Naked Put Backtesting Methodology (Part 4)

I continued last time talking about fixed notional risk. When backtesting this way, limited notional risk results in decreased granularity and significant error.

To better understand this, I listed the strikes used throughout the 15-year backtest in a spreadsheet. For each strike I calculated contract size corresponding to a defined notional risk. I then rounded and determined the error as a percentage of the calculated contract size. I started by keeping a cumulative tally of the error to see how that differed across a range of notional risk. Error may be positive or negative depending on whether the calculated contract size is rounded down or up, respectively. The cumulative tally therefore went up and down over the range of strikes and was not very helpful.

I then looked at the maximum and minimum values of cumulative error. This is what I found:

The greater the notional risk used, the lower the range of cumulative error. This illustrates the granularity issue. More granular (larger) position sizing means decreased error. Decreased error means more stability in notional risk, which I am attempting to hold constant throughout.

Backtesting my account size would have limited contract size significantly and introduced a large amount of error due to the lack of granularity. I therefore decided to increase notional risk (250x) to minimize error.

One question that remains is whether I have created an artificial situation that is incompatible with live trading. More than anything else, I am trying to get a good sense of maximum drawdown when trading this way and for this reason, I believe backtesting will provide useful information unlike any backtesting results I have seen before.

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.

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.

Click here

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.

Naked Put Backtesting Methodology (Part 1)

I’ve run into a buzzsaw with regard to my naked put (NP) backtesting so I want to review the development of my methodology to date.

I started with a generalized disdain for the way so much option backtesting is done regarding fixed days to expiration (DTE). Quite often I see “start trade with X DTE.” I believe this is a handicap for two reasons. First, I can only backtest one trade per month. This limits my overall sample size. Second, I don’t believe anything is special about X DTE as opposed to X + 1, X + 4, X – 5, etc. Since they should be similar, why not do them all? This is similar to exploring the surrounding parameter space and would also solve the sample size problem.

To this end, I backtested the NP trade by starting a new position on every single trading day. This is not necessarily how I would trade in real life because I might run out of capital. However, the idea was to see how the trade fares overall. This would give me over 3500 occurrences and that is a very robust sample.

From the very beginning, my aim was to keep position size fixed to ensure drawdowns were being compared in a consistent manner. In the first backtest I therefore sold a constant contract size of naked puts with defined premium (first strike priced at $3.50 or less).

This large sample size gave me a healthy set of trade statistics. I had % wins (losses). I had average win (loss) and largest win (loss: maximum drawdown). I had average days in trade (DIT) for the winners (losers). I had standard deviation (SD) of the winners (losers) and of DIT for both. I had the profit factor. I was also able to compare these statistics to a long shares position by creating a complementary shares trade over the same time interval. I then calculated the same statistics and the NP strategy seemed clearly superior.

The analysis thus far was done to study trade efficacy rather than, as mentioned above, to represent how the trade would be experienced live. To further develop the latter guidelines I would need to generate and study an equity curve. Thankfully I already had a fixed-position-size backtest so I could at least compare the drawdowns throughout the backtesting interval.

Upon further review, however, I discovered some problems that I will describe in the next post.

Stop at the Equity Curve (20) (Part 3)

The end-of-trade PnL equity curve filter looked promising but mark-to-market (MTM) is what I would encounter in real-time.

To do this, I replicated a previous backtest from 5/1/2008 through 3/16/2009 and tracked daily account value. The 239 days between 6/17/2008 and 2/4/2009 was the shortest elapsed time to get four exit signals.

I expected the MTM equity curve to largely parallel the equity curve generated previously. I expected some evidence of future shift since the end-of-trade PnL (spreadsheet) approach counts the final trade PnL on the date of trade inception:

The future shift is evident along with much more volatility in the MTM daily curve. With regard to filter efficacy:

I was disappointed with MTM daily’s performance with the 20-SMA trade filter. It worked well until Feb 2009 when it suffered a very large drawdown (DD). This was the maximum DD seen with the MTM daily equity filter and a larger DD than seen without! This suggests winning (losing) days were (not) filtered out: a dangerous combination.

A closer look at the data shows the MTM daily equity filter was more active than the end-of-trade PnL filter. The former (latter) generated 13 (4) signals. Of the 13 signals, five or two lasted one or two days, respectively. This suggests a large number of whipsaws because such a filter will be effective by signalling a big market decline to remain on the sidelines for an extended period. The MTM filter was particularly ineffective in March 2009 as the strategy in the market on March 2 to lose $220K and out of the market on March 4 to miss a $175K gain.

The graph shows the MTM equity curve filter did about $200K better than no filter at all. However, with all the whipsaws I am not convinced it is any more effective. I would need a longer MTM backtest to be convinced.

Backtesting made it clear why the MTM daily filter was so much more volatile. The end-of-trade PnL method only gains or loses the value of one trade per day. Although this is big money for the largest losers, on big down days the MTM daily filter method loses big money on all of the open trades.

While the end-of-trade PnL filter was quite effective, as I suspected it is very artificial and looks nothing like the MTM daily filtered equity. If I want to continue studying an equity curve approach then I should backtest over a longer period. Alternatively, I could look to price action of the underlying for DD minimization.