Friday, 13 February 2009

Horses for Courses










Is the Financial World just a bad Casino? Are the Finance Regulators the worse bookmakers ever? Should Alan Greenspan and Mervyn King be tried for crimes against Humanity a priori? Or are they just ignorant?
The answer is "Yes" to all the above questions. In the Anglo-Saxon society it is common to say that "ignorance is bliss". In my country, Portugal, we have a totally different approach as in our opinion "ignorance kills". And although we should be forgiving towards ignorant people "because they don't know what they are doing" there is no redemption for the worst human sin... stupidity.
Today I shall talk about horses, bets, odds, uncertainty in an attempt to find some parallel between this world and Finance. It all starts with statistics, probability, and the concept of 1 or 100%. What is the probability of winning the lottery if I buy all the tickets? 1! What if I do not buy any? 0... I have no chance of winning. Probability gives an estimate for an event to occur in due time against all possible events. In the 49 number lottery is about 1 to 14 million, the odds are 1 to 14 million... the chance of winning... very slim. So how do bookmakers earn their living? Very simple... at any given time the sum of the odds for a race has to be lower than 1. The odds are permanently being updated to reflect this; to be around 0.95 in total so 0.05 (or 5%) of the total of the bets is a fixed profit to the bookmaker regardless of the race outcome.
So... I bet $100 on the 2011 Kentucky Derby on a horse called Credit Crunch. The odds are now at 1/150 which means that if my horse wins, the bookmaker will have to pay me $15,000. I have to wait a couple of years, until the race completes, to either loose $100 for good or cash $15,000. The bookmaker will have in the meantime to assure that he has enough money to pay any possible outcome of the race. He manages the sum of the odds to be always below 1. If he makes a quoting mistake he will have to pay more than the total of the bets placed, a loss. This only happens if the sum of the odds is bigger than 1.
Hang on... wait a minute. I gave $100 to the bookie and now I have a piece of worthless paper. That's not very good. But this paper could be worth $15,000. Sure I can get some return on it already. So, I go back to the bookie and explain: "Listen, I am sure I will win $15,000 in the Kentucky Derby of 2011. Could I have $5,000 of it already?" He starts laughing on my face and evicts me from his business premises alleging that I am mentally disturbed (he might have a point). On exit someone whispers to me "For what you want, you need a Financial Engineer". So on the next day, after talking with one, I bring home not $5,000 but only $3,800 because that was the figure calculated by the "Broker" after applying the Black-Scholes formula. I had to pay a $25 premium though but now, I am the proud owner of a derivative (and $3,800!)
The Black-Scholes environment gives a price to anything and everything for a certain date in the future. The problem is, although calculating a price based on probability its Universe, or universal application is always bigger than 1. It also dilutes time as you can have and trade "assets" based on the formula immediately, it generates instant "wealth" based on a future event for which there is no control whatsoever. Worse, as opposite to horse racing (where the more money is placed on a horse the worse is your return) the more you use it the better your odds, you get a better valuation of your "asset". The financial world has been accepting these for decades where the probabilities are above 1, sometimes 10, with the inverted thinking "the higher the better". These products "feed" on themselves, the more, the higher they get, the faster they "produce". There is only one problem. When Credit Crunch finishes the race in 2nd place ("oh that was so close, our model almost worked!" says the Broker) it is payback time. And guess what... the broker goes broke, the bank that supports his genius goes bust.
You can always hedge your bet. For my $100 I can always go "each way" instead of "to win". This is a basic way of spreading your costs and increasing your chances of a positive return, totally acceptable and controllable in the bookmakers' world. However Finance Engineers tend to hedge their bets by inventing new events, new universes. For instance, I could hedge my $100 bet on Credit Crunch by creating a probability like "If the odds of Credit Crunch on the day of the race are longer than 5/1 (i. e. 4/1, 3/1 etc.) I will win $100 per each 0.1 above. On the contrary if they are shorter I will have to pay $10 per 0.1". There are equivalent "proven" formulas for this type of events. These products unfortunately are not controlled by a single bookie and worldwide, their probability is always bigger than 1.
Although the BS formula has the look of a probability its use is always to "price" better. If, in my Credit Crunch derivative, the formula would have come up with $10 only, I wouldn't have bothered.
Ah... to finalise... I can always pick up my (worthless) piece of paper of the hedge fund and get another derivative for it... then hedge this one ... ad eternum. If I do it enough times there is not enough money in the world to pay for it all.
By the way... has anyone tried to integrate the BS formula and check if its final value is... 1?

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