Tangencies of the Efficient Frontier and Individual Utility Functions

by Justin Wai

Submitted : Fall 2010

First I had to generate data on 20 different asset classes and find the return over each month for the last 5 years. Then, found the difference between each month returns and the average. Next use that data to produce a covariance-variance matrix. Then using solver, the covariance-variance matrix, returns and restrictions find different points on the efficient frontier. Use these points to graph an efficient frontier. Because the efficient frontier is not a smooth constant slope, use Easy fit software to find the best equation for the given line.

After finding the equation to the efficient frontier use four different utility functions and find the first derivative of them. Next find the point that maximizes the utility of these individuals by setting the first derivative of the efficient frontier and each individual utility curve equal to each other. Now for a given utility curve we can substitute the values in to find the x value. Plugging that back into original equation to find the y and then using that to find the asset allocation.

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