Which stock outperforms this year?

Question

Stock A's annual return is normally distributed with mean 8% and standard deviation 6%. Stock B's annual return is normally distributed with mean 5% and standard deviation 8%. The two returns are independent.

What is the probability that A outperforms B this year?

Accepted Answer

To compare two normal quantities, study their difference. Let D = (	ext{A's return}) - (	ext{B's return}). "A outperforms" means D 0. The difference of two independent normals is normal: the mean subtracts, and the variances add (combining independent quantities always increases the spread). Mean of D: \;8 - 5 = 3\%. Variance of D: \;6^2 + 8^2 = 36 + 64 = 100, so the standard deviation of D is \sqrt{100} = 10\%. So D is normal with mean 3 and standard deviation 10. Convert 0 to a z-score: z = \frac{0 - 3}{10} = -0.3. We want the area to the right of z = -0.3, about 0.6179: P(D 0) \approx 0.…

Which stock outperforms this year?

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