A stock has an annual standard deviation of 14.1% and an expected annual return of 11.5%. What is the smallest expected loss for the next 6 months given a probability of 2.5%?
A)8.90%
B)13.79%
C)14.57%
D)15.38%
E)16.67%

Question

Quizplus · Accepted Answer

Using the formula: Expected loss = - [ Z-score * standard deviation * sqrt(time) + expected return * time ]
We are given:
Standard deviation = 14.1%
Expected annual return = 11.5%
Time = 6 months = 0.5 years
Probability = 2.5%
Using the Z-score table, the corresponding value for a probability of 2.5% is -1.96
Expected loss = - [(-1.96) * 14.1% * sqrt(0.5) + 11.5% * 0.5] = -13.79%
Therefore, the smallest expected loss for the next 6 months given a probability of 2.5% is 13.79%. 
Hence, the answer is B.

A Stock Has an Annual Standard Deviation of 14