Question 1

The variance of a stock's returns can be calculated as the:
A) average value of deviations from the mean.
B) average value of squared deviations from the mean.
C) square root of the average value of deviations from the mean.
D)sum of the deviations from the mean.

Accepted Answer

The variance is the average value of squared deviations from the mean. It is a measure of how spread out the returns are from their average. Option A, C, and D are incorrect definitions of variance.

Question 2

Over a 20-year period an investment of $1,000 in common stocks returned an average of 11% in nominal terms and 4% in real terms. At the end of the 20 years, the portfolio value was:
A) $1,800 in real terms.
B) $3,679.19 in real terms.
C) $7,870.59 in nominal terms.
D)$8,062.31 in nominal terms.

Accepted Answer

FV_Nominal = $1,000(1.11)²⁰ = $8,062.31FV_Real = $1,000(1.04)²⁰ = $2,191.12

Question 3

The wider the dispersion of returns on a stock, the:
A) lower the expected rate of return.
B) higher the standard deviation.
C) lower the real rate of return.
D)lower the variance.

Accepted Answer

The wider the dispersion of returns on a stock, the higher the standard deviation. This is because standard deviation measures the amount of variability or dispersion of a set of data points. Therefore, a wider dispersion means higher standard deviation.

Question 4

The idea that investors in a common stock may expect a lower total return if they purchase a stock with limited price volatility rather than one with high price volatility suggests that:
A) investors are irrational.
B) there is a relationship between risk and return.
C) real rates of return will be lower during periods of price stability.
D)stocks should be avoided when inflation is low.

Accepted Answer

The concept of risk and return is a fundamental principle in finance. It suggests that the higher the risk of an investment, the higher the potential return. Investors who choose a stock with limited price volatility may expect a lower total return as it is considered a lower-risk investment. Therefore, option B is the correct answer. Option A is incorrect because the statement does not imply that investors are irrational. Option C is also incorrect as there is no evidence to suggest that real rates of return will be lower during periods of price stability. Option D is also incorrect as it is not related to the concept of risk and return.

Question 5

What is the standard deviation of returns of a 4-stock portfolio (each stock being equally weighted) that produced returns of 20%, 20%, 25%, and 30%?
A) 2.15%
B) 3.15%
C) 4.15%
D)5.15%

Accepted Answer

Mean = (20% + 20 + 25 + 30)/4 = 23.75%Variance = {(20 - 23.75)² + (20 - 23.75)² + (25 - 23.75)² + (30 - 23.75)²}/4 = 17.1875Std dev = 17.1875^.5 = 4.15%

Question 6

What is the standard deviation of a portfolio's returns if the mean return is 15%, the variance of returns is 184, and there are three stocks in the portfolio?
A) 7.83%
B) 13.56%
C) 41.00%
D)225.00%

Accepted Answer

Std dev = 184^.5 = 13.56%

Question 7

A stock is expected to return 11% in a normal economy, 19% if the economy booms, and lose 8% if the economy moves into a recessionary period. The economists predict a 65% chance of a normal economy, a 25% chance of a boom, and a 10% chance of a recession. What is the expected return on the stock?
A) 11.98%
B) 12.06%
C) 11.10%
D)11.23%

Accepted Answer

E(R) = (0.65 × 0.11) + (0.25 × 0.19) + (0.10 × -0.08) = 0.1110, or 11.10%

Question 8

What is the variance of returns of a 3-stock portfolio (with unequal weights 25%, 50%, and 25%) that produced returns of 20%, 25%, and 30%, respectively?
A) 10.00
B) 12.50
C) 15.00
D)20.00

Accepted Answer

Mean = .25 × 20% + .50 × 25% + .25 × 30% = 25%Variance = .25 × (20 - 25)² + .50 × (25 - 25)² + .25 × (30 - 25)² = 12.50

Question 9

An estimation of the opportunity cost of capital for projects that have an "average" level of risk is the rate of return on:
A) Treasury bills.
B) the market portfolio.
C) the market portfolio minus the rate of return on Treasury bills.
D)Treasury bonds plus a maturity premium.

Accepted Answer

The rate of return on the market portfolio is often used as an estimate of the opportunity cost of capital for projects with an "average" level of risk. This is because the market portfolio is considered to represent the average risk in the market, making it a suitable benchmark for such projects.

Question 10

The variance of an investment's returns is a measure of the:
A) volatility of the rates of return.
B) probability of a negative return.
C) historic return over long time periods.
D)average value of the investment.

Accepted Answer

The variance measures the dispersion of returns around the average or mean return. A high variance indicates greater volatility and risk, while a low variance indicates relatively stable and consistent returns. Therefore, option A is the best choice as it accurately describes the relationship between variance and the volatility of returns. Options B, C, and D do not accurately describe the role of variance in measuring investment returns.

Question 11

If the standard deviation of a portfolio's returns is known to be 30%, then its variance is:
A) 5.48%.
B) 5.48% squared.
C) 900.00%.
D)900.00% squared.

Accepted Answer

30%² = 900%²

Question 12

Which one of the following guarantees is offered to common stock investors?
A) Guarantee to receive dividends
B) Guarantee to receive capital gains
C) Guarantee only to receive a refund of principal
D)No guarantees of any form

Accepted Answer

Common stock investors do not have any guarantees. Their return on investment is dependent on the performance of the company and the stock market. They may receive dividends and capital gains, but there is no guarantee. The only guarantee is that they own a portion of the company and have voting rights at shareholder meetings.

Question 13

What is the approximate standard deviation of returns if over the past 4 years an investment returned 8%, -12%, -12%, and 15%?
A) 9.26%
B) 10.26%
C) 11.26%
D)12.01%

Accepted Answer

Mean = (8% - 12 - 12 + 15)/4 = -0.25%Variance = {[8 - (-0.25)]² + [-12 - (-0.25)]² + [-12 - (-0.25)]² + [15 - (-0.25)]²}/4 = 144.1875Std dev = 144.1875^.5 = 12.01%

Question 14

When the annual rate of return on U.S. Treasury bills is historically high, investors expect the risk premium on the stock market to be:
A) considerably lower than normal.
B) considerably higher than normal.
C) approximately normal.
D)approximately equal to zero.

Accepted Answer

The answer of When the annual rate of return on...

Question 15

In a year in which common stocks offered an average return of 18%, Treasury bonds offered 10%, and Treasury bills offered 7%. The risk premium for common stocks was:
A) 1%.
B) 3%.
C) 8%.
D)11%.

Accepted Answer

Risk premium = 18% - 7% = 11%

Question 16

What is the variance of returns of a 3-stock portfolio (each stock being equally weighted) that produced returns of 20%, 25%, and 30%?
A) 16.67
B) 33.33
C) 50.00
D)100.00

Accepted Answer

Mean = (20% + 25 + 30)/3 = 25%Variance = {(20 - 25)² + (25 - 25)² + (30 - 25)²}/3 = 16.67

Question 17

From a historical perspective (1900-2013), what would you expect to be the approximate return on a diversified portfolio of common stocks in a year that Treasury bills offered 7.5%?
A) 14.3%
B) 12.3%
C) 15.1%
D)16.5%

Accepted Answer

7.5% + 7.6% (historical risk premium on common stocks) = 15.1%

Question 18

Which one of the following security classes has the highest standard deviation of returns?
A) Common stocks
B) Long-term Treasury bonds
C) Treasury bills
D)Corporate bonds

Accepted Answer

Common stocks have a higher standard deviation of returns compared to other security classes due to their relatively high volatility in the market. While long-term Treasury bonds and Treasury bills usually offer a lower return, they also have a lower risk and standard deviation of returns. Corporate bonds also have a lower standard deviation compared to common stocks as they represent a lower risk of default by the issuing company.

Question 19

The appropriate opportunity cost of capital is the return that investors give up on alternative investments that:
A) possess the same level of risk.
B) earn the risk-free rate of return.
C) are included in the S&P 500 index.
D)earn the average market rate of return.

Accepted Answer

The appropriate opportunity cost of capital takes into consideration the return that investors could earn on alternative investments that carry the same level of risk.

Question 20

What is the approximate variance of returns if over the past 3 years an investment returned 8%, -12%, and 15%?
A) 31
B) 131
C) 182
D)961

Accepted Answer

Mean = (8% - 12 + 15)/3 = 3.67%Variance = {(8 - 3.67)² + (-12 - 3.67)² + (15 - 3.67)²}/3 = 131

Quiz 11: Introduction to Risk, Return, and the Opportunity Cost of Capital

The variance of a stock's returns can be calculated as the:

Over a 20-year period an investment of $1,000 in common stocks returned an average of 11% in nominal terms and 4% in real terms. At the end of the 20 years, the portfolio value was:

The wider the dispersion of returns on a stock, the:

The idea that investors in a common stock may expect a lower total return if they purchase a stock with limited price volatility rather than one with high price volatility suggests that:

What is the standard deviation of returns of a 4-stock portfolio (each stock being equally weighted) that produced returns of 20%, 20%, 25%, and 30%?

What is the standard deviation of a portfolio's returns if the mean return is 15%, the variance of returns is 184, and there are three stocks in the portfolio?

A stock is expected to return 11% in a normal economy, 19% if the economy booms, and lose 8% if the economy moves into a recessionary period. The economists predict a 65% chance of a normal economy, a 25% chance of a boom, and a 10% chance of a recession. What is the expected return on the stock?

What is the variance of returns of a 3-stock portfolio (with unequal weights 25%, 50%, and 25%) that produced returns of 20%, 25%, and 30%, respectively?

An estimation of the opportunity cost of capital for projects that have an "average" level of risk is the rate of return on:

The variance of an investment's returns is a measure of the:

If the standard deviation of a portfolio's returns is known to be 30%, then its variance is:

Which one of the following guarantees is offered to common stock investors?

What is the approximate standard deviation of returns if over the past 4 years an investment returned 8%, -12%, -12%, and 15%?

When the annual rate of return on U.S. Treasury bills is historically high, investors expect the risk premium on the stock market to be:

In a year in which common stocks offered an average return of 18%, Treasury bonds offered 10%, and Treasury bills offered 7%. The risk premium for common stocks was:

What is the variance of returns of a 3-stock portfolio (each stock being equally weighted) that produced returns of 20%, 25%, and 30%?

From a historical perspective (1900-2013) , what would you expect to be the approximate return on a diversified portfolio of common stocks in a year that Treasury bills offered 7.5%?

Which one of the following security classes has the highest standard deviation of returns?

The appropriate opportunity cost of capital is the return that investors give up on alternative investments that:

What is the approximate variance of returns if over the past 3 years an investment returned 8%, -12%, and 15%?