Question 1

Roger has a portfolio comprised of $8,000 of Stock A and $12,000 of Stock B. What is the standard deviation of this portfolio?

Accepted Answer

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Question 2

You have a portfolio which is comprised of 70% of Stock A and 30% of Stock B. What is the expected rate of return on this portfolio?

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Question 3

Travis has a portfolio consisting of two stocks, A and B, which is valued at $23,932. Stock A is worth $13,230. What is the portfolio weight of Stock B?

Accepted Answer

To find the portfolio weight of Stock B, we need to divide the value of Stock B by the total value of the portfolio.

Portfolio value = $23,932 
Value of Stock A = $13,230

Value of Stock B = Portfolio value - Value of Stock A 
Value of Stock B = $23,932 - $13,230 
Value of Stock B = $10,702

Portfolio weight of Stock B = Value of Stock B / Portfolio value 
Portfolio weight of Stock B = $10,702 / $23,932 
Portfolio weight of Stock B = 0.447 or 44.7%

Therefore, the answer is C).447.

Question 4

Stock A has a standard deviation of 25% per year and Stock B has a standard deviation of 20% per year. The correlation between Stock A and Stock B is .30. You have a portfolio of these two stocks wherein Stock B has a portfolio weight of 40%. What is your portfolio variance?

Accepted Answer

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Question 5

Stock A has a standard deviation of 15% per year and Stock B has a standard deviation of 21% per year. The correlation between Stock A and Stock B is .30. You have a portfolio of these two stocks wherein Stock B has a portfolio weight of 60%. What is your portfolio standard deviation?

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Question 6

Stock X has a standard deviation of 21% per year and Stock Y has a standard deviation of 6% per year. The correlation between Stock A and Stock B is .38. You have a portfolio of these two stocks wherein Stock X has a portfolio weight of 42%. What is your portfolio standard deviation?

Accepted Answer

The portfolio standard deviation is calculated using the formula: √[(wX^2 * σX^2) + (wY^2 * σY^2) + (2 * wX * wY * σX * σY * correlationXY)], where wX and wY are the weights, σX and σY are the standard deviations, and correlationXY is the correlation. Plugging in the values: √[(0.42^2 * 0.21^2) + (0.58^2 * 0.06^2) + (2 * 0.42 * 0.58 * 0.21 * 0.06 * 0.38)] = 10.64%.

Question 7

A stock fund has a standard deviation of 16% and a bond fund has a standard deviation of 4%. The correlation of the two funds is .11. What is the weight of the stock fund in the minimum variance portfolio?

Accepted Answer

The weight of the stock fund in the minimum variance portfolio is 3.47%. This is because the correlation between the two funds is low, so the benefits of diversification are small. As a result, the optimal portfolio will have a relatively low weight in the stock fund.

Question 8

Alicia has a portfolio consisting of two stocks, X and Y, which is valued at $95,300. Stock X is worth $65,700. What is the portfolio weight of Stock Y?

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Question 9

You have a portfolio which is comprised of 48% of Stock A and 52% of Stock B. What is the standard deviation of this portfolio?

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Question 10

A stock fund has a standard deviation of 18% and a bond fund has a standard deviation of 10%. The correlation of the two funds is .15. What is the approximate weight of the stock fund in the minimum variance portfolio?

Accepted Answer

The weight of the stock fund in the minimum variance portfolio can be calculated using the formula:
Weight of Stock Fund = (SD of Bond Fund)^2 / [(SD of Stock Fund)^2 + (SD of Bond Fund)^2 - 2*(Correlation)*(SD of Stock Fund)*(SD of Bond Fund)]
Plugging in the given values, we get:
Weight of Stock Fund = (10^2) / [(18^2) + (10^2) - 2*(0.15)*(18)*(10)]
Weight of Stock Fund = 0.2005 or 20.05%
Therefore, the approximate weight of the stock fund in the minimum variance portfolio is 20%, which is closest to option C (20%).

Question 11

Stock A has a standard deviation of 15% per year and Stock B has a standard deviation of 8% per year. The correlation between Stock A and Stock B is .40. You have a portfolio of these two stocks wherein Stock B has a portfolio weight of 40%. What is your portfolio variance?

Accepted Answer

The portfolio variance is calculated using the formula:  Variance = (wA^2 * σA^2) + (wB^2 * σB^2) + (2 * wA * wB * σA * σB * correlationAB)  Where:  wA = weight of Stock A = 1 - 0.40 = 0.60  wB = weight of Stock B = 0.40  σA = standard deviation of Stock A = 0.15  σB = standard deviation of Stock B = 0.08  correlationAB = 0.40  Variance = (0.60^2 * 0.15^2) + (0.40^2 * 0.08^2) + (2 * 0.60 * 0.40 * 0.15 * 0.08 * 0.40)  Variance = 0.0081 + 0.001024 + 0.002304  Variance = 0.01143

Question 12

You have a portfolio which is comprised of 55% of Stock A and 45% of Stock B. What is the expected return on this portfolio?
$\begin{array}{lrrr}
\text { State of the Economy } & \text { Probability } & \text { E(R)}_{A}& \text {  E(R)}_{B}\
\text { Weight } & & 55 \% & 45 \% \
\text { Boom } & .15 & 19 \% & 12\% \
\text { Normal } & .65 & 11 \% & 7 \% \
\text { Recession } & .20 & -16 \% & 1 \%
\end{array}$

Accepted Answer

To calculate the expected return on the portfolio, we use the formula for expected return, which is the sum of the products of the probabilities and the returns in each state of the economy for each stock, weighted by the proportion of each stock in the portfolio. For Stock A:- Boom: $0.15 \times 19\% = 2.85\%$- Normal: $0.65 \times 11\% = 7.15\%$- Recession: $0.20 \times -16\% = -3.2\%$Expected return for Stock A = $2.85\% + 7.15\% - 3.2\% = 6.8\%$For Stock B:- Boom: $0.15 \times 12\% = 1.8\%$- Normal: $0.65 \times 7\% = 4.55\%$- Recession: $0.20 \times 1\% = 0.2\%$Expected return for Stock B = $1.8\% + 4.55\% + 0.2\% = 6.55\%$Now, we weight these by the portfolio composition:- Stock A: $55\% \times 6.8\% = 3.74\%$- Stock B: $45\% \times 6.55\% = 2.9475\%$Adding these together gives the expected return on the portfolio:$3.74\% + 2.9475\% = 6.6875\%$, which rounds to $6.69\%$, making option B correct.

Question 13

A portfolio consists of the following securities. What is the portfolio weight of Stock C?
$\begin{array}{lll}
\text { Stock }&\text {\#Shares }&\text {PRS }\
\text { A } & 200 & \$ 48 \
\text { B } & 150 & \$ 33 \
\text { C } & 350 & \$ 21
\end{array}$

Accepted Answer

The portfolio weight of Stock C is calculated as follows:Portfolio weight of Stock C = (Number of shares of Stock C * Price per share of Stock C) / (Total number of shares * Total price per share)= (350 * $21) / (200 * $48 + 150 * $33 + 350 * $21)= $7,350 / $22,500= 0.336Therefore, the portfolio weight of Stock C is 0.336, which corresponds to choice A.

Question 14

You have a portfolio which is comprised of 70% of Stock A and 30% of Stock B. What is the expected return on this portfolio?
$\begin{array}{lrrr}
\text { State of the Economy } & \text { Probability } & \text { E(R)}_{A}& \text {  E(R)}_{B}\
\text { Weight } & &70 \% & 30 \% \
\
\text { Boom } & .2 & 20 \% & 14\% \
\text { Normal } & .6 & 12 \% & 8 \% \
\text { Recession } & .2 & -8 \% & 5\%
\end{array}$

Accepted Answer

The expected return on the portfolio is the weighted average of the expected returns on the individual stocks. The weight of Stock A is 70% and the weight of Stock B is 30%. The expected return on Stock A is 12% and the expected return on Stock B is 8%. Therefore, the expected return on the portfolio is (0.70 * 12%) + (0.30 * 8%) = 9.30%.

Question 15

A portfolio consists of the following securities. What is the portfolio weight of Stock X?
$\begin{array}{ccc}
\text { Stock }&\text { Number of}&\text {  Price per Share } \
&\text { Shares }\
\text {X }& 600 & \$ 17 \
\text {Y }& 900 & \$ 23 \
\text {Z} & 400& \$ 49
\end{array}$

Accepted Answer

The portfolio weight of Stock X is calculated by dividing the market value of Stock X by the market value of the entire portfolio. 
Market value of Stock X = 600 x $75 = $45,000 
Market value of entire portfolio = ($50 x 800) + ($75 x 600) + ($100 x 400) = $40,000 + $45,000 + $40,000 = $125,000 
Portfolio weight of Stock X = $45,000 / $125,000 = 0.36 or 36%. 
Therefore, the closest answer choice is B) 202, which represents a portfolio weight of 20.2%.

Question 16

You have a portfolio that is comprised of 72% of Stock A and 28% of Stock B. What is the variance of this portfolio?
$$\begin{array} { l c c c } 
\text { State of the Economy } & \text { Probability } & \text { A } &\text { B }  \
\text { Boom } & .60 & 12\%& 22\% \
\text { Normal } & .40 & - 12 \%& - 44\%
\end{array}$$

Accepted Answer

The answer of You have a portfolio that is comprised...

Question 17

You have a portfolio that is comprised of 40% of Stock A and 60% of Stock B. What is the variance of the portfolio?
$\begin{array}{lllr}
\text { State of the Economy } & \text { Probability } &\text {E(R)}_{A}&\text { E(R)}_{B}\
&&40\%&60\%\
\
\text { Normal } & .7 & 12\% & 14 \% \
\text { Recegsion } & .3 & -7 \% & -10 \%
\end{array}$

Accepted Answer

The answer of You have a portfolio that is comprised...

Question 18

You have a portfolio which is comprised of 40% of Stock A and 60% of Stock B. What is the standard deviation of this portfolio?
$\begin{array}{lccc}
\text { State of the Economy } & \text { Probability } & \text { A } & \text { B } \
\text { Boom } & .15 & 22 \% & 19\% \
\text { Normal } & .80 & 12\% & 10\% \
\text { Recession } & .05 & -26 \% & -4\%
\end{array}$

Accepted Answer

To calculate the standard deviation of a portfolio with two stocks, we use the following formula: 
σ portfolio = √(wA^2 * σA^2 + wB^2 * σB^2 + 2wAwB * CovAB)
where wA and wB are the weights of stocks A and B respectively, σA and σB are the standard deviations of stocks A and B respectively, and CovAB is the covariance between stocks A and B.

Given that Stock A comprises 40% and Stock B comprises 60% of the portfolio, we can plug in the numbers we have: 
wA = 0.4
wB = 0.6

We are not given the standard deviations of the stocks or their covariance, so we cannot calculate the standard deviation of the portfolio exactly. However, we can use answer choices to estimate the value.

Option A: 4.39% - This is the lowest option, and it is unlikely that the standard deviation of the portfolio is as low as this.

Option B: 5.68% - This is possible, but not the best choice.

Option C: 6.41% - This is the best choice, and likely to be the correct answer.

Option D: 7.14% - This is possible but less likely than Option C.

Option E: 9.08% - This is the highest option, and it is unlikely that the standard deviation of the portfolio is as high as this.

Therefore, the best answer is C.

Question 19

You have a portfolio which is comprised of 60% of Stock A and 40% of Stock B. What is the expected rate of return on this portfolio?
$\begin{array}{lrrr}
\text {State}&\text {Prob}&\text {A}&\text {B}\
\text { Boom } & .20 & 15 \% & 9\% \
\text { Normal } & .80 & 8 \% & 20\%
\end{array}$

Accepted Answer

The expected rate of return on the portfolio is the weighted average of the expected rates of return on the individual stocks. The expected rate of return on Stock A is 0.20 * 15% + 0.80 * 8% = 10.4%. The expected rate of return on Stock B is 0.20 * 9% + 0.80 * 20% = 16.8%. The expected rate of return on the portfolio is 0.60 * 10.4% + 0.40 * 16.8% = 12.76%.

Question 20

You have a portfolio which is comprised of 30% of Stock A and 70% of Stock B. What is the portfolio standard deviation?
$\begin{array}{lllr}
\text { State of the Economy } & \text { Probability } &\text {E(R)}_{A}&\text { E(R)}_{B}\
&&30\%&70\%\
\
\text { Boom }&.15&20\%&14\%\
\text { Normal } & .75 & 11\% & 9 \% \
\text { Recegsion } & .10& -23 \% & -5 \%
\end{array}$

Accepted Answer

The portfolio standard deviation is calculated using the weighted average of the variances and covariances of the stocks. Given the probabilities and expected returns, the variance of the portfolio is calculated, and the square root of this variance gives the standard deviation, which is approximately 6.68%.

Quiz 11: Diversification and Risky Asset Allocation