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	.33	.36	.43	.18	.43	.16	.36
BP	.33	1.00	.36	.18	.16	.30	.48	.19
Fiat Chrysler	.36	.36	1.00	.10	.11	.03	.37	.08
Heineken	.43	.18	.10	1.00	.24	.51	.30	.33
Korea Electric	.18	.16	.11	.24	1.00	.01	.16	.13
Nestlé	.43	.30	.03	.51	.01	1.00	.23	.08
Sony	.16	.48	.37	.30	.16	.23	1.00	.19
Tata Motors	.36	.19	.08	.33	.13	.08	.19	1.00
Standard deviation (%)	26.80	36.10	50.06	14.54	34.83	11.10	47.64	41.21

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 Nestl?
	BP and Sony
	BP and Korea Electric
	BP and Tata Motors

Answer 1

A. To Find : Portfolio Variance

Formula = (Standard Deviation A * Weight of A )² + (Standard Deviation B * Weight of B )² + (2 *Standard Deviation A * Weight of A* Standard Deviation B * Weight of B * Correlation between A & B )

Where, A & B are the stocks in which the amount is invested

and Weights are calculated as follows : Amount invested in Stock / Total investment

Now,

Total investment = $100,000 in which they have invested $50,000 in the BP shares and remaining $ 50,000 is invested in one another share

Hence, Weights for the two Shares is 0.5 as equally invested in both the shares. ( 50000/100000)

Potfolio	S.D (A)	S.D2 (A2)	W (A)	W2 (A2)	S.D (B)	S.D 2 (B2)	W (B)	W2 (B2)	R(A & B	Portfoliio Variance
BHP (A) & BP (B )	0.2680	0.07182	0.5	0.25	0.3610	0.13032	0.5	0.25	0.33	0.067
Fiat (A) &n BP (B)	0.5006	0.2506	0.5	0.25	0.3610	0.13032	0.5	0.25	0.36	0.12776
Heinkenen (A) & BP (B)	0.1454	0.02114	0.5	0.25	0.3610	0.13032	0.5	0.25	0.18	0.04259
Korea (A) & BP (B)	0.3483	0.12131	0.5	0.25	0.3610	0.13032	0.5	0.25	0.16	0.07297
Nestle(A) & BP (B)	0.1110	0.01232	0.5	0.25	0.3610	0.13032	0.5	0.25	0.30	0.04167
Sony (A) & BP (B)	0.4764	0.22696	0.5	0.25	0.3610	0.13032	0.5	0.25	0.48	0.13059
Tata Motors (A) & BP(B)	0.4121	0.16983	0.5	0.25	0.3610	0.13032	0.5	0.25	0.19	0.08917

Explanation

S.D. = Standard Deviation

W = Weight

R = Correlation

B. Most Safest Attainable portfolio is BP & Nestle because it has the smallest risk factor than others combination