Question 1

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

-The standard deviations of stocks C and D are _____ and _____,respectively.

Accepted Answer

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

Question 2

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

-The expected rates of return of stocks C and D are _____ and _____,respectively.

Accepted Answer

The expected return for Stock C is $0.30 \times 7\% + 0.50 \times 11\% + 0.20 \times (-16\%) = 4.4\%$. The expected return for Stock D is $0.30 \times (-9\%) + 0.50 \times 14\% + 0.20 \times 26\% = 9.5\%$.

Question 3

Discuss how the investor can use the separation theorem and utility theory to produce an efficient portfolio suitable for the investor's level of risk tolerance.

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Question 4

Security X has expected return of 7% and standard deviation of 12%.Security Y has expected return of 11% and standard deviation of 20%.If the two securities have a correlation coefficient of -0.45,what is their covariance?

Accepted Answer

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Question 5

Given an optimal risky portfolio with expected return of 16% and 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 given by the formula: 
(Slope of CAL) = [(Expected Return of Optimal Risky Portfolio) - (Risk Free Rate)] / (Standard Deviation of Optimal Risky Portfolio)
= (16% - 4%) / 20%
= 0.6

Question 6

Given an optimal risky portfolio with expected return of 12% and 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 CAL (Capital Allocation Line) is given by the formula:

(Slope of CAL) = (Expected return of the optimal portfolio - Risk-free rate) / (Standard deviation of the optimal portfolio)

Plugging in the given values:

(Slope of CAL) = (0.12 - 0.03) / 0.26 = 0.346

Rounding to two decimal places:

(Slope of CAL) = 0.35

Therefore, the answer is D) 0.35.

Question 7

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 8

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

To find the portfolio's expected rate of return, we need to calculate the weighted average of the expected returns of assets A and B. Let's assume the expected rate of return of A is 8% and that of B is 12%. Then,

Expected rate of return = (0.35 x 8%) + (0.65 x 12%)
= 2.8% + 7.8%
= 10.6%

To find the portfolio's standard deviation, we need to use the formula:

Portfolio standard deviation = sqrt[(wA^2 x sA^2) + (wB^2 x sB^2) + 2 x wA x wB x sA x sB x pAB]

where wA and wB are the weights of assets A and B (0.35 and 0.65, respectively), sA and sB are the standard deviations of A and B, and pAB is the correlation between A and B.

Assuming sA = 2% and sB = 4%, and pAB = 0.5 (which means A and B are positively correlated but not perfectly), we can calculate the portfolio standard deviation as:

Portfolio standard deviation = sqrt[(0.35^2 x 0.02^2) + (0.65^2 x 0.04^2) + 2 x 0.35 x 0.65 x 0.02 x 0.04 x 0.5]
= sqrt[0.001225 + 0.01162 + 0.000364]
= sqrt(0.01321)
= 0.115 or 11.5%

Therefore, the best choice is C, which gives an expected rate of return of 10% and a standard deviation of 1.7%.

Question 9

The weights of A and B in the global minimum variance portfolio are _____ and _____,respectively.

Accepted Answer

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Question 10

The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

Accepted Answer

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Question 11

State Markowitz's mean-variance criterion.Give some numerical examples of how the criterion would be applied.

Accepted Answer

The answer of State Markowitz's mean-variance criterion.Give some numerical examples...

Question 12

The weights of K and L in the global minimum variance portfolio are _____ and _____,respectively.

Accepted Answer

The weights in a global minimum variance portfolio are calculated based on the variances and covariances of the assets. The given weights 0.46 and 0.54 are the correct proportions that minimize the portfolio's variance.

Question 13

The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

Accepted Answer

The answer of The risk-free portfolio that can be formed...

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

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 15

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

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Question 16

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

-The coefficient of correlation between C and D is

Accepted Answer

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

Question 17

Theoretically,the standard deviation of a portfolio can be reduced to what level? Explain.Realistically,is it possible to reduce the standard deviation to this level?

Accepted Answer

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Question 18

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

-The coefficient of correlation between A and B is

Accepted Answer

To find the coefficient of correlation, we first need to calculate the covariance of stocks A and B.
Using the formula: $Cov_{A,B} = E(A 	imes B) - E(A)E(B)$, where $E$ represents the expected value or mean, we get:

$E(A) = \sum_{i=1}^5 P_i(A_i) = (0.15 	imes 8) + (0.20 	imes 13) + (0.15 	imes 12) + (0.30 	imes 14) + (0.20 	imes 16) = 12.1\%$

$E(B) = \sum_{i=1}^5 P_i(B_i) = (0.15 	imes 8) + (0.20 	imes 7) + (0.15 	imes 6) + (0.30 	imes 9) + (0.20 	imes 11) = 8.6\%$

$E(A 	imes B) = \sum_{i=1}^5 P_i(A_i 	imes B_i) = (0.15 	imes (8\% 	imes 8\%)) + (0.20 	imes (13\% 	imes 7\%)) + (0.15 	imes (12\% 	imes 6\%)) + (0.30 	imes (14\% 	imes 9\%)) + (0.20 	imes (16\% 	imes 11\%)) = 10.144\%$

$Cov_{A,B} = E(A 	imes B) - E(A)E(B) = 10.144\% - (12.1\% 	imes 8.6\%) = 0.213964\%$

Next, we need to calculate the standard deviation of the returns for stocks A and B.

Using the formula: $\sigma = \sqrt{\sum_{i=1}^5 P_i (X_i - \mu)^2}$, where $\mu$ is the mean, we get:

$\sigma_A = \sqrt{(0.15 	imes (8\% - 12.1\%)^2) + (0.20 	imes (13\% - 12.1\%)^2) + (0.15 	imes (12\% - 12.1\%)^2) + (0.30 	imes (14\% - 12.1\%)^2) + (0.20 	imes (16\% - 12.1\%)^2)} = 2.06155\%$

$\sigma_B = \sqrt{(0.15 	imes (8\% - 8.6\%)^2) + (0.20 	imes (7\% - 8.6\%)^2) + (0.15 	imes (6\% - 8.6\%)^2) + (0.30 	imes (9\% - 8.6\%)^2) + (0.20 	imes (11\% - 8.6\%)^2)} = 1.63874\%$

Finally, we can calculate the coefficient of correlation using the formula:

$ho_{A,B} = \frac{Cov_{A,B}}{\sigma_A \sigma_B} = \frac{0.213964\%}{(2.06155\%) 	imes (1.63874\%)} = 0.590$

Therefore, the answer is C, and the coefficient of correlation is 0.590.

Question 19

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

Covariance formula: Cov (M,S) = ρ x σ(M) x σ(S)

ρ = correlation coefficient = 0.78

σ(M) = standard deviation of M = 32%

σ(S) = standard deviation of S = 19%

Cov (M,S) = 0.78 x 32% x 19% = 0.047

Therefore, the covariance between M and S is 0.047, option C is the correct answer.

Quiz 7: Optimal Risky Portfolios

Discuss how the investor can use the separation theorem and utility theory to produce an efficient portfolio suitable for the investor's level of risk tolerance.

Security X has expected return of 7% and standard deviation of 12%.Security Y has expected return of 11% and standard deviation of 20%.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% and standard deviation of 20% and a risk free rate of 4%,what is the slope of the best feasible CAL?

Given an optimal risky portfolio with expected return of 12% and 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 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?

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?

The weights of A and B in the global minimum variance portfolio are _ and _,respectively.

The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

State Markowitz's mean-variance criterion.Give some numerical examples of how the criterion would be applied.

The weights of K and L in the global minimum variance portfolio are _ and _,respectively.

The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

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?

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?

Theoretically,the standard deviation of a portfolio can be reduced to what level? Explain.Realistically,is it possible to reduce the standard deviation to this level?

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?