Question

An analyst believes GM stock could provide several different rates of return depending on different possible economic conditions. In a strong economic environment with high corporate profits, the investor expects the rate of return on GM stocks during the next year to reach as high as 10%. In contrast, if there is a slight economic decline, the analyst expects the rate of return on GM common stocks during the next year to be 5%, and if the economy enters a recession, the analyst expects the return to be-10%. Finally, with no major change in the economy, the rate of return during the next year would probably approach the long-run average of 7%. The analyst estimates probabilities for each of these economic scenarios based on past experience and the current outlook as follows: Economic Conditions Strong economy Declining economy Recession No major change Probability 10% 15% 10% 65% What are the expected return and the standard deviation of the GM stock over the next year?

Answer 1

(1)

Expected return (%) = 10 x 0.1 + 15 x 0.05 - 10 x 0.1 + 65 x 0.07 = 1 + 0.75 - 1 + 4.55 = 5.3% (= 0.053 in decimal form)

(2)

Variance = 10 x (0.1 - 0.053)² + 15 x (0.05 - 0.053)² + 10 x (- 0.1 - 0.053)² + 65 x (0.07 - 0.053)²

= 10 x (0.047)² + 15 x (- 0.003)² + 10 x (- 0.153)² + 65 x (0.017)²

= 10 x 0.002209 + 15 x 0.000009 + 10 x 0.023409 + 65 x 0.000289

= 0.02209 + 0.000135 + 0.23409 + 0.018785

= 0.2751

= 27.51%

Standard deviation = (Variance)^0.5 = (0.2751)^0.5 = 0.5245 = 52.45%