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?

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Shahzaibfaraz Shahzaibfaraz · Answer 1 · 2020-04-13T04:41:05+02:00

Answer:

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

Tundexi Tundexi · Answer 2 · 2021-12-23T12:36:10+01:00

The amount that i will invest in X and Y is $6904.76 and $3095.24 respectively.

Let investment in X = $x

So, the investment in Y will be (10,000-x)

Portfolio return = Respective return*Respective weight

10.85 =(x/10,000*11.5) + (10,000-x) / 10,000*9.4

(10.85*10,000) = 11.5x + (10,000-x)*9.4

108500 = 11.5x + 94000 - 9.4x

x = (108500 - 94000) / (11.5-9.4)

x = $6904.76

Thus, the investment in X equals $6904.76.

Investment in Y = (10,000-x)

Investment in Y = (10,000 - 6904.76

Investment in Y = $3095.24

In conclusion, the amount that i will invest in X and Y is $6904.76 and $3095.24 respectively.

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