Leverage Causes Fat Tails and Clustered Volatility

Good paper here via  quantivity on Twitter discussing the effect of fund managers borrowing on margin to purchase assets.  This is something I’ve discussed previously in my many posts on margin debt and why it matters (see here for a good explanation or just read on).

Many analysts correctly note that margin debt is a coincident indicator, but that misses the point. Borrowing on margin can exacerbate volatility in both directions by helping fund managers to purchase more of an asset than they normally would.  The reasoning for this is rather simple and it’s classic herding behavior, recency bias and optimism bias.  When the market rallies it often becomes a self fulfilling prophecy in which recent positive performance causes overconfidence about future performance.

When the herd becomes overly optimistic it can result in volatility clusters which lead to abnormal divergences from the mean and what looks like a permanently high market.  As the herd grows this effect is magnified.  And one way the herd grows is by essentially borrowing to make the herd larger than it really should be.  So fund managers borrow to purchase more stock and irrationally bid up prices.  The problem is that this works both ways – on the upside and the downside.  And when the market reverses the herd reverses course causing not only a negative psychological volatility cluster, but the margin call effect in which fund managers become FORCED sellers of positions.  If you remember 2008 and talked to any fund managers during that period you know what I mean.

Anyhow, a lot of this is common sense stuff, but it’s important.  Of course, right now, the herd is running full steam ahead and gaining momentum in large part thanks to borrowing (see here for the data).  Said differently, the supposed stability creates overconfidence which can lead to instability (and greater risk as investors become more confident of future market action).  Who knows when it reverses course or why, but if it does you’ll want to make sure you’re not in the way of this stampede.  It looks like a mighty big one already.


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Cullen Roche

Cullen Roche

Mr. Roche is the Founder of Orcam Financial Group, LLC. Orcam is a financial services firm offering research, private advisory, institutional consulting and educational services. He is also the author of Pragmatic Capitalism: What Every Investor Needs to Understand About Money and Finance and Understanding the Modern Monetary System.

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  1. What the takeaway then? That the market is becoming increasingly risky as margin debt rises?

  2. It’s not always leverage. You can actually show mathematically that fat tails come from nonlinear payoffs and convexity effects. So any situation which involves nonlinear payoffs and/or convexity effects usually has fat tailed distributions.

    This is really easy to show mathematically by doing a Monte Carlo simulation of a given probability distribution over different types of payoffs. If the payoffs are convex/concave, you will get fat tails. Those kinds of payoffs do very often show up in levered systems though.

    The interesting thing about fat tails is that outside of the “middle 99%” of the normal, there are actually less events, but the events are of greater magnitude.

  3. The quants seem fixated with ‘fat tails’ because they think they are the major cause of the problem. What they fail to realize is that even “normal” (i.e. normally distributed) risk is bad enough, because the volatility of a “normal” market still increases with time. the ‘quants’ somehow misunderstand “regression to the mean” as “reversion to the mean”.

    My point is: you do not need fat tails to experience large portfolio drawdowns. This is the entire reason that makes most of Modern Portfolio Theoary flawed. The idea that “expected returns” can be achieved under a “normal” random process is flawed.

    Fat tails are only a second order detail and not really the main part of the problem.

  4. The key is nonlinear payoffs as I stated earlier. That’s what creates the primary downside risk and can also create major upside benefit.

  5. Cullen posting of this article is valid……. The volatility could erupt and with high levels of margin debt…….. it could get really interesting over the next few weeks for investors and traders alike.

    We have a Euro crisis. We have a Federal Reserve pumping billions into the EU. We have Assad’s vision of building a gas pipeline. We have a US Government pressuring Europe to support our pipeline asset strikes in Syria……..We have a pipeline which connects Syria, Europe, Russia, the Middle Kingdom and China. We have the Russians and the Chinese who want to protect their large infrastructure investments……… We have local European countries that do not support a strike in Syria, but an EU which is dependent on Federal Reserve’s support, supporting the strikes…… hmmmmm. How would you retaliate against targeted asset strikes in Syria??????? Maybe, close the pipeline valve? Erupt Europe in crises before the German election? Maybe, slow your purchases of Treasury debt…….. Maybe build OPEC 2.0 and reinvent the 1970’s……..? Maybe create and economic blockade?


  6. Absolutely right about not dismissing as merely a coincident indicator. This is a nice simple example why economists & especially monetarists fail in understanding the monetary system. There are many actors which create money to chase other assets in a carry trade. There is no ‘rational actor’, it’s just trend following up/down with corresponding growing/impaired balance sheets. Many economists said the same thing about housing: oh yah, Mr. Econ dude … so why was the total change in res mortgage debt 5-7x higher than the total assuming only new homes!

  7. Looks like the Q’s want higher along with the rest. Other parts of the world are trying, maybe Merkel bails out euroland after the elections and China gets its groove back and Japan grows at 3.5% forever. Or maybe we just crash and burn, who knows. I couldn’t blame a guy for wanting out now but it looks like there is more to come. I would keep some cash in this market until it is clearly broken. We are just not there yet.

  8. Could you please explain the difference between “regression to the mean” and “reversion to the mean”.

  9. There an important difference. See here:

    A common misunderstanding in finance is to think that when returns are “normally” distributed, then stock prices will have a high probability of being close to the historical mean in the “long run”. This simple misunderstanding explains why long term strategic asset allocation is flawed.

  10. A wikipedia article written by people who have little or no real academic experience in mathematics and statistics?

    Perhaps an understanding of real statistics would help. Statistical Mechanics is a necessary requirement for anyone discussing statistics. Financial markets do not satisfy the ergodic hypothesis, thus much of the stuff people write and read and comment on is complete crap.

  11. The article on wikipedia provides a reasonably good, and yet readable explanation of the difference between “regression to the mean” and “reversion to the mean”. It is a purely statistical concept and it has nothing to do with the ergodic hypothesis or statistical mechanics/ You are either showing your ignorance in not having understood what I was talking about, or you have not read the comment very carefully.

    Otherwise, you’d have provided a more technically qualified answer than “much of the stuff …. is complete crap”.

    But I agree on one point. Much financial theory is flawed because of an incomplete understanding of statistical mechanics.