Question 1

The risk-free rate of return is currently 3 percent, whereas the market risk premium is 6 percent. If the beta of Lenz, Inc., stock is 1.8, then what is the expected return on Lenz?

Accepted Answer

The expected return on Lenz, Inc. can be calculated using the Capital Asset Pricing Model (CAPM) as: 
Expected Return = Risk-Free Rate + Beta * Market Risk Premium 
Expected Return = 3% + 1.8 * 6% 
Expected Return = 13.8% 
Therefore, the expected return on Lenz is 13.8%. The best choice is (C).

Question 2

Most of the risk-reduction benefits from diversification can be achieved in a portfolio consisting of

Accepted Answer

While there is no exact number that guarantees the benefits of diversification, studies have shown that a well-diversified portfolio should consist of at least 15 to 20 different stocks across various industries and sectors. This helps to minimize the risk of exposure to any single company or sector and allows for the potential benefits of growth in different areas of the market. However, it is important to note that diversification alone does not guarantee a profit or eliminate all risks.

Question 3

The beta of RicciCo.'s stock is 3.2, whereas the risk-free rate of return is 9 percent. If the expected return on the market is 18 percent, then what is the expected return on RicciCo.?

Accepted Answer

According to the capital asset pricing model (CAPM),
Expected Return on Stock = Risk-Free Rate + (Beta x (Expected Return on Market - Risk-Free Rate))
= 9% + (3.2 x (18% - 9%))
= 9% + (3.2 x 9%)
= 9% + 28.8%
= 37.8%

Question 4

Batman Stock has exhibited a standard deviation in stock returns of 0.5, whereas Superman Stock has exhibited a standard deviation of 0.6. The correlation coefficient between the stock returns is 0.5. What is the variance of a portfolio composed of 70 percent Batman and 30 percent Superman?

Accepted Answer

First, we need to calculate the portfolio's weighted average standard deviation using the formula:

portfolio standard deviation = sqrt(w1^2 * SD1^2 + w2^2 * SD2^2 + 2*w1*w2*r*SD1*SD2)

where:
w1 = 0.7 (weight of Batman stock)
SD1 = 0.5 (standard deviation of Batman stock)
w2 = 0.3 (weight of Superman stock)
SD2 = 0.6 (standard deviation of Superman stock)
r = 0.5 (correlation coefficient between the stock returns)

Plugging in the numbers, we get:

portfolio standard deviation = sqrt(0.7^2 * 0.5^2 + 0.3^2 * 0.6^2 + 2*0.7*0.3*0.5*0.5*0.6) = 0.4326

Next, we need to square the portfolio standard deviation to get the variance:

portfolio variance = 0.4326^2 = 0.1869

Finally, we need to adjust for the weights of the individual stocks to get the variance of the portfolio composition. Since we have 70% Batman and 30% Superman, we can calculate the variance as:

portfolio variance = 0.7^2 * 0.5^2 + 0.3^2 * 0.6^2 + 2*0.7*0.3*0.5*0.5*0.6 = 0.2179

Therefore, the answer is B) 0.2179.

Question 5

A portfolio with a level of systematic risk the same as that of the market has a beta that is

Accepted Answer

A portfolio with a level of systematic risk the same as that of the market has a beta of 1. A beta of 0 would mean the portfolio has no systematic risk and a negative beta is not possible as it would imply an inverse relationship between the returns of the portfolio and the market.

Question 6

You have invested 40 percent of your portfolio in an investment with an expected return of 12 percent and 60 percent of your portfolio in an investment with an expected return of 20 percent. What is the expected return of your portfolio?

Accepted Answer

The expected return of the portfolio can be calculated by multiplying the weight of each investment by its expected return and then summing these products. For the first investment: 0.40 * 12% = 4.8%. For the second investment: 0.60 * 20% = 12%. Adding these together gives an expected return of 16.8% for the portfolio.

Question 7

Given the returns for two stocks with the following information, calculate the correlation coefficient of the returns for the two stocks. Assume the expected return for Stock 1 is 10.8 percent and 9.7 percent for Stock 2.
Prob
Stock 1
Stock 2
0)4
0)09
0)11
0)5
0)11
0)08
0)1
0)17
0)13

Accepted Answer

The correlation coefficient is a measure of the linear relationship between two variables. It can take on values between -1 and 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.In this case, the correlation coefficient between the returns for the two stocks is 0.230967. This indicates that there is a weak positive correlation between the returns for the two stocks. This means that when the return for Stock 1 is high, the return for Stock 2 is also likely to be high, and when the return for Stock 1 is low, the return for Stock 2 is also likely to be low.

Question 8

Which of the following investors should be willing to pay the highest price for an asset?

Accepted Answer

The answer of Which of the following investors should be...

Question 9

The beta of Elsenore, Inc., stock is 1.6, whereas the risk-free rate of return is 8 percent. If the expected return on the market is 15 percent, then what is the expected return on Elsenore?

Accepted Answer

Using the Capital Asset Pricing Model (CAPM):
E(Ri) = Rf + βi(E(Rm) - Rf)
Elsenore's expected return = 8% + 1.6(15% - 8%) = 19.20%

Question 10

The expected return on Kiwi Computers stock is 16.6 percent. If the risk-free rate is 4 percent and the expected return on the market is 10 percent, then what is Kiwi's beta?

Accepted Answer

The CAPM formula states that the expected return on a security is equal to the risk-free rate plus the security's beta multiplied by the expected market risk premium (the difference between the expected return on the market and the risk-free rate). Mathematically: 
Expected Return = Risk-Free Rate + Beta x (Expected Market Return - Risk-Free Rate)
Substituting the given values: 
16.6% = 4% + Beta x (10% - 4%)
Solving for Beta: 
Beta = (16.6% - 4%) / (10% - 4%) = 2.1

Question 11

Given the returns for two stocks with the following information, calculate the covariance of the returns for the two stocks. Assume the expected return is 10.8 percent for Stock 1 and 9.7 percent for Stock 2.
Prob
Stock 1
Stock 2
0)4
0)09
0)11
0)5
0)11
0)08
0)1
0)17
0)13

Accepted Answer

The covariance of the returns for the two stocks is 0.000094. This is calculated by multiplying the covariance of the returns for the two stocks by the probability of each return. The covariance of the returns for the two stocks is 0.000094, and the probability of each return is 0.4, 0.09, 0.11, 0.5, 0.11, 0.08, 0.1, 0.17, and 0.13.

Question 12

Horse Stock returns have exhibited a standard deviation of 0.57, whereas Mod T Stock returns have a standard deviation of 0.63. The correlation coefficient between the returns is 0.078042. What is the covariance of the returns?

Accepted Answer

The answer of Horse Stock returns have exhibited a standard...

Question 13

The covariance of the returns between Einstein Stock and Bohr Stock is 0.0087. The standard deviation of Einstein is 0.26, and the standard deviation of Bohr is 0.37. What is the correlation coefficient between the returns of the two stocks?

Accepted Answer

The correlation coefficient is calculated as the covariance divided by the product of the standard deviations. Therefore, the correlation coefficient between the returns of the two stocks is 0.0087 / (0.26 * 0.37) = 0.090437.

Question 14

You have invested 20 percent of your portfolio in Homer, Inc., 40 percent in Marge Co., and 20 percent in Bart Resources. What is the expected return of your portfolio if Homer, Marge, and Bart have expected returns of 2 percent, 18 percent, and 3 percent, respectfully?

Accepted Answer

The expected return for the portfolio is calculated as follows:
Portfolio Expected Return = (Weight of Homer x Expected Return of Homer) + (Weight of Marge x Expected Return of Marge) + (Weight of Bart x Expected Return of Bart)
= (0.20 x 0.02) + (0.40 x 0.18) + (0.20 x 0.03)
= 0.004 + 0.072 + 0.006
= 0.082 or 8.2%
Therefore, the best choice is option B.

Question 15

The expected return on Mike's Seafood stock is 17.9 percent. If the expected return on the market is 13 percent and the beta for Kiwi is 1.7, then what is the risk-free rate?

Accepted Answer

The answer of The expected return on Mike's Seafood stock...

Question 16

Sayers purchased a stock with a coefficient of variation equal to 0.125. The expected return on the stock is 20 percent. What is the variance of the stock?

Accepted Answer

The answer of Sayers purchased a stock with a coefficient...

Question 17

The covariance of the returns between Wildcat Stock and Sun Devil Stock is 0.09875. The variance of Wildcat is 0.2116, and the variance of Sun Devil is 0.1369. What is the correlation coefficient between the returns of the two stocks?

Accepted Answer

The formula for correlation coefficient is:
Correlation Coefficient = Covariance / (Standard Deviation of Stock1 x Standard Deviation of Stock2)

We first need to calculate the standard deviation of both stocks:
Standard Deviation of Wildcat = √Variance of Wildcat = √0.2116 = 0.4600
Standard Deviation of Sun Devil = √Variance of Sun Devil = √0.1369 = 0.3700

Now we can substitute the given values in the formula of correlation coefficient:
Correlation Coefficient = 0.09875 / (0.4600 x 0.3700) = 0.578731

Therefore, the best choice is D, with a correlation coefficient of 0.578731.

Question 18

You invested $3,000 in a portfolio with an expected return of 10 percent and $2,000 in a portfolio with an expected return of 16 percent. What is the expected return of the combined portfolio?

Accepted Answer

The expected return of the combined portfolio is calculated by taking the weighted average of the expected returns of the individual portfolios. For the $3,000 investment with a 10% expected return: ($3,000/$5,000) * 10% = 6%. For the $2,000 investment with a 16% expected return: ($2,000/$5,000) * 16% = 6.4%. Adding these together gives an expected return of 12.4% for the combined portfolio.

Question 19

Braniff Ground Services stock has an expected return of 9 percent and a variance of 0.25 percent. What is the coefficient of variation for Braniff?

Accepted Answer

The coefficient of variation is the ratio of the standard deviation to the expected return. 
Coefficient of variation = (standard deviation / expected return)
= sqrt(0.25%) / 9%
= 0.5% / 9%
= 0.05556 or 0.5556% (rounded to four decimal places) 
Therefore, the best choice is B.

Question 20

Aquaman Stock has exhibited a standard deviation in stock returns of 0.7, whereas Green Lantern Stock has exhibited a standard deviation of 0.8. The correlation coefficient between the stock returns is 0.1. What is the standard deviation of a portfolio composed of 70 percent Aquaman and 30 percent Green Lantern?

Accepted Answer

To find the standard deviation of a portfolio with two stocks, we use the formula:

σportfolio = √(w1^2σ1^2 + w2^2σ2^2 + 2w1w2ρσ1σ2)

where w1 and w2 are the weights of the two stocks in the portfolio, σ1 and σ2 are the standard deviations of the two stocks, ρ is the correlation coefficient between the two stocks.

Given:

w1 = 0.7, w2 = 0.3
σ1 = 0.7, σ2 = 0.8
ρ = 0.1

Substituting the values in the formula, we get:

σportfolio = √(0.7^2*(0.7)^2 + 0.3^2*(0.8)^2 + 2*0.7*0.3*0.1*0.7*0.8)
= √(0.34522)
= 0.56676

Therefore, the standard deviation of the portfolio is 0.56676, which corresponds to choice C.

Quiz 7: Risk and Return