Question 1

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?

Accepted Answer

Real rate = (1.12/1.03) - 1 = 8.74%

Question 2

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

Accepted Answer

Squaring the deviations from the mean prevents the sum of the deviations from always equaling zero (I) and exaggerates the effects of large positive and negative deviations (II). However, the unit of variance is not percentage of returns but a squared unit of the original data, such as (percentage)^2 in this case.

Question 3

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?

Accepted Answer

(.2)(30%) + (.5)(10%) + (.3)(-6%) = 9.2%

Question 4

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

Accepted Answer

According to historical data, long-term U.S. Treasury bonds provided the lowest real return during the 1926-2013 period.

Question 5

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

Accepted Answer

LN[1 + .09] = 8.62%

Question 6

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

Accepted Answer

Large U.S. stocks had the greatest Sharpe ratio during the 1926-2013 period, indicating they provided the best risk-adjusted returns among the given asset classes.

Question 7

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

Accepted Answer

Using the average historical excess returns for the asset under consideration can provide an estimate of the risk premium, which is the additional return investors require to compensate for the increased risk of holding that asset over a risk-free investment. This method examines how much more return an investor has historically received holding the asset when compared to a risk-free investment, and assumes that such excess return will continue in the future. The other options listed do not directly provide an estimate of the risk premium.

Question 8

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

Accepted Answer

The geometric mean return on small-firm stocks during the 1926-2013 period was 11.82%. This is a historical statistic often cited in financial literature.

Question 9

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?

Accepted Answer

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

Question 10

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

Accepted Answer

The Sharpe ratio measures the excess return per unit of risk, with risk measured by volatility. During the 1986-2013 period, long-term U.S. Treasury bonds had the lowest Sharpe ratio, indicating lower excess return per unit of risk compared to the other asset classes.

Question 11

The market risk premium is defined as ________.

Accepted Answer

The market risk premium is the difference between the return on a risky asset and the risk-free rate (which is typically measured by the return on Treasury bills). Choice A is the only option that correctly defines the market risk premium in this manner.

Question 12

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?

Accepted Answer

E(r_p) = (.4)(15%) + (.5)(10%) + (.10)(−3%) = 10.7% σ(r_p) = .4(.15 − .107)² + .5(.10 − .107)² + .10(−.03 − .107)² σ(r_p) = 5.14%

Question 13

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

Accepted Answer

According to efficient market theory, higher returns are typically associated with higher risk. Therefore, the fact that small-firm stocks have earned higher returns than large-firm stocks suggests that small firms are riskier than large firms.

Question 14

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.

Accepted Answer

Treasury bills are considered risk-free and have a fixed rate of return, which is known at the beginning of the holding period. On the other hand, risky assets have variable rates of return that are not known until the end of the holding period.

Question 15

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

Accepted Answer

Historical evidence suggests that stocks of small firms have generally had higher returns compared to stocks of large firms. This phenomenon is known as the small-cap premium and is attributed to higher risk and less efficiency in small firms, leading to higher expected returns.

Question 16

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

Accepted Answer

An investor requires a risk premium to take on the risk, which means they expect a higher return for taking on more risk. This is different from a gambler who is willing to take on any risk without the expectation of a higher return. The other choices are not accurate.

Question 17

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

Accepted Answer

The reward-to-volatility ratio is measured by the slope of the capital allocation line, which represents the excess return per unit of volatility (risk) of the portfolio.

Question 18

The excess return is the ________.

Accepted Answer

Excess return is the rate of return in excess of the Treasury-bill rate. It represents the additional return gained from investing in a risky asset compared to a risk-free investment like treasury bills. Therefore, option B is the correct choice. Option A is incorrect because there is no rate of return that can be earned with certainty. Option C is incorrect because it does not refer to excess return. Option D is also incorrect because index return refers to the return on a market index, not excess return.

Question 19

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

Accepted Answer

EAR = e^.075 - 1 = 7.79% e = 2.71828

Question 20

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

Accepted Answer

The geometric mean return on Treasury bonds during the 1926-2013 period was 5.07%. This figure is often used to provide a more accurate representation of average returns over time, especially for investments that experience volatility.

Quiz 5: Risk, Return, and the Historical Record