Question 1

Diversification reduces the risk of a portfolio because the prices of different securities do not move exactly together.

Accepted Answer

Diversification helps to spread risk across different securities, which may not always move in the same direction or at the same magnitude. This reduces the overall risk of the portfolio as losses from one security can be offset by gains from another.

Question 2

According to the authors, a reasonable range for the risk premium in the United States is 5 percent to 8 percent.

Accepted Answer

The statement is true, as mentioned in the article.

Question 3

For log normally distributed returns, the annual geometric average return is greater than the arithmetic average return.

Accepted Answer

For log normally distributed returns, the annual geometric average return is equal to the arithmetic average return.

Question 4

The correlation coefficient between stock B and the market portfolio is 0.8.The standard deviation of stock B is 35 percent and that of the market is 20 percent.Calculate the beta of the stock.

Accepted Answer

Beta of the stock = Correlation coefficient * (Standard deviation of stock / Standard deviation of market) = 0.8 * (35%/20%) = 1.4

Question 5

Treasury bills typically provide higher average returns, both in nominal terms and in real terms, than long-term government bonds.

Accepted Answer

Treasury bills, being short-term securities, generally offer lower average returns than long-term government bonds due to the lower risk associated with their shorter maturity periods.

Question 6

The standard statistical measures of the variability of stock returns are beta and covariance.

Accepted Answer

Beta and covariance are measures of the relationship between the returns of a stock and the returns of the overall market, not measures of variability. Measures of variability include variance and standard deviation.

Question 7

Which of the following portfolios will have the highest beta?

Accepted Answer

U.S. common stocks are generally more volatile and have a higher beta compared to U.S. Treasury bills or government bonds. Therefore, a portfolio of U.S. common stocks will have the highest beta.

Question 8

For a portfolio of N-stocks, the formula for portfolio variance contains

Accepted Answer

The formula for portfolio variance includes the covariance between each pair of stocks in the portfolio. Since there are N stocks, there are N(N-1)/2 different pairs of stocks, and therefore the portfolio variance formula contains N(N-1)/2 covariance terms.

Question 9

What is the beta of a security where the expected return is double that of the stock market, there is no correlation coefficient relative to the U.S.stock market, and the standard deviation of the stock market is .18?

Accepted Answer

The beta of a security measures the volatility of the security relative to the market. A beta of 1.0 indicates that the security has the same volatility as the market. A beta greater than 1.0 means that the security is more volatile than the market, while a beta less than 1.0 means that the security is less volatile than the market.

Given that the expected return of the security is double that of the stock market, it implies that the security is riskier than the stock market. However, the fact that it has no correlation coefficient relative to the U.S. stock market means that it does not move with the market at all. Therefore, it is impossible to calculate the beta of the security.

The best answer, in this case, is A) 0.00, which represents a security with zero correlation to the market, and thus beta cannot be calculated.

Question 10

The beta of the market portfolio is

Accepted Answer

The beta of the market portfolio is defined as 1.0 by definition.

Question 11

The portfolio risk that cannot be eliminated by diversification is called market risk.

Accepted Answer

Market risk is the risk that affects the overall stock market and cannot be eliminated by diversification as it is systematic or non-diversifiable. It includes factors such as economic conditions, interest rates, political events, and natural disasters, which can affect the entire market and all the stocks within it.

Question 12

The portfolio risk that cannot be eliminated by diversification is called unique risk.

Accepted Answer

The portfolio risk that cannot be eliminated by diversification is called systematic risk or market risk, not unique risk. Unique risk, also known as unsystematic risk, is specific to a single company or industry and can be reduced through diversification.

Question 13

The historical nominal returns for stock A were -8 percent, +10 percent, and +22 percent.The nominal returns for the market portfolio were +6 percent, +18 percent, and 24 percent during this same time.Calculate the beta for stock A.

Accepted Answer

First, we need to calculate the average nominal returns for both stock A and the market portfolio.
Average nominal return of stock A: (-8% + 10% + 22%) / 3 = +8%
Average nominal return of market portfolio: (6% + 18% + 24%) / 3 = +16%

Then, we can calculate stock A's beta using the following formula:
Beta of stock A = (average nominal return of stock A - risk-free rate) / (average nominal return of the market portfolio - risk-free rate)

Assuming the risk-free rate is 3%, we get:
Beta of stock A = (8% - 3%) / (16% - 3%) = 1.64

Therefore, the best choice is A, with a beta of 1.64.

Question 14

If the standard deviation of returns on the market is 20 percent, and the beta of a well-diversified portfolio is 1.5, calculate the standard deviation of this portfolio.

Accepted Answer

The standard deviation of a well-diversified portfolio can be calculated as the product of the market's standard deviation and the portfolio's beta. Here, it's 20% * 1.5 = 30%.

Question 15

A risk premium is the difference between a security's return and the Treasury bill return.

Accepted Answer

This statement is true. A risk premium is the additional return that investors require to accept the risk of investing in a particular security or asset. It is calculated as the difference between the return on the investment and the risk-free rate, typically represented by the yield on Treasury bills.

Question 16

For each additional 1 percent change in market return, the return on a stock having a beta of 2.2 changes, on average, by

Accepted Answer

A stock's beta measures its sensitivity to market movements. A beta of 2.2 indicates that the stock's return is expected to change by 2.2 percent for each 1 percent change in market return. Therefore, the answer is C: 2.20 percent.

Question 17

The correlation coefficient between a stock and the market portfolio is +0.6.The standard deviation of return of the stock is 30 percent and that of the market portfolio is 20 percent.Calculate the beta of the stock.

Accepted Answer

The answer of The correlation coefficient between a stock and...

Question 18

The annual returns for three years for stock B were 0 percent, 10 percent, and 26 percent.Annual returns for three years for the market portfolio were +6 percent, 18 percent, and 24 percent.Calculate the beta for the stock.

Accepted Answer

Using the formula for beta:

Beta = (Covariance of stock returns and market returns) / (Variance of market returns)

First, we need to calculate the covariance of stock B returns and the market portfolio returns. We can use the following formula:

Covariance = Σ [(Ri - R̄i) * (Rm - R̄m)] / (N-1)

where 
- Ri is the return for stock B
- R̄i is the average return for stock B
- Rm is the return for the market portfolio
- R̄m is the average return for the market portfolio
- N is the number of observations

Calculating for each year:

Year 1: [(0% - (10%+6%)/2) * (6% - 12%)] = 0.03
Year 2: [(10% - (10%+6%)/2) * (18% - 12%)] = 0.12
Year 3: [(26% - (10%+6%)/2) * (24% - 12%)] = 0.52

Summing up the yearly covariances:

Covariance = 0.03 + 0.12 + 0.52 = 0.67

Next, we need to calculate the variance of the market portfolio returns. We can use the following formula:

Variance = Σ [(Rm - R̄m)^2] / (N-1)

Calculating for each year:

Year 1: (6% - 12%)^2 = 36
Year 2: (18% - 12%)^2 = 36
Year 3: (24% - 12%)^2 = 144

Summing up the yearly variances:

Variance = 36 + 36 + 144 = 216

Finally, we can calculate the beta:

Beta = 0.67 / 216 = 0.003 (rounded to two decimal places)

Therefore the answer is B)1.36

Question 19

The covariance between YOHO stock and the S&P 500 is 0.05.The standard deviation of the stock market is 20 percent.What is the beta of YOHO?

Accepted Answer

The formula for beta is β = cov(ri , rM ) / var(rM)
Given that cov(YOHO, S&P 500) = 0.05 and the standard deviation of the stock market is 20%, we need to calculate the variance of the S&P 500.
Variance of S&P 500 = (20%)^2 = 0.04
Now substituting the values in the formula,
β = 0.05 / 0.04 = 1.25
Therefore, the correct answer is C) 1.25.

Question 20

Beta is a measure of

Accepted Answer

Beta measures market risk, which is the risk that is inherent in investing in the overall market. It is a statistical measure that compares the volatility of a stock's returns to the volatility of the overall market. A beta of 1 indicates that a stock's returns correlate perfectly with the market, while a beta of less than 1 indicates lower volatility than the market and a beta of greater than 1 indicates higher volatility than the market. Beta does not measure unique risk, total risk, or liquidity risk.

Quiz 7: Introduction to Risk and Return