Hey DQYDJ readers, remember that whole real estate bubble popping thing which started a few years ago? Now, there is plenty of blame for that little incident to go around, but one of the largest issues with the bubble and the ensuing collapse was the use of improper valuation techniques in securities related to real estate. We’ll go a step more abstract: today we’re going to discuss the usage of financial models, and a theoretical framework for how financial models can break down.
If you want me to be more specific and less abstract, I’ll gladly comply. David X. Li introduced his gaussian copula to the world in 2000, meaning for it to be a model which could predict the performance of CDOs – collateralized debt obligations – and won a Nobel Prize for it. Take note of that word, ‘predict’.
Real Life vs. Predictions in Financial Models
Now, David Li isn’t the villain here. Humble about the prospects of his own work, he even seems to have predicted the issues with the overuse of his model in a 2005 WSJ article where he stated, “The most dangerous part is when people believe everything coming out of it.” Right he was, eerily enough.
In fact, high finance faces the same modeling limitations as does hard science – the truth is, models generally work out to be a very good approximation of actual behavior, instead of describing it perfectly. Just as unified field theory is an area in constant search for hidden variables, high finance is a constant search for higher correlation to real life behavior. The problem comes when people conflate a model’s predictions with truth, and ignore the corner cases (or the black swans and long tails.) You see, for the uninitiated in the audience, a copula is a distribution function, while ‘Gaussian’ refers to a ‘normal’ distribution – think a bell curve in however many dimensions (variables) a formula has. That’s right – a normal curve, by definition an approximation of a larger population.
The vicious cycle of collapse is pretty obvious at this point – and it will continue to repeat itself. With no better model, it works something like this:
- Pre-model, a market works in a certain way – organically, depending on the whims of individual traders and investors operating worldwide
- A model is introduced, either academically or internally to a finance company, which attempts to predict the market in question
- If no competing models are developed, the singular model is disseminated
- The model itself, no longer the individual traders, starts to dictate the movements of the market. This is because of algorithmic trading – at some point, the trades made predicting the individual traders represent more volume than the original trades.
- The model collapses in on itself – since every one of the common cases is already covered, the market itself is driven to the extremes – areas where the model is undefined.
- Inevitable collapse, as the behavior of the market is not hedged in the models used.
I don’t think I’m breaking any new ground with this 6 step model, but if I am, contact me and we can co-author a paper and win a Nobel Prize. In all seriousness, I’m just describing feedback – where previous information influences the present. Think pointing a microphone at a monitor speaker – it quickly escalates to a point which neither the microphone or the speaker are designed to handle. That’s right – the exact same inevitability which can rip speaker cones can collapse a market.
Why Doesn’t Collapse Happen Everywhere there is Algorithmic Trading Relying on Financial Models?
Sometimes, the sheer volume of trades is enough to cover up negative feedback effects. Consider a farmer who, for some reason, sells corn into the marketplace yet purchases corn at the store. His purchase lowers the supply of corn at the same time as his growing increases it – he affects the price on both sides, yet he is such a small player he doesn’t noticeably move the market. Another reason would be model improvements. When some people recognize the weakness in a model it can be improved – either with an improvement to the model itself (known as heuristics to my computer science bretheren) or with a new model entirely. This is the case in the options market, where Black Scholes is but one of a number of options models employed by finance firms.
That’s right – subtle differences in similar models between firms means that collapse is asymmetric. Bear Sterns might collapse simply because there model didn’t flag a concern until one day after Goldman Sachs, for example. Marginal improvements in processing power, latency, and yes, improved heuristics, might be all that separates a massive gain from a bankruptcy. Just like Warren Buffett said, sometimes it really is like picking up nickels in front of a steamroller.
The other reason? For whatever reason, perhaps the models haven’t imploded yet. Otherwise, perhaps the spread is so low that an inefficiency in a proposed model is worthless to exploit (some inefficiencies are smaller than the transaction costs to correct them). The truth is, any ‘perfect’ model would have to also predict its own effect on the market (and the proportion of the market affected!), a near impossible task… although conceptually possible.
The best way to prevent this sort of stuff? Stop treating models and predictions as truth. The fact remains – any model is a guess. Just like you don’t know the value of your house until it sells, you can’t know the price of a security until it sells.
Beware of false precision – and take this to heart. The best move you can do in your own portfolio is to build in error tolerance into your own predictions. Maybe you think that $8 stock is worth $20? Don’t be the CDO market – treat that second number as a range of $16-$20!
Does this help explain the potential problem with financial models?