You have been given this probability distribution for the holding-period return for a stock: $\begin{array}{lcc}
\text { Stock of the Economy } & \text { Probability} & \text {HPR } \
\text { Boom } &0.40&22\%\
\text { Normal growth } &0.35&11\%\
\text { Recession }&0.25&-9\%
\end{array}$

What is the expected variance for the stock?
A) 142.07%
B) 189.96%
C) 177.04%
D) 128.17%
E) None of the options are correct.

Question

You have been given this probability distribution for the holding-period return for a stock: $\begin{array}{lcc}
  \text { Stock of the Economy } & \text {  Probability} & \text {HPR  } \
 \text { Boom } &0.40&22\%\
 \text { Normal growth } &0.35&11\%\
\text { Recession }&0.25&-9\%
\end{array}$

What is the expected variance for the stock?
A) 142.07%
B) 189.96%
C) 177.04%
D) 128.17%
E) None of the options are correct.

Quizplus · Accepted Answer

To find the expected variance, we first calculate the expected return (mean) and then use it to calculate the variance. Expected return (mean) = $0.40 \times 22\% + 0.35 \times 11\% + 0.25 \times (-9\%)$ = $8.8\% + 3.85\% - 2.25\% = 10.4\%$.Now, we calculate the variance using the formula for expected variance, which involves squaring the difference between each outcome and the mean, multiplying by the probability of each outcome, and summing these products:Variance = $0.40 \times (22\% - 10.4\%)^2 + 0.35 \times (11\% - 10.4\%)^2 + 0.25 \times (-9\% - 10.4\%)^2$= $0.40 \times (11.6\%)^2 + 0.35 \times (0.6\%)^2 + 0.25 \times (-19.4\%)^2$= $0.40 \times 0.0134 + 0.35 \times 0.000036 + 0.25 \times 0.0376$= $0.00536 + 0.0000126 + 0.0094$= $0.0147726$To convert to percentage, we multiply by 100^2 (since the returns are in percentages, and variance is in squared units):Variance = $0.0147726 \times 100^2 = 147.726\%$.Since none of the provided options exactly match this calculation, the correct answer is E) None of the options are correct.

You Have Been Given This Probability Distribution for the Holding-Period