Hedging the Lower Tail Risk

What I learned from Robert Waldmann: Almost no professional portfolio manager worries about the lower tail, because if you are in the lower tail the whole world has gone to hell in a handbasket and people have other, more important things to worry about than whether one's portfolio manager had appropriately hedged whatever risk is now roosting on the roof.

Felix Salmon disagrees:

RGE - Economonitor: Brad DeLong responds to my entry on Bob Rubin thusly:

The lower tail--both in its economic and political aspects--is still ferocious and scary. But it is still the lower tail. And I can understand why finance professionals would rather not price it at all than price it into their forecasts and so run a high probability of lagging their peers' performance.

He has a point: If there's a 90% probability of the market going up by 15% and a 10% probability of the market going down by 60%, how do you position yourself? You want to be long, even on the balance of probabilities. So in practice you simply do what you would have done if the lower tail didn't exist. But of course today's markets have more options than simply long/short.

Specifically, it's possible to hedge against a large downside risk by buying long-dated, far-out-of-the-money put options which cost almost nothing using Black-Scholes but which act as a very good hedge against lower-tail events. Such positions don't even need to be a dead loss if the lower-tail event doesn't happen, since even an increase in the perceived probability of such an event is likely to drive their price higher.

What's more, DeLong seems to be saying ("it is still the lower tail") that scary events like the ones Rubin was talking about ("nuclear proliferation, Islamic radicalism, the endgame in Iraq, instability in countries that mean a great deal to us in the Middle East, what's going to happen in Pakistan, and many other issues as well") are still low probability. Many geopolitical strategists might disagree, in which case it might make sense simply on the balance of probabilities to position oneself defensively.

It is the case that the cost of buying the long-dated out-of-the-money put options is a constant drag on one's performance in those high-probability states of the world in which you don't wind up in the lower tail. But Felix has a good point: in a world of derivatives, you buy puts if you think that the market will raise its estimate of the chance of a lower-tail event. And you do so even if you think the lower tail remains very unlikely.

Comments

[elliottg]

Any lower tail fall out will be handled by someone else. What incentive exists for any portfolio manager to risk their job in this manner - maybe if you work for Berkshire Hathaway - but not if you work for Goldman Sachs. It's pretty easy to model that any incentive system with threshold rewards leads to riskier behavior and discounting of the lower tail.

[Gerard MacDonelll]

I'll bet the good doctor can prove that put/call parity makes the point about options redundant as regards the net length of the average investor.

[P O'Neill]

One thing I don't understand. Insurance companies are in the business of worrying about the lower tail. But they don't deal with it by buying securities that payoff when a lower tail event occurs. They deal with by piling up enough safe assets so that they can cushion it when it happens. What exactly would make another financial institution more willing to play a more aggressive contigent security?

[Jon Gallagher]

While I am a firm believer in markets, I am agnostic on the ability of markets to foresee extreme risk.

For example, Niall Ferguson (who, despite lack of persipcaciousness[ viz. http://delong.typepad.com/sdj/2006/09/niall_ferguson_.html], is at least energetic in providing primary sources) points out (in his new book "War of the World") that bond markets did not start reacting to the possibility of WW1 until the last week of July 1914, after the Austro-Hungarian ultimatum to Serbia. Even the Rothschilds were caught short, despite having family/partners in Vienna.

Since reading that, I've been trying to model how you could have protected yourself after Princip fired and the Archduke and Duchess died. Puts on Russian bonds? Move everything into commodities (Ferguson notes that insurance was *not* available even at the beginning of the war for shipping gold across the Atlantic)? Corner the market on ammonium or nitrates (guano anyone?)?

And what would be the hedge against nuclear proliferation, Iraqi meltdown, an idiot in the White House? Is there anything that doesn't make you sound like a new "landowner" in the Idaho panhandle burying guns and packets of freeze-dried food?

[wcw]

Short answer: there is nothing you can do in the markets. Cf also my response at http://delong.typepad.com/sdj/2006/10/why_isnt_the_lo.html#comment-23712569 on the previous thread, with its personal recollection. Now, my father's father therein was no trader, but his countrymen who were got bombed just the same.

The lower-tail risk that interests me is not that experienced when society collapses, but when society does not. Take the '29 crash; FDR rescued capitalism and made it worth the while of those who considered the risk of such an event and the chances it would not destroy markets entirely.

[Matt]

There's a point you're missing here. If the long-dated put option is truly far out of the money, the world in which it would be exercised is also a world in which it might not be honored. To take you example, can you imagine that stock prices go down by 60 percent without the collapse of a number of major financial institutions and at least a temporary breakdown in the payments process? And note here, there is no lender of last resort to guarantee that holders of put options get their money. If margin can't be posted, and the clearinghouse runs out of credit, the holder of the put option is screwed.

This is another reason why financial market participants so rarely buy insurance against downside tail event. The circumstances in which that insurance would be valuable are also circumstances in which insurance obligations might not be honored.

[Oskar Shapley]

http://www.gladwell.com/2002/2002_04_29_a_blowingup.htm

Nassim Taleb is betting that the lower tail happens.

[Barkley Rosser]

There is lower tail risk and there is lower tail risk, at least partly meaning that it depends how far down the tail one wants to insure against. Many of the above comments amount to noting that there are real limits to doing so for the further out contingencies, e.g. those that start to look like the Idaho panhandle option, get diamonds, guns, gold, a bomb shelter, or whatever, because the markets will not be functioning anyway.

For lower degrees of this, in fact many hedge funds are dealing with the volatility smile of conditional skewness and ubiquitous kurtosis of returns by variations on Black-Scholes of various sorts on asset combos where there is still assumed to be some degree of standard covariance across assets.

Things get a bit hairier once one recognizes that the higher moments also covary, for which the new fad is copulas, used at a minimum by some insurance companies and also certain cautious entities like some Swiss banks. But, again, there are serious limits on all this. In the end there is Keynesian uncertainty that cannot be hedged, or as Rummie put it, "the unknown unknowns."

[christofay]

I'd love to be in LA earthquake insurance, that's a no-brainer. Collect premiums until the big one hits, then declare bankruptcy.

Woody Harrelson, Doc Hollywood, or words to that effect

[christofay]

I'd love to be in LA earthquake insurance, that's a no-brainer. Collect premiums until the big one hits, then declare bankruptcy.

Woody Harrelson, Doc Hollywood, or words to that effect

[Hal Varian]

I strongly recommend:
Mark Rubinstein and Jens Jackwerth (1996) "Recovering Probability Distributions from Option Prices", Journal of Finance (December)

They look at the probability distribution on the S&P futures index implied by options prices. Before 1987 it was more or less normal. After then it was bimodel, with far out of the money options have a higher price than implied by normally distributed returns. It seems that the possibility of another Oct 1987 meltdown was definitely incorporated into options prices.

Since then the bump in the lower tail has been getting smaller and smaller.

I take this as some evidence that the market prices tail events...but maybe it has too short a memory.

[Jon Fernquest]

Paper referenced by professor Varian above:

Mark Rubinstein and Jens Jackwerth(1996) "Recovering Probability Distributions from Option Prices", Journal of Finance (December)

Available online:
http://www.haas.berkeley.edu/finance/WP/RPF-250REV.pdf

Source:
http://www.haas.berkeley.edu/finance/WP/WEBrpfwps.html
from

[a]

"To take you example, can you imagine that stock prices go down by 60 percent without the collapse of a number of major financial institutions and at least a temporary breakdown in the payments process?"

Well let's see. Eurostoxx50 hit a high of 5522 in March 2000 and then went to 2040 in April 2003. That's a 63% decline. Where was the collapse?

"Since then the bump in the lower tail has been getting smaller and smaller."

Since when? It goes up, it goes down. You also have to watch the level of the at-the-money volatility, since a smile of 10 is very different if the atm is 30 or if it is 10.

At the beginning of 2006 the Eurostoxx50 5-year 50% put's implicit volatility was almost 50% higher than the 100% put's. That's a lot.

[Ken Houghton]

Anyone claiming a 60% drop in the market would be a world-changing event either has a very short memory or has forgotten NASDAQ.

To be clear, using round numbers: (5000-2000)/5000 = 60%

Also, those long-dated OOM thingies aren't ONLY good for a significant event, guys. They're ****ing OPTIONS. With very little time decay.

Until the market drops 10 or 20% (think 1987, 1989, et seq.), at which point they're not so OOM and have a significant ROC.

P O'Neill - "What exactly would make another financial institution more willing to play a more aggressive contigent security?" In two words: capital considerations. (The other half is that your premise is incorrect: options are not a "more aggressive contingent"; they are, in one small part, the rational response of the market to the need for a more efficient hedging method than the insurance companies use.)

[Tim Francis-Wright]

I figure that a lot of fund managers were ruing not buying some long-term puts on key NASDAQ stocks (think big stock prices but no profits) at the height of Web 1.0.

You did not need an earth-shattering event to make these puts very valuable, just a bursting of the Internet stock bubble.

Similarly, buying the right sort of interest derivative two or three years ago would have made these fund managers quite successful. And all theyr needed to do was to realize that rates could not stay this low forever. (If you locked in a fixed-term mortgage rate at the time, you were making this sort of bet on a more human scale.)

[centrist]

What was the market response to nk nuke test....to rally and the vix barely moved! I deal options and it gave me pause.

[wcw]

As someone who was buying puts towards the end of the bubble, I can assure you it was not an easy trade. Implied vols were very high, and buying puts ate up your relative returns. My piddly retirement account gave up almost a thousand beeps (not a typo) versus the indexes in 1999.

If I had been doing that as a fund manager instead of with my own money, I'd have been fired before I made it all back and then some in the next year alone.