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?
$\begin{array}{lrrr}
\text { State of the Economy } & \text { Probability } & \text { E(R)}_{A}& \text { E(R)}_{B}\
\text { Weight } & & 55 \% & 45 \% \
\text { Boom } & .15 & 19 \% & 12\% \
\text { Normal } & .65 & 11 \% & 7 \% \
\text { Recession } & .20 & -16 \% & 1 \%
\end{array}$
A)5.45%
B)6.69%
C)7.14%
D)7.60%
E)8.22%

Question

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?
$\begin{array}{lrrr}
\text { State of the Economy } & \text { Probability } & \text { E(R)}_{A}& \text {  E(R)}_{B}\
\text { Weight } & & 55 \% & 45 \% \
\text { Boom } & .15 & 19 \% & 12\% \
\text { Normal } & .65 & 11 \% & 7 \% \
\text { Recession } & .20 & -16 \% & 1 \%
\end{array}$
A)5.45%
B)6.69%
C)7.14%
D)7.60%
E)8.22%

Quizplus · 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.

You Have a Portfolio Which Is Comprised of 55% of Stock