Question

Consider the following information about three stocks:

Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom 25 .21 .36 .55 .60 .17 Normal Bust .13 -.28 .15 .00 -.45

a. If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio expected return? The variance? The standard deviation?

b.If the expected T-bill is is 3.80 percent, what is the expected premium on the portfolio?

c. If the expected inflation rate is 3.50 percent, what are the appropriate and exact expected real returns on the portfolio?What are the approximate and exact expected real risk premiums on the portfolio?

please answer all parts

Answer 1

State of Economy	Probability	Stock A	Stock B	Stock C
Boom	0.25	0.10	0.10	0.05
Normal	0.6	0.24	0.24	0.12
Bust	0.15	0.06	0.06	0.03
Weights		0.40	0.40	0.20
T.bill rate	3.80%
Inflation rate	3.50%
	a	b	c=a*b	(b-sum of c)
State of Economy	Probability	Portfolio return	Product	Return Deviation	Squared Deviation	Product
Boom	0.25	0.338	0.0845	0.201	0.040401	0.0101
Normal	0.6	0.138	0.0828	0.001	0.000001	6E-07
Bust	0.15	-0.202	-0.03	-0.339	0.114921	0.017238
Weights		E ( R )	0.137		Variance	0.027339

Standard deviation	Square of variance	0.165345
2
Expected Risk premium	E ( R ) - Risk free return	0.137-0.038	0.099
Approximate real return	0.137 - 0.035	0.102
exact real return	1 + E(R) = (1 + h)[1 + e(ri)]	1+0.137= (1+0.038)(1+E(R))
		E ( R ) = (1.137/1.038)-1	0.0954
Approximate real risk premium	Risk premium - infation rate	0.137-0.035	0.102
exact real return	real risk premium /1+inflation rate	0.102/1.035	0.0986