Question

In: Finance

Your eccentric Aunt Claudia has left you $50,000 in BP shares plus $50,000 cash. Unfortunately her...

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

Solutions

Expert Solution

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.


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