The rate of return on the common stock of Lancaster Woolens is expected to be 21 percent in a boom economy, 11 percent in a normal economy, and only 3 percent in a recessionary economy. The probabilities of these economic states are 10 percent for a boom, 70 percent for a normal economy, and 20 percent for a recession. What is the variance of the returns on this common stock?

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The rate of return on the common stock of Lancaster Woolens is expected to be 21 percent in a boom economy, 11 percent in a normal economy, and only 3 percent in a recessionary economy. The probabilities of these economic states are 10 percent for a boom, 70 percent for a normal economy, and 20 percent for a recession. What is the variance of the returns on this common stock?

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Emilio Mccoy · Answer 1

0.002244

Explanation:

We will first calculate the expected return. It is: E (r)

E (r) = (0.10 0.21) + (0.70 0.11) + (0.20 0.03)

= 0.104

Var = 0.10 (0.21 - 0.104) 2 + 0.70 (0.11 - 0.104) 2 + 0.20 (0.03 - 0.104) 2

= 0.002244