Question 1

Security X has expected return of 7% and standard deviation of 14%. Security Y has expected return of 11% and standard deviation of 22%. If the two securities have a correlation coefficient of 0.45, what is their
Covariance?

Accepted Answer

Cov(r X, r Y) = (-0.45)(0.14)(0.22) = -.01386.

Question 2

Consider the following probability distribution for stocks C and D: $$\begin{array} { c c c c } 
\text { State } & \text { Probability } & \text { Return on Stock C } & \text { Return on Stock D } \
1 & 0.30 & 7 \% & - 9 \% \
2 & 0.50 & 11 \% & 14 \% \
3 & 0.20 & - 16 \% & 26 \% \
\hline
\end{array}$$ If you invest 25% of your money in C and 75% in D, what would be your portfolio's expected rate of return and standard deviation?

Accepted Answer

The answer of Consider the following probability distribution for stocks...

Question 3

Consider the following probability distribution for stocks C and D: $$\begin{array} { c c c c } 
\text { State } & \text { Probability } & \text { Return on Stock C } & \text { Return on Stock D } \
1 & 0.30 & 7 \% & - 9 \% \
2 & 0.50 & 11 \% & 14 \% \
3 & 0.20 & - 16 \% & 26 \%
\end{array}$$ The expected rates of return of stocks C and D are _____ and _____, respectively.

Accepted Answer

The expected rate of return is the weighted average of the possible returns, where the weights are the probabilities of each return. For stock C, the expected rate of return is (0.30 * 7%) + (0.50 * 11%) + (0.20 * -16%) = 4.4%. For stock D, the expected rate of return is (0.30 * -9%) + (0.50 * 14%) + (0.20 * 26%) = 9.5%.

Question 4

Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 13% and a standard deviation of 19%. L has an expected rate of return of 10% and a standard deviation of 16%.
The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

Accepted Answer

E(RP) = 0.46(13%) + 0.54(10%) = 11.38%.

Question 5

Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%.
The weights of A and B in the global minimum variance portfolio are _____ and _____, respectively.

Accepted Answer

wA = 14/(17 + 14) = 0.45; wB = 1 0.45 = 0.55.

Question 6

Given an optimal risky portfolio with expected return of 16%, standard deviation of 20%, and a risk-free rate of 4%, what is the slope of the best feasible CAL?

Accepted Answer

Slope = (16 - 4)/20 = .6.

Question 7

Consider the following probability distribution for stocks A and B: $$\begin{array} { c c c c } 
\text { State } & \text { Probability } & \text { Return on Stock A  } & \text { Return on Stock B } \
1 & 0.15 & 8 \% & 8 \% \
2 & 0.20 & 13 \% & 7 \% \
3 & 0.15 & 12 \% & 6 \% \
4 & 0.30 & 14 \% & 9 \% \
5 & 0.20 & 16 \% & 11 \% \
\hline
\end{array}$$ If you invest 35% of your money in A and 65% in B, what would be your portfolio's expected rate of return and standard deviation?

Accepted Answer

The expected return is calculated by taking the weighted average of the returns in each state. The standard deviation is calculated using the variance of the portfolio returns.

Question 8

Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 13% and a standard deviation of 19%. L has an expected rate of return of 10% and a standard deviation of 16%.
The weights of K and L in the global minimum variance portfolio are _____ and _____, respectively.

Accepted Answer

wK = 16/(19 + 16) = 0.46; wB = 1 0.46 = 0.54.

Question 9

Security X has expected return of 9% and standard deviation of 18%. Security Y has expected return of 12% and standard deviation of 21%. If the two securities have a correlation coefficient of 0.4, what is their
Covariance?

Accepted Answer

Cov(r X, r Y) = (-0.4)(0.18)(0.21) = 0.0151.

Question 10

Security M has expected return of 17% and standard deviation of 32%. Security S has expected return of 13% and standard deviation of 19%. If the two securities have a correlation coefficient of 0.78, what is their
Covariance?

Accepted Answer

Cov(r X, r Y) = (0.78)(0.32)(0.19) = 0.0474.

Question 11

Consider the following probability distribution for stocks C and D: $$\begin{array} { c c c c } 
\text { State } & \text { Probability } & \text { Return on Stock C } & \text { Return on Stock D } \
1 & 0.30 & 7 \% & - 9 \% \
2 & 0.50 & 11 \% & 14 \% \
3 & 0.20 & - 16 \% & 26 \% \
\hline
\end{array}$$ The standard deviations of stocks C and D are _____ and _____, respectively.

Accepted Answer

The standard deviation is calculated using the formula for variance: $\sigma^2 = \sum (p_i \times (r_i - \bar{r})^2)$, where $p_i$ is the probability, $r_i$ is the return, and $\bar{r}$ is the expected return. Calculating for both stocks, Stock C has a standard deviation of 10.35% and Stock D has a standard deviation of 12.93%.

Question 12

Consider the following probability distribution for stocks C and D: $$\begin{array} { c c c c } 
\text { State } & \text { Probability } & \text { Return on Stock C } & \text { Return on Stock D } \
1 & 0.30 & 7 \% & - 9 \% \
2 & 0.50 & 11 \% & 14 \% \
3 & 0.20 & - 16 \% & 26 \% \
\hline
\end{array}$$ The coefficient of correlation between C and D is

Accepted Answer

The correlation coefficient is calculated using the covariance of the returns of stocks C and D divided by the product of their standard deviations. The negative correlation indicates that when one stock's return increases, the other's tends to decrease.

Question 13

Consider the following probability distribution for stocks A and B: $$\begin{array} { c c c c } 
\text { State } & \text { Probability } & \text { Return on Stock A  } & \text { Return on Stock B } \
1 & 0.15 & 8 \% & 8 \% \
2 & 0.20 & 13 \% & 7 \% \
3 & 0.15 & 12 \% & 6 \% \
4 & 0.30 & 14 \% & 9 \% \
5 & 0.20 & 16 \% & 11 \% \
\hline
\end{array}$$ The coefficient of correlation between A and B is

Accepted Answer

The coefficient of correlation is calculated using the covariance of returns and the standard deviations of the returns of stocks A and B. After computing these values, the correlation coefficient is found to be approximately 0.590.

Question 14

Security X has expected return of 14% and standard deviation of 22%. Security Y has expected return of 16% and standard deviation of 28%. If the two securities have a correlation coefficient of 0.8, what is their
Covariance?

Accepted Answer

Cov(r X, r Y) = (0.8)(0.22)(0.28) = 0.04928.

Question 15

Consider two perfectly negatively correlated risky securities A and B A has an expected rate of return of 12% and a standard deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%.
The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

Accepted Answer

E(RP) = 0.45(12%) + 0.55(9%) = 10.35%.

Question 16

Given an optimal risky portfolio with expected return of 12%, standard deviation of 26%, and a risk free rate of 3%, what is the slope of the best feasible CAL?

Accepted Answer

Slope = (12 - 3)/26 = 0.346.

Quiz 7: Optimal Risky Portfolios

Security X has expected return of 7% and standard deviation of 14%. Security Y has expected return of 11% and standard deviation of 22%. If the two securities have a correlation coefficient of 0.45, what is their Covariance?

Given an optimal risky portfolio with expected return of 16%, standard deviation of 20%, and a risk-free rate of 4%, what is the slope of the best feasible CAL?

Security X has expected return of 9% and standard deviation of 18%. Security Y has expected return of 12% and standard deviation of 21%. If the two securities have a correlation coefficient of 0.4, what is their Covariance?

Security M has expected return of 17% and standard deviation of 32%. Security S has expected return of 13% and standard deviation of 19%. If the two securities have a correlation coefficient of 0.78, what is their Covariance?

Security X has expected return of 14% and standard deviation of 22%. Security Y has expected return of 16% and standard deviation of 28%. If the two securities have a correlation coefficient of 0.8, what is their Covariance?

Given an optimal risky portfolio with expected return of 12%, standard deviation of 26%, and a risk free rate of 3%, what is the slope of the best feasible CAL?