Exercises [1]: Consider the following expected return, E(r i ), variance, s i 2
ID: 3273405 • Letter: E
Question
Exercises[1]:
Consider the following expected return, E(ri ), variance, si2 , and correlation value, rij, for the three securities listed below: (Hint: calculate the standard deviation for each stock first! )
Security
E(ri ),
si2
r12
r13
r23
1
.06
.04
.60
2
.12
.08
-.40
3
.18
.18
.20
a. What is the portfolio expected return for each of the following combinations:
(i) W1 = .2, W2 = .4, W3 = .4.
(ii) W1 = .3, W2 = .2, W3 = .5
b. What is the portfolio variance for each of the combinations in Part a?
c. Which of the two portfolios would you choose? Why?
[1] Roundup your calculations to 0.0001.
Security
E(ri ),
si2
r12
r13
r23
1
.06
.04
.60
2
.12
.08
-.40
3
.18
.18
.20
Explanation / Answer
a)
Portfolio expected return of (a)=w1*E(r1)+ w2*E(r2)+w3*E(r3)
=0.2(0.06)+0.4(0.12)+0.4(0.18)
= 0.132
Portfolio expected return of (b)=w1*E(r1)+ w2*E(r2)+w3*E(r3)
=0.3(0.06)+0.2(0.12)+0.5(0.18)
= 0.132
b)
Variiance of (a) =w112+ w112+ w112+2*w1*w2*w3*r12*r13*r23
=0.2*0.04+0.4*0.08+0.4*0.18+ 2*0.2*0.4*0.4*0.6*(-0.4)*0.2
=0.112-0.003072
=0.1089
Variiance of (b) =w112+ w112+ w112+2*w1*w2*w3*r12*r13*r23
=0.3*0.04+0.2*0.08+0.5*0.18+2*0.3*0.2*0.5*0.6*(-0.4)*0.2
=0.118-0.00288
=0.1151
c)
Both having portfolio expected return is same and 2nd standard deviation is more than the 1st one , so i preferred part b
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