Ch 5

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

You have an APR of 7.5% with continuous compounding. The EAR is

e^0.075 - 1 = 7.79%

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 measure of downside risk predicts the worst loss that will be suffered with a given probability?

value at risk

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%

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?

E(rp) = (0.4)(15%) + (0.5)(10%) + (0.10)(−3%)=10.7% σ(rp) = 0.4(0.15 − 0.107)2 + 0.5(0.10− 0.107)2 + 0.10(−0.03− 0.107)2 σ(rp) = 5.14%

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.

E(RP) = 0.7(0.15) + 0.3(0.05) = 12% STD DEV = 0.70(0.05)^1/2=15.7%

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 ____

4% + 3.5/50 = 11%

The arithmetic average of -11%, 15%, and 20% is

(-11)+15+20/3 = 8%

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?

(0.2)(30%)+(0.5)(10%)+(0.3)(-6%) = 9.2%

The buyer of a new home is quoted a mortgage rate of .5% per month. What is the APR on the loan?

.5% × 12 = 6%

A loan for a new car costs the borrower .8% per month. What is the EAR?

1.008^12 - 1 = 10.03%

Suppose you pay $9,700 for a $10,000 par Treasury bill maturing in 3 months. What is the holding-period return for this investment?

10,000 - 9,700/9,700 = 3.09%

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 ratio of

15-4.5/25 = 0.42

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

28+2.25-29 / 29 = 4.31%

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

HPR = (P1 + DIV - P0)/P0 HPR × P0 = P1 + DIV - P0 HPR × P0 - P1 + P0 = DIV .25 × $16 - $18 + $16 = $2

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 HPR × P0 = P1 + DIV - P0 P1 = HPR × P0 - DIV + P0 P1 = .32 × $25 - $1.50 + 25 = $31.50

Which of the following arguments supporting passive investment strategies is (are) correct?

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.

Security A has a higher standard deviation of returns than security B. We would expect that:

I. Security A would have a risk premium equal to 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.

You invest all of your money in 1-year T-bills. Which of the following statements is (are) correct?

I. Your nominal return on the T-bills is riskless III. Your nominal Sharpe ratio is zero.

You have an EAR of 9%. The equivalent APR with continuous compounding is

LN[1+0.09] = 8.62%

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?

Nominal rate = (1.08)(1.03) - 1 = 11.24%

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?

Nominal return on stock: (50 + 3)/55 - 1 = -3.64% Real return: (1 + R) = (1 + r)(1 + i) 1 + r = (1 - .0364)/(1.03) = .935 R = .935 - 1 = -.0644

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%

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

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

[(1+-0.12)*(1+0.20)*(1+0.25)]-1 = 9.70%

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

[0.4(0.15) + 0.6(0.05)] - 0.06 = .03 = 3%

Suppose you pay $9,400 for a $10,000 par Treasury bill maturing in 6 months. What is the effective annual rate of return for this investment?

[10,000/9,400]^12/2 - 1 = 13.17%

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

One method of forecasting the risk premium is to use the

average historical excess returns for the asset under consideration

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

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 formula e(rp)-rf/std. dev. is used to calculate the

sharpe ratio

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

The holding period return on a stock is equal to

the capital gain yield over the period plus the dividend yield

The market risk premium is defined as

the difference between the return on an index fund and the return on Treasury bills

The complete portfolio refers to the investment in

the risk-free asset and the risky portfolio combined