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.

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 1.

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

James decides to follow her wife’s suggestion. But, he would prefer a lower volatility for his investment. He decides to invest 40% of his wealth into the T-bills, and 60% in Rachel’s portfolio.

What is the proportion of his investments in each asset?

He would invest   % into the T-bills,   % into Microsoft, and   % into Coca-Cola.

Note: please fill in a whole number for each blank.

Answer 1

a). 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%

b). James would invest 40% in T-bills

Investment in Microsoft = Weight of Rachel's Portfolio * Weight of Microsoft in Rachel's Portfolio

= 0.60 * 0.60 = 0.36, or 36%

Investment in Coca Cola = Weight of Rachel's Portfolio * Weight of Coca Cola in Rachel's Portfolio

= 0.60 * 0.40 = 0.24, or 24%