Deck 5: Risk, Return, and the Historical Record

Question 1

Which one of the following measures time-weighted returns and allows for compounding?

A) geometric average return
B) arithmetic average return
C) dollar-weighted return
D) historical average return

Answer 1

A

Question 2

Published data on past returns earned by mutual funds are required to be ________.

A) dollar-weighted returns
B) geometric returns
C) excess returns
D) index returns

Answer 2

B

Question 3

Rank the following from highest average historical standard deviation to lowest average historical standard deviation from 1926 to 2017.
I) Small stocks
II) Long-term bonds
III) Large stocks
IV) T-bills

A) I, II, III, IV
B) III, IV, II, I
C) I, III, II, IV
D) III, I, II, IV

Answer 3

C

Question 4

Rank the following from highest average historical return to lowest average historical return from 1926 to 2017.
I) Small stocks
II) Long-term bonds
III) Large stocks
IV) T-bills

A) I, II, III, IV
B) III, IV, II, I
C) I, III, II, IV
D) III, I, II, IV

Question 5

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?

A) 6.38%
B) 12.77%
C) 13.17%
D) 14.25%

Question 6

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 ________.

A) 4%
B) 3.5%
C) 7%
D) 11%

Question 7

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 ________.

A) geometric average return
B) arithmetic average return
C) dollar-weighted return
D) index return

Question 8

The complete portfolio refers to the investment in ________.

A) the risk-free asset
B) the risky portfolio
C) the risk-free asset and the risky portfolio combined
D) the risky portfolio and the index

Question 9

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

A) 15.67%
B) 8%
C) 11.22%
D) 6.45%

Question 10

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

A) 8.42%
B) 11%
C) 9.7%
D) 18.88%

Question 11

An investment earns 10% the first year, earns 15% the second year, and loses 12% the third year. The total compound return over the 3 years was ________.

A) 41.68%
B) 11.32%
C) 3.64%
D) 13%

Question 12

The holding period return on a stock is equal to ________.

A) the capital gain yield over the period plus the inflation rate
B) the capital gain yield over the period plus the dividend yield
C) the current yield plus the dividend yield
D) the dividend yield plus the risk premium

Question 13

Suppose you pay $9,800 for a $10,000 par Treasury bill maturing in 2 months. What is the annual percentage rate of return for this investment?

A) 2.04%
B) 12 %
C) 12.24%
D) 12.89%

Question 14

The dollar-weighted return is the ________.

A) difference between cash inflows and cash outflows
B) arithmetic average return
C) geometric average return
D) internal rate of return

Question 15

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?

A) 3.01%
B) 3.09%
C) 12.42%
D) 16.71%

Question 16

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 ________.

A) dollar-weighted return
B) geometric average return
C) arithmetic average return
D) index return

Question 17

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?

A) dollar-weighted return
B) geometric average return
C) arithmetic average return
D) index return

Question 18

The ________ measure of returns ignores compounding.

A) geometric average
B) arithmetic average
C) IRR
D) dollar-weighted

Question 19

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

A) [1 + (APR/n)]n - 1
B) (APR)(n)
C) (APR/n)
D) (periodic rate)(n)

Question 20

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?

A) dollar-weighted return
B) geometric average return
C) arithmetic average return
D) mean holding-period return

Question 21

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?

A) 5.48%
B) 8.74%
C) 9%
D) 12%

Question 22

In 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 for which the unit is percentage of returns

A) I only
B) I and II only
C) I and III only
D) I, II, and III

Question 23

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?

A) 12.8%
B) 11%
C) 8.9%
D) 9.2%

Question 24

During the 1926-2013 period which one of the following asset classes provided the lowest real return?

A) Small U.S. stocks
B) Large U.S. stocks
C) Long-term U.S. Treasury bonds
D) Equity world portfolio in U.S. dollars

Question 25

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

A) 8.47%
B) 8.62%
C) 8.88%
D) 9.42%

Question 26

During the 1926-2013 period the Sharpe ratio was greatest for which of the following asset classes?

A) small U.S. stocks
B) large U.S. stocks
C) long-term U.S. Treasury bonds
D) bond world portfolio return in U.S. dollars

Question 27

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

A) coefficient of variation of analysts' earnings forecasts
B) variations in the risk-free rate over time
C) average historical excess returns for the asset under consideration
D) average abnormal return on the index portfolio

Question 28

During the 1926-2013 period the geometric mean return on small-firm stocks was ________.

A) 5.31%
B) 5.56%
C) 9.34%
D) 11.82%

Question 29

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?

A) 3%
B) 8%
C) 11%
D) 11.24%

Question 30

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

A) small U.S. stocks
B) large U.S. stocks
C) long-term U.S. Treasury bonds
D) equity world portfolio in U.S. dollars

Question 31

The market risk premium is defined as ________.

A) the difference between the return on an index fund and the return on Treasury bills
B) the difference between the return on a small-firm mutual fund and the return on the Standard & Poor's 500 Index
C) the difference between the return on the risky asset with the lowest returns and the return on Treasury bills
D) the difference between the return on the highest-yielding asset and the return on the lowest-yielding asset

Question 32

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?

A) 5.14%
B) 7.59%
C) 9.29%
D) 8.43%

Question 33

Historically, small-firm stocks have earned higher returns than large-firm stocks. When viewed in the context of an efficient market, this suggests that ________.

A) small firms are better run than large firms
B) government subsidies available to small firms produce effects that are discernible in stock market statistics
C) small firms are riskier than large firms
D) small firms are not being accurately represented in the data

Question 34

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.

A) risky assets; Treasury bills
B) Treasury bills; risky assets
C) excess returns; risky assets
D) index assets; bonds

Question 35

Historical returns have generally been ________ for stocks of small firms as (than) for stocks of large firms.

A) the same
B) lower
C) higher
D) none of these options (There is no evidence of a systematic relationship between returns on small-firm stocks and returns on large-firm stocks.)

Question 36

Both investors and gamblers take on risk. The difference between an investor and a gambler is that an investor ________.

A) is normally risk neutral
B) requires a risk premium to take on the risk
C) knows he or she will not lose money
D) knows the outcomes at the beginning of the holding period

Question 37

The reward-to-volatility ratio is given by ________.

A) the slope of the capital allocation line
B) the second derivative of the capital allocation line
C) the point at which the second derivative of the investor's indifference curve reaches zero
D) the portfolio's excess return

Question 38

The excess return is the ________.

A) rate of return that can be earned with certainty
B) rate of return in excess of the Treasury-bill rate
C) rate of return to risk aversion
D) index return

Question 39

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

A) 7.5%
B) 7.65%
C) 7.79 %
D) 8.25%

Question 40

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

A) 5.07%
B) 5.56%
C) 9.34%
D) 11.43%

Question 41

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 ________.

A) $.25
B) $1
C) $2
D) $4

Question 42

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 ________.

A) security A
B) security B
C) security C
D) security D

Question 43

Two assets have the following expected returns and standard deviations when the risk-free rate is 5%:
Asset A E(rA) = 10% σA = 20%
Asset B E(rB) = 15% σB = 27%
An investor with a risk aversion of A = 3 would find that ________ on a risk-return basis.

A) only asset A is acceptable
B) only asset B is acceptable
C) neither asset A nor asset B is acceptable
D) both asset A and asset B are acceptable

Question 44

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 ________.

A) 1%
B) 3%
C) 6%
D) 9%

Question 45

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 ________.

A) $28.50
B) $33.20
C) $31.50
D) $29.75

Question 46

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 ________.

A) 1.040
B) )80
C) )50
D) )25

Question 47

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%.

A) 100%
B) 90%
C) 45%
D) 10%

Question 48

The formula is used to calculate the ________.

A) Sharpe ratio
B) Treynor measure
C) coefficient of variation
D) real rate of return

Question 49

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 ________.

A) invest $125,000 in the risk-free asset
B) invest $375,000 in the risk-free asset
C) borrow $125,000
D) borrow $375,000

Question 50

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%. A portfolio that has an expected value in 1 year of $1,100 could be formed if you ________.

A) place 40% of your money in the risky portfolio and the rest in the risk-free asset
B) place 55% of your money in the risky portfolio and the rest in the risk-free asset
C) place 60% of your money in the risky portfolio and the rest in the risk-free asset
D) place 75% of your money in the risky portfolio and the rest in the risk-free asset

Question 51

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.
III) The Sharpe ratio of A will be higher than the Sharpe ratio of B.

A) I only
B) II only
C) II and III only
D) I, II, and III

Question 52

Most studies indicate that investors' risk aversion is in the range ________.

A) 1-3
B) 1.5-4
C) 3-5.2
D) 4-6

Question 53

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 ________.

A) -3.57%
B) -3.45%
C) 4.31%
D) 8.03%

Question 54

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) 8.67%
B) 9.84%
C) 21.28%
D) 14.68%

Question 55

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.

A) 10%; 6.7%
B) 12%; 22.4%
C) 12%; 15.7%
D) 10%; 35%

Question 56

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 ________.

A) )22
B) )60
C) )42
D) )25

Question 57

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 ________.

A) stocks
B) bonds
C) money market funds
D) Treasury bills

Question 58

In the mean standard deviation graph, the line that connects the risk-free rate and the optimal risky portfolio, P, is called the ________.

A) capital allocation line
B) indifference curve
C) investor's utility line
D) security market line

Question 59

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%?

A) $6,000
B) $4,000
C) $7,000
D) $3,000

Question 60

Consider the following two investment alternatives: First, a risky portfolio that pays a 20% rate of return with a probability of 60% or a 5% rate of return with a probability of 40%. Second, a Treasury bill that pays 6%. If you invest $50,000 in the risky portfolio, your expected profit after one year would be ________.

A) $3,000
B) $7,000
C) $7,500
D) $10,000

Question 61

What is the geometric average return of the following quarterly returns: 3%, 5%, 4%, and 7%?

A) 3.72%
B) 4.23%
C) 4.74%
D) 4.90%

Question 62

What is the geometric average return over 1 year if the quarterly returns are 8%, 9%, 5%, and 12%?

A) 8%
B) 8.33 %
C) 8.47%
D) 8.5 %

Question 63

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 ________.

A) 6%
B) 8.75 %
C) 10%
D) 16.25%

Question 64

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?

A) long-term Treasury bonds
B) corporate bonds
C) common stocks
D) preferred stocks

Question 65

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 ________.

A) 68.26%
B) 95.44%
C) 99.74%
D) 100%

Question 66

Which one of the following would be considered a risk-free asset in real terms as opposed to nominal?

A) money market fund
B) U.S. T-bill
C) short-term corporate bonds
D) U.S. T-bill whose return was indexed to inflation

Question 67

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.

A) 19%
B) 25%
C) 36%
D) 50%

Question 68

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.
II) Your real return on the T-bills is riskless.
III) Your nominal Sharpe ratio is zero.

A) I only
B) I and III only
C) II only
D) I, II, and III

Question 69

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?

A) 6.58%
B) 8.86%
C) 14.47%
D) 18.66%

Question 70

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?

A) )8
B) )6
C) 9
D) 1

Question 71

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%. 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%.

A) $162; $595; $243
B) $243; $162; $595
C) $595; $162; $243
D) $595; $243; $162

Question 72

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?

A) -3.64%
B) -6.36%
C) -6.44%
D) -11.74%

Question 73

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?

A) 3.92%
B) 4%
C) 4.12%
D) 6%

Question 74

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

A) )50%
B) 5%
C) 6%
D) 6.5%

Question 75

You have the following rates of return for a risky portfolio for several recent years:
2013 35.23%
2014 18.67%
2015 −9.87%
2016 23.45%
If you invested $1,000 at the beginning of 2013, your investment at the end of 2016 would be worth ________.

A) $2,176.60
B) $1,785.56
C) $1,645.53
D) $1,247.87

Question 76

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

A) )80%
B) 6.87%
C) 9.6%
D) 10.03%

Question 77

You have the following rates of return for a risky portfolio for several recent years:
2013 35.23%
2014 18.67%
2015 −9.87%
2016 23.45%
The annualized (geometric) average return on this investment is ________.

A) 16.15%
B) 16.87%
C) 21.32%
D) 15.60%

Question 78

From 1926 to 2013 the world stock portfolio offered ________ return and ________ volatility than the portfolio of large U.S. stocks.

A) lower; higher
B) lower; lower
C) higher; lower
D) higher; higher

Question 79

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.

A) 0%; 60%; 40%
B) 25%; 45%; 30%
C) 40%; 24%; 16%
D) 50%; 30%; 20%

Question 80

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%. 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 ________.

A) $300; $450
B) $150; $100
C) $100; $150
D) $450; $300