Question

Your eccentric Aunt Claudia has left you $50,000 in BP shares plus $50,000 cash. Unfortunately her will requires that the BP stock not be sold for one year and the $50,000 cash must be entirely invested in one of the stocks shown below. The table provides estimates of the standard deviations of returns for each stock and the correlation between the returns of each pair of stocks.

	BHP	BP	Fiat Chrysler	Heineken	Korea Electric	Nestlé	Sony	Tata Motors
BHP	1.00	.30	.45	.35	.17	.35	.13	.37
BP	.30	1.00	.37	.17	.13	.30	.47	.20
Fiat Chrysler	.45	.37	1.00	.11	.12	.04	.38	.09
Heineken	.35	.17	.11	1.00	.23	.50	.31	.32
Korea Electric	.17	.13	.12	.23	1.00	.01	.16	.13
Nestlé	.35	.30	.04	.50	.01	1.00	.23	.08
Sony	.13	.47	.38	.31	.16	.23	1.00	.19
Tata Motors	.37	.20	.09	.32	.13	.08	.19	1.00
Standard deviation (%)	25.80	35.10	49.06	15.04	33.83	10.90	47.24	40.91

a. Calculate the portfolio variance for seven different portfolios. (Use decimals, not percents, in your calculations. Do not round intermediate calculations. Enter your answers as a decimal rounded to 5 places.)

	Portfolio Variance
BHP
Fiat Chrylser
Heinkenen
Korea Electric
Nestlé
Sony
Tata Motors

b. What is the safest attainable portfolio under these restrictions?

	BP and BHP
	BP and Fiat
	BP and Heineken
	BP and Nestlé
	BP and Sony
	BP and Korea Electric
	BP and Tata Motors

Answer 1

First you need to calculate variance of each stock which is just the square of standard deviation

	Variance of each security
BHP	7%
BP	12%
Fiat Chrysler	24%
Heineken	2%
Korea Electric	11%
Nestlé	1%
Sony	22%
Tata Motors	17%

Now, variance of each stock w.r.t to BP

Variance = W1^2*Var1+W2^2*Var2+2*Var1*Var2*cov(1,2)

Worth noting that, W1 and W2 will remain same as 0.5 for all our calculations as investment is same. Also, Stock 2 will be BP in all out cases.

	Covariance	Variance of each stock	Variance of the portfolio
BHP	0.30000	0.06656	0.048671
Fiat Chrysler	0.37000	0.24069	0.096458
Heineken	0.17000	0.02262	0.036692
Korea Electric	0.13000	0.11445	0.060328
Nestlé	0.30000	0.01188	0.03399
Sony	0.47000	0.22316	0.093052
Tata Motors	0.20000	0.16736	0.074703

Now analysis the same, if the variance is high, then risk is high, so BP &BHP, BP&Heineken and BP &Nestle are good to use.