Time Decay and the Parable of the Iceberg Salesman

Source: Wikipedia

The inexorable nature of "time decay"--the quality of options that make them naturally lose value over time--is something that anyone who invests using options must understand and deal with. Option sellers are helped by time decay; option buyers are hurt by it. It is a hard concept to grasp for someone used to investing in stocks, but the following Parable of the Iceberg Salesman should implant it firmly in your mind.

Assume that you are a business person living near the equator in the late 1800s. Everyone in your town is in need of ice to store food. You own a boat and hit upon the idea of using your boat to transport icebergs down to the place where you live, where you can cut up and sell individual blocks to your neighbors. You gear up and travel to Alaska, where you harpoon an iceberg and head back toward your home country. As you travel further and further south, your iceberg is warmed by the surrounding waters and it grows a little smaller each day. Will there be any ice left to sell when you get back to your home port? If there is ice left to sell, will it generate enough revenue to cover your capital expenditures to outfit your expedition?

The money you make will be directly related to the amount of ice left when you get back to shore. You have already spent a fixed dollar amount on outfitting the ship, and you hope that there will at least be enough ice left when you return to cover that expense. Your payoff for this venture can be represented with the following diagram:

Of course, looking at the payoff in this light, it is easy for anyone who has read through an option book that uses the typical hocky stick graphs to represent option payoffs to see that the situation of the iceberg salesman is exactly that of the holder of a call option. The fixed amount spent on outfitting the ship is eqivalent to the premium paid for the call option. If there is any ice left when you reach home port, this is equivalent to a call option expiring In-the-Money (ITM) and the amount of gross profit you realize is directly related to how much ice you have or how far ITM your option is. The melting of the ice en route is equivalent to what is known in the options world as “time decay” (or “Theta” for those familiar with the option “Greeks”).

On page 66 of The IntelligentOption Investor, I talk about the dynamics of time decay and point out that options losing value quicker the closer to expiration is due completely to the shape of the BSM Cone and the slope of lines tangent to the Cone.

The dynamics of time decay also make sense with respect to the story of our iceberg salesman. The iceberg shrinks more quickly the closer you draw to your home port in the tropics because the water there is warmer than it did when you were still off the shore of Vancouver.

In Chapter 9 of The Intelligent Option Investor, the chapter covering “Gaining Exposure”, I talk about ways that one can lessen the effect of time decay on an investment in a purchased option. That discussion is integrally related to a discussion of investment leverage, and that is a topic large enough for another blog posting!