But financial mathematics has an attraction. It brings an appearance of precision to some very imprecise arts.
But my test as to whether you really understand financial mathematics is whether you can meaningfully apply it to simple real world problems. If you can get maths to do that it is not wasted and can add something to your risk management.
So – in this line – think of this post as a second year university financial mathematics course without the maths.
David – the financial salesperson extrovert and his sports betting junkie
David (not his real name) was financial sales guy I knew kind of well. Like most financial sales guys he was an extrovert. He worked with analysts – and they were all introverts. If you put him in a bus with his colleagues on the way back from some Christmas function he would try to get everyone singing Scottish football songs. This was amusing but usually unsuccessful. To the extent it was successful I blame alcohol and not David’s out-of-tune lead. [Dave – if you are reading this – your singing wasn’t bad – it was just memorable.]
Anyway Dave had fifty bucks left in an old sports betting account. He reckoned that he could bet the entire sum every week for six months and end up with more money than he started with.
This sounded impossible – and I was prepared to fund the experiment if I was wrong.
David may have been a sales guy – but he was no fool. He divided his stake into five equal amounts and bet on five near certainties. A typical sort of bet might be for Roger Federer to win the second round at
He wouldn’t get great odds – the bets often paid only 1.05 times the sum wagered. But he would win all five bets most weeks.
The odd week he would lose one – and the four winners would wind up losing 16% (=1-4*1.05/5). It would take him a few weeks to recover – but he recovered – and little harm was done.
I lost track of how David was going – but you can see what is going to happen. Week in, week out the David will make a profit. He might have a setback – but it would be manageable. He looked like a consistent winner.
Of course if he did it for long enough his number would be up – and he would bet on five losers. It is highly unlikely to happen in any particular week – but done for long enough it was inevitable.
The strategy will have the property of making regular seemingly-consistent profits – but taking irregular large losses. Off six months of data it was almost impossible to tell if he was adding value with his wagering – but my guess is he probably wasn’t.
So what has this got to do with financial mathematics?
Well what David was doing was betting on likely outcomes. If you bet on likely outcomes you make money most the time but when you lose you lose big.
I call this selling volatility in the sports betting market. You can model it just like selling volatility in the finance market (but hey – I am saving you doing a financial maths course).
Selling volatility in financial markets is just betting on the world staying within likely parameters. I can design you a hedge fund that would make a profit almost all the time –and has fantastic consistent returns.
Maybe I could even convince rating agencies I am a genius. But the only strategies I know that are consistent have a blow-up risk. That is what selling volatility is all about. I know several Australian funds (and there were many more) which blew up precisely this way late last year.
If you watch for long enough it is amazing how often you see people selling volatility. And they often don’t even know they are doing it. Over times I hope to point a few out. But that is subject matter for later posts.
6 comments:
If I recall correctly, V Niederhoffer blew up exactly this way ie he was writing options. And the person on the other side buying is Nassem Taleb of the Black Swan fame. Selling volatility will not go away, because it is psychologically attractive to have consistent small wins.
OK, but it's possible to be short vol without having unlimited risk by using exotics, e.g. instead of selling strangles you buy a range accrual note or a DNT.
It would be just as possible if my friend David divided his pot into two equal piles. One pile he invested in treasuries. The other pile he sports bet on.
In no week is it possible for him to go to zero - but if all five fail he will drop half.
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Given he can never go to zero time will tell whether he is superior to the bookmaker. If he is superior he will eventually go to infinity. If he is inferior he will asymptotically travel to zero.
By removing the blow up risk you can sell volatility and if you actually generate alpha it will show in the end.
An interesting intellectual exercise is to model out Dave assuming he is either 1% better or 1% worse than the bookmakers. Assume he does the divide pot in two and bet half rule.
If he is 1% better it will show.
But the question: how many weeks/months/years.
You need a lot of data to know anything to any degree of certainty!!!
In the long term David is either bankrupt or makes a slight loss unless he knows better than hte sports market. If he knows as much as the market he of vourse breaks even but will no doubt pay some sort of commission or profit to the bookmaker.
What David doesnt do is bet more where there is more value and less where there is less. Indeed you make no mention of value.
You post is therefore (as im sure you intended) simply about bankruptcy risk - which as Peter mentioned Taleb covers in his books. However Taleb also doesnt talk about value. I can only assume Taleb believes volatility is underpriced (due to the reasons you refer) and therefore buying it will profit over the long term.
Trouble is the long term is very long so we dont ever find out.
Great blog, thanks!
To put this into numeric perspective, his strategy is optimal in the sense of maximizing long-term growth if he is able to correctly identify the winner in 96% of bets, which is only slightly better than the odds assigned by the dealer (about 95%). If he is right in more than 96% of bets he should put a larger fraction on each bet and make smaller number of bets each week, e.g. if his success rate is 97% he should make 3 bets instead of 5. On the other hand, if he is wrong more than 5% of the time he will slowly bleed money. Even if he is better than the bookmaker, it is not guaranteed he will go to infinity; there is non-zero chance to lose all the money if he is extremely unlucky, see Kelly criterion.
If he is 1% better than the bookmaker, his mean growth rate is 1% a week, whereas volatility is above 16% (as your calculation suggests). So he'll have to bet for five years or so before the long term growth overtakes random noise and it is clear whether he is skillful or just lucky.
John, just found your blog via Felix Salmon. I like your combination of facts and seat of the pants analysis.
This post points out the fact that statistics work for large groups and are worthless on a case by case basis. Your buddy is done the first time he loses 2 of 5. 40% loss that he can never earn back. In the hedge fund world he then makes riskier bets to try to earn it back and speeds up his death spiral.
I will add you to the blog roll at my own lightly read blog:
hppt://timplaehn.com
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