Question

Question 1 gives you the information of the stocks and their correlation, which will be used in many of the following questions.

James, a portfolio manager, would like to form the following portfolio between Microsoft and Coca-Cola:

            Expected return (%)      Standard Deviation (%) Weight

Microsoft                 28                          42                    0.4                  

Coca-Cola              12.5                         21                    0.6

The correlation between the two stocks is 0.5.

What is the expected return of the portfolio? ______%

Rachel, James’ wife, suggests a portfolio which consists 60% of Microsoft and 40% of Coca-Cola.

The information of the stocks’ standard deviation and their correlation is from question the question above

What is the standard deviation of Rachel’s portfolio? ______%

Answer 1

a). Expected Return = $\sum_{i=1}^{n}$ [Weight_i * Return_i]

= [0.4 * 28%] + [0.6 * 12.5%] = 11.2% + 7.5% = 18.7%

b). Rachel's Portfolio Expected Return = $\sum_{i=1}^{n}$ [Weight_i * Return_i]

= [0.6 * 28%] + [0.4 * 12.5%] = 16.8% + 5% = 21.8%

Rachel's Portfolio $\sigma$ = [(Weight_MSFT * $\sigma$_MSFT)² + (Weight_CC * $\sigma$_CC)² + (2 * Weight_MSFT * Weight_CC * $\sigma$_MSFT * $\sigma$_CC * Correlation(MSFT,CC)]^1/2

= [(0.6 * 42%)² + (0.4 * 21%)² + (2 * 0.6 * 0.4 * 42% * 21% * 0.5)]^1/2

= [635.04%² + 70.56%² + 211.68%²]^1/2 = [917.28%²]^1/2 = 30.29%