COMMON STOCK A COMMON STOCK B PROBABILITY RETURN PROBABILITY

COMMON STOCK A

COMMON STOCK B

PROBABILITY

RETURN

PROBABILITY

RETURN

.20

10?%

.10

?6?%

.60

16%

.40

0.20

18%

.40

14?%

.10

21?%

?(Expected rate of return and risk?)

Summerville Inc. is considering an investment in one of two common stocks. which investment is? better, based on the risk? (as measured by the standard? deviation) and return of? each?

Solution

Return of common stock A = Probability * return

Return of common stock A = 0.2 * 0.1 + 0.6 * 0.16 + 0.2 * 0.18

Return of common stock A = 0.02 + 0.096 + 0.036

Return of common stock A = 0.152 or 15.2%

Return of common stock B = 0.1 * -0.06 + 0.4 * 0.07 + 0.4 * 0.14 + 0.1 * 0.21

Return of common stock B = -0.006 + 0.028 + 0.056 + 0.021

Return of common stock B = 0.099 or 9.9%

Variance of common stock A = [0.2( 0.1 - 0.152)² + 0.6(0.16 - 0.152)² + 0.2(0.18 - 0.152)²]

Variance of common stock A = [ 0.000541 + 0.000038 + 0.000157]

Variance of common stock A = 0.000736

Standard deviation of stock A = ( 0.000736 )^1/2

Standard deviation of stock A = 0.027129 or 2.7129%

Variance of common stock B = [0.1( -0.06 - 0.099)² + 0.4(0.07 - 0.09)² + 0.4(0.14 - 0.099)² + 0.1(0.21 - 0.099)²]

Variance of common stock B = [ 0.002528 + 0.00016 + 0.000672 + 0.001232]

Variance of common stock B = 0.004592

Standard deviation of stock B = ( 0.004592 )^1/2

Standard deviation of stock B = 0.067764 or 6.78%

Investment in common stock A is better as it has the highest return and lowest risk.