Fall 2011
Homework Assignment #6
In the first step of the analysis, two stocks from the DIJA Index were chosen. In order to obtain a low correlation coefficient ( less than 0.5) the stocks from different market segments were chosen: WalMart and Exxon. According to the monthly data from the last two years, the average returns of WalMart and Exxon are -0.58% and -0.92% , while the standard deviations are 3.97% and 5.11% respectively. The correlation between the two assets is 0.49, which is consistent with the problem requirements (See Excel file for detailed calculations).
As a second step, a portfolio with the two selected assets, which form an efficient frontier with different weights, was created. In order to do so, different portfolio weights (from a full investment in WalMart stock (1.0) and no investment in the stock Exxon (0) till the opposite scenario with a 100% of investment in Exxon portfolio and 0% in WalMart portfolio) were simulated. According to the data, the efficient frontier can be represented by the following graph.
If the risk free rate is assumed to be equal to 4%, the tangency portfolio can be calculated using variance-covariance matrix. The point of tangency, also known as the optimal combination of risky assets is the combination of 52% of WalMart and 48% of Exxon stocks. The expected return and the standard deviation of this portfolio are respectively -0.74% and 22.52%.
Finally, the tangency portfolio is combined with the risk free asset, assuming an expected return of 12%. In this way the standard deviation decreases, reaching 19.36%. This result is achieved by investing 76% in the tangency portfolio and 24% in the risky portfolio.
