Question 1

Two companies Amber and Bolt are manufacturers of glass.The securities of the companies are listed and traded in the New York Stock Exchange.An investor's portfolio consists of these two securities in the proportion of 5/6 and 1/6 respectively.Amber's security has an expected return of 20% and a standard deviation of 8%.Bolt has an expected return of 15% and a standard deviation of 5%.The correlation coefficient between the two securities is 0.6.Calculate the expected return and the standard deviation of the investor's portfolio.
A) $\bar { R } _ { P } = 19.17 \% ; \sigma _ { P } = 7.20 \%$
B) $\bar { R } _ { P } = 20.19 \% ; \sigma _ { P } = 8.20 \%$
C) $\bar { R } _ { P } = 17 \% ; \sigma _ { P } = 7.0 \%$
D) $\bar { R } _ { P } = 18.19 \% ; \sigma _ { P } = 8.0 \%$

Accepted Answer

The expected return of the portfolio ($\bar { R } _ { P }$) is calculated as the weighted average of the expected returns of the individual securities, which is $0.8333 \times 20\% + 0.1667 \times 15\% = 19.17\%$. The standard deviation of the portfolio ($\sigma _ { P }$) is calculated using the formula for the standard deviation of a two-asset portfolio, which incorporates the weights of the assets, their standard deviations, and the correlation coefficient between them. The calculation yields a standard deviation of approximately $7.20\%$.

Question 2

If the returns on different assets are uncorrelated:
A) an increase in the number of assets in a portfolio may bring the standard deviation of the portfolio close to zero.
B) there will be little gain from diversification.
C) diversification will result in risk averaging but not in risk reduction.
D) the expected return on a portfolio of such assets should be zero.

Accepted Answer

When the returns on different assets are uncorrelated, diversification can significantly reduce the portfolio's risk, potentially bringing the standard deviation of the portfolio close to zero, as uncorrelated assets do not move in tandem, smoothing out the overall volatility.

Question 3

Using the Sharpe single-index model with a random portfolio of U.S.common stocks,as one increases the number of stocks in the portfolio,the total risk of the portfolio will:
A) approach zero.
B) approach the portfolio's systematic risk.
C) approach the portfolio's non-systematic risk.
D) not be affected.

Accepted Answer

According to the Sharpe single-index model, the total risk of a portfolio can be decomposed into systematic risk (measured by beta) and non-systematic risk (measured by residual risk). As the number of stocks in the portfolio increases, the non-systematic risk decreases because it becomes more diversified. However, the systematic risk remains the same regardless of the number of stocks in the portfolio. Therefore, as the portfolio becomes more diversified, the total risk of the portfolio will approach the portfolio's systematic risk, which is measured by beta.

Question 4

Consider the probability distribution below.(Note that the expected returns of A and B have already been computed for you.)
 $$\begin{array} { | c | c | c | c | } 
\hline \text { State } & \mathbf { p } ( \mathbf { s } ) & \mathbf { r } _ { \mathrm { A } } & \mathbf { r } _ { \mathrm { B } } \
\hline \text { Recession } & 0.3 & - 0.11 & 0.16 \
\text { Normal } & 0.4 & 0.13 & 0.06 \
\text { Boom } & 0.3 & 0.27 & - 0.04 \
\hline \text { Expected Return: } && 0.1 & 0.06 \
\hline
\end{array}$$ a.Calculate the standard deviations of A and B.
b.Calculate the covariance and correlation between A and B.
c.Calculate the expected return of the portfolio that invests 30% in stock A and the rest in stock B.
d.Calculate the standard deviation of the portfolio in part b.

Accepted Answer

The answer of Consider the probability distribution below.(Note that the...

Question 5

Discuss whether the following statement is true or false:
One can always construct a multi-index model that explains more of the returns on a security than a single-index model does.

Accepted Answer

The single-index model assumes that the stock prices move together only because of common movement in the market.Hence,the single index-model derives returns on securities with the help of the market movement in which the securities are being traded.Although,according to many researchers,there are influences beyond the market that cause stocks to move together.The multi-index model includes two different types of schemes that have been put forth for handling additional influences.Hence,the multi-index model takes into consideration the return on securities by introducing additional sources of covariance.By adding these additional influences,the multi-index model explains more of the returns to the general return equation of the single-index model.

Question 6

With the help of a diagram show,how would you identify a ray with the greatest slope as an efficient frontier where riskless lending and borrowing is present?

Accepted Answer

The answer of With the help of a diagram show,how...

Question 7

Which of the following is correct of how the returns on assets move together?
A) Positive and negative deviations between assets at similar times give a negative covariance.
B) Positive and negative deviations between assets at dissimilar times give a negative covariance.
C) Positive and negative deviations between assets give a zero covariance.
D) Positive and negative deviations between assets at dissimilar times give a positive covariance.

Accepted Answer

Covariance measures the extent to which the returns on two assets move together. Positive and negative deviations between assets at dissimilar times give a negative covariance, which means that when one asset is performing well, the other is not and vice versa. This is because dissimilar times refer to different market conditions, affecting asset returns differently. Therefore, option B is the correct answer.

Question 8

Discuss whether the following statement is true or false:
A multi-index model will predict returns better than a single-index model.

Accepted Answer

The multi-index model lies in an intermediate position between the full historical correlation matrix and the single-index model in its ability to reproduce the historical correlation matrix.Adding more indexes complicates things but result in a more accurate representation of the historical correlation matrix.However,this does not imply that future correlation matrices will be forecast more accurately.

Question 9

Describe what is semivariance? Give reasons why semivariance is not used as a measure of dispersion.

Accepted Answer

The answer of Describe what is semivariance? Give reasons why...

Question 10

Under what condition will adding a security with a high standard deviation decrease the risk of a portfolio?

Accepted Answer

The answer of Under what condition will adding a security...

Question 11

Which of the following is true of a cutoff rate?
A) The cutoff rate is be determined by dividing the Beta with the difference between average return and return on the riskfree rate of the securities.
B) All securities whose return is above the cutoff rate are selected in the market portfolio.
C) The cutoff rate is computed from the characteristics of all securities in the optimum portfolio.
D) All securities whose risk is below the cutoff rate are selected in the optimum portfolio.

Accepted Answer

The answer of Which of the following is true of...

Question 12

Consider the following historical data for the returns on assets A and B and the market portfolio:
$\begin{array}{|c|c|c|c|}
\hline \text { Period } & \text { Asset A } & \text { Asset B } & \text { Market Portfolio } \
\hline 1 & 10 \% & 6 \% & 4 \% \
\hline 2 & 3 \% & 6 \% & 1 \% \
\hline 3 & 5 \% & 2 \% & 5 \% \
\hline 4 & 2 \% & 4 \% & 2 \% \
\hline 5 & 1 \% & 2 \% & 1 \% \
\hline
\end{array}$

a. What is the covariance between asset A and asset B?
b. If the beta of asset B is 0.5, what is the systematic return and non-systematic return for asset B in each period?

Accepted Answer

The answer of Consider the following historical data for the...

Question 13

Consider the following data for assets A and B: $\bar { R } _ { \mathrm { A } } = 10 \%$ ; $\bar { R } _ { B } = 19 \%$ ; $\sigma _ { \mathrm { A } } = 3 \%$ ; $\sigma _ { B } = 5 \%$ ; $\beta _ { \mathrm { A } } = 0.6$ ; $\beta _ { B } = 1.4$ ; $\rho _ { A B } = 0.4$ . 
a. Calculate the expected return, variance, and beta of a portfolio constructed by investing 1/3 of your funds in asset A and 2/3 in asset B.
b. If only the riskless asset and assets A and B are available, find the optimum risky-asset portfolio if the risk-free rate is 8%.

Accepted Answer

The answer of Consider the following data for assets A...

Question 14

The risk on a portfolio of assets:
A) is different from the risk on the market portfolio.
B) is not influenced by the risk of individual assets.
C) is different from the risk of individual assets.
D) is negatively correlated to the risk of individual assets.

Accepted Answer

The risk of a portfolio of assets is different from the risk of individual assets, as diversification can reduce the overall risk through the combined effect of the different asset classes. The risk of the portfolio is influenced by the correlation between the assets, the diversification, and the weight of each asset in the portfolio. The risk on the market portfolio may be used as a benchmark to compare the risk of a portfolio, but it is not the same as the risk of a portfolio. Therefore, A and B are incorrect. It cannot be concluded that the risk of the portfolio is negatively correlated to the risk of individual assets in general, so D is also incorrect.

Question 15

The annual returns of Wonder Widgets,Inc.and the S&P 500 Composite Index over the last ten years were as follows: $\begin{array} { r c c } \text { Year } & \text { Wonder Widgets } & \text { S\&P } 500 \ \hline 1 & - 15 \% & - 8.5 \% \ 2 & 10 \% & 4.0 \% \ 3 & 12 \% & 14.0 \% \ 4 & 20 \% & 15.0 \% \ 5 & - 20 \% & - 14.0 \% \ 6 & - 15 \% & - 26.0 \% \ 7 & 25 \% & 37.0 \% \ 8 & 30 \% & 24.0 \% \ 9 & - 10 \% & - 7.0 \% \ 10 & 3 \% & 6.5 \% \end{array}$ Find the following for Wonder Widgets: a. Beta ($\beta$_W, slope of regression line) b. Alpha ($\alpha$_W, intercept of regression line) c. Unsystematic variance ($\sigma$²_W -$\beta$²_W$\sigma$²_m) d. Correlation coefficient ( )

Accepted Answer

The answer of The annual returns of Wonder Widgets,Inc.and the...

Question 16

Stock A has an expected return of 8% and a standard deviation of 40%.Stock B has an expected return of 13% and standard deviation of 60%.The correlation between A and B is -1 (i.e.,they are perfectly negatively correlated).Show that you can form a zero risk portfolio by investing $w _ { A } = \frac { \sigma _ { B } } { \sigma _ { A } + \sigma _ { B } }$ in A and the rest in B.

Accepted Answer

The answer of Stock A has an expected return of...

Question 17

Consider the following data for assets A,B,and C $\bar { R } _ { A } = 12 \%$ ; $\bar { R } _ { B } = 8 \%$ ; $\bar { R } _ { C } = 6 \%$ ; $\beta _ { \mathrm { A } } = 1.1$ ; $\beta _ { B } = 0.8$ ; $\beta _ { C } = 0.9$ ; $\sigma _ { e A } ^ { 2 } = 10$ ; $\sigma _ { e B } ^ { 2 } = 15$ ; $\sigma _ { e C } ^ { 2 } = 5$ .
Assume the variance of the market portfolio is 20 and that a riskless asset exists.Set up the first-order conditions for the optimum risky-asset portfolio.

Accepted Answer

The answer of Consider the following data for assets A,B,and...

Question 18

What is the concept behind the indexes used in the Fama and French Model?
A) Form portfolios with standard deviations that mimic the impact of the variables.
B) Form portfolios with returns that are opposite to the impact of the variables.
C) Form portfolios with returns that mimic the impact of the variables.
D) Form portfolios with standard deviations that are opposite to the impact of the variables.

Accepted Answer

The concept behind the indexes used in the Fama and French model is to form portfolios with returns that mimic the impact of the variables. Specifically, the model uses three factors--market risk, size, and value--to explain differences in stock returns. By forming portfolios that reflect exposure to these factors, the Fama and French model aims to capture more of the variation in stock returns than traditional models that rely only on market risk. Therefore, choice C is the correct answer as it reflects the concept behind the Fama and French indexes.

Question 19

An efficient frontier is:
A) a combination of securities that have the highest expected return for each level of risk.
B) the combination of two securities or portfolios represented as a convex function.
C) a combination of securities that lie below the minimum variance portfolio and the maximum return portfolio.
D) a combination of securities that have an average expected return for each level of risk.

Accepted Answer

An efficient frontier represents the combination of securities or portfolios that have the highest possible expected return for each level of risk. It is a curve that plots the expected return on the vertical axis and the risk, usually represented by standard deviation, on the horizontal axis. The portfolios that lie on the curve are considered "efficient," meaning that no other portfolio can offer a higher expected return for the same level of risk, or a lower level of risk for the same expected return. Therefore, the efficient frontier represents the optimal portfolio choices for an investor seeking to maximize returns while minimizing risk.

Question 20

The following diagram shows the investment opportunity set for portfolios containing stocks A and B.You need to know that:
•Point A on the graph represents a portfolio with 100% in stock A
•Point B represents a portfolio with 100% in stock B  a.Is the correlation between A and B greater than,equal to,or less than 1.How do you know?
b.Which labeled point on the graph represents the minimum variance portfolio?
c.Which labeled point on the graph represents a portfolio with 88% invested in stock A and the rest in B? 
d.If A and B are the only investments available to an investor,which of the labeled portfolios are efficient? 
e.Suppose a risk-free asset exists,allowing an investor to invest or borrow at the risk-free rate of 3%.If the above graph is drawn perfectly to scale,which labeled point represents the optimal risky portfolio.
f.Under the assumptions in part (e),would it be wise for an investor to invest all of his or her money in stock A? Why or why not?

Accepted Answer

The answer of The following diagram shows the investment opportunity...

Quiz 2: Portfolio Analysis

If the returns on different assets are uncorrelated:

Using the Sharpe single-index model with a random portfolio of U.S.common stocks,as one increases the number of stocks in the portfolio,the total risk of the portfolio will:

Discuss whether the following statement is true or false: One can always construct a multi-index model that explains more of the returns on a security than a single-index model does.

With the help of a diagram show,how would you identify a ray with the greatest slope as an efficient frontier where riskless lending and borrowing is present?

Which of the following is correct of how the returns on assets move together?

Discuss whether the following statement is true or false: A multi-index model will predict returns better than a single-index model.

Describe what is semivariance? Give reasons why semivariance is not used as a measure of dispersion.

Under what condition will adding a security with a high standard deviation decrease the risk of a portfolio?

Which of the following is true of a cutoff rate?

The risk on a portfolio of assets:

What is the concept behind the indexes used in the Fama and French Model?

An efficient frontier is: