________ of the current investment opportunity set.
left and above
Some diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities is _____________.
less than 1
Rational risk-averse investors will always prefer portfolios _____________.
located on the capital market line to those located on the efficient frontier
From 1926 to 2008 the world stock portfolio offered _____ return and _____ volatility than the portfolio of large U.S. stocks.
lower; lower
Reward-to-variability ratios are ________ on the ________ capital market line.
lower; steeper
Beta is a measure of security responsiveness to _________.
market risk
In a single factor market model the beta of a stock ________.
measures the stock's contribution to the standard deviation of the market portfolio
The possibility of arbitrage arises when ____________.
mis-pricing among securities creates opportunities for riskless profits
You put half of your money in a stock portfolio that has an expected return of 14% and a standard deviation of 24%. You put the rest of you money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 12%. The stock and bond portfolio have a correlation 0.55. The standard deviation of the resulting portfolio will be ________________.
more than 12% but less than 18% s2p = 0.02592 = (.52)(.242) + (.52)(.122) + 2(.5)(.5)(.24)(.12)0.55; s = 16.1%
To eliminate the bias in calculating the variance and covariance of returns from historical data the average squared deviation must be multiplied by _________.
n/(n - 1)
Diversification is most effective when security returns are _________.
negatively correlated
Two assets have the following expected returns and standard deviations when the risk-free rate is 5%: Asset A E(rA) = 10%. A = 20% Asset B E(rA) = 15%. B = 27% An investor with a risk aversion of A = 3 would find that _________________ on a risk return basis.
neither Asset A nor Asset B is acceptable A = 0.5 + (1/2(3)(.20)^2) = 11% B = 0.5 + (1/2(3)(.27)^2) = 15.94%
Diversification can reduce or eliminate __________ risk.
non-systematic
An investor's degree of risk aversion will determine his or her ______.
optimal mix of the risk-free asset and risky asset
Security X has an expected rate of return of 13% and a beta of 1.15. The risk-free rate is 5% and the market expected rate of return is 15%. According to the capital asset pricing model, security X is _________.
overpriced
According to the capital asset pricing model, a security with a _________.
positive alpha is considered underpriced
The excess return is the _________.
rate of return in excess of the Treasury bill rate
The most significant conceptual difference between the arbitrage pricing theory (APT) and the capital asset pricing model (CAPM) is that the CAPM _____________.
recognizes only one systematic risk factor
Beta is a measure of ______________.
relative systematic risk
Both investors and gamblers take on risk. The difference between an investor and a gambler is that an investor _______.
requires a risk premium to take on the risk
The measure of unsystematic risk can be found from an index model as _________.
residual standard deviation
Which of the following is a correct expression concerning the formula for the standard deviation of returns of a two asset portfolio where the correlation coefficient is positive?
s2rp < (W12s12 + W22s22)
Consider a treasury bill with a rate of return of 5% and the following risky securities: Security A: E(r) = .15; variance = .0400 Security B: E(r) = .10; variance = .0225 Security C: E(r) = .12; variance = .1000 Security D: E(r) = .13; variance = .0625 The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. The security the investor should choose as part of his complete portfolio to achieve the best CAL would be _________.
security A A has the steepest slope; found as: (.15-.05)/(.04)^.5 = .5000
Empirical results estimated from historical data indicate that betas _________.
seem to regress toward one over time
Historically small firm stocks have earned higher returns than large firm stocks. When viewed in the context of an efficient market, this suggests that ___________.
small firms are riskier than large firms
A measure of the riskiness of an asset held in isolation is ____________.
standard deviation
If an investor does not diversify their portfolio and instead puts all of their money in one stock, the appropriate measure of security risk for that investor is the ________.
stock's standard deviation
Historically the best asset for the long term investor wanting to fend off the threats of inflation and taxes while making his money grow has been ____.
stocks
A portfolio of stocks fluctuates when the treasury yields change. Since this risk can not be eliminated through diversification, it is called __________.
systematic risk
Investors require a risk premium as compensation for bearing ______________.
systematic risk
Market risk is also called __________ and _________.
systematic risk, nondiversifiable risk
Harry Markowitz is best known for his Nobel prize winning work on _____________.
techniques used to identify efficient portfolios of risky assets
An important characteristic of market equilibrium is _______________.
the absence of arbitrage opportunities
In the mean-standard deviation graph, the line that connects the risk-free rate and the optimal risky portfolio, P, is called _________.
the capital allocation line
The holding period return on a stock is equal to _________.
the capital gain yield over the period plus the dividend yield
The beta of a security is equal to _________.
the covariance between the security and market returns divided by the variance of the market's returns
Arbitrage is __________________________.
the creation of riskless profits made possible by relative mispricing among securities
The term excess-return refers to ______________.
the difference between the rate of return earned and the risk-free rate
The market risk premium is defined as __________.
the difference between the return on an index fund and the return on Treasury bills
One of the main problems with the arbitrage pricing theory is __________.
the model fails to identify the key macroeconomic variables in the risk-return relationship
Suppose that a stock portfolio and a bond portfolio have a zero correlation. This means that ______.
the returns on the stock and bond portfolio tend to vary independently of each other
The complete portfolio refers to the investment in _________.
the risk-free asset and the risky portfolio combined
The term "complete portfolio" refers to a portfolio consisting of _________________.
the risk-free asset combined with at least one risky asset
The reward/variability ratio is given by _________.
the slope of the capital allocation line
According to capital asset pricing theory, the key determinant of portfolio returns is _________.
the systematic risk of the portfolio
The expected rate of return of a portfolio of risky securities is _________.
the weighted sum of the securities' expected returns
Many current and retired Enron Corp. employees had their 401k retirement accounts wiped out when Enron collapsed because ___.
their 401k accounts were not well diversified
The correlation coefficient between two assets equals to _________.
their covariance divided by the product of their standard deviations
Standard deviation of portfolio returns is a measure of ___________.
total risk
Firm specific risk is also called __________ and __________. A. systematic risk, diversifiable risk
unique risk, diversifiable risk
In a well diversified portfolio, __________ risk is negligible.
unsystematic
Adding additional risky assets to the investment opportunity set will generally move the efficient frontier _____ and to the ______.
up, left
The values of beta coefficients of securities are __________.
usually positive, but are not restricted in any particular way
Which of the following statistics cannot be negative?
variance
According to the capital asset pricing model, fairly priced securities have _________.
zero alphas