Question 1

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

The slope of the best feasible CAL is equal to the ratio of the expected return of the risky portfolio to its standard deviation. In this case, the slope is 16% / 20% = 0.8.

Question 2

Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 13% and a standard deviation of 21%. L has an expected rate of return of 10% and a standard deviation of 15%. The weights of K and L in the global minimum variance portfolio are _____ and _____, respectively.

Accepted Answer

For two perfectly negatively correlated securities, the weights in the global minimum variance portfolio can be calculated using the formula: $w_K = \frac{\sigma_L}{\sigma_K + \sigma_L}$ and $w_L = \frac{\sigma_K}{\sigma_K + \sigma_L}$, where $w_K$ and $w_L$ are the weights of securities K and L, respectively, and $\sigma_K$ and $\sigma_L$ are the standard deviations of securities K and L, respectively. Plugging in the given standard deviations, $w_K = \frac{15}{21 + 15} = \frac{15}{36} = 0.4167$ and $w_L = \frac{21}{36} = 0.5833$.

Question 3

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

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 rate of return is calculated by taking the weighted average of the returns in each state. The standard deviation is calculated by finding the square root of the weighted average of the squared deviations from the expected return.

Question 4

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

The covariance between two securities can be calculated using the formula: Cov(X,Y) = ρ(X,Y) * σX * σY, where ρ(X,Y) is the correlation coefficient between securities X and Y, σX is the standard deviation of X, and σY is the standard deviation of Y. Plugging in the given values: Cov(X,Y) = -0.4 * 0.18 * 0.21 = -0.01512, which rounds to -0.0151.

Question 5

Two securities have a covariance of 0.022. If their correlation coefficient is 0.52 and one has a standard deviation of 15%, what must be the standard deviation of the other security?

Accepted Answer

The answer of Two securities have a covariance of 0.022....

Question 6

A portfolio contains 3 stocks with expected returns of 15%, 18%, and 12%, with corresponding weights of 25%, 45%, and 30%, respectively. What is the expected return of the portfolio?

Accepted Answer

The answer of A portfolio contains 3 stocks with expected...

Question 7

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

The 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. After calculating, the standard deviations for stocks C and D are 10.35% and 12.93%, respectively.

Question 8

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

The coefficient of correlation between C and D is

Accepted Answer

The correlation coefficient is calculated using the covariance of returns and the standard deviations of the stocks. The negative correlation indicates that when one stock performs well, the other tends to perform poorly, which is consistent with the given returns.

Question 9

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

Accepted Answer

The expected rate of return for a stock is calculated by multiplying each possible return by its probability and then summing these products. For Stock C: $E(R_C) = 0.30(7\%) + 0.50(11\%) + 0.20(-16\%) = 2.1\% + 5.5\% - 3.2\% = 4.4\%$. For Stock D: $E(R_D) = 0.30(-9\%) + 0.50(14\%) + 0.20(26\%) = -2.7\% + 7\% + 5.2\% = 9.5\%$.

Question 10

Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 12% and a standard deviation of 17%. L has an expected rate of return of 9% and a standard deviation of 11%. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

Accepted Answer

The answer of Consider two perfectly negatively correlated risky securities,...

Question 11

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

The covariance between two securities is calculated using the formula: Cov(X,Y) = ρ(X,Y) * σX * σY, where ρ(X,Y) is the correlation coefficient between X and Y, σX is the standard deviation of X, and σY is the standard deviation of Y. Plugging in the given values: Cov(X,Y) = 0.8 * 0.22 * 0.28 = 0.04912, which rounds to 0.049.

Question 12

Two securities have a covariance of 0.076. If their respective standard deviations are 13% and 22%, what is their correlation coefficient?

Accepted Answer

The correlation coefficient is calculated using the formula: correlation coefficient = covariance / (standard deviation of X * standard deviation of Y). Plugging in the given values: 0.076 / (0.13 * 0.22) = 0.38.

Question 13

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

The answer of Consider two perfectly negatively correlated risky securities...

Question 14

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

The slope of the best feasible CAL is equal to the Sharpe ratio, which is calculated as (Expected return - Risk-free rate) / Standard deviation. In this case, the Sharpe ratio is (12% - 3%) / 26% = 0.35.

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

The risk-free portfolio's rate of return can be calculated using the formula for the expected return of a portfolio consisting of two perfectly negatively correlated assets, A and B: $E(R_p) = \frac{\sigma_B - \sigma_A}{\sigma_B + \sigma_A}E(R_A) + \frac{\sigma_A - \sigma_B}{\sigma_A + \sigma_B}E(R_B)$. Plugging in the given values: $E(R_p) = \frac{14 - 17}{14 + 17} * 12\% + \frac{17 - 14}{17 + 14} * 9\% = \frac{-3}{31} * 12\% + \frac{3}{31} * 9\% = -0.116\% + 0.871\% = 10.4\%$.

Question 16

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

Covariance is calculated using the formula: Cov(X,Y) = ρ(X,Y) * σX * σY, where ρ(X,Y) is the correlation coefficient between X and Y, σX is the standard deviation of X, and σY is the standard deviation of Y. Substituting the given values: Cov(X,Y) = -0.45 * 14% * 22% = -0.45 * 0.14 * 0.22 = -0.01386, which rounds to -0.0139.

Question 17

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

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 18

Two securities have a covariance of 0.092. If their respective standard deviations are 23% and 31%, what is their correlation coefficient?

Accepted Answer

The answer of Two securities have a covariance of 0.092....

Question 19

A portfolio contains 3 stocks with expected returns of 12%, 15%, and 9%, with corresponding weights of 30%, 35%, and 35%, respectively. What is the expected return of the portfolio?

Accepted Answer

The answer of A portfolio contains 3 stocks with expected...

Question 20

Security M has expected return of 17% and standard deviation of 28%. Security S has expected return of 13% and standard deviation of 15%. If the two securities have a correlation coefficient of 0.78, what is their covariance?

Accepted Answer

Covariance = Correlation coefficient * Standard deviation of Security M * Standard deviation of Security S= 0.78 * 0.28 * 0.15= 0.033

Quiz 7: Efficient Diversification

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?

Two securities have a covariance of 0.022. If their correlation coefficient is 0.52 and one has a standard deviation of 15%, what must be the standard deviation of the other security?

A portfolio contains 3 stocks with expected returns of 15%, 18%, and 12%, with corresponding weights of 25%, 45%, and 30%, respectively. What is the expected return of the portfolio?

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?

Two securities have a covariance of 0.076. If their respective standard deviations are 13% and 22%, what is their correlation coefficient?

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?

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?

Two securities have a covariance of 0.092. If their respective standard deviations are 23% and 31%, what is their correlation coefficient?

A portfolio contains 3 stocks with expected returns of 12%, 15%, and 9%, with corresponding weights of 30%, 35%, and 35%, respectively. What is the expected return of the portfolio?

Security M has expected return of 17% and standard deviation of 28%. Security S has expected return of 13% and standard deviation of 15%. If the two securities have a correlation coefficient of 0.78, what is their covariance?