### Optionality

My latest favorite read is a book called the Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty by Sam L Savage in which Mr. Savage tackles such mind numbingly complex statistical ideas as covariance, correlation, null hypothesis, the p test and makes them not only understandable but completely relevant to our everyday life as traders and businessmen.

One the more interesting examples that Mr. Savage presents is the evaluation of the gas well problem. Suppose, he write, the current market price of natural gas is \$10, but it costs you \$9.50 to extract it. Your company is looking to buy the well which has a million units but the transaction can take a few months to complete and you have no idea what the price of gas will be at that time.

Your boss asks you to estimate the price of gas one month forward so that he can properly value the property and come up with a reasonable bid price. You learn that natural gas has averaged about \$10 per unit over the past several months so that’s the number you give him. Fine, he says and bids \$500,000 for the property. He is promptly outbid by every other interested buyer and loses the deal.

Was your boss smart or dumb? By this time you should know that this a loaded question – the boss is always dumb, but in this case he actually is dumb to have made such a low bid.

Why?

On the face value the boss appears to have made a fair offer willing to pay no more than the potential cash flow from the property. Most businessmen would have applauded his disciplined approach. But the gas well problem is a perfect example of how our common sense often lead us astray in evaluating risk.

The key to properly valuing the gas well deal is to understand that if the price moves below the \$9.50 recovery cost you can simply shut down the well incurring only minimum maintenance costs while you wait for the price to rally. Suppose that six months forward the price rallies to \$15/unit. Your profit potential on the property is then a whopping \$5 million rather than \$500,000 that your boss initially bid. No wonder he lost the deal.

The gas well problem is embedded with what’s called optionality – effectively an asymmetrical payoff function between risks and rewards that skews favorably towards the buyer. Generally in business you always want to look for deals that offer convexity – that is deals where the downside is limited, but the upside is limitless and the payoff function slopes in the upward fashion from lower left corner to upper right corner.

That may seem obvious in retrospect, but how many of us follow this rule in real life? One quick and easy way to achieve a degree of optionality in trading is to always use stop losses. Yet many traders do the exact opposite – they limit their profits while letting their losses run. This is not a just a sin of your typical retail trader but of every major bank on Wall Street (toxic debt anyone?) and most of the hedge fund community as well (can you spell LTCM?).

When it comes to trading the dynamics are a bit more complex than the simple cut-your-losses-short-and-let-your-profits run maxim, but the underlying principle is inviolable. Cutting your losses is the only way to achieve optionality in trading. In other words, if you want the option to survive financially you must always use a stop loss . Don’t take my word for it. It’s a statistical fact.