Spectral window gates for index long puts

A 100-day sample and an 82-day window

The case fed a spectral moving-window procedure the maximum allowed sample of 100 daily closes on an exchange stock index from 24 August 1983 through 16 January 1984. That moving-window-spectrum fitted overlapping wave components on a fixed-length recent sample rather than a single trend line. The window was set at 82 observations to match a previously seen cycle of about 78 to 82 days. Differencing was applied so that successive changes replaced levels and long-term trend did not dominate the spectrum.

Forecast path and later comparison

The resulting forecast path was later plotted against realized index values that were unknown when the forecast was made. The forecast specified an 11.4 percent decline over about 30 trading days, from roughly 227 to 202, including a turning point against then-prevailing bullish sentiment.

The forecast-gate tests

A forecast-gate is a pair of precommitted tests, a minimum percent change and a minimum duration, that decide whether any option is bought. A position was contemplated only when the forecast showed a move of about 6 percent or more lasting about 20 trading days or longer. This run cleared both gates.

Index long-put structures

A long-put is a purchased put whose loss is limited to the premium and whose value rises if the underlying index falls. Index options were chosen over single-name options so that one-security misspecification risk was reduced, loss stayed limited to premium paid, and capital stayed leveraged to the forecasted index path.

Two purchase structures were defined. An in-the-money-put has a strike already on the profitable side of the index, so little of the premium is pure time value. The case allowed well in-the-money puts with little time premium. An out-of-the-money-put has a strike still beyond the current index, so the entire premium is time value unless the forecasted decline crosses that strike. The case also allowed far out-of-the-money puts whose strike was expected to be crossed if the forecasted decline occurred. The case used the far out-of-the-money structure, buying February 210 puts at a price of 1/8.

The later path and the inspection table

During the forecast horizon the index fell from a recent high of 227 to a low of 204. Half the puts were later closed at 1 and the rest at 4. A subsequent table of index closes and option prices was supplied so both purchase structures could be inspected against the same later path.