Question

The rate of return on the common stock of Flowers by Flo is expected to be 14 percent in a boom economy, 8 percent in a normal economy, and only 2 percent in a recessionary economy. The probabilities of these economic states are 20 percent for a boom, 70 percent for a normal economy, and 10 percent for a recession. What is the standard deviation of returns for this investment? Round to the nearset hundredth percent. Answer in the percent format. Do not include % sign in your answer (i.e. If your answer is 4.33%, type 4.33 without a % sign at the end.)

Answer 1

Answer: The standard deviation of the stock is 3.23 percentage

Explanation:

First we shall calculate the epected weighted average return of the stock.

We shall multiply the probability of the scenario with its expected return and then take the sum of the expected returns of different scenarios,

E(x) = (0.2 x 14%) + (0.7 x 8%) + (0.1 x 2%)

E(x) = 8.6%

We shall use the follwing formula to calculate the Variance of the stock,

σ²(x) = ∑ P($x_{i}$) × [$x_{i}$ - E(r)]²

σ²(x)  = (0.2) (0.14 - 0.086)² + (0.7) (0.08 - 0.086)² + (0.1) (0.02 - 0.086)²

σ²(x) = 0.001044

To find the standar deviation,

σ(x) = $\sqrt{0.001044}$

σ(x) = 0.0323109

in percentage it would be 3.23%