The Benefits Of Diversification

We have discussed how diversification works and shown examples, but what about how it works in your portfolio? A recent article in Money discusses how much you should have invested in stocks depending on your age. And while we don't want to take a position in this, we would like to point out the "Finding the Right Mix" figure shown in the article. As you can see, in general, the range of possible returns declines as you increase the percentage of bonds in a portfolio. This is the decline in volatility that is also exhibited in the lower standard deviation from adding bonds to a stock portfolio. 

Market Efficiency Wins Again

Skeptics of stock market efficiency are always ready to argue "evidence" that the stock market is grossly inefficient. One piece of evidence that has been used in recent years is the performance of hedge funds. An oft reported statistic is that the average hedge fund return since 1996 was 12.6 percent per year. A recent article highlights research that indicates this claim is incorrect. Overstated hedge funds returns are due to the fact that hedge funds self-report returns. So, if a fund has poor returns, it stops reporting returns. Additionally, when a hedge fund is started, it will often not report returns until it has "something to brag about."  After removing these biases, the researchers found that the average annual hedge fund return since 1996 was only 6.3 percent, half of the reported average!

Diversification In A Multi-Factor World

Our guest blogger this week is Dr. Richard Roll from UCLA. Dr. Roll has published more than 100 articles and is perhaps most famous for stating that CAPM would never be tested in his lifetime as CAPM holds theoretically but is almost impossible to test empirically. Originally an aeronautical engineer, Dr. Roll wrote the operating manual for NASA's Saturn V rocket. Here, he discusses how correlation does not affect diversification in a multi-factor world.

In a multi-factor world, diversification benefits do not generally depend on correlation. This is because correlation, say between two investment portfolios, is a very poor measure of whether the portfolios are explained by the same underlying factors. If the factor loading (betas) are disparate, two portfolios can be perfectly explained by the same factors, yet their simple correlation can be zero or even negative.

In general, the individual assets in two portfolios can be re-weighted to make portfolio betas congruent. This implies that true diversification benefits depend only on the idiosyncratic volatility that remains after re-weighting to align betas. Similarly, the risk reduction from adding an asset to an existing portfolio does not depend on the asset’s correlation with the portfolio, contrary to the prescription in many investment textbooks.

These implications evince the fundamental importance of measuring the underlying factors and estimating factor sensitivities for every asset. Several methods for measuring factors have been investigated in previous literature, but an easy-to-implement general method is simply to specify a group of heterogeneous indexes or traded portfolios. Exchange Traded Funds (ETFs) could be well-suited for this purpose.

Multiple Regression Using Excel

While we certainly hope that Excel Master helped explain how to estimate a regression equation in Excel, there are definitely more uses for regression equations than CAPM or APT. For a quick look at another use, check out this regression analysis by Excel guru Bill Jelen. http://www3.cfo.com/article/2012/6/spreadsheets_excel-regression-analysis