Question

Nancy is considering investing in a company's stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Use the following table of returns and probabilities to determine the coefficient of variation for the investment. (Round answer to 5 decimal places, e.g. 0.07680.)

          Probability Return

Boom     0.3          25.00%

Good      0.4         15.00%

Level      0.2          10.00%

Slump     0.1         -5.00%

Use the table of returns and probabilities above to determine the expected return on Nancy’s investment? (Round answer to 3 decimal places, e.g. 0.076.)

Expected return_______

Use the table of returns and probabilities above to determine the standard deviation of the return on Nancy's investment? (Round answer to 5 decimal places, e.g. 0.07680.)Standard deviation____

Answer 1

State of the Economy	Probability	return	E(X)	E(X^2)
Boom	0.3	25.00%	0.075	0.01875
Good	0.4	15.00%	0.06	0.009
Level	0.2	10.00%	0.02	0.002
Slump	0.1	-5.00%	-0.005	0.00025
		mean	15.00%	0.03
		variance	0.0075
		standard deviation	8.66%

Expected return = sum of (probability of state * return of state)

E(X^2) =  sum of (probability of state * return of state^2)

variance = E(X^2) - (E(X))^2

Standard deviation = sqrt(variance)