Question

After some study of the economy, your forecast for next year is that a boom economy has a 30% chance of occurring, a neutral economy 50%, and a bust economy a 20% chance of occurring. You also estimate that a certain stock would have a return of 31% in a boom economy next year, 16% in a neutral economy , and -14% in a bust economy. The risk-free rate is 4.4%. What is the standard deviation of expected returns for this stock next year? (Answer to the nearest tenth of a percent, but do not use a percent sign).
  

	Probability	Return
Boom Economy	30%	31%
Neutral Economy	50%	16%
Bust Economy	20%	-14%

Risk-Free Rate = 4.4%

Answer 1

Economy	Probability	Return
	(P)	( R)	(P) *(R )
Boom	0.3	0.31	0.093
Neutral	0.5	0.16	0.08
Bust	0.2	-0.14	-0.028
Expected return			0.145
Expected Return of Portfolio = 14.50%
Standard deviation:
Economy	Probability	Return	Deviation	Squared	Sq. Deviation*(P)
	(P)	( R)	E - (R )	Deviation
Boom	0.3	31	-16.5	272.25	81.675
Neutral	0.5	16	-1.5	2.25	1.125
Bust	0.2	-14	28.5	812.25	162.45
			VARIANCE		245.25
Std deviation = (Variance)^2 = (245.25)^2 = 15.66%
Answer is 15.66%