Question

Prob.	Ret(A)	Ret(B)
10%	-5.00%	-2.00%
20%	0.00%	1.00%
40%	5.00%	3.00%
20%	10.00%	4.00%
10%	15.00%	5.00%

1) Please calculate covariance and correlation between A and B.

2) Please calculate the variance of a portfolio consisting of 45% of A and 55% of B.

3) Please find the MVP based on a portfolio consisting of A and B. What is the expected return of the MVP? What is the risk for the MVP?

4) Please find the optimal portfolio (calculate W_A and W_B) corresponding to 4% of return.

Answer 1

Solution:

This excel table shows all the calculations to be used.

probability (p)	R (A)	R (B)	p.R (A)	p.R (B)	(R - E (RA))	(R -E(RB))	P.(R-E(RA))^2	P.(R-E(RB))^2	P.(R-E(RA)).(R-E(RB))
0.1	-5	-2	-0.5	-0.2	-10	-4.5	10	2.025	4.5
0.2	0	1	0	0.2	-5	-1.5	5	0.45	1.5
0.4	5	3	2	1.2	0	0.5	0	0.1	0
0.2	10	4	2	0.8	5	1.5	5	0.45	1.5
0.1	15	5	1.5	0.5	10	2.5	10	0.625	2.5
			5	2.5			30	3.65	10

1. The covariance between return A and B is calculated as follows

10 (From the above table)

The correlation between returns A and B is calculated as follows

[These values are obtained from the table]

= 0.9556

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2. The variance of the portfolio, is calculated as follows

= (0.45)^2*30 + 0.55^2*3.65 + 2*0.45*0.55*10

= 12.1291 (%)^2

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3.

To find the minimum variance, we use the following formula

= 1.465

= -0.465 (5%) + 1.465 (2.5%)

= 1.34%

The risk for the MVP is calculated as follows

= 0.8342

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4. The optimal portfolio with 4% return

= 1.667