What is the expected return and standard deviation for the following stock? $$\begin{array} { l c c }
{ \text { State of } } & \text { Probability of } & \text { Rate of Return } \
\text { Econony } & \text { State of Economy } & \text { if State Occurs } \
\text { Boorn } & .06 & - .06 \
\text { Normal } & .74 & .07 \
\text { Recession } & .20 & .18
\end{array}$$
A) 8.53 percent; 5.69 percent
B) 8.53 percent; 5.74 percent
C) 8.42 percent; 5.69 percent
D) 8.80 percent; 5.74 percent
E) 8.42 percent; 5.74 percent

Question

What is the expected return and standard deviation for the following stock? $$\begin{array} { l c c } 
 { \text { State of } } & \text { Probability of } & \text { Rate of Return } \
\text { Econony } & \text { State of Economy } & \text { if State Occurs } \
\text { Boorn } & .06 & - .06 \
\text { Normal } & .74 & .07 \
\text { Recession } & .20 & .18
\end{array}$$
A) 8.53 percent; 5.69 percent
B) 8.53 percent; 5.74 percent
C) 8.42 percent; 5.69 percent
D) 8.80 percent; 5.74 percent
E) 8.42 percent; 5.74 percent

Quizplus · Accepted Answer

To calculate the expected return, we use the formula:

Expected return = (probability of state 1 x return in state 1) + (probability of state 2 x return in state 2) + (probability of state 3 x return in state 3)

Expected return = (0.06 x -0.06) + (0.74 x 0.07) + (0.20 x 0.18) = 0.0084 = 8.42%

To calculate the standard deviation, we first need to calculate the variance. We use the formula:

Variance = (probability of state 1 x (return in state 1 - expected return)^2) + (probability of state 2 x (return in state 2 - expected return)^2) + (probability of state 3 x (return in state 3 - expected return)^2)

Variance = (0.06 x (-0.06 - 0.0842)^2) + (0.74 x (0.07 - 0.0842)^2) + (0.20 x (0.18 - 0.0842)^2) = 0.000324

Then we take the square root of the variance to get the standard deviation:

Standard deviation = sqrt(0.000324) = 0.017994 = 1.7994%

Therefore, the expected return is 8.42% and the standard deviation is 1.7994%. Choice (C) is the best answer.

What Is the Expected Return and Standard Deviation for the Following