Question

1.

Suppose there are two assets, Asset 1 and Asset 2. You are given the following information about the two assets.

E(R₁)   = 0.12                       E(s₁)   = 0.05

E(R₂)   = 0.20                       E(s₂)   = 0.08

1. Calculate the expected returns and expected standard deviations of a two-stock portfolio in which Stock 1 has a weight of 70 percent under the following conditions.

1. r_1,2    =    1.00
2. r_1,2    =   0.50
3. r_1,2    =   0.00
4. r_1,2    = –0.50
5. r_1,2    = –1.00

Show your calculations.

2. Which of these portfolios has the most risk? Why?

Answer 1

The Expected return of the portfolio of 2 ASSETS is calculated as

Exp return = w1*r1 +w2*r2

Expected return on the portfolio = w1*r1 +w2*r2

Where the weights are given

W1=0.7

So W2 = (1-w1)

W2= 0.3

Standard Deviation of a portfolio of 2 Assets

Std dev = ((w1^2)(sd1)^2) + (W2^2 sd2^2) + (2*w1*w2*sd1*sd2*correlation ) ) ^ 1/2

A    Corell = 1.0

Expected return = ( 0.7*12) +(0.3 * 20) = 14.4%

Standard Deviation

= (( 0.7^2 * 0.05^2) +( 0.3^2 * 0.08^2)+ ( 2* 0.05*0.08*0.7*0.3*1)) ^ 1/2

= 0.059 or 5.9%

	Return %	Std Dev	Weight	Correlation
Asset 1	12	0.05	0.7	1
Asset 2	20	0.08	0.3
Expected Return	14.400
Variance	0.003481
Std Dev	0.059

b   Corell = 0.50

Expected return = ( 0.7*12) +(0.3 * 20) = 14.4%

Standard Deviation

= (( 0.7^2 * 0.05^2) +( 0.3^2 * 0.08^2)+ ( 2* 0.05*0.08*0.7*0.3*0.50)) ^ 1/2

= 0.051390661 or 5.13%

	Return %	Std Dev	Weight	Correlation
Asset 1	12	0.05	0.7	0.5
Asset 2	20	0.08	0.3
Expected Return	14.400
Variance	0.002641
Std Dev	0.051390661

C Corell = 00

Expected return = ( 0.7*12) +(0.3 * 20) = 14.4%

Standard Deviation

= (( 0.7^2 * 0.05^2) +( 0.3^2 * 0.08^2)+ ( 2* 0.05*0.08*0.7*0.3*0)) ^ 1/2

= 0.04243819

	Return %	Std Dev	Weight	Correlation
Asset 1	12	0.05	0.7	0
Asset 2	20	0.08	0.3
Expected Return	14.400
Variance	0.001801
Std Dev	0.04243819

D Corell = -0.5

Expected return = ( 0.7*12) +(0.3 * 20) = 14.4%

Standard Deviation

= (( 0.7^2 * 0.05^2) +( 0.3^2 * 0.08^2)+ ( 2* 0.05*0.08*0.7*0.3*0)) ^ 1/2

= 0.031

	Return %	Std Dev	Weight	Correlation
Asset 1	12	0.05	0.7	-0.5
Asset 2	20	0.08	0.3
Expected Return	14.400
Variance	0.000961
Std Dev	0.031

E Corell = -1.00

Expected return = ( 0.7*12) +(0.3 * 20) = 14.4%

Standard Deviation

= (( 0.7^2 * 0.05^2) +( 0.3^2 * 0.08^2)+ ( 2* 0.05*0.08*0.7*0.3*0)) ^ 1/2

= 0.011

	Return %	Std Dev	Weight	Correlation
Asset 1	12	0.05	0.7	-1
Asset 2	20	0.08	0.3
Expected Return	14.400
Variance	0.000121
Std Dev	0.011

Part II

The most riskiest or risky case is CASE 1 with Corell with Corell(1,2) = 1

This is because the portfolio having the highest standard deviation is the most risky portfolio

Thanks