Naked Put Backtesting Methodology (Part 3)

In my last post I described the need to keep short delta as well as notional risk constant in order to have a valid backtest throughout. Today I delve deeper into implications of maintaining constant notional risk.

Notional risk can be held relatively constant by selecting proportionate contract size. Contract size is calculated by dividing the desired (constant) notional risk by the option strike price multiplied by 100. The strike price in the denominator gets multiplied by 100 because the notional risk in the numerator has already been multiplied by 100.

Understanding the impact of rounding is important with regard to this “normalization” process. The calculated number must be rounded because fractional contracts cannot be traded. I would therefore round to the nearest whole number and this introduces error. For example, if the above calculation yields 1.3235 then I would trade one contract. One is 0.3235 less than the actual number, which represents an error of (0.3235 / 1.3235) * 100% = 24.4%. I will get back to this shortly.

My next issue was deciding what notional risk to apply. Since I was going to spend several weeks on a backtest, I decided to select a value similar to my live trading account so I could get a feel for what drawdowns I might actually see.

Trading this level of notional risk resulted in a range of contract sizes from 5 to 1. The latter is problematic because as the underlying price continues to increase into the future, the one contract would represent increasing—not fixed—notional risk. No matter how high this becomes, I cannot decrease because zero contracts is no trade.

Aside from this floor effect for contract size is a problem with granularity. By multiplying the notional risk by five, I found that over the range of strikes used in my 15-year backtest, contract sizes varied from 25 to 4. This is much less granular than the 5-to-1 seen above and would result in a much smaller error.

I will illustrate this granularity concept in the next post.