Question 1

Which portfolio had the highest average annual return in real terms between 1900 and 2017?

Accepted Answer

According to historical data, the portfolio of U.S. common stocks had the highest average annual return in real terms between 1900 and 2017, with an average yearly return of 6.5%. The portfolio of U.S. government bonds had an average yearly return of 2.5%, and the portfolio of Treasury bills had an average yearly return of 0.8%. Therefore, option A is the best choice for the portfolio with the highest average annual return in real terms.

Question 2

What has been the average annual nominal rate of return on a portfolio of U.S. common stocks over the past 117 years (from 1900 to 2017)?

Accepted Answer

The average annual nominal rate of return on a portfolio of U.S. common stocks over the past 117 years (from 1900 to 2017) has been greater than 11%. This reflects the long-term growth and resilience of the U.S. stock market despite various economic downturns and crises.

Question 3

Which portfolio has had the highest average risk premium during the period 1900-2017?

Accepted Answer

According to historical data, common stocks have provided the highest average risk premium during the period 1900-2017, with an average annual return of 9.8% and a risk premium of approximately 6.4%. Government bonds and Treasury bills have lower average returns and therefore lower risk premiums.

Question 4

What has been the average annual real rate of interest on Treasury bills over the past 117 years (from 1900 to 2017)?

Accepted Answer

The average annual real rate of interest on Treasury bills over the past 117 years has been less than 2%, reflecting the relatively low-risk and low-return nature of these government securities.

Question 5

What has been the average annual rate of return in real terms for a portfolio of U.S. common stocks between 1900 and 2017?

Accepted Answer

According to the data provided by NYU Stern, the average annual rate of return in real terms for a portfolio of U.S. common stocks between 1900 and 2017 was approximately 8.6%. This is greater than 8% and makes option D the correct choice.

Question 6

Which of the following countries has had the lowest risk premium?

Accepted Answer

The risk premium is the extra return required by investors to invest in a risky asset instead of a risk-free asset. Denmark has had historically low levels of risk premium due to its stable economy and fiscal policies, making it an attractive destination for investment with low risk. In contrast, Italy has had higher levels of risk premium due to its volatile economy and high levels of debt, while Germany and the United States have had moderate levels of risk premium. Therefore, the best choice is B) Denmark.

Question 7

A standard error measures

Accepted Answer

A standard error measures the reliability of an estimate. It is a statistical term that quantifies the amount of variation or dispersion that exists in a sample dataset. It gives an idea of how much the estimate of a population parameter (such as mean or standard deviation) is likely to differ from the true population parameter. It is commonly used in hypothesis testing and confidence interval estimation. It is not related to the nominal or real annual rate of return on a portfolio or to the risk of a portfolio.

Question 8

Spill Drink Company's stocks had -8 percent, 11 percent, and 24 percent rates of return, respectively, during the last three years; calculate the (arithmetic)average rate of return for the stock.

Accepted Answer

To calculate the average rate of return, we take the sum of the rates of return and divide by the number of years.
Average rate of return = (-8% + 11% + 24%) / 3 = 9%
Therefore, the best choice is B, with an average rate of return of 9 percent per year.

Question 9

For long-term U.S. government bonds, which risk concerns investors the most?

Accepted Answer

For long-term U.S. government bonds, interest rate risk concerns investors the most because as interest rates rise, the market value of existing bonds declines, leading to capital losses for investors who need to sell their bonds before maturity.

Question 10

Which portfolio has had the lowest average annual nominal rate of return during the 1900-2017 periods?

Accepted Answer

The portfolio of Treasury bills has had the lowest average annual nominal rate of return during the 1900-2017 period. Treasury bills are considered one of the most conservative investments, with very low risk but also very low returns. Therefore, they are not expected to have high average returns compared to other investments such as stocks or bonds.

Question 11

What has been the average annual nominal rate of interest on Treasury bills over the past 117 years (1900-2017)?

Accepted Answer

The average annual nominal rate of interest on Treasury bills over the past 117 years (1900-2017) has been greater than 3%. This reflects the long-term historical performance of these securities, taking into account various economic cycles, including periods of high inflation and interest rates, particularly during the late 20th century.

Question 12

If the average annual rate of return for common stocks is 11.7 percent, and 4.0 percent for U.S. Treasury bills, what is the average market risk premium?

Accepted Answer

The market risk premium is the difference between the average annual rate of return for common stocks (11.7%) and the rate of return for U.S. Treasury bills (4.0%), which is 7.7% (11.7% - 4.0%). Therefore, the correct choice is C.

Question 13

Assume the following data: Risk-free rate = 4.0 percent; average risk premium = 7.7 percent. Calculate the required rate of return for the risky asset.

Accepted Answer

The required rate of return for the risky asset can be calculated using the formula:
Required rate of return = Risk-free rate + Average risk premium
= 4.0% + 7.7%
= 11.7%
Therefore, the best choice is C.

Question 14

One dollar invested in a portfolio of long-term U.S. government bonds in 1900 would have grown in nominal value by the end of year 2017 to:

Accepted Answer

The answer of One dollar invested in a portfolio of...

Question 15

Which of the following portfolios has the least risk?

Accepted Answer

Treasury bills are considered to have the least risk because they are backed by the U.S. government and have a low volatility compared to other investments. Long-term U.S. government bonds have slightly higher risk due to interest rate changes, U.S. common stocks of small firms have higher risk associated with the company's performance, and U.S. common stocks of large firms have moderate risk associated with market fluctuations.

Question 16

For log normally distributed returns, annual compound returns equal

Accepted Answer

For log-normally distributed returns, the annual compound return equals the arithmetic average return minus half the variance. This is because the compound return is adjusted for the volatility drag, which is represented by subtracting half the variance of the returns.

Question 17

Which of the following is an estimate of the standard error of the mean?

Accepted Answer

The standard error of the mean is calculated by dividing the standard deviation by the square root of the number of observations. Therefore, the correct choice is C, which divides the standard deviation of returns by the square root of the number of observations. A is the formula for calculating the standard deviation, but not the standard error of the mean. B is the formula for calculating the standard deviation, but not the standard error of the mean. D is the formula for calculating the variance, but not the standard error of the mean.

Question 18

One dollar invested in a portfolio of U.S. common stocks in 1900 would have grown in nominal value by the end of year 2017 to

Accepted Answer

This question is testing knowledge of long-term stock market performance. According to historical data, including dividends reinvested, the average annual return of the US stock market has been about 9-10% per year over the very long-term (100+ years). Using this average annual return, a $1 investment in 1900 would be worth approximately $47,661 in nominal value by the end of 2017. Therefore, choice A is the correct answer. The other answer choices are significantly lower and do not reflect the long-term growth potential of the stock market.

Question 19

Which of the following provides a correct measure of the opportunity cost of capital regardless of the timing of cash flows?

Accepted Answer

The answer of Which of the following provides a correct...

Question 20

If the standard deviation of annual returns is 19.8 percent and the number of years of observation is 107, what is the standard error?

Accepted Answer

The formula for standard error (SE) is SE = standard deviation / square root of sample size. Plugging in the given values, we get SE = 19.8% / sqrt(107) = 1.91%. Therefore, the correct answer is choice B.

Quiz 7: Introduction to Risk and Return