SPX Monthly Returns And Tail Risk

I had some time yesterday while waiting for an appointment, and re-read "A Comparison of Tail Risk Protection Strategies in the U.S. Market".  One particular sentence in the paper caught my attention:

"Remarkably, of the 24 months with greater than 5% loss in the S&P 500 between March 1990 and March 2011, 17 of them (or 71%) occurred with the S&P 500 below its 10-month moving average.7"

The footnote associated with this sentence stated:

"The ten-month or 200-day moving average is a popular technical indicator among market participants; its effectiveness in asset class timing is documented by Faber (2005)"

I ran the same study in AmiBroker and Excel using the monthly closing prices of the SPX.  I calculated the 10 month moving average of SPX closing prices, and compared this value with the closing value of the first day of the next month.  For example, on March 1 1990, the closing price was 332.74, and the 10 month average of monthly closing prices was 338.59 (May 1989 through Feb 1990).  In this situation, March 1990 started below it's 10 month moving average.

Looking at the same period of time as the Tail Risk Article (March 1990 - March 2011; 253 months), I found the following:

• 70 of 253 months started below the 10 month moving average (28%)
• 183 of 253 months started above the 10 month moving average (72%)
• 25 of 253 months experienced a loss of 5% or more
• 16 of these 25 months occurred when the month started below the 10 month moving average (64%)

There were a few other points to note regarding winning and losing months:

• 103 of 253 months were losing months (41%)
• 36 of these 103 losing months occurred when the month started below the 10 month moving average (35%)
• 150 of 253 months were winning months (59%)
• 34 of these 150 winning months occurred when the month started below the 10 month moving average (23%)
• 29 of these 150 winning months had monthly returns of greater than 5% (19%)
• 14 of these 29 occurred when the month started below the 10 month moving average (48%)

A few takeaways:

• A greater percentage of the 5%+ monthly losses occurred when a month stated below the 10 month moving average
• A month starting below the 10 month moving average is not a good indicator of whether the month will end with any loss ... the SPX has a positive bias
• A month starting above the 10 month moving average is a good indicator of whether the month will end as a win (77%)
• The numbers are similar when the range is expanded through March 2017

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80 DTE Iron Condor Results Summary

This article reviews the backtest results for iron condors (IC) entered at 80 days to expiration (DTE). These tests covered 9 IC variations, with short strike deltas at four locations (8, 12, 16, 20), utilizing 12 exits.  In all, there were 432 test runs (9 variations x 4 deltas x 12 exits). Each test run executed an average of 165 SPX IC trades between the January 2007 expiration and the September 2016 expiration.  A total of 432 ten year backtests.  I used weekly options for this testing, so there were more than 12 trades per year.  In total, there were 71,388 total trades entered for the 80 DTE testing.

You can find the prior SPX IC posts in this series at the links below:

• New Iron Condor Series Introduction
• 38 DTE SPX Iron Condor Results Summary
• 38 DTE SPX Iron Condor Results Summary - Part 2
• 45 DTE SPX Iron Condor Results Summary
• 45 DTE SPX Iron Condor Results Summary - Part 2
• 52 DTE SPX Iron Condor Results Summary
• 59 DTE SPX Iron Condor Results Summary
• 66 DTE SPX Iron Condor Results Summary
• 73 DTE SPX Iron Condor Results Summary

Normalized P&L per Day

The P&L per day values shown in the charts below are expressed as a percentage of the max risk for that test run.  Each of the different wing width ICs (25 point, 50 point, 75 point) will have a different max risk, and it is important to normalize daily returns by the associated max risk number.  For example, a 25 point IC will have slightly less than $25K max risk (margin), while a 75 point IC will have slightly less than $75K max risk (margin).  Since the 25 point IC will have approximately 1/3 the risk/margin, the $ returns need to be normalized by these varying max risk / margin numbers for proper strategy variation comparison.

The results:

1. We continue to see more variability in P&L per day readings in the 25 point wing ICs, than in the larger wing width ICs
2. Similar to the prior test runs, as the delta of the short strikes increases, the variability in the P&L per day readings increases
3. The largest reading was 0.19%, which is the largest value we've seen in this series of IC tests.  There was one strategy variation with a 0.19% value:
1. ST (NA:50), 25 point wings, 20 delta
4. The next best readings came in at 0.18% and were associated with two test runs: 
1. ST (NA:50), 25 point wings, 8 delta
2. ST (200:50), 25 point wings, 20 delta
5. 88 strategy variations had P&L per day readings of 0.12% or greater:
1. Of these 88, 61 used the profit taking level of 50%
2. Of these 88, 55 used the standard balanced (ST) IC structure
3. Of these 88, 38 did not use a loss taking level (loss taking % = NA)
4. Of these 88, 34 used wing widths of 50 points
5. Of these 88, 32 used a short strike delta of 20 (30 used a delta of 16)

(click to enlarge)

Normalized P&L per Trade

The normalized P&L per trade charts display returns expressed as a percentage of the max risk for a given test run.  As trade duration increases with increasing DTE, overall P&L per trade increases. Due to this fact, the max value of the y-axis on the 80 DTE P&L per trade charts was increased from 6% to 12% (similar to the 73 DTE P&L per trade charts).  At 80 DTE, all delta variations had some values exceeding the 6% level.

The results:

1. The variability in normalized P&L per trade again increases as the delta of the short strike increases, and decreases with increasing wing width
2. In general, the returns per trade increase with increasing loss taking %, and this trend continues to be more pronounced as the trades move out in time / DTE
3. The largest normalized P&L per trade was 9.4% and was associated with one strategy variation:
1. ST (300:NA), 50 point wings, 16 delta
4. 174 variations had P&L per trade values of 5.0% or greater...really large number!:
1. 86 of these 174 were standard (ST) structures (45 were DN structures)
2. 75 of these 174 did not use a loss taking exit (64 used the 300% level)
3. 67 of these 174 did not use a profit taking level (59 used the 75% level)
4. 66 of these 174 used a short strike delta of 20 (53 used 16 delta)
5. 65 of these 174 used 50 point wings (58 used 75 point wings)
5. The 80 DTE ICs have the largest average P&L per trade readings:
1. 80 DTE: mean 4.60% / SD 1.98%
2. 73 DTE: mean 3.92% / SD 1.73%
3. 66 DTE: mean 2.79% / SD 1.09%
4. 59 DTE; mean 2.75% / SD 1.20%
5. 52 DTE: mean 2.33% / SD 0.88%
6. 45 DTE: mean 2.23% / SD 0.87%
7. 38 DTE: mean 1.88% / SD 0.75%

(click to enlarge)

Win Rate

The win rate trends have been consistent across the DTEs tested:

1. In general, win rates tend to increase as wing widths increase
2. Win rates tend to decrease as the delta of the short strikes increases
1. At 20 delta, there is only a slight increase in win rate when taking losses greater than 200%
3. The 50% profit taking level has the highest win rates
4. The top win rate was 99%, and was associated with four strategies:
1. EL (NA:50), wing width 25, 8 delta
2. ST (NA:50), wing width 75, 8 delta
3. EL (NA:50), wing width 75, 8 delta
4. DN (NA:50), wing width 75, 8 delta
5. 82 strategies had win rates of 91% or better:
1. Of these 82 , 57 took profits at 50%
2. Of these 82 , 49 did not use loss exits (they exited at 2 DTE; loss taking % = NA)
3. Of these 82 , 43 had short strike deltas of 8
4. Of these 82 , 32 had wing widths of 75 points
6. The strategies with the top win rates also had some of the largest single losses...and this is consistent across the DTEs tested

(click to enlarge)

Largest Loss

The next charts show the normalized largest loss for each of the test runs  These largest losses are expressed as a percentage of the max risk found in the roughly 165 trades in each test run.

The results:

1. Typically, the largest loss percentage increases with increasing loss taking level
2. There were three strategy variations that had losses measurably greater than 100% of risk.  They were the 25 point wing, 20 delta shorts, DN using a loss taking level of 300%.  These variations hit a loss of 126% of risk due to bad data.
1. This bad quote was associated with the 17-Sep-2011 expiration, and occurred on 24-Aug-2011. This was the same expiration that was hit with bad data in other DTE trades.
3. 36 strategy variations had largest loss readings of 95% or greater:
1. Of these 36, 27 did not use a loss taking level (loss taking % = NA)
2. Of these 36, 18 used wing widths of 25 points
3. Of these 36, 18 used the DN structure
4. 34 strategy variations had largest losses that were 29% or smaller:
1. Of these 34, 32 used a loss taking level of 100%
2. Of these 34, 23 had short strike deltas of 8
3. Of these 34, 18 used the extra long put (EL) structure
4. Of these 34, 18 used a profit taking level of 50%
5. Of these 34, 16 used wing widths of 75 points
5. The top three smallest losses were associated with the following strategies:
1. EL (100:50), 75 point wings, 8 delta -> 16% loss  (win rate 80%)
2. DN (100:50), 75 point wings, 8 delta -> 17% loss  (win rate 82%)
3. DN (100:50), 50 point wings, 8 delta -> 18% loss  (win rate 82%)

(click to enlarge)

Profit Factor

The profit factor results are listed below:

1. Profit factors increase for variations not using a loss taking % (loss taking % = NA)
1. This trend is most pronounced at the short strike delta of 8
2. 216 strategy variations had profit factors of 2.0 or greater...this is a big increase again from the number of variations meeting this criteria lower DTE.
1. 100 of these 216 took profits at 50%
2. 85 of these 216 did not use a loss taking exit (loss taking % = NA)
3. 82 of these 216 used the standard IC structure (ST) (73 used the DN structure)
4. 78 of these 216 had short strike deltas of 8 (61 used 12 delta)
3. The top tree performers were:
1. DN (NA:50), 75 point wings, 12 delta -> profit factor of 3.1 (win rate 95%)
2. DN (NA:50), 50 point wings, 8 delta -> profit factor of 3.0 (win rate 95%)
3. EL (NA:50), 50 point wings, 8 delta -> profit factor of 3.0 (win rate 96%)

(click to enlarge)

Average DIT For Winning Trades

This metric was derived by averaging all of the DIT for all of the winning trades in a test run. The trends associated with this metric are consistent with the prior DTE test runs:

1. As short strike deltas increase, trade duration increases
2. As profit taking level increases, trade duration increases
3. The 50% profit taking level should have you out of your trade between 24 and 47 days for a 80 DTE IC, depending on short strike delta
4. The smallest winning trade DIT of 24 was associated with 8 delta short strikes, 25 point wings, profit taking at 50%, loss taking at 100%, and the EL structure.  The same configuration but using either the ST or DN structures yielded a an average DIT for winning trades of 27
5. There were 50 variations with winning trade DIT values less than 35:
1. All 50 took profits at 50%
2. 36 of these 50 used 8 delta short strikes
3. 19 of these 50 used the loss taking level of 100%

(click to enlarge)

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