Question

Problem 3.Refer to the following information on the return distribution for two assets in which you are contemplating to invest in;

State of Economy	Probability that the state of economy occurs	Return if the state occurs              Asset AA	Return if the state occurs              Asset BB
BOOM	10%	40%	60%
AVERAGE	40%	20%	30%
BELOW AVERAGE	20%	20%	10%
POOR	30%	-20%	-30%

In addition to the above return distribution the two assets (AA& BB) operate in different industries and hence characterized by a market risk (Beta) of 2 and 3respectively. The market risk premium (RM- RF) or the slope for fairly correctly priced assets is 14%. In the same economy government treasury bills reward a risk free return of about 11%.

Required:

Calculate the expected return for assets AA & BB respectively

Calculate the required rate of return assets AA & BB respectively using the CAPM

Calculate the standard deviation for assets AA& BB respectively

If the company wants to invest in the two assets with the ratio of 45:55 what is the Portfolio standard deviation and Portfolio return

Answer 1

Working Note 1)

State of Economy	Probability that the state of economy occurs (A)	Return if the state occurs              Asset AA (B)	Expected return = probability * return of asset (c)	Deviation from Expected Value of 10% (d)	Squared (d)2
BOOM	10%	40%	4%	4-10= -6%	(-6)2 =36
AVERAGE	40%	20%	8%	8-10= -2%	(-2)2 =4
BELOW AVERAGE	20%	20%	4%	4-10= -6%	(-6)2 =36
POOR	30%	-20%	-6%	-6-10 =16%	(-16)2 =256
			Expected return = 10% (4+8+4-6)		332%2

Expected return for assets AA = 10%

required rate of return assets AA  = R_{f +} B(RM- RF)

= 11% + 2(14%)

=39%

Standard deviation (σ) is found by taking the square root of variance:

Standard deviation of Asset AA = (332%)^1/2

⁼18.22%

Working note 2)

State of Economy	Probability that the state of economy occurs (A)	Return if the state occurs    Asset BB	Expected return = probability * return of asset	Deviation from Expected Value of 11%	Squared
BOOM	10%	60%	6%	6-11= -5%	-52 =25
AVERAGE	40%	30%	12%	12-11= 1%	(-1)2 =1
BELOW AVERAGE	20%	10%	2%	2-11= -9%	(-9)2 =81
POOR	30%	-30%	-9%	-9-11 =-20%	(20)2 =400
			Expected return = 11% (6+12+2-9)		507%2

Expected return for assets AA = 11%

required rate of return assets AA  = R_{f +} B(RM- RF)

= 11% + 3(14%)

=53%

Standard deviation (σ) is found by taking the square root of variance:

Standard deviation Asset BB =( 507%²) ^1/2

⁼22.516%

If the company wants to invest in the two assets with the ratio of 45:55 what is the Portfolio standard deviation and Portfolio return

Portfolio return = 45/100* 10% + 55/100* 11%

=4.5% + 6.05

=10.55%

Working note 3) Computation of Covariance between assets

Deviation from Expected Value of 10% i.e Expected return of Asset AA- Actual return of Asset AA) (please refer working note 1 (d)             A	Deviation from Expected Value of 11% i.e (Expected return of Asset BB- Actual return of Asset BB) please refer working note 2 (d)            B	Probability that the state of economy occurs C	D= A*B*C
-6%	-5%	.10	3
-2%	1%	.40	-.8
-6%	-9%	.20	10.8
-16%	-20%	.30	96
		1.00	109

Covariance between the two Assets:

Sum of (Expected return of Asset AA- Actual return of Asset AA) * (Expected return of Asset BB- Actual return of Asset BB) * Probabilty

=109 (Check working note 3 for computation)

Calculation of Standard Deviation of portfolio

Standard Deviation of portfolio= 16.568% (CHECK WORKING NOTE 4)

WORKING NOTE 4)