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Those working in the two fields of actuarial science and quantitative finance have not always been totally appreciative of each others’ skills. Actuaries have been dealing with randomness and risk in finance for centuries. Quants are the relative newcomers, with all their fancy stochastic mathematics. Rather annoyingly for actuaries, quants come along late in the game and thanks to one piece of insight in the early ‘70s completely change the face of the valuation of risk. The insight I refer to is the concept of dynamic hedging, first published by Black, Scholes and Merton in 1973. Before 1973 derivatives were being valued using the “actuarial method,” i.e. in a sense relying, as actuaries always have, on the Central Limit Theorem. Since 1973 and the publication of the famous papers, all that has been made redundant. Quants have ruled the financial roost.

But this might just be the time for actuaries to fight back.

I am putting the finishing touches to this article a few days after the first anniversary of the “day that quant died.” In early August 2007 a number of high-profile and previously successful quantitative hedge funds suffered large losses. People said that their models “just stopped working.” The year since has been occupied with a lot of soul searching by quants, how could this happen when they’ve got such incredible models?

In my view the main reason why quantitative finance is in a mess is because of complexity and obscurity. Quants are making their models increasingly complicated, in the belief that they are making improvements. This is not the case. More often than not each ‘improvement’ is a step backwards. If this were a proper hard science then there would be a reason for trying to perfect models. But finance is not a hard science, one in which you can conduct experiments for which the results are repeatable. Finance, thanks to it being underpinned by human beings and their wonderfully irrational behaviour, is forever changing. It is therefore much better to focus your attention on making the models robust and transparent rather than ever more intricate. As I mentioned in a recent wilmott.com blog, there is a maths sweet spot in quant finance. The models should not be too elementary so as to make it impossible to invent new structured products, but nor should they be so abstract as to be easily misunderstood by all except their inventor (and sometimes even by him), with the obvious and financially dangerous consequences. I teach on the Certificate in Quantitative Finance and in that our goal is to make quant finance practical, understandable and, above all, safe.

When banks sell a contract they do so assuming that it is going to make a profit. They use their complex models, with sophisticated numerical solutions, to come up with the perfect value. Having gone to all that effort for that contract they then throw it into the same pot as all the others and risk manage en masse. The funny thing is that they never know whether each individual contract has “washed its own face.” Sure they know whether the pot has made money, their bonus is tied to it. But each contract? It makes good sense to risk manage all contracts together but it doesn’t make sense to go to such obsessive detail in valuation when ultimately it’s the portfolio that makes money, especially when the basic models are so dodgy. The theory of quant finance and the practice diverge. Money is made by portfolios, not by individual contracts.

In other words, quants make money from the Central Limit Theorem, just like actuaries, it’s just that quants are loath to admit it! Ironic.

It’s about time that actuaries got more involved in quantitative finance. They could bring some common sense back into this field. We need models which people can understand and a greater respect for risk. Actuaries and quants have complementary skill sets. What high finance needs now are precisely those skills that actuaries have, a deep understanding of statistics, an historical perspective, and a willingness to work with data.

Now when I just said that I suspected I knew what certain people would say, those certain people are Americans. Around the table were folk from all over Europe, Australia, one from Iceland, and some Americans. So I asked the question of one of the Americans. He did not disappoint, and he gave the answer that I expected, but feared. His answer was "Seven or eight."

Had I asked for the names of the seven or eight I would probably have got the answer "Cheez Wiz, cheese slices,...and Monterey Jack." If you are from Europe you will have a better idea of the correct answer, which I suspect is in the thousands.

Now I love America and Americans so much that I married one. But the uniformity of the tastes of this large, rich country, or any, large, rich country, has the potential to damage smaller producers of niche products. Combine uniform tastes with easy global transport and hypermarkets within reach of everyone and you've got a recipe for evolution towards blandness. We are told that French wines are suffering from globalization. But then we also hear about record years for French wines. So what is happening?

Timescales are very important here, and we have the competing effects of globalization on the one hand and education on the other, together with the natural timescale for businesses to grow or collapse. Which will win?

It would be a shame if cheese or wine were to suffer, since I fully intend my retirement years to be spent sitting by a pool, somewhere warm, catching up on my reading, while working my way through the wines and cheeses of the world!

Finally, a question for you, how many varieties of apple are there? (Not that I care much for fruit or veg, where I come from chips count as one of my five portions per day!)

P

1) On average hedge funds will probably have done not much better or worse than the market as a whole. However, that average performance will hide a lot of extremes. Many funds, thanks to lady luck and leverage will be up record amounts. But that means many funds will be down record amounts too, and the downside is severely limited by zero! Therefore expect to see many funds announcing blow ups soon, maybe 30% of funds will close up shop for one reason or another.

2) After the blow ups expect to see the lawsuits. There will be many managers who have broken the terms of their prospectuses, many will have taken risks that they ought not to have taken. If they made money then they'll get away with it, if they've lost money then they will be on the wrong end of suits for damages. (Not that there's ever really a right end of a lawsuit!) And there will also be opportunistic suits in cases where no wrong has been done. In the US anybody can sue anyone for anything remember. There will be a three- to six-month delay between the big losses and the big lawsuits. They will take many years before they are completed.

3) When the dust has settled expect to see small, boutique funds being popular. They will have managers with very specialised experience and they will work closely with investors. There will necessarily be more transparency. Because investors will have the upper hand in negotiations leading up to investments expect to see investors taking a shareholding in hedge funds.

The above is what probably will happen. Now for something I personally would like to see happen.

For several years now I have been advising that potential investors in funds really need to take their due diligence far more seriously than they do at the moment. Current practice is that if an investor is very keen on a particular fund, perhaps because of a very persuasive salesman, then they tend not to perform as many background checks as they ought. The reason is simple, if they do the checks then they might find something that means they are unable to invest, therefore they reckon it's better if they don't do the checks. This leaves them the freedom to invest where they want. This is naive and dangerous.

In any random walk through life one encounters people who should not be left in charge of a pair of scissors never mind billions of dollars. These are people who, following formative experiences, are excessively risk seeking, or panic in a crisis, or who have a false idea of their own talents or who are simply dishonest. You may be unlucky enough to meet one person with all of these characteristics! Put this person in a sharp suit, send them to how-to-be-a-fund-manager finishing school and, hey presto, you’ve got a front-page Wall Street Journal scandal. There are a lot of clever people out there, people of talent, but how can you tell them from the disasters in waiting? I would very strongly advise that investors take the background checking far more seriously than at present. Speak to managers' colleagues, partners in previous funds, previous employers and previous employees, etc. Double and triple check CVs and qualifications.

I doubt whether it will catch on, sadly, but I’ve also been advocating for years that there should be a process of psychometric testing, along the line of Myers-Briggs, for fund managers. This is actually not uncommon in other business scenarios involving large loans, buyouts, etc. and ought to be standard practice for any position of serious responsibility.

P

Maybe that was because the specially picked panel was made up of sensible and respectable managers, those who would do well, and importantly, act conservatively, whatever the state of the markets.

But such managers are unfortunately rather rare.

While highly regulated banks can collapse any day of the month, hedge funds tend to report their performance on a monthly basis and can sometimes cling on to life, limping along until they can keep the sorry state of their business secret no longer. With the wild swings in the market of late it seems reasonable that it won't be too long before we start hearing about the collapsing of hedge funds, and maybe some big names among them.

P

The figure shows the 252-day rolling SAC for the Dow Jones Industrial index. It is clear from this that there has been a longstanding trend since the late 1970s going from extremely positive SAC to the current extremely negative SAC. (I imagine you’ve all noticed this lately!) Positive SAC is rather like trend following, negative SAC is rather like profit taking. (I use ‘rather like’ because technically speaking trending is, in s.d.e. terms, the function of the growth or dt term, whereas SAC is in the random term.) The current level has been seen before, in the early thirties, mid 1960s and late 1980s. (Note that what I have plotted here is a very simplistic SAC measure, being just a moving window and therefore with all the well-known faults. The analysis could be improved upon dramatically, but the consequences would not change.)

As far as pricing and hedging of derivatives is concerned there are three main points of interest (as I say, mentioned in very, very few quant books!).

1) The definition of ‘volatility’ is subtly different when there is SAC. The sequence +1, -1, +1, -1, +1, has perfect negative SAC and a volatility of zero! (The difference between volatility with and without SAC is a factor of SQR(1 – rho^2), where rho is the SAC coefficient.

2) If we can hedge continuously then we don’t care about the probability of the stock rising or falling and so we don’t really care about SAC! (A fun consequence of this is that options paying off SAC always have zero value theoretically.)

3) In practice, however, hedging must be done discretely. And this is where non-zero SAC becomes important. If you expect that a stock will oscillate up and down wildly from one day to the next, like the above +1, -1, +1, -1, example, then what you should do depends on whether you are long or short gamma. If gamma is positive then you trade to capture the extremes if you can. Whereas if you are short gamma then you can wait, because the stock will return to its current level and you will have gained time value. Of course this is very simplistic, and for short gamma positions requires nerves of steel!

That’s just a brief introduction to a much-ignored topic. I hope it will inspire some discussion!

P