In part one of “Holes in Some of Finance’s Critical Assumptions,” Kevin Harney of the hedge fund Massif Partners discussed some of the market distortions arising from critical finance assumptions like Brownian motion and normal distributions used in options pricing. What are some of the effects of these choices? What can be done differently? Here is what Harney said.

Jason Voss: If I may interrupt you there for a moment. . . . You just said something, in passing, that is, to me, rather profound, and I want to make sure that I have this right. Are you saying that much of the trading in derivatives is not based on a real, objective price, but rather on prices created by agreed upon models? In other words, the real agreement is in valuation methodology, not an agreement as to value? So if new models were developed that were widely accepted, they might spit out suggested values that differed substantively from the previous ones? Did I get that right?

Kevin Harney: That’s rather a strong interpretation of what I said. If you lose money consistently you’ve got to explain why and do so pretty quickly. It’s efficient and self-correcting. And derivatives are zero-sum instruments — someone wins and someone loses (which is not to say that they don’t create value through risk-transfer).

Advances in models tend to be shared quite quickly — people move around between organizations and a lot of the intellectual property effectively ends up in the public domain (though I will note a number of successful hedge funds that are much more vigorous in protecting their intellectual property). Thus the core models for “vanilla” derivatives tend to be widely known and used. If someone starts to make money systematically because of a better model, then that tends to become known quite quickly. And since prices are effectively publicly available, you can see if you are diverging from the “market” price and address why (it may be that you are correct, but you have to know why). There are lots of smart people involved who have a lot of money at stake. That tends to lead to efficient (correct) pricing. And you’ve seen a large growth in the number of market participants — particularly hedge funds always looking for opportunities. So in some sense, pricing for liquid derivatives must be correct, if only because there’s a market price and lots of educated participants and a natural tendency for arbitrage opportunities to dissipate — like in any liquid market. If you are systematically underpricing, you’ll be picked off. And conversely, you won’t make any money if you are systematically overpricing. And so, in answer to the question of whether those prices are model-driven or market-driven, if a better model appeared that allowed for a systematic profit (relative to prior models), then you can be assured it will be used and, for some period, it will allow the holder to earn a profit on that modeling investment, before it makes its way into the mainstream, and the market price adjusts accordingly. You can see many examples of this over the years — from option pricing when the initial Black-Scholes model hit the mainstream in the 70s through to the SABR model, which became a de facto standard in interest-rate derivative pricing about six years ago.

But as liquidity falls off, and the model valuation becomes more sensitive to large moves in underlying variables, then you may have much more disparate pricing and consequently opportunities to take advantage of model mispricing. For example, if you are pricing a very out-of-the-money equity option, then you will get much wider disparities in model prices, depending on how the probability of a large move in the underlying equity price has been modeled (the “tail-event”). And someone with a better model (or even a more accurate assessment) of equity return distributions can make money from those whose models don’t accurately reflect those potential returns, at least until everyone else is doing the same thing.

Another “vanilla” model (at least based on this liquidity definition) is MBS pricing. And MBS pricing is highly contingent on prepayment models (i.e., mortgage holders refinance when interest rates fall enough to make it worth their while). As you can imagine, an inordinate amount of intellectual energy is devoted to modeling that behavior. Anyone with a better model of prepayments (particularly it it’s tailored to a specific set of mortgages or a geographic region) would be well-placed to make a substantial amount of money.

But the lack of market pricing for exotic derivatives — which I’ve used to define “exotic” — provides a much more substantial opportunity for things to go wrong. A great opportunity is to find a flaw in a model that doesn’t take into account some market nuance — for example, the fact that volatility might be expected to spike around certain dates because of the release of certain government data. Now, obviously, as with the earlier arguments, through time that opportunity inevitably disappears. But, because of the complexity of the instrument (and its underlying model), there are ample opportunities to exploit real-world factors that cannot be incorporated into a valuation model. Of course traders are meant to supplant the model and appropriately price the risk in the model itself, but it’s a battle of wits.

And, with a nascent market, the core model may just have been wrong to start with. And you charge a large premium for that risk. But it may not have been large enough.

An example that’s of specific interest to me is longevity (being a specific risk for pension plan sponsors). The market for longevity swaps in Europe is growing and is something that we’ll see in the United States shortly (it’s a bigger risk for European pension plans because they tend to provide inflation-linked benefits upon retirement unlike in the US and thus the longevity risk is amplified). This is a highly-illiquid market with few providers and very large premiums. And thus pricing is highly dependent on modeling mortality for a group of pension beneficiaries (or a proxy that may be based on a national population). On the one hand, you will find people predicting that growing obesity will have a very large impact on mortality, and on the other, those who predict that advances in medicine will have a large opposite impact. It’s unlikely they’re both going to be right. Or maybe they will be and it will net out in the end. This is one of the most extreme examples — it will take decades to determine if the models were accurate. But that’s not going to stop a market from developing.

Let me give one final example — blackjack. Casinos were happy to have their original payout scheme and then they realized people were counting cards — i.e., those players had a better model than the casinos who were mispricing the payout. Now, in this case, the casinos “banned” the new model rather than accepting it and modifying the payout downwards. But the point is the same. And it would be the same if a roulette player discovered that a flaw in a particular table meant that 0 comes up 10% of the time. I am exaggerating of course — casinos are very, very, good at making sure this is not the case. But the principle is the same. If the distribution is found to be wrong, then either the price changes to reflect the new distribution or someone is going to make money with that information — until the opportunity goes away.

The above leads me to my two fundamental laws of finance: (1) the price of an asset is how much you can sell it for when you need to sell it; and (2) caveat emptor. It would be nice to have those embedded in any valuation models.

Without giving away the secrets of the shop, do you have any suggestions about proper starting points?

Caveat emptor. There is too much asymmetry of information and expertise in the exotic derivatives business for anyone other than the most sophisticated buyers. We only use very vanilla derivatives for a very specific purpose.

It has been my experience that most people in finance have never deconstructed the calculation of variance and standard deviation. If they did they would discover that it is a weighted averaging technique that unnecessarily aggregates information into a summary number that obscures the preponderance of upside volatility relative to downside volatility.

What’s your opinion of using semi-standard deviation or semi-variance to improve the accuracy of derivative pricing models due to a better dissection of volatility?

To be honest, I don’t know enough about moving away from a symmetric definition of volatility and how it would be incorporated. But clearly most people with a long position in an asset are only interested in downside volatility. And the economic research is clear that people are much more sensitive to losses than gains.

What are some of the holes in finance that you have spent time researching that we haven’t covered so far?

I’ve spent the last six years working with corporate pension plans — and their key issues are asset allocation and immunizing their liability. Asset allocation has been dominated by mean-variance optimization for 50 years now, but once you step back from it and look at the underlying assumptions, it’s so clear that it’s absolutely inappropriate for use in the real world. Here again, we have a lovely, simple idea which was taken to an extreme. The key flaw with this is the normality assumption about joint distributions of asset returns — and this falls down so badly in reality. The quick way of explaining this is that diversification doesn’t work just when you need it, and thus asset risk is always higher than predicted. And, at its core, MVO is a one-period model. Which begs the question, what period is being used? And it’s a very sensitive model — continuous admittedly — but not in a nice way. A model with 30 assets is going to require around 500 inputs . . . all of which have to come from somewhere. It’s too easy to hide behind the façade of mathematical sophistication. But I suppose one could call it a vanilla model at this point. . . . It just happens to be blatantly wrong.

There’s no doubt that many people are looking for an alternative. And while there isn’t an established replacement on the horizon, there are better ways of doing it that are available.

Pension plans are very interesting from a modeling perspective, and they actually contain a number of features that should be treated like options. There’s one in particular that is ignored, or rather assumed away, because it’s very difficult to model, but it has a very significant impact on estimating risk and reward in a pension plan’s asset allocation, with the uniformly unfortunate consequence that risk is overestimated — which can be just as deleterious as underestimating risk.

Any model must lose information — either because the reality is too complex or the calculation is impossible to complete in a time that makes it useful. The balance, as Einstein said, it making it as simple as possible, but no simpler.

Kevin, thank you for sharing your expertise with us about some of the critical holes in financial assumptions.

Originally published on CFA Institute’s  Enterprising Investor.