You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 11.5% and Stock Y with an expected return of 9.4%. If your goal is to create a portfolio with an expected return of 10.85%, how much money will you invest in Stock X? In Stock Y?

Investment in stock X is $6900 while that in stock Y is $3100.

Explanation:

The portfolio return is a function of the weighted average of the individual stock returns.

Let x be the weightage of stock X in the portfolio.

1-x is the weightage of stock Y in the portfolio.

0.1085  =  x * 0.115  +  (1-x) * 0.094

0.1085 = 0.115x  +  0.094  -  0.094x

0.1085 -0.094  =  0.021x

0.0145 / 0.021  =  x

x = 0.69047 or 69.047% rounded off to 69%.

(1-x) = 1 - 0.69 = 0.31 or 31%

Money invested in stock X = 0.69 * 10000 = $6900

Money invested in stock Y = 0.31 * 10000 = $3100