Question

Consider the following scenario analysis:

		Rate of Return
Scenario	Probability	Stocks		Bonds
Recession	0.3	-6	%	14	%
Normal economy	0.5	15		11
Boom	0.2	26		5

Assume a portfolio with weights of 0.60 in stocks and 0.40 in bonds.

a. What is the rate of return on the portfolio in each scenario? (Enter your answer as a percent rounded to 1 decimal place.)

b. What are the expected rate of return and standard deviation of the portfolio? (Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

State of economy	Probability of state	return	bonds		portfolio
good	0.3	-0.06	0.14		0.02
normal	0.5	0.15	0.11		0.134
bad	0.2	0.26	0.05		0.176
expected return		10.90%	10.70%		0.1082
E(X^2)		0.02585	0.01243
variance		0.013969	0.000981
standard deviation		11.82%	3.13%		0.0834426823

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

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

Variance = E(X^2) - expected return^2

Standard deviation = sqrt(variance)

a)

rate of return in recession = 2%

rate of return in normal = 13.4%

rate of return in boom = 17.6%

b)

Expected return = 10.82%

standard deviation = 8.34%