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Rekenthaler Report

The Drawback of Diversification

Its lunch is indeed a bargain, but it's not quite free.

Skewed Results
The practice of diversification is justly popular, not only because it reduces portfolio risk but also because, at least for equity investors, it improves the odds of landing a winner. Most stocks disappoint. Equity funds thrive not because they hold many stocks that perform well, but instead because their relatively few successes outweigh their more-numerous failures. After all, a stock can only lose 100% of its value, but it can gain a great deal more.

Statistically, this condition is termed "positive skewness." Under a normal distribution, as many subjects exceed the norm as trail it. With positive skewness, however, most subjects lag the average, which is bolstered by the happy few. For example, 50 students graduated from Wake Forest University in 1997 with degrees in psychology. The average career earnings for those graduates now stands at $6.5 million--thanks to the one student who made $250 million.

(I confess: I do not know exactly how many students received Wake Forest psychology degrees in 1997, and how much money the graduates not named "Tim Duncan" have earned. But you get the point.)

Passing Quietly Through the Night
As Morningstar's James Xiong and Thomas Idzorek point out in "Quantifying the Skewness Loss of Diversification," published this spring in the Journal of Investment Management, the stock market's positive skewness is ignored by conventional asset-allocation techniques. Traditional techniques assume that stocks are normally distributed. The inputs into "efficient frontier" asset-allocation programs typically include the expected mean and standard deviation for an asset--the first and second statistical moments--but not skewness, which is the third moment, and which identifies the asymmetry of a distribution.

This has the effect of showcasing diversification's strength, while covering up a potential weakness. It is well known that holding many stocks rather than a single security reduces variability. That is why 401(k) plans offer mutual funds, not individual equities. What few realize, however, is that the process of diversification reduces positive skewness, over short to intermediate time horizons. And positive skewness is a useful attribute; it has the potential to supersize performance.  

Running the Numbers
Curtailing skewness cannot be beneficial--but it may not be particularly harmful, either. What matters is the size of the damage. Which is where Morningstar's paper comes in. Previous authors have discussed diversification's effect on skewness but have not measured the amount. Xiong and Idzorek give the numbers.

Their calculations, by necessity, are indirect. After all, they must assess that which is not present: the amount of skewness that would exist for a stock market portfolio, if it were not a stock market portfolio. (That sounds like a Zen paradox.) Such a task does not lend itself to straightforward methods. Options provide the solution. By buying put options for the market portfolio and call options for a single stock, one can estimate the economic value of skewness loss that resulted from diversification (for further details, refer to the original paper).

The price of this strategy can readily be computed, since options are publicly quoted. Voila! Xiong and Idzorek now have an estimate of the value of skewness, by determining the "economic cost" of replicating the attribute.

The Longer, the Better
That cost is high indeed for day traders. By the authors' calculation, those with a one-day time horizon who hold the market portfolio would need to shell out an annualized 28% in options purchases to recover the skewness that was lost through diversification. Talk about a steep investment hurdle! The moral of the story: If you are rash enough to day trade, do so with single securities, not pooled funds.

The price drops precipitously if the time horizon is extended to one month. Rather than 28%, the bill becomes an annualized 2%. Nonetheless, while far below the day traders' handicap, 2% is notably pricey by today's standards. Index-fund providers jostle over a basis point here, two basis points there. To concede 200 basis points in foregone skewness, without even recognizing the loss, stings.

For long-term investors, the cost drops to almost nothing. Due to compounding effects, the market portfolio's returns over time fit a lognormal distribution (when measured cumulatively, as opposed to in annualized terms), rather than the roughly normal (albeit subject to occasional huge losses) pattern that they show for daily performance. Over the long term, returns for both the market portfolio and a single stock converge to be lognormally distributed, which means that they are similarly skewed.

The Lottery Effect
So far, so good: The drawback of diversification is merely academic for anybody who invests for the reasonably long haul. Investment professionals might be chided for ignoring an important part of performance when not accounting for skewness with their advice, but their oversight is harmless.

That is true, but with an asterisk.

The asterisk being that an individual equity's combination of positive skewness and large standard deviation leads to performance that, in some respects, resembles that of a lottery ticket. Usually, the payoff is minimal, or even a small loss. On occasion, though, the investor can enjoy almost unimagined success. Of course, the same holds true for the market portfolio, but that process takes longer--several decades, rather than (as with a particularly fortunate stock) only a few years.

Investors prize this feature, although they generally can't put words to the feeling. As Xiong and Idzorek point out, the academic literature has long puzzled why many people are underdiversified, holding only a handful of stocks. The reason being, they seek positive skewness, accompanied by high variability. In nontechnical terms, they wish to get rich quickly, not slowly. For that goal, diversification is an impediment.

Says Xiong, "The standard advice to 401(k) participants is never to own company stock. But I would argue that if investors have a strong preference for skewness, it might be optimal to own some individual equities--just as long as it is not company stock." He adds, "We recommend diversification. We only argue that it's not completely free."

Xiong and Idzorek haven't revolutionized money management. Pooled funds have become the retail shareholder's mainstay, not individual stocks. That condition will not be changing. But their paper is a useful reminder that although investment practices have advanced far from their early, intuitive days, they do not and cannot capture all nuances. Sometimes, investors may seek something different--and not necessarily be illogical when doing so.

John Rekenthaler has been researching the fund industry since 1988. He is now a columnist for and a member of Morningstar's investment research department. John is quick to point out that while Morningstar typically agrees with the views of the Rekenthaler Report, his views are his own.