Monday, March 12, 2007

Hedgeability: The premise that is false

Find the trend whose premise is false and bet against it. - George Soros

Last week brought news of the death of Jean Baudrillard, or not as the case may be, whose rather esoteric works were highlighted in the film, The Matrix. While I didn't agree with his pessimism (see Bumming out with Baudrillard) I too have stared into the abyss of incoherence- the fear that there is no truth, and it left me as shaken as a character in an H.P. Lovecraft tale shouting Cthulhu at the top of his lungs. During periods of mass mania, if you are one of those stubborn souls who refuses to toe the party line, it can seem as if the truth does not matter.

But the truth does matter, or so I believe. One can swallow the party line that, for example, the economy is doing well only so long as one has enough food to eat. The old economic adage that it is a recession when your neighbor loses his job but a depression when you do still holds true.

And one needs to believe there is a truth, and that it matters, i.e. that it will force people to change behavior, if one is to make use of Soros' trading maxim above.

In response to a few comments on Too big to bail (out) today's musings will focus on how a supposedly well hedged portfolio, i.e. with minimal VaR (value-at-risk), can become a huge liability.

Back when I was an FX-Options dealer I would begin my day by getting the volatility "runs," the current volatility prices for at-the-money straddles- straddles being a equal amount of puts and calls with the same expiration and strike. I would then enter that data in our risk-analysis computer along with any overnight trades and then publish a few reports. The two key reports were with respect to time (theta) and underlying instrument price (gamma).

A typical gamma report for a portfolio long front month options might look something like:

GBP price Delta P/L
1.9500 2.2M +50.0K
1.9250 1.0M +17.5K
1.9000 0.0M 0.0
1.8750 -1.0M +17.5K
1.8500 -2.2M +50.0K

What the table means is that as spot GBP rises the portfolio becomes longer GBP and as it falls it becomes shorter. If getting longer as spot rises and shorter as spot falls seems too good to be true, it is. The catch is that good gamma, as the above is known in the trade, comes at a cost of time decay.

A typical theta, or time decay, report of the same portfolio might look something like:

Delta P/L
March 11, 2007 0.0M 0.0
March 12, 2007 0.0M -8.0K
March 13, 2007 0.0M -16.0K
March 14, 2007 0.0M -25.0K
March 15, 2007 0.0M -33.5K
March 18, 2007 0.0M -60.0K

That is, each day the portfolio loses about 8K and these losses will increase over time until expiration.

While there are many different strategies one can employ which might produce a similar report, thus leading to the conclusion that not all VaR neutral reports are equal, I've assumed an at-the-money straddle whose notional value might be 15M GBP per leg, i.e. a 15M GBP put and a 15M GBP call. Assuming nothing else in the portfolio (an assumption very rarely seen in the major trading house wherein one usually finds thousands of options of $100Bs of notional worth with wildly varying strikes and expirations along with spot and forward hedges) the true value-at-risk is the cost of the options.

If the portfolio had instead sold the options in question the true risk would be equivalent to a 15M GBP spot position mitigated by the receipt of the cost of the options. In that case the risk reports above would have their signs flipped- the portfolio would be getting shorter as spot rose, and vice versa (known as bad gamma) and would be earning money each day in the event spot remained the same (positive time decay.)

Let's assume, as is general practice in the industry, that the portfolio will be hedged in a sense, automatically. That is, each time, for instance, the delta reaches 1.0M GBP (one could choose a different amount), it would be "hedged" by entering a spot (or forward) trade of equal amount. In our example, the portfolio would then become a mix of both options and spot (or forward) deals.

This hedging would be done assuming that one or the other leg would be exercised which brings us to the first big risk options portfolios encounter, counter-party risk. In our initial example of a long options position, with spot rising, the portfolio would be short GBPs against the expected purchase at the strike price on exercise. If that counter-party defaults, as New Financial has apparently done, but not, I believe, in the FX options market, then the portfolio is just short GBPs sold at lower levels. That is, what seemed well hedged wasn't.

Thus you can hopefully see how LTCM's billions of $ of defaults were a major problem. Dealers who had bought options from or sold options to LTCM had hedged assuming LTCM would hold up their end of the deal. They assumed that all dealing institutions would exist in perpetuity, a rather silly assumption given the intermittent failure of financial institutions over the decades. Often though, counter-party risk is a secondary effect of a primary cause, a hedging failure.

The false premise, in my view, standing at the heart of our dilemma is the assumption of constant hedgeability. Option models, like Black-Scholes or their variants which we used to produce the hypothetical reports above, and which are used to produce reports throughout the financial universe, are based on this assumption of continuous pricing.

But what happens if markets don't exhibit continuous pricing? Let's assume we were managing the short side of the portfolio above and GBP gapped up from 1.900 to 2.000 in a few moments, say because Britain decided to join the ERM, as happened in October 1990. In that case, as they delicately put it on Wall St., you're screwed. In a few brief moments following an announced economic policy change, your nicely hedged portfolio becomes a disaster- you're now short 15M GBP from 10 cents lower (leading to a current loss of US$1.5M, far more than you collected in premium) in a rapidly rising market.

Perhaps you can now see how the Nobel Prize winning economists who founded LTCM, whose members included Myron Scholes of Black-Scholes fame, got blind-sided when emerging market debt prices became very volatile in the summer of 1998, a period which included Russia's default of sovereign debt. Markets which had seemed liquid enough to hedge suddenly became very illiquid. Prices were changing by large amounts (not exhibiting continuous pricing) and few wanted to take the other side of the trades, like buying Russian debt which was about to default, LTCM needed to make to stay hedged.

Thus the tremors of fear that emanated from financial centers around the world when China's market dropped 9% in a day and particularly when "calculation problems" caused an apparently instantaneous 200 point drop in the Dow. If you had been using the Dow Jones Index as spot price to "automatically" hedge, you didn't. (to be fair, from what I understand most equity hedging strategies used the relevant futures which were unaffected).

In other words, when markets gap up or down substantially the premise of continuous pricing upon which option pricing models are based is proved false. Moreover, as the LTCM case makes clear, even if you are well hedged and not directly involved in the volatile markets, exposure to other institutions who are involved can still get you. Thus the term, contagion.

Given that markets have, from time to time, exhibited just such discontinuous pricing (imagine a Wahhabi inspired coup in Saudi Arabia) many times in the past, basing a risk model which will serve as VaR calculator for portfolios which carry notional amounts (in our case above the notional amounts total 30M GBP) of many multiples of global GDP seems downright silly.

To be fair to Fischer Black and Myron Scholes, I'll bet that if they were told their theoretical musings would become the cornerstone of modern day portfolios they would likely have thought differently. So long as dynamic hedging flows (we referred to them above as automatic hedges) remained small relative to real trade flows, their assumptions, while not perfect, were, in a sense, workable. As these dynamic hedging and other speculative flows have grown, now swamping real trade flows, the flaws in the assumptions are laid bare.

Thus the ever increasing need for governments to engage in "market smoothing operations." Of course, market smoothing doesn't change the underlying fundamentals that gave rise to the discontinuities, they merely, if they work, foster the illusion of an "efficient market," and in so doing, lead more and more to join the party- thus begging the un-smooth-able.

Ultimately, I fear, we will regret the growth of the derivatives monster from manageable to unmanageable size. Political coups, abrupt decisions to not accept this or that currency and even economic warfare will, as they have in the past, appear. Certain financial institutions will get caught and their contagion effect will shake the whole house. We will, I fear, test whether these derivative dealing institutions have become Too Big to Bail (out).

p.s. many thanks to those who linked to this blog and brought thousands of new readers, although I hope one new reader so directed, the US Treasury's Executive Office of Asset Forfeiture, is just interested in my musings and not my house. (lol, I hope)