Question 13.2: Going back to Example 13.1, what are the variances on the tw...

Fundamentals of Corporate Finance

Going back to Example 13.1, what are the variances on the two stocks once we have unequal probabilities? The standard deviations?

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We can summarize the needed calculations as follows:

(1) State of Economy	(2) Probability of State of Economy	(3) Return Deviation from Expected Return	(4) Squared Return Deviation from Expected Return	(5) Product (2) x (4)
Stock L
Recession	.80	-.20-(-.02) = -.18	.0324	.02592
Boom	.20	.70-(-.02)= .72	.5184	$\underline{0.10368}$ $σ^{2}_{L}= .12960$
Stock U
Recession	.80	.30 – .26 = .04	.0016	.00128
Boom	.20	.10-.26 = -.16	.0256	$\underline{.00512}$
$σ^{2}_{U}= .00640$

Based on these calculations, the standard deviation for L is $\sigma _{L}=\sqrt{.1296}=.36, or \text{ }36\%$ . The standard deviation for U is much smaller: $\sigma _{U}=\sqrt{.0064}=.08, or \text{ }8\%$ .

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