What is the expected return on portfolio which is invested 20% in share A, 50% in share B, and 30% in share C?
$\begin{array} { | l | l | l | l | l | }
\hline & & \multicolumn{3}{|l|} { \text { Rate of Return if State Occurs } } \
\hline \text { State of Economy } & \text { Probability of State of Economy } & \text { Share A } & \text { Share B } & \text { Share C } \
\hline \text { Boom } & 20 \% & 18 \% & 9 \% & 6 \% \
\hline \text { Normal } & 70 \% & 11 \% & 7 \% & 9 \% \
\hline \text { Recession } & 10 \% & - 10 \% & 4 \% & 13 \% \
\hline
\end{array}$
A)7.40%
B)8.25%
C)8.33%
D)9.45%
E)9.50%

Question

What is the expected return on portfolio which is invested 20% in share A, 50% in share B, and 30% in share C?
$\begin{array} { | l | l | l | l | l | } 
\hline & & \multicolumn{3}{|l|} { \text { Rate of Return if State Occurs } } \
\hline \text { State of Economy } & \text { Probability of State of Economy } & \text { Share A } & \text { Share B } & \text { Share C } \
\hline \text { Boom } & 20 \% & 18 \% & 9 \% & 6 \% \
\hline \text { Normal } & 70 \% & 11 \% & 7 \% & 9 \% \
\hline \text { Recession } & 10 \% & - 10 \% & 4 \% & 13 \% \
\hline
\end{array}$
A)7.40%
B)8.25%
C)8.33%
D)9.45%
E)9.50%

Quizplus · Accepted Answer

The expected return on the portfolio can be calculated by multiplying the returns of each share by their respective weights in the portfolio and the probability of each state of the economy, then summing these products across all states. For Share A: - Boom: $0.20 \times 0.18 = 0.036$- Normal: $0.70 \times 0.11 = 0.077$- Recession: $0.10 \times (-0.10) = -0.01$Weighted return for Share A: $0.20 \times (0.036 + 0.077 - 0.01) = 0.0206$For Share B: - Boom: $0.20 \times 0.09 = 0.018$- Normal: $0.70 \times 0.07 = 0.049$- Recession: $0.10 \times 0.04 = 0.004$Weighted return for Share B: $0.50 \times (0.018 + 0.049 + 0.004) = 0.0355$For Share C: - Boom: $0.20 \times 0.06 = 0.012$- Normal: $0.70 \times 0.09 = 0.063$- Recession: $0.10 \times 0.13 = 0.013$Weighted return for Share C: $0.30 \times (0.012 + 0.063 + 0.013) = 0.0264$Total expected return on the portfolio: $0.0206 + 0.0355 + 0.0264 = 0.0825$ or $8.25\%$.

What Is the Expected Return on Portfolio Which Is Invested