Credit Suisse: Making Fat Tails Work for You

Both theory and empirical evidence on the success of certain “modified risk techniques” show that they can do what they are designed to do. They can accommodate fat tail events and diversify a portfolio’s sources of return.

That is the gist of a Credit Suisse white paper prepared by Yogi Thambiah and Nicolo’ Foscari.

The paper is entitled, “New Normal Investing: Is the (Fat) Tail Wagging Your Portfolio?” a title that neatly encapsulates two bits of finance jargon. First, there is the phrase “new normal,” coined by PIMCO in 2009, to express the view that investors and managers shouldn’t wait for any return of the good-old-days of the boom in real estate and its derivatives. They should, rather, accustom themselves to the world that the bust-ups of 2007-08 have created.

The new normal, on Thambiah’s and Foscari’s account, includes an enhanced role by central banks, implementing monetary policies through open market operations, closer interconnections of banking institutions worldwide, much painful de-leveraging, and persistently high levels of unemployment.

The Tails on a Bell Curve

The second buzz phrase, “fat tail,” is drawn from the world of statistics, and plays off the familiar Gaussian distribution, or “bell curve.”

In this distribution, more than 68 percent of outcomes will be found with one standard deviation of the mean, and 95 percent of the outcomes will be found within two standard deviations. The “tails,” the bits of the curve at or outside three standard deviations, are then quite skinny.

But finance is not a Gaussian world. Extreme events simply occur more frequently than they would in such a world. It isn’t quite right to say that in the ‘old normal’ distribution was Gaussian and in the ‘new normal’ it isn’t. The distribution of outcomes in finance may never have been Gaussian. They certainly didn’t seem Gaussian in October 1987 for example. But various models and equations in modern finance theory incorporate Gaussian distribution at least as a matter of convenience.

It is fair to say that the financial world from circa 1973 to 2007 was one in which many participants (wrongly) assumed skinny tails. That “old normal” won’t return. As the renowned mathematician Benoit Mandelbrot has explained, the volatility of a market exhibits a “power law,” i.e. a correlation in which the size of a price change varies with a power of the frequency of the change.

To render this idea intuitive, consider the possibility that ABC Inc.’s share price will change from $75 to $76 in the course of an hour’s trading. Now, consider the possibility that ABC Inc.’s share price will change from $76 to $176 in the next hour’s trading. Even non-quants would consider the latter much less likely than the former. The larger price changes are much less frequent, for any fixed amount of time, than the smaller ones.

How much more frequent? This is the question of identifying the power for the “power law.” The bell curve is but a special case: one in which the power equals -2. Another special case, the “Cauchy distribution,” one with much greater volatility, is what results if we set the power as -1. We can call -2 the “mild” power and -1 the “wild” power.

As a matter of empirical fact, the fluctuation of stock prices exhibits a fractional power, somewhere between mild and wild. This isn’t quite how Thambiah and Foscari put matters, but at least part of their underlying point is Mandelbrot’s.

Since the Crisis

They also maintain that underlying realities have changed since the crisis and as a consequence thereof. The tails, always perhaps fatter than theory would have it, have become fatter than they were. Governments responded to the crisis of 2007-08 by borrowing large sums of money. This will eat into the growth of their national economies in the years to come. The “new normal” will see a persistence of high unemployment.

The consequence, as the Credit Suisse authors observe, is that “investors relying on mean-variance optimization and normal distribution models can potentially underestimate a portfolio’s drawdown risk and end up with sub-optimal portfolio allocations.”

What to do? Institutional investors can protect themselves against fat tails by using derivatives to hedge against volatility (variance swaps); or by using tail-risk protection indexes that aggregate variance swaps; or by following equity options strategies such as traditional put options, or option collars.

Also, these authors suggest, investors can make use of extreme value theory, and Conditional Value at Risk (CVaR) optimization, not merely to protect against the fatness of tails but to make that fatness work in their favor.

For illustrative purposes only, the authors have designed a portfolio that, on their calculations, ought to provide investors with a better return than has the S&P 500 index as a matter of history and that ought to do so while significantly reducing risk as measured against the same benchmark.

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5 Comments

  1. s jay
    April 26, 2012 at 10:07 am

    But consider the recent research published by Artemis Capital Management that calculates the market implied probability of 21% (based on options prices) of a 50% crash in equity prices in one year. This versus their estimate of the historical realized frequency of 2.9%. If anything, fat tails on the downside are dramatically overpriced at this point, and likely not a source of interesting returns. The suggestions in the paper for hedging the downside fat tail are coincident with the pricing observed in the marketplace. It’s a crowded trade.


  2. George
    April 26, 2012 at 3:51 pm

    “They certainly didn’t seem Gaussian in October 1987 for example. ”

    Why not? It is an extreme event, but why would a single event would ever be considered as defying Gaussian.
    I would expect that only a frequency of extreme events would be considered as a deviation from normal distribution.

    G


  3. Christopher
    April 26, 2012 at 8:29 pm

    S Jay,

    You raise an important point. Clearly there must be more to a particular “fat tail” strategy than simply the confidence that if one bets on the fatness of tails, all will come out well. It is because so many parties are crowding this trade that alphas are becoming betas, and both are becoming zero. As I recently heard some one say, the search for alpha is like the act of peeling an onion. Every time a given layer is routinized, it becomes beta, and you have to peel deeper.

    George,

    You, too, raise a good point, and my comment on October 1987 may have seemed facetious. But I was thinking of Mandelbrot’s career, which I referenced in the following paragraph. As Justin Fox has written: back in the mid 1960s, Mandelbrot was part of the “random walk gang,” with Eugene Fama and the rest. He drifted away, though, applying his fractal ideas to other fields, in part because his colleagues in quantitative finance were in his view too enamoured of Gaussian distributions.

    He reportedly said of the field around the time the Black-Scholes papers came out, “well, it won’t last. I’ll come back when it’s gone.” The 1987 crash was the precipitating event that caused Mandelbrot again to begin paying attention to finance, and that led some modelers to begin paying him attention in return.

    Here’s the url for Fox’s discussion of the point in a Reuters blog:

    http://blogs.reuters.com/justinfox/2010/10/18/why-didn%E2%80%99t-people-in-finance-pay-attention-to-benoit-mandelbrot/


  4. Robert S.
    April 30, 2012 at 11:05 am

    What the CS paper says is basic stuff that should be known by every serious practitioner by now. I simply can’t believe that there is still anyone out there who continues to use mean-variance optimization… And regarding their conclusion, it is so blantantly self-serving that the whole paper can only be aimed to their own unsophisticated client base.


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