Investment Management Chapter 5
Security 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 ratio of A will be higher than the Sharpe ratio of B.
I and II only
Suppose your expectations regarding the stock market are as follows: State of the Economy Probability HPR Boom 0.3 41% Normal growth 0.6 24 Recession 0.1 -18 Use above equations to compute the mean and standard deviation of the HPR on stocks. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Mean = [0.3 × 0.41] + [0.6 × 0.24] + [0.1 × (-0.18)] = 0.249 or 24.90% Standard Deviation = Var = [0.3 × (0.41 - 0.249^2] + [0.6 × (0.24 - 0.249^2] + [0.1 × (-0.18 - 0.249)^2 = 0.0262 Standard Deviation = Sq. rt 0.0262 = .1620 = 16.20%
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 _____.
Note that the expected return minus 2 standard deviations is 18% - (2 × 23%) = -28% and the expected return plus 2 standard deviations is 18% + (2 × 23%) = 64%. The probability of a return falling within ± 2 standard deviations is 95.44%.
If you are promised a nominal return of 12% on a 1-year investment, and you expect the rate of inflation to be 3%, what real rate do you expect to earn?
Real Rate = (1.12/1.03) - 1 = 8.74%
You manage an equity fund with an expected risk premium of 11.2% and a standard deviation of 26%. The rate on Treasury bills is 4.2%. Your client chooses to invest $70,000 of her portfolio in your equity fund and $30,000 in a T-bill money market fund. What is the reward-to-volatility ratio for the equity fund? (Round your answer to 4 decimal places.)
Reward to volatility ratio = Portfolio Risk Premium / Standard Deviation of portfolio excess return 11.2% / 26% = .4308
Consider the following two investment alternatives: First, a risky portfolio that pays a 15% rate of return with a probability of 40% or a 5% rate of return with a probability of 60%. Second, a Treasury bill that pays 6%. The risk premium on the risky investment is _________.
Risk Premium = [.4(.15) + .6(.05)] - .06 = .03 = 3%
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 her complete portfolio to achieve the best CAL would be _________.
Security A
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%. The slope of the capital allocation line formed with the risky asset and the risk-free asset is approximately _________.
Slope = (16-6)/20 = .50
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
Which measure of downside risk predicts the worst loss that will be suffered with a given probability?
Value at risk
The geometric average of -12%, 20%, and 25% is _________.
[(1+-.12)(1+.2)(1+.25)]^1/3 - 1 = 9.70%
One method of forecasting the risk premium is to use the _______.
average historical excess returns for the asset under condiseration
The stock of Business Adventures sells for $40 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: Dividend Stock Price Boom $2.80 $48 Normal economy 1.80 43 Recession .90 34 b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 5%. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
b. E(r) = (0.5 × 8.75%) + (0.5 × 5%) = 6.88% σ = 0.5 × 16.39% = 8.19%
The excess return is the _________.
rate of return in excess of the T-Bill rate
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%. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 9%.
ôc = y x op 9% = y x 20% =45%
You have the following rates of return for a risky portfolio for several recent years: 2011 35.23% 2012 18.67% 2013 −9.87% 2014 23.45% If you invested $1,000 at the beginning of 2011, your investment at the end of 2014 would be worth_____
$1,000(1.3523)(1.1867)(1 + -.0987)(1.2345) = $1,785.56
If you believe you have a 60% chance of doubling your money, a 30% chance of gaining 15%, and a 10% chance of losing your entire investment, what is your expected return?
(.60 x 100%) + (.30 x 15%) + (.10 x -100%) = 54.5%
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 _________.
y x .16 + (1-y) x 0.08 = .22 .16y - .08y + .08 = .22 .08y = .14 y = 1.75 Put 1.75 × $500,000 = $875,000 in the risky asset by borrowing $375,000.
If the 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?
1 + r = (1 + R)/(1 + i) - 1 1 + r = 1.06/1.02 - 1 = .0392
During the 1926-2013 period the geometric mean return on Treasury bonds was _________.
5.07%
Treasury bills are paying a 4% rate of return. A risk-averse investor with a risk aversion of A = 3 should invest entirely in a risky portfolio with a standard deviation of 24% only if the risky portfolio's expected return is at least ______.
A = E(rq) - rf/ o^2q 3 = ( E(rq) - .04 ) / .24^2 =21.28%
The CAL provided by combinations of 1-month T-bills and a broad index of common stocks is called the ______.
CML
The stock of Business Adventures sells for $40 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: Dividend Stock Price Boom $2.80 $48 Normal economy 1.80 43 Recession .90 34 a. Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
HPR = Ending Price - Beginning Price + Cash Dividend / Beginning Price a. The holding period returns for the three scenarios are: Boom: (48 - 40 + 2.8)/40 = 0.27 = 27% Normal: (43 - 40 + 1.8)/40 = 0.120 = 12.0% Recession: (34 - 40 + .90)/40 = -0.1275 = -12.75% = [(1/3) × 0.27] + [(1/3) × 0.120] + [(1/3) × (-0.1275) =0.08750 or 9% Variance = [(1/3) × (0.27 - 0.08750)^2] + [(1/3) × (0.120 - 0.08750)^2] + [(1/3) × (-0.1275 - 0.08750)^2] = .026863 Std. Dev = Sq. Rt .026863 = .16390 = 16.39%
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 _________.
HPR = P1 + DIV - P0/P0 .32 = P1 + 1.50 - 25/25 = $31.50