Question

You have performed the XXXX optimization on a portfolio with 3 assets whose risk/return characteristics are summarized in the table below:

	Asset 1	Asset 2	Asset 3
E[r]	5.00%	10.00%	15.00%
s.d.	10.00%	15.00%	20.00%

The ‘bordered matrix’ for the optimal risky portfolio based on these three assets is given below:

Bordered matrix		W1	W2	W3
		-1.522	1.585	0.938
W1	-1.522	0.0232	-0.0261	-0.0044
W2	1.585	-0.0261	0.0565	-0.0033
W3	0.938	-0.0044	-0.0033	0.0352

1)Find the optimal risky portfolio’s expected return. Express your answer as a percentage with 3 digits after the decimal point.

2)Find the optimal risky portfolio’s standard deviation return. Express your answer as a percentage with 3 digits after the decimal point.

Answer 1

Answer :

(1). The optimal risky portfolio's expected Return = 22.31%

#	Weights	Expected Return	Weight*Expected Return
Asset 1	-1.522	5	-7.61
Asset 2	1.582	10	15.85
Assets 3	0.938	15	14.07
-	1.000	-	22.310

(b). The optimal risky portfolio's standard deviation return = 59.61%

Bordered matrix

-	-	W1	W2	W3
-	-	-1.522	1.585	0.938
W1	-1.522	0.0232	-0.0261	-0.0044
W2	1.585	-0.0261	0.0565	-0.0033
W3	0.938	-0.0044	-0.0033	0.0352

Bordered matrix

	A	B	C	D	E
1	Bordered matrix	-	-	-	-
2	-	-	W1	W2	W3
3	-	-	-1.522	1.585	0.938
4	W1	-1.522	0.0232	-0.0261	-0.0044
5	W2	1.585	-0.0261	0.0565	-0.0033
6	W3	0.938	-0.0044	-0.0033	0.0352

59.610 => (((B4*C3*C4)+(B4*D4*D3)+(B4*E4*E3)+(B5*C5*C3)+(B5*D5*D3)+(B5*E5*E3)+(B6*C3*C6)+(B6*D3*D6)+(B6*E6*E3))^(1/2))