(19,700 / 20,660) - 1 = - 0.04647 <- note the negative sign, a loss
return on Hess: (70/80) - 1 = - 0.125
return on XOM: (80/83) - 1 = - 0.03614
let x = weight of Hess in the portfolio,
thus (1 - x) = weight of XOM in the portfolio
-0.125x + [ (1 - x)(-0.03614) ] = - 0.04647
-0.125x -0.03614 + 0.03614x = - 0.04647
-0.125x + 0.03614x = - 0.04647 + 0.03614
- 0.08886x = - 0.01032
x = -0.01032 / -0.08886
x = 0.11617
so, (1 - x) = 0.88383
at this point you can either use beginning total and beginning per share prices, or end total and end share prices...we'll use beginning
$ amt invested in Hess: 0.11617 * $20,660 = $2,400
$2,400 / begin price $80 = 30 shares of Hess
shares of XOM: (total begin - amt in Hess) = 20,660 - 2400 = $18,260
$18,260 / begin price $83 = 220 shares
OR another way...as we calculated for Hess...
weight of XOM * total invested: 0.88383 * 20,660 = $18,260
$18,260 / 83 = 220 shares
check math:
Hess: 30 shares * end price $70 = $2,100
XOM: 220 shares * end price $80 = $17,600
Sum: $19,700 = total end value
In the two-month period June 1–July 31, 2011, Hess Corp. (HES) stock decreased from $80 to $70 per share, and Exxon Mobil (XOM) stock decreased from $83 to $80 per share.? If you invested a total of $20,660 in these stocks at the beginning of June and sold them for $19,700 at the end of July, how many shares of each stock did you buy?
