Most Popular ArticlesSeptember 1, 2009
Quantifying diversification
Mr. Katz asserts that the Merriman portfolio is “massively diversified” because it holds so many stocks (11,000). The problem with simply counting holdings is that this is a poor measure of the diversification within a portfolio. As Professor William Goetzmann of Yale succinctly notes:
While the number of stocks in a portfolio is a useful heuristic for identifying the degree of diversification, this measure is insufficient to accurately characterize the diversification characteristics of a portfolio. To measure diversification more accurately, we exploit the covariance structure of investors’ portfolios…
This means that we can only properly account for portfolio diversification if we account for the correlations between positions—which is one of my key points. Holding thousands of stocks that are highly correlated (as a group) to the broader market means that you may, in fact, be relatively undiversified. I asserted that this is the case for the original Merriman portfolio. While Mr. Katz takes issue with this concept, he provides no substantive arguments to the contrary. Instead, he argues (with no quantitative support) that we should simply ignore the high correlations between the components of the Merriman portfolio because they might go away in the future.
For those readers who do not have the time to follow the references provided, I will simply note that all of these studies are authored by leading academics in finance—these are not fringe ideas.
Default risk and individual stocks
One of the standard arguments in favor of having very low exposure to any single stock is that this minimizes exposure to default risk if one company fails. This is clearly true. On the other hand, the argument for including individual stocks is that we can choose high quality stocks that have low Beta, low volatility, and a long history of stable performance—and this is a specific strategy that Bill Gross recommends for the New Normal. Choosing stocks based on low Beta and volatility exposes the investor to lower levels of default risk than choosing stocks at random. I explored this issue in depth in an article in March of 2008. While I did not include Bank of America (BAC) in my New Normal portfolio, Mr. Katz notes that if I had, a position in this one stock could have taken a big bite out of the portfolio in 2008.
Let’s look at this example more closely. For the 12-month period through July of 2009, BAC is down 53%. IYF, an ETF that tracks the U.S. financial sector is down 33%. By Mr. Katz’s logic, this shows that an individual stock is too risky relative to a broader aggregation of stocks. This does not tell the whole story.
When I calculate the Beta of the Merriman portfolio with respect to IYF (and using data through July 08), I get a value of 23.1%. When I calculate Beta with respect to IYF for my New Normal portfolio (using the same date range), I get a value of 14.8%. These Betas tell us how much either portfolio will tend to respond to a move in IYF. For the next twelve months, IYF dropped 33%, and this move tended to generate a loss of 7.8% in the Merriman portfolio (23.1% x -33%) vs. a loss of 5.0% in my New Normal portfolio. Now, let’s assume that we had invested 3% of the portfolio in BAC (just based on Mr. Katz’s assertion) and the remaining 97% in the original New Normal portfolio. The BAC position would contribute a 1.6% loss to the portfolio, so the total portfolio return for the 12-month period would be -6.4% (-1.6% - 0.97*5% ). In other words, based upon the net exposure to financials that we would have estimated back in July 2008, the Merriman portfolio still fared worse than my New Normal in the last 12-months, even with a 3% allocation to BAC.
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