Sample Question #113 (finance – portfolio theory)

What’s the efficient frontier? What makes the efficient frontier "efficient"? In practice, how does one derive the efficient frontier?

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Sample Question #113 (finance – portfolio theory)

What’s the efficient frontier? What makes the efficient frontier "efficient"? In practice, how does one derive the efficient frontier?

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ANSWER

Given any portfolio of assets, we can calculate its expected return and expected risk, usually measured as expected standard deviation. (Well, we "can" do this in the sense that the expectation can be anything we want it to be!) In other words, we can plot portfolios in the Risk-vs.-Return space, with expected risk on the x-axis and expected return on the y-axis.

Modern portfolio theory says that for each given level of risk, there’s a portfolio that has a maximum return. When we trace out these maximum-return portfolios for different risk levels, we get the efficient frontier curve. This curve tells us that, given our assumptions, no portfolio can lie above the curve, since by definition no portfolio can have a higher expected return than the maximum-return portfolio for a given level of risk.

In practice, one derives the efficient frontier by first forming expected returns for the assets that will be included in the portfolio as well as expected variances and correlations. (Bonus question: given n assets, how many such estimations do you need to carry out?) Then we can use Excel’s Solver functionality to calculate the maximum-return portfolios for a range of standard deviation measures. Of course, don’t forget to constraint the weights of the assets; e.g., are short sells allowed in the portfolios?