Question

a. 15.46%

b. 12.65%

c. 14.45%

d. 28.43%

e. 16.86%

A stock will have a loss of 13.9 percent in a recession, a return of 12.6 percent in a normal economy, and a return of 27.3 percent in a boom. There is 30 percent probability of a recession, 33 percent probability of normal economy, and 37 percent probability of boom. What is the standard deviation of the stotk's returns? Multiple Choice Ο 15.46% Ο 12.65% Ο 14.45% Ο 28.43%

Answer 1

Economy	Probability (a)	Rate of return (b)	c = a x b	Deviation from expected return d = b - E(R)	Squared Deviation e = d2	f = a x e
Recession	0.30	-0.139	-0.0417	-0.23989	0.057547212	0.017264164
Normal	0.33	0.126	0.04158	0.02511	0.000630512	0.000208069
Boom	0.37	0.273	0.10101	0.17211	0.029621852	0.010960085
	Expected Return E(R)	0.10089		Variance	0.028432318
	Standard Deviation	0.168618854

Expected Return E(R) = -0.0417 + 0.04158 + 0.10101 = 0.10089

Variance = 0.017264164 + 0.000208069 + 0.010960085 = 0.028432318

Standard Deviation = √ Variance

                                = √ 0.028432318 = 0.168618854 = 16.86 %

Standard deviation of the stock return is 16.86 %

Hence option “e. 16.86 %” is correct answer.