Question

state of economy	probability	return on stock J	return on stock K
bear	0.23	-0.013	0.041
normal	0.58	0.145	0.069
bull	0.19	0.225	0.099

Calculate the standard deviation for each of the stocks

Stock J    %

Stock K     %

Answer 1

Standard Deviation for Stock J

Expected Return

Expected Return = Sum[Returns x Probability]

= [-1.30% x 0.23] + [14.50% x 0.58] + [22.50% x 0.19]

= -0.30% + 8.41% + 4.28%

= 12.39%

Variance of the returns

Variance of the returns = [(-1.30 – 12.39)² x 0.23] + [(14.50 – 12.39)² x 0.58] + [(22.50 – 12.39)² x 0.19]

= [187.42 x 0.23] + [4.45 x 0.58] + [102.21 x 0.19]

= 43.1057 + 2.5822 + 19.4203

= 65.1082

Standard Deviation for the Stock J

Standard Deviation of the return = Square Root of 65.1082 or [65.1082]^1/2

= 8.07%

Standard Deviation for Stock K

Expected Return

Expected Return = Sum[Returns x Probability]

= [4.10% x 0.23] + [6.90% x 0.58] + [9.90% x 0.19]

= 0.94% + 4.00% + 1.89%

= 6.83%

Variance of the returns

Variance of the returns = [(4.10 – 6.83)² x 0.23] + [(6.90 – 6.83)² x 0.58] + [(9.90 – 6.83)² x 0.19]

= [7.4529 x 0.23] + [.0049 x 0.58] + [9.4249 x 0.19]

= 1.7142 + 0.0028 + 1.7907

= 3.5077

Standard Deviation for the Stock K

Standard Deviation of the return = Square Root of 3.5077 or [3.5077]^1/2

= 1.87%

Therefore,

Standard Deviation for the Stock J = 8.07%

Standard Deviation for the Stock K = 1.87%