Question 1

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

Accepted Answer

Beta measures how much a stock moves in relation to the overall market. It is calculated as the covariance of the stock with the market divided by the variance of the market.

Beta = Covariance(AMZN, S&P 500) / Variance(S&P 500)

We are given that the covariance between Amazon and the S&P 500 is 0.05. We are also told that the standard deviation (which is the square root of the variance) of the S&P 500 is 20%.

So, 
Beta = 0.05 / (0.2^2) 
Beta = 1.25

Therefore, the answer is C, 1.25.

Question 2

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 0.18?

Accepted Answer

A security with no correlation coefficient relative to the U.S. stock market indicates that it is not affected by the movements of the stock market, thus making its beta 0. The expected return being double that of the stock market is irrelevant when calculating beta. The standard deviation of the stock market is also not used in calculating beta.

Question 3

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

Accepted Answer

Diversification allows investors to spread their investments across different securities, asset classes, industries, and geographies. Since the prices of different securities do not move exactly together, diversification reduces the risk of a portfolio. If one investment underperforms, the impact on the overall portfolio will be minimized by the performance of other investments.

Question 4

Beta is a measure of

Accepted Answer

Beta is a measure of market risk, which is the risk associated with investing in the overall market. It measures how volatile a stock or portfolio is, in relation to the overall market. It is not a measure of unique risk, total risk, or liquidity risk.

Question 5

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

To calculate beta, we need to first calculate the average returns for both the stock and the market:

Stock B: (0% + 10% + 26%) / 3 = 12%
Market: (+6% + 18% + 24%) / 3 = 16%

Next, we calculate the covariance between the stock and the market:

Covariance = [(0-12) x (6-16) + (10-12) x (18-16) + (26-12) x (24-16)] / 2

Covariance = -240/2 = -120

Finally, we calculate beta:

Beta = Covariance / Variance of the market
Variance of the market = [(6-16)^2 + (18-16)^2 + (24-16)^2] / 3 = 64

Beta = -120/64 = -1.875

Therefore, the answer is not one of the choices given. However, if we take the absolute value of beta to make it positive, the answer becomes 1.875. This is closest to choice B, 1.36. But we must remember that we should not take the absolute value of beta in reality.

Question 6

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

The beta of a stock represents the sensitivity of its returns to the market returns. A beta of 2.2 indicates that the stock's returns are expected to change 2.2 times more than the market returns. Therefore, for each 1 percent change in the market return, we can expect a 2.2 percent change in the return of the stock. Thus, the answer is C.

Question 7

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

Accepted Answer

The authors suggest that a reasonable range for the risk premium in the US is between 5% and 8%, as stated in the statement.

Question 8

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 9

Which of the following portfolios will have the highest beta?

Accepted Answer

Stocks, specifically common stocks, typically have a higher beta than bonds or Treasury bills. Therefore, a portfolio of U.S. common stocks will have the highest beta among the given options.

Question 10

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 11

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

Accepted Answer

The formula for portfolio variance for a portfolio of N-stocks contains N variance terms, one for each stock in the portfolio. These terms account for the individual risk associated with each stock.

Question 12

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 13

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

Accepted Answer

Beta and covariance are both measures of the relationship between the returns of different securities, but they are not measures of variability. Variability measures include standard deviation and variance.

Question 14

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

Accepted Answer

This is the definition of a risk premium. It represents the additional return that investors demand for taking on the uncertainties associated with a particular investment, compared to the return on a risk-free asset such as a Treasury bill.

Question 15

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

Accepted Answer

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

Question 16

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 17

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 measures the systematic risk of an asset relative to the market. The formula for beta is: 
Beta = (Correlation coefficient * Standard deviation of stock B) / Standard deviation of the market 
Substituting the given values: 
Beta = (0.8 * 35%) / 20% = 1.4 
Therefore, the answer is B, 1.4.

Question 18

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 19

The beta of the market portfolio is

Accepted Answer

The beta of the market portfolio is, by definition, 1.0. This means that the market portfolio has the same level of systematic risk as the overall market. A beta of less than 1.0 indicates that a security is less volatile than the market, while a beta of greater than 1.0 indicates that a security is more volatile than the market.

Question 20

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

Using the formula for beta:

Beta = Covariance(stock A, market) / Variance(market)

We first need to calculate the covariance between stock A and the market:

Covariance = [(-8%-6%)(10%+18%)+(10%-6%)(22%+18%)+(22%-6%)(24%+18%)] / 3
Covariance = 293/3

Next, we need to calculate the variance of the market:

Variance = [(6%-12.67%)^2 + (18%-12.67%)^2 + (24%-12.67%)^2] / 3
Variance = 46.22%

Beta = Covariance / Variance = (293/3) / 0.4622 = 1.64

Therefore, the answer is A) 1.64.

Quiz 7: Introduction to Risk and Return

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

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 0.18?

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

Beta is a measure of

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.

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

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

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

Which of the following portfolios will have the highest beta?

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.

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

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.

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

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

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

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

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.

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

The beta of the market portfolio is

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.