Question

The rate of return on the common stock of Flowers by Flo is expected to be 13 percent in a boom economy, 11 percent in a normal economy, and only 6 percent in a recessionary economy. The probabilities of these economic states are 15 percent for a boom, 80 percent for a normal economy, and 5 percent for a recession. What is the variance of the returns on this stock?

Answer 1

Expected return of stock = sum of (Return of stock in each economic state * probabilities of respective economic states)

= 13% * 0.15 + 11% * 0.8 + 6% * 0.05

= 11.05%

Variance of the returns on this stock =

= {avg. of (Return of stock in each economic state – Expected return of stock) ^2}

= {(13%-11.05%) ^2 + (11% - 11.05%) ^2 + (6% -11.05%) ^2}/3

= {3.80 + 0.0025 +25.5025}/3

= 29.3075/3 = 9.77%

Variance of the returns on this stock is 9.77%