Question

Consider the following probability distributions for stocks A and B:

State	Probability	Return on A	Return on B
1	.3	7%	-9%
2	.5	11%	14%
3	.2	-16%	26%

a) What is the standard deviation of returns for stock A? Please give your answer in percent rounded to the nearest basis point.

b) What is the standard deviation of returns for stock B? Please give your answer in percent rounded to the nearest basis point.

Answer 1

Question a:

Expected Return of stock A = Σ (Probability * Return)

= (0.30 * 7%) + (0.50 * 11%) + (0.20 * -16%)

= 2.1% + 5.5% - 3.2%

= 4.4%

Variance of Stock A = Σ Probability * (Return - Expected Return)^2

= [0.30 * (7% - 4.4%)^2] + [0.50 * (11% - 4.4%)^2] + [0.20 * (-16% - 4.4%)^2]

= [0.30 * 0.000676] + [0.50 * 0.004356] + [0.20 * 0.041616]

= 0.0002028 + 0.002178 + 0.0083232

= 0.010704

Standard deviation of Stock A = Square root of Variance

= (0.010704)^(1/2)

= 0.103460137

= 10.35%

Therefore, standard deviation of Stock A is 10.35%

Question b:

Expected Return of stock B = Σ (Probability * Return)

= (0.30 * -9%) + (0.50 * 14%) + (0.20 * 26%)

= -2.7% + 7% + 5.2%

= 9.5%

Variance of Stock B = Σ Probability * (Return - Expected Return)^2

= [0.30 * (-9% - 9.5%)^2] + [0.50 * (14% - 9.5%)^2] + [0.20 * (26% - 9.5%)^2]

= [0.30 * 0.034225] + [0.50 * 0.002025] + [0.20 *0.027225 ]

= 0.010268 + 0.001013 + 0.005445

= 0.016725

Standard deviation of Stock B = Square root of Variance

= (0.016725)^(1/2)

= 0.129325

= 12.93%

Therefore, standard deviation of Stock B is 12.93%