Bernie Madoff and Stock Options

We'll resume our discussion of stock options from where we were here. The above photographed felon will come into our discussion soon enough.

Options can be part of broader strategies that limit exposure in either direction. You can combine puts and calls to create a “collar” around the market price of the underlying stock, limiting both your own profit and your own risk.

The word “straddle” has connotations similar to “collar,” suggesting that options allow the straddler to be on both sides of the same underlying asset at the same time. Yet “straddle” has a more aggressive sound to it.

As it happens, Bernie Madoff used to tell prospective clients that he was following an options-based straddle strategy. Of course, he wasn’t following any strategy, but he needed to sell a story, and that was it.

Such a straddle strategy, by the way, can work when carried out legitimately. It can do roughly what Madoff claimed that he was using it to do – produce a slow-but-steady stream of equity market profits. But (and this is a big “but,”) it can’t do so on anything like the scale on which Madoff claimed he was working. He had $17 billion on his books at his height, and the options markets just don’t do the volume that would support that much hedging.

A Hedge in Both Directions

But, since we've justified our visual, let us return from Madoff-inspired fantasies to the real world. We spoke in the last chapter of the intuitive risk-return trade-off, and here we’ve just described the value of stock options as a hedge against risk. I suggest that we dig further into this notion of risk, especially as it applies in the market for corporate equities.

Remember that risk in financial economics is conventionally identified as the standard deviation, or the width of the bell curve representing outcome for a portfolio within a defined period.

But we have thus far assumed that the shape of the curve representing those outcomes is the “normal” bell. If it isn’t, then perhaps the tails are fatter than they should be. That’s a problem, because of course the “tail” of the curve on the left hand side of the graph represents disastrously bad outcomes. If the tail is fatter than normal, disasters are more likely than any calculations based upon that curve will presume.

There are at least two different ways in which the curves can be non-normal, yielding bigger tails. However we draw a hypothetical curve, it will have to cover just as much space, have as much volume within the resulting shape, as does the normal distribution, because in any event 100 percent of the possibilities must be present and accounted for.

The most obvious way to re-jigger the distribution, then, is simply to flatten the curve, and make up the loss of space by raising the tails on each side. This makes the ‘normal; result somewhat less compelling, and the extremes, both the very big dogs and the very small dogs, somewhat more common, while preserving horizontal symmetry – that is, while leaving the result unskewed.

A less obvious way to end up with fat tails is to make the bell pointier. That is, take the normal curve, move its central point upward, and fatten the tails, while ‘paying’ for this by lowering the shoulders. In probability terms, this indicates a situation in which the median is more likely than in the normal curve, extreme results are also more likely, and the moderately off-center results are less likely.

A Story About Coleridge

This is a quote from a memoir by Dorothy Wordsworth, reflecting on a trip she took with two famous poets, her brother, William Wordsworth, and their similarly gifted companion, Samuel Taylor Coleridge. We sat upon a bench, placed for the sake of one of these views, whence we looked down upon the waterfall, and over the open country ... A lady and gentleman, more expeditious tourists than ourselves, came to the spot; they left us at the seat, and we found them again at another station above the Falls. Coleridge, who is always good-natured enough to enter into conversation with anybody whom he meets in his way, began to talk with the gentleman, who observed that it was a majestic waterfall. Coleridge was delighted with the accuracy of the epithet, particularly as he had been settling in his own mind the precise meaning of the words grand, majestic, sublime, etc., and had discussed the subject with William at some length the day before. “Yes, sir,” says Coleridge, “it is a maj...

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John Searle has become the object of accusations of improper conduct. These accusations even have some people in the world of academic philosophy saying that instructors in that world should try to avoid teaching Searle's views. That is an odd contention, and has given rise to heated exchanges in certain corners of the blogosphere. At Leiter Reports, I encountered a comment from someone describing himself as "grad student drop out." GSDO said: " This is a side question (and not at all an attempt to answer the question BL posed): How important is John Searle's work? Are people still working on speech act theory or is that just another dead end in the history of 20th century philosophy? My impression is that his reputation is somewhat inflated from all of his speaking engagements and NYRoB reviews. The Chinese room argument is a classic, but is there much more to his work than that?" I took it upon myself to answer that on LR. But here I'll tak...

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I've written about Nassim Taleb on earlier occasions in this blog. I'll let you do the search yourself, dear reader, for the full background. The short answer to the question "who is Taleb?" is this: he is a 57 year old man born in Lebanon, educated in France, who has been both a hedge fund manager and a derivatives trader. He retired from active participation from the financial world sometime between 2004 and 2006, and has been a full-time writer and provocateur ever since. Taleb's writings for the general public began where one might expect -- in the field where he had made his money -- and he explained certain financial issues to a broad audiences in a very dramatic non-technical way. Since then, he has widened has fields of study, writing about just about everything, applying the intellectual tools he honed in that earlier work. As you might have gather from the above, I respect Taleb, though I have sometimes been critical of him when my own writing ab...

Jamesian Philosophy Refreshed

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