Question

Use the following scenario analysis for stocks X and Y to answer CFA Questions

Question: What are the standard deviations of returns on stocks X and Y?

Short answer

The correct answer is:

σx = 24.33%

σy = 13.23%

Step-by-step solution

Given information

Probability (scenario- Bear Market) = 0.2

Probability (scenario-Normal Market) = 0.5

Probability (scenario- Bull Market) = 0.3

Return for Stock X (all 3 scenarios) = --20%, 18% and 50%

Return for Stock Y (all 3 scenarios) = --15%, 20% and 10%

Calculation of standard deviation of returns on stocks X and Y.

(Standard Deviation)² =[Probability (Scenario x Deviation from mean in Scenario)]²

Hence,

σx² = [0.2 x (–20 - 20)²] + [0.5 x (18 -20)²] + [0.3 x (50- 20)²] = 592

σx=Ö592= 24.33%

σy² = [0.2 x (–15 -10)²] + [0.5 x (20 – 10)²] + [0.3 x (10 -10)²] = 175

σy = Ö175= 13.23%