Question

You have $1,000,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 18 percent and Stock Y with an expected return of 10 percent. Your goal is to create a portfolio with an expected return of 13 percent. All money must be invested. How much will you invest in Stock X?

Answer 1

How much will you invest in Stock X?

$                 3,75,000

• The Expected Return of a portfolio is the weighted average return of the individual securities in the portfolio, where the weights are the proportions invested in each security.
• Let P be the proportion of Stock X in the portfolio. Then the proportion of Stock Y in the portfolio is 1-P

Stock	Expected return (%)	Proportion	Expected return of portfolio (%)
	a	b	c = a × b
X	18	P	18P
Y	10	1-P	10(1-P)
Expected return of portfolio (target)			13

• 18P + 10(1-P) = 13
• 18P + 10 - 10P = 13
• 8P = 13 - 10
• P = 3 ÷ 8 = 0.375
• Therefore, proportion of stock X & Y:

  • X	P	0.375	37.5%
    Y	1-P	1 - 0.375 = 0.625	62.5%

• Verification:

  • Stock	Expected return (%)	Proportion	Expected return of portfolio (%)
    	a	b	c = a × b
    X	18	0.375	6.75
    Y	10	0.625	6.25
    Expected return of portfolio (target)			13.00

• HOW MUCH TO INVEST IN EACH STOCK:

  • Stock	Computation		Amount invested
    X	$1,000,000 × 37.5%		$                 375,000
    Y	$1,000,000 × 62.5%		$                 625,000
    Total			$               1,000,000