Question

QUESTION 28 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, 21% in a neutral economy , and -10% in a bust economy. The risk-free rate is 4.5%. 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% 21% Bust Economy 20% -10% Risk-Free Rate = 4.5%

Answer 1

State of Economy	Probability = P	Return = R	Product = P x R
Boom	0.30	31.00%	9.30000%
Neutral	0.50	21.00%	10.50000%
Bust	0.20	-10.00%	-2.00000%
		Average Return = Total =	17.80000%

Average Return

17.80%

Standard deviation of return = [Sum (Probability x (Return - Average return)]^0.5                                  

Standard deviation of return = (0.3*(31%-17.8%)^2+0.5*(21%-17.8%)^2+0.2*(-10%-17.8%)^2)^0.5       

Standard Deviation = 14.6%

Standard Deviation = 14.6 Percent