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

ID: 2710519 • Letter: Y

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.

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

Explanation / Answer

Company -BP

Variance

BHP

=(1/2)2 x (30.0%)2 + (1/2)2 x (41.8%)2+ 2 x 1/2 x 1/2 x (0.34) x (30.0%) x (41.8%) =

0.087499

Fiat

=(1/2)2 x (52.8%)2 + (1/2)2 x (41.8%)2+ 2 x 1/2 x 1/2 x (0.29) x (52.8%) x (41.8%) =

0.145379

Heineken

=(1/2)2 x (28.3%)2 + (1/2)2 x (41.8%)2+ 2 x 1/2 x 1/2 x (0.14) x (28.3%) x (41.8%) =

0.071984

Nestle

=(1/2)2 x (22.0%)2 + (1/2)2 x (41.8%)2+ 2 x 1/2 x 1/2 x (0.16) x (22.0%) x (41.8%) =

0.063138

Sony

=(1/2)2 x (42.5%)2 + (1/2)2 x (41.8%)2+ 2 x 1/2 x 1/2 x (0.36) x (42.5%) x (41.8%) =

0.120814

TAM

=(1/2)2 x (50.4%)2 + (1/2)2 x (41.8%)2+ 2 x 1/2 x 1/2 x (-0.07) x (50.4%) x (41.8%) =

0.099811

Tata Motors

=(1/2)2 x (52.5%)2 + (1/2)2 x (41.8%)2+ 2 x 1/2 x 1/2 x (0.12) x (52.5%) x (41.8%) =

0.125754

Safest Portfolio has lowest variance.i.e. nestle and BP