Risk Latte - Analyzing Futures and Forwards - A Trainer's agony!

Analyzing Futures and Forwards - A Trainer's agony!

Rahul Bhattacharya
April 9, 2007

Legend has it that a few years ago, a well known financial trainer from a famous UK based training and financial consultancy company (which also happens to have a base in Hong Kong these days) was faced with an agonizing question from a graduate trainee of a bank. The graduate trainee had asked the trainer the question: why is there a difference in the pricing of a futures contract and a forward contract? More specifically, why is a futures contract almost always less than that of a forward contract?

What a question it was. For the trainer, a veteran of 15 years in this area, it was a walk in the park. He took ten minutes to explain the difference, including a detailed expose - without much math, of course - on how convexity causes the difference in pricing. The trainee was not convinced. He wanted an intuitive explanation of the difference in price of a futures and forwards and how then can that intuitive explanation be put into math framework. The trainer went back to all that he had memorized from John Hull's textbook and against his best judgment, even spitted out a lot of math that he had memorized. The trainee was still not satisfied. His point was: there has to be a very simple explanation in terms of financial markets as to why futures and forwards are differently priced and the underlying math should be able to justify that. Not the other way round, as a lot of trainers try to preach.

Legend has it that the trainees were new recruits - some MBAs, some Ph.D.s - in the investment bank CSFB (this is a good 6 or 7 years back) and were going through orientation programme in the bank's London office. Legend also has it that they had somehow attended a working session by one of the bank's desk "quants" prior to that training session and this particular trainee simply wanted to put this external trainer through some rigour. We don't know what is true or false, or whether it was indeed CSFB or some other bank. But one thing we must admit. CSFB in the late nineties and early two thousand did indeed have an intake of very sharp Ph.D.s - that much is certain and around 2001 and 2002 CSFB also had some of the best known and well respected quants in the area of fixed income in London those days. So the story is quite plausible.

The trainer was made to sweat a lot that afternoon, despite a cool autumn breeze outside and the temperature hitting 18 degrees Celsius. In the end, the guy stood up and answered his own question in a strongly accented, sing song English (some call it "curry" English and we call it the "Raj" English) and to the delight of his other colleagues in that room, and to the sheer misery of the trainer, he explained the difference between the two.

Most often than not we are tempted to present a math formula or a model and then try to justify that by our observations in the financial markets. There is nothing wrong in that. Theoretical physicists work like that. Albert Einstein formulated his General Theory of Relativity using his imagination and mathematical modeling and much later was the proof of the theory discovered in the Universe. But finance is not theoretical physics and the quants or the academicians who come out with financial models to explain products and markets Einstein or Dirac. Empirical observation is important in finance. Modelling - and by that we mean math modeling - in finance needs to based on empirical observations. The math has to consistently and accurately explain what we observe and observations are made a priori.

Thus on that autumn afternoon, a rather simple and a trivial question like why forwards are generally more expensive than the futures hung in the air like some unexplained equation of General Relativity needing an Einstein or a novice to unravel its mystery. To a novice all complexities of life are explained away by the trivia.

We asked this question to a shipbroker friend of ours who has no formal education or training in finance or banking but has over a span of twenty years made a fortune by investing in derivatives and other financial instruments. His response was: what a stupid question, Ronny! You pay nothing upfront to the bank for the forward contract and you can roll it over if you make a loss - at least we could do that in good old days - but in the case of futures you need to settle at the end of the day by paying cash. So of course, the bank is going to charge you more for the forward contracts. There's no free lunch, man!

Well, in the following article we will present a slightly more formal explanation in English and then some using Math as to why the futures and forwards are differently priced. And we will use Bruce Tuckman's explanation there (which we believe is the best). By the way, Bruce Tuckman was a Managing Director in the Fixed Income and Derivatives division of CSFB in the early two thousands.

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