Question

		Rate of Return
Scenario	Probability	Stocks		Bonds
Recession	.20	−8	%	+16	%
Normal economy	.50	+19		+9
Boom	.30	+25		+6

Consider a portfolio with weights of .6 in stocks and .4 in bonds.

a.	What is the rate of return on the portfolio in each scenario? (Do not round intermediate calculations. Round your answers to 1 decimal place.)

Scenario	Rate of Return
Recession	%
Normal economy	%
Boom	%

b.	What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected rate of return	%
Standard deviation	%

c.	Which investment would you prefer?
	Portfolio Bonds Stocks

Answer 1

Sol:

a) Rate of return on the portfolio can be calculated using the following equation:

E(r)_P = [E(r)_Stocks x W_Stocks] + [E(r)_Bonds x W_Bonds]

Here,

E(r)_p= Return on the portfolio

E(r)_Stocks = Return on the Stocks

W_Stocks = Weight of the Stocks

E(r)_Stocks= Return on the Bonds

W_Bonds = Weight of the Bonds

Calculate the rate of return on the portfolio can in Recession as follows:

E(r)_P-_Recession = [ E(r)_Stocks x W_Stocks ] + [ E(r)_Bonds x W_Bonds ]

=[(-8%) x 0.50 ] + [16% x 0.40 ]

=( -4%) + 6.40%

= 2.40%

Calculate the rate of return on the portfolio can in Normal Economy as follows:

E(r)_{P-Normal Economy} = [ E(r)_Stocks x W_Stocks ] + [ E(r)_Bonds x W_Bonds ]

= [19%) x 0.50 ] + [9% x 0.40 ]

= 9.5% + 3.6%

   = 13.10%

Calculate the rate of return on the portfolio can in Bonds as follows:

E(r)_P-Boom = [ E(r)_Stocks x W_Stocks ] + [ E(r)_Bonds x W_Bonds ]

= [25%) x 0.50 ] + [6% x 0.04 ]

= 12.5% +2.40%

   = 14.90%

Following table shows the rate of return on the portfolio in each scenario :

Scenario	Stocks	Bonds	Rate of return
Recession	-8%	16%	2.40%
Normal Economy	19%	9%	13.10%
Boom	25%	6%	14.90%

b) Expected return = (2.40 *.20)+(13.10* .50)+(14.90*.30)

= .48+6.55+ 4.47

= 11.50%

Variance = (2.40-11.50)^2 + (13.10-11.50)^2 + (14.90-11.50)^2

   = (-9.10)^2 + (1.60)^2 + (3.40)^2

= -82.81+ 2.56+11.56

= 68.69

Standard deviation = Square root of 68.69

                             = 8.29%

c) Investment in stock is better as expected return in stock is higher than expected return in bond .