Time Spread Backtesting Concepts (Part 3)

Today I conclude this brief mini-series detailing background concepts about time spreads.

Theta is one parameter I found insidious in manual backtesting. 2020-2021 time spreads generally have a lot of “jump.” They seem to hit profit targets quickly and sometimes completely out of the blue (e.g. with PnL small or negative just a day or two beforehand). 2017 time spreads, in contrast, move very slowly. Weeks go by without any significant profit and loss is more common. Perhaps because I monitored the TD ratio per guidelines shown here, I did not think to track theta itself.

2017 volatility is extremely low and I eventually realized that position theta is extremely low with these guidelines, too. Over a given period, the market can be expected to move within a probability cone. When theta is much lower, profit will not accumulate to offset this movement. Without normalizing theta by adjusting spread width, these guidelines really describe entirely different strategies for 2017 and 2020/2021. As shown in the table here, width will affect MR, which can then be normalized as discussed in that final paragraph.

Eventually, I would like to do a study with no profit targets or stop-losses. Track MFE with DTE, MAE with DTE, and then visualize to check for optimal values. This should be done in walk-forward fashion to avoid generalized curve-fitting. Maybe every month I visualize a chart of MAE/MFE over the previous six months to see what values are optimal based on recent history. These values may or may not be stable going forward.

To get started, something simpler like backtesting with a straight 10% profit target and -20% max loss could be done. I should then try to generate a variety of combinations to verify the strategy as profitable in all cases. Other pairs could be 10%/-10%, 15%/-20%, 20%/-20%, 20%/-15%, etc. Of course, the higher the number the longer the trades. For this reason, some measure of PnL%/day also makes sense…

…and by now I have lost the “simpler” part. Keeping complexity out is certainly one of the larger challenges here.

Rewind: start with +10%/-20%. I can then compare strike selection from -5% to ATM to +5% by increments of 1%, 2%, or 2.5% to assess directional bias. Transaction fees should be included, and avoiding less-liquid strikes is a possibility.

As one last piece of theoretical complexity, I suspect an X% change in horizontal skew has less effect on PnL as DTE decreases. Lower DTE means less extrinsic value remains in the short option to be affected by IV change in the first place. Tracking horizontal skew % may therefore be misleading unless done with regard to DTE.

Time Spread Backtesting Concepts (Part 2)

Today I want to continue with background on time spreads before moving forward with Python backtesting.

How horizontal skew reacts to different types of market rallies and/or selloffs is hard to predict. In selloffs when fear spikes, traders tend to buy near-term options pressuring term structure toward backwardation (increasing horizontal skew). In theory, increased IV is good for vega-positive time spreads. If horizontal skew becomes more positive, then although the long leg increases in value (good) due to IV, short-leg value may increase more (bad). The overall effect on PnL depends on how decreased spread value from higher skew compares with increased spread value from higher long option prices.

You can imagine other permutations for cases where horizontal skew is initially positive or negative, becomes more positive or negative based on different magnitudes of rally/selloff, etc. I am interested to see if any significant association exists between [changes in] horizontal skew and profitability.

I am also interested to see if any significant association exists between IV and profitability. Conventional wisdom says vega-positive time spreads should be purchased when IV is low. Could horizontal skew have a significant interaction here?

Margin requirement (MR) varies from one time spread to another and I have had difficulty putting my finger on this. MR is proportional to IV. MR should be inversely proportional to DTE since all else being equal, time spread price increases over time and maximum potential risk is the cost. Width (days between expirations) is directly proportional to MR because for the same short option, long options farther out in time are more expensive. Horizontal skew should also be inversely proportional to MR because the higher skew means a more-expensive near-term option and lower overall cost.

To simplify things a bit:

Perhaps Python can aid with some analysis here.

With MR so variable, some consideration must be given to position sizing. One possibility is a fixed position size backtest where each trade is done with number of contracts (rounded down) equal to position size ($) / MR. Alternatively, a fixed percentage of the total account could be allocated. This would allow for compounding. Drawdowns across the equity curve could then be compared as percentages off the highwater mark to normalize for temporal sequence. This seems logical at first glance.

I will continue next time.

Practice Trades Cal 1.13

Cal 1.13 (guidelines here) begins 2/18/20 (87 DTE) with SPX 3370 and trade -$168 (-2.6%). TD = 1, MR $6,498 (two contracts), IV 11.9%, horizontal skew -0.85%, NPD 6.8, and NPV 231.

What jumps out at you when looking at the initial risk graph?

This is the second Cal example where the same strike is unavailable in the back month (see Cal 1.4 here). Placing the long leg lower gives the trade a bullish bias, which is something discussed in the fifth paragraph here.

Notice that a bullish bias is achieved whether I diagonalize the long leg (lower) or whether I raise the calendar strike. The former preserves profit potential at current underlying price at the cost of raising MR. Each has pros and cons.

As mentioned in the third paragraph here, I may want to come up with some alternative downside management since TD = 1 at inception unless I plan to let it go to ML.

On 84 DTE, trade -4.4% with market down 0.85 SD in three days.

Exit 81 DTE for loss of $1,478 (-22.8%). This is the 4.33 SD down day, which comes without warning. Over 6 days, SPX down 2.73 SD with IV up 83%. Horizontal skew has increased slightly to -0.62%. TD = 0 (rounded).

Unlike Cal 1.2, SOH to see how the market “shakes out” would be a terrible decision here:

Highlighted is my first opportunity to exit at max loss (with market far outside profit tent and TD 0 unlike third paragraph here where Cal 1.12 is still well-positioned with TD strong). I have to take the loss immediately: no reason not to.

HEED WARNING DISCRETIONARY TRADERS!

I think one of the biggest risks of discretionary trading is the tendency to see something that seems to work while conveniently forgetting other instances where it does not. You may be confident in something that, on the whole, adds no benefit (or worse). A large-sample-sized systematic backtest to assess strategy guidelines can prevent this from happening.

Practice Trades Cal 1.12 (Part 2)

I left off questioning whether I should exit Cal 1.12 at max loss despite being well-positioned inside the profit tent.

From a systematic, programming standpoint, I don’t see how to do breakeven (BE) estimation with time spreads without Black-Scholes and/or volatility skew modeling. This precludes implementation of a Python backtester.

From an “art of trading” standpoint, my gut says “no way no how” do I take max loss when I am well inside the profit tent (strongly supportive of a high TD) like this.* To convince me otherwise, I will be on the lookout for cases where I remain in such trades only to meet a horrific demise.

Exit two trading days later at 73 DTE for profit of $552 (15.3%). SPX is up 0.13 SD to 3011 with IV up 5.9% over the 5 days, TD = 96, and horizontal skew remaining at +1.8%.

Part of me wonders if it might require extraordinary discipline to exit still being positioned near the center with TD so high.

If I stayed in, then when would I look to exit?

Moving ahead to 11 DTE:

I am now approaching the downside BE. While still 140 points away, I am certainly getting to the “slim pickins'” portion of the graph compared to what lies to the right. TD is 10 at this point and trade is +42.5%, which would be an absurd amount to lose should the market continue lower.

This would be a decent time to exit. I may not be able to code this discretionary interpretation, but said “art of trading” still seems alluring as a viable tool.

Finally, I’m a bit curious about the margin requirement (MR). I mentioned in this third paragraph that high IV may cause time spreads to be expensive. Such is not the case with Cal 1.12. I will grant that Cal 1.12 IV (~35%) is nowhere near that seen in Cal 1.3, but it still seems relatively high whereas MR seems relatively low. With starting DTE, horizontal skew, and [average] IV [proprietarily calculated over the whole option matrix in ONE] all potential contributing factors, how can this be explained?

I will pick up here next time.

* — This is 31.3% of the way between BEs.

Practice Trades Cal 1.12 (Part 1)

Cal 1.12 (guidelines here) begins 2/27/20 (78 DTE) with SPX 2995 and trade -$168 (-4.3%). MR is $3,608 (two contracts), TD 53, IV 35.2%, horizontal skew +1.8%, NPD 0.8, and NPV 224.

“Conventional wisdom” (see second paragraph) would probably suggest skipping this day for entry given a crazy market down 3.1 SD! I can imagine a volatile, whipsaw market causing hefty slippage, but looked at another way if I place a limit order and just wait, then I can imagine having a good chance to be filled precisely because of the market’s wild movement.

The positive horizontal skew provides me with a little extra bonus compensation for the risk taken in a volatile market.

How much compensation, you ask?

I admittedly zoomed in to make this look super large. However, what is no joke is 460 points between expiration breakevens (BE)—a full 15% of the underlying’s current price. If volatility tanks then the graph will move down and BEs will narrow, but as the positive skew reverts, T+0 will rise. Lots of moving parts here.

Surprisingly [to me], the official max loss (-$728, -20.2%) is hit the very next day with market down 1.1 SD:

Should I exit this trade?

The market is down 59 points, but I still have 166 points to downside BE. Distance between expiration BEs has increased to 530 points with IV now at 45.4%. Horizontal skew has increased and I still expect a reversion to negative horizontal skew to follow (recall last paragraph here). TD 25 also suggests solid potential for profit potential going forward.

I will continue next time.