Chapter 5 Quiz

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+0.3523)*(1+0.1867)*(1-0.0987)*(1+.2345)-1)= 78.56% 1000*(1+.7856)= 1785.56

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?

(.6 x 1) + (.3 x .15) + (.1 x -1) = *54.5%*

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?

(1+i)=(1+r)(1+e) r=8.7%

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 two 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%. 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.

.6 x .14 + .4 x .1=12.4% 12.4x + (1-x) x .05=.08 x=40.54% 40.54 x .6= 24% 40.54 x .4 = 16%

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?

1.06/1.02=1+r r= 3.92%

During the 1926-2013 period the geometric mean return on Treasury bonds was _________.

5.07%

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%

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(rm)-rf/std dev^2 21.28%

The CAL provided by combinations of 1-month T-bills and a broad index of common stocks is called the ______.

CML- Capital Market Line

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

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 _________.

E R c= Rf + \sigmac * Slope of Line 16 = 6 + 20* Slope of Line Slope of Line = (16-6)/20 Slope of Line = 0.50

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 two 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%. To form a complete portfolio with an expected rate of return of 11%, you should invest __________ of your complete portfolio in Treasury bills.

E(rp)=.6 x .14 + .4 x .1= 12.4% 12.4x +(1-x) x .05= .11 12.4x + .05 -.05x = .11 .074x +.05 = .11 .074x = .06 x= 81% 1-.81= 19%

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= (End-Beg+Div)/ Beg *$31.50*

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.

II only

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%.

New std dev= invested% x old std dev 9%= y x .2 y=.45

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

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 _________.

W x .16 + (1-W) x .08=.22 .16w +.08 -.08w=.22 .08w +.08=.22 .08w=.14 w=1.75 500,000 x 1.75= 875,000 875,000-500,000=375,000 *Borrow 375,000*

The geometric average of -12%, 20%, and 25% is _________.

[(1+(-.12)x(1+.2)x(1+.25)]^1/3 -1 9.7%

Annual percentage rates can be converted to effective annual rates by means of the following formula:

[1 + (APR/n)]n - 1

One method of forecasting the risk premium is to use the _______.

average historical excess returns for the asset under consideration

During the 1986-2013 period, the Sharpe ratio was lowest for which of the following asset classes?

long-term U.S. Treasury bonds

The excess return is the _________.

rate of return in excess of the Treasury-bill rate

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 portfolio expected return = 0.4 * 15% + 0.6 * 5% = 9% risk premium = expected return - risk free rate = 9% - 6% = 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 _________.

std dev: sqrt(variance)... Coef. of var.: stdv/e(r) A has least amount of variability i.e. less risky