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You have $ 10 comma 000 to invest. You decide to invest $ 20 comma 000 in Google and short sell $ 10 comma 000 worth of​ Yahoo! Google's expected return is 15 % with a volatility of 30 % and​ Yahoo!'s expected return is 12 % with a volatility of 25 %. The stocks have a correlation of 0.90. What is the expected return and volatility of the​ portfolio? The expected return is

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Answer:

expected return is 18%

volatility of the​ portfolio 13.23 %

Explanation:

Your Investment: $ 10,000

Invest $ 20,000 in Google, Google's expected return is 15 %

Sell $ 10,000 worth of​ Yahoo! Yahoo! Yahoo!'s expected return is 12 %

=> The weight of your portfolio is 2 for the Google stock, and -1 for the Yahoo stock.  The negative sign for the Yahoo stock indicates a short position in the stock. The expected return is the weighted average of the returns on the two stocks:

  • 2 * 15% + (-1) * 12% = 18%

The volatility of the portfolio is:

[tex]\sqrt{2^{2}*0.15^{2} + -1^{2}*0.25^{2} +2*2*(-1)*0.9*0.15*0.25 }[/tex] = 13.23 %

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