Question

A company’s stock trades at $75 per share. You estimate in a year there is a 40% chance the stock goes to $100 per share, a 40% chance the stock stays right at $75, and a 20% chance it drops in value to $60. What is the expected return, in dollar and percentage terms? What is the variance and standard deviation?

Answer 1

If stock goes to $100;

r = [$100 - $75] / $75 = $25 / $75 = 33.33%

If stock stays at $75;

r = [$75 - $75] / $75 = $0 / $75 = 0%

If stock drops to $60;

r = [$60 - $75] / $75 = -$15 / $75 = -20%

E(r) = $\sum_{i=1}^{n}$ [Pi x Ri]

= [0.40 x 33.33%] + [0.40 x 0%] + [0.20 x -20%] = 13.33% + 0% + (-4%) = 9.33%

Dollar Return = Initial Investment x r% = $75 x 9.33% = $7

$\sigma$² = $\sum_{i=1}^{n}$ [Pi x {E(r) - Ri}²]

= [0.40 x {9.33% - 33.33%)²] + [0.40 x {9.33% - 0%)²] + [0.20 x {9.33% + 4%)²]

= 230.40%² + 34.84%² + 35.56%² = 300.80%²

$\sigma$ = [$\sigma$²]^1/2 = [300.80%²]^1/2 = 17.34%