Consider the following information on three stocks: $$\begin{array} { l ccccc }
{ \text { State of } } & { \text { Probability of } } &&\text { Rate of Return }\
\text { Economy } & \text { State of Economy } & &{ \text { if State Occurs } } \
& & \text { Stock A } & \text { Stock B } & \text { Stock C } \
\text { Boom } & .25 & .27 & .15 & .11 \
\text { Normal } & .65 & .14 & .11 & .09 \
\text { Bust } & .10 & - .19 & - .04 & .05
\end{array}$$
A portfolio is invested 45 percent each in Stock A and Stock B and 10 percent in Stock C. What is the expected risk premium on the portfolio if the expected T-bill rate is 3.2 percent?
A) 11.47 percent
B) 12.38 percent
C) 1.67 percent
D) 4.29 percent
E) 8.71 percent

Question

Consider the following information on three stocks: $$\begin{array} { l ccccc } 
 { \text { State of } } &   { \text { Probability of } } &&\text { Rate of Return }\
\text { Economy } & \text { State of Economy } &  &{ \text { if State Occurs } } \
& & \text { Stock A } & \text { Stock B } & \text { Stock C } \
\text { Boom } & .25 & .27 & .15 & .11 \
\text { Normal } & .65 & .14 & .11 & .09 \
\text { Bust } & .10 & - .19 & - .04 & .05
\end{array}$$
A portfolio is invested 45 percent each in Stock A and Stock B and 10 percent in Stock C. What is the expected risk premium on the portfolio if the expected T-bill rate is 3.2 percent?
A) 11.47 percent
B) 12.38 percent
C) 1.67 percent
D) 4.29 percent
E) 8.71 percent

Quizplus · Accepted Answer

To calculate the expected risk premium on the portfolio, first, we need to calculate the expected return of the portfolio and then subtract the T-bill rate (risk-free rate) from it.The expected return of the portfolio (E(Rp)) can be calculated using the formula:$$E(Rp) = w_A \cdot E(R_A) + w_B \cdot E(R_B) + w_C \cdot E(R_C)$$where $w_X$ is the weight of the investment in stock X and $E(R_X)$ is the expected return of stock X.The expected return of each stock can be calculated using the formula:$$E(R_X) = \sum (P_i \cdot R_{X,i})$$where $P_i$ is the probability of state $i$ occurring and $R_{X,i}$ is the return of stock X in state $i$.For Stock A:$$E(R_A) = 0.25 \cdot 0.27 + 0.65 \cdot 0.14 - 0.10 \cdot 0.19 = 0.0675 + 0.091 - 0.019 = 0.1395$$ or 13.95%For Stock B:$$E(R_B) = 0.25 \cdot 0.15 + 0.65 \cdot 0.11 - 0.10 \cdot 0.04 = 0.0375 + 0.0715 - 0.004 = 0.105$$ or 10.5%For Stock C:$$E(R_C) = 0.25 \cdot 0.11 + 0.65 \cdot 0.09 + 0.10 \cdot 0.05 = 0.0275 + 0.0585 + 0.005 = 0.091$$ or 9.1%Now, calculate the expected return of the portfolio:$$E(Rp) = 0.45 \cdot 13.95\% + 0.45 \cdot 10.5\% + 0.10 \cdot 9.1\% = 6.2775\% + 4.725\% + 0.91\% = 11.9125\%$$The expected risk premium on the portfolio is the expected return of the portfolio minus the T-bill rate:$$Risk\ Premium = E(Rp) - T\text{-}bill\ Rate = 11.9125\% - 3.2\% = 8.7125\%$$Therefore, the expected risk premium on the portfolio is approximately 8.71 percent.

Consider the Following Information on Three Stocks A Portfolio Is Invested 45 Percent Each in Stock a ccccc