You have $130,000 to invest in a portfolio containing Stock X and Stock Y. Your

Question

You have $130,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 14.6 percent. Stock X has an expected return of 12.8 percent and a beta of 1.30, and Stock Y has an expected return of 7.8 percent and a beta of 1.05.

You have $130,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 14.6 percent. Stock X has an expected return of 12.8 percent and a beta of 1.30, and Stock Y has an expected return of 7.8 percent and a beta of 1.05.

Explanation / Answer

Let the contribution in Stock Y be 'p'. So, the contribution in Stock X = 1-p

As per question,

14.6% = Return of Stock X * (1-p) + Return of Stock Y * p

=> 14.6% = 12.8% * (1-p) + 7.8% * p

=> p = -0.36

So, the investor would sell 36%* $130,000 = $46,800 worth of Stock Y and buy 136% * $130,000 = $176,800 worth of Stock X.

Investment in Stock Y = -$46,800

Beta of portfolio = 1.36 * 1.30 - 0.36 * 1.05

= 1.390

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