Naked Put Backtesting Methodology (Part 2)

Last time I began to describe my naked put (NP) backtesting methodology. I thought I implemented constant position sizing—important for reasons described here—but such was not the case.

I held contract size constant and collected a constant premium for every trade. How could I have gone wrong?

The first thing I noticed was a gradual shift in moneyness of the options traded. I sold options with a constant premium. Earlier in the backtest this corresponded to deltas between 9-13. Later in the backtest this corresponded to deltas between 5-9. Pause for 30 seconds and determine whether you see a problem with this.

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Do you have an answer?

The probability of profit is greater when selling smaller deltas than it is when selling larger ones. The equity curve would probably be smoother in the latter case with relatively large drawdowns. These are different trading strategies.

Even selling constant-delta options left the equity curve with an exponential feel, however. As discussed here, exponential curves do not result from fixed position size. I did notice the growing premiums collected during the course of the backtest but I thought by normalizing delta and contract size I had achieved a constant position size.

If you’re up to the challenge once again, take 30 seconds to figure out what’s wrong with this logic.

Figure it out?

The root of the problem is variable notional risk. Normalized delta and fixed contract size does not mean constant risk if strike price changes. Remembering the option multiplier of 100 for equities, a short 300 put has a gross notional risk of $30,000. Later in the backtesting sequence when the underlying has tripled in price, a short 900 put has a gross notional risk of $90,000. Returns are proportional to notional risk (e.g. return on investment is usually given as a percentage) and this explains the exponential equity curve.

So not only did I need to hold delta constant, I also needed to normalize notional risk. A constant contract size is not necessarily a constant position size. The latter is achieved by keeping notional risk constant and calculating contract size accordingly.

I will continue with this in the next post.