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Tuesday, December 12, 2017

Iron Condor Results Summary - Part 6 - IC Returns vs Initial Conditions Correlation

In the last article, we looked at correlations between Iron Condor returns and Iron Condor structures / trade management. Specifically, we started with the following list of areas to investigate:

  1. Correlation between Iron Condor strategy structure / management and result metrics
  2. Which result metrics most influence equity curve shape
  3. Correlation between result metrics
  4. Correlation between initial trade conditions and trade outcome based on strategy variation

In the last article we looked at items 1 and 2, and in this article we will look at items 3 and 4. We will start with the correlation between result metrics. For reviewing the correlation numbers, I'll use the following guidelines:

  • -0.5 to -1.0 or +0.5 to +1.0: strong correlation
  • -0.3 to -0.5 or +0.3 to + 0.5: moderate correlation
  • -0.1 to -0.3 or +0.1 to +0.3: weak correlation
  • -0.1 to +0.1: no correlation

While there is not 100% agreement on these levels across experts, these levels are fairly close to the common ranges listed in a number of statistics articles and books.


3. Correlation Between Result Metrics
The correlation matrices below show the results for all 3024 strategy variations, and also the subset of 1512 strategy variations that just contain profit targets and stops. There isn't any surprising information in these two matrices. The strong correlations in the tables are exactly where you would expect strong correlations to exist.

(click to enlarge)
(click to enlarge)


4. Correlation Between Initial Trade Conditions and Returns
This is the most interesting topic. I've analyzed if there is any relationship between the conditions at trade entry and the P&L for a trade. For initial conditions, I used the following indicator values from the day a trade was initiated:

  • IV Correlation: average implied volatility (IV) of the at the money (ATM) call and put
  • VIX Correlation: VIX
  • Skew 10: skew calculation based on 10 delta and 50 delta calls and puts (see note below)
  • Skew 25: skew calculation based on 25 delta and 50 delta calls and puts (see note below)
  • Skew 40: skew calculation based on 40 delta and 50 delta calls and puts (see note below)
  • Put Slope: indicator based on IV of 10 puts at various deltas (8, 12, 16, 20, 25, 30, ... , 50)
  • Slope(50-12): indicator based on slope of IVs at 12 delta and 50 delta
  • Slope(50-30): indicator based on slope of IVs at 30 delta and 50 delta
  • Credit: credit received per trade
  • Above/Below MA(50): whether the SPX is above/below it's MA(50) (-1, 0, +1)
  • Above/Below MA(200): whether the SPX is above/below it's MA(200) (-1, 0, +1)
  • ATR-50: indicator based on the number of ATRs the SPX is above/below it's MA(50)
  • ATR-200: indicator based on the number of ATRs the SPX is above/below it's MA(200)
Note: skew calculation based on Mixon paper: What Does Implied Volatility Skew Measure?

The 25th percentile, mean, and 75th percentile values for each of these indicators at 80 DTE is displayed in the table below. This will give you an idea of the distribution of the indicator values between January, 2007 and September, 2016.

(click to enlarge)

The correlation between returns and these indicators is shown in correlation tables below. Each table is for a specific DTE, short strike delta, wing width, stop loss, and profit target. Each table also includes the three Iron Condor starting structures (DN - delta neutral, EL - extra long put, and ST - standard balanced). Each row corresponds to a particular wing width, and each column corresponds to a particular stop loss level. My biggest take away was that there was either weak correlation or no correlation between indicator values at trade initiation and the final trade results.

The nine correlation tables below are for the 80 DTE Iron Condor variations with 8 delta short strikes. Across these tables, there were only 11 values of 0.2 / 20% or greater. 7 of these values occurred with the DN structure. 4 of these 11 values were associated with the VIX. Overall, though, any correlation of returns with initial conditions was weak for these trade variations.

(click to enlarge)

The nine correlation tables below are for the 80 DTE Iron Condor variations with 12 delta short strikes. Across these tables, there were only 41 values of 0.2 / 20% or greater. A much larger number than for the variations with 8 delta short strikes. 17 of these values occurred with the EL structure, 15 with the ST structure. 14 of these 41 values were associated with the Slope(50-12) indicator, and 10 with the Credit. Again, overall, any correlation of returns with initial conditions was weak for these trade variations.

(click to enlarge)

For the sake of completeness, the indicator values and correlations at 66 DTE are included below. There are six correlation tables for the 66 DTE Iron Condor variations with 12 delta short strikes. Across these tables, there were only 21 values of 0.2 / 20% or greater. 9 of these values occurred with the ST structure. 10 of these 21 values were associated with the Skew 40 indicator, and 6 with the ATR-50 indicator. Incidentally, the Skew 40 indicator also had one correlation value that hit 0.3. Regardless, any correlation of returns with initial conditions was also weak for these trade variations.

(click to enlarge)
(click to enlarge)

I think the big take away from this correlation analysis is that the market conditions at trade initiation, specifically indicator readings, have almost no ability to predict the final returns for these Iron Condors. So, don't overthink your entries.

I'm still reflecting on a quote from Euan Sinclair on the Talton Capital Management blog and how it relates to these results:
"always use the simplest method possible. Trading is a business. Problems are to be solved, not treated as sources of amusement or intellectual challenges. Brute force is often a perfectly acceptable technique."
I think the correlation results for these simple Iron Condors fall under the category of "brute force is often a perfectly acceptable technique." Decent results are possible with static profit targets and static stop loss levels. Spend your time managing your trades, not overthinking your entries.


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Wednesday, December 6, 2017

Iron Condor Results Summary - Part 5 - IC Structure vs Metrics Correlation

In the last article, posted way back in August, I looked at the Iron Condor structures that appeared to perform the best for each of the seven metrics I tracked. Recall that I tested 3024 different Iron Condor strategy variations over the period from January 2007 through September 2016. This testing generated more than 600,000 Iron Condor trades. The past articles can be found at:



Background
After writing those four articles, I was a bit disappointed with the results. In Part 3, I looked at three strategy variations that appeared to be some of the strongest based on the results in Part 1 and Part 2. These variations did not have the equity curves that I was anticipating. In Part 4, I ranked the 3024 different Iron Condor strategy variations by seven metrics in order to create a composite rank for each of variation. I then looked at the top scoring variation for each of the seven metrics, while also noting that variation's composite rank. These top performing strategy variations were a bit disappointing as well.

My next step was to identify four "families" of Iron Condor strategies that had some of the best composite rank scores. Those Iron Condor "families" included:

  • 80 DTE, 25 point wings, 8 delta short strikes
  • 80 DTE, 25 point wings, 12 delta short strikes
  • 80 DTE, 50 point wings, 16 delta short strikes
  • 66 DTE, 25 point wings, 12 delta short strikes

For these "families" I looked at all of the combinations of profit targets, and stop loss for each of the different starting structures (DN, EL, ST). I tweeted the results from this analysis starting September 16 and running through October 11. Quite a few of these variations looked promising.


Correlations
Since that time, I've been looking more closely at a number of features related to the result metrics, including:

  1. Correlation between Iron Condor strategy structure / management and result metrics
  2. Which result metrics most influence equity curve shape
  3. Correlation between result metrics
  4. Correlation between initial trade conditions and trade outcome based on strategy variation


1. Correlation Between Iron Condor Structure and Metrics
Let's take a quick look at the results from bullet one above, the correlation between Iron Condor strategy structure / management and result metrics. The correlation matrices below show the results for all 3024 strategy variations, and also the subset of 1512 strategy variations that just contain profit targets and stops.

(click to enlarge)
(click to enlarge)

A few points to note from the correlation matrices:

  • P&L / Trade vs DTE:
    The trades entered at higher DTE (i..e 80), generated greater returns per trade. You'd expect this, since we have more days of theta generation. Assuming we have two variations, with the only difference being DTE, you'd expect the higher DTE trade to generate a greater return since its DIT will typically be greater.

  • P&L / Trade vs Short Delta:
    Higher delta short strikes generate greater returns per trade than lower delta short strikes. For example, a variation with 20 delta short strikes will typically generate greater P&L / trade than a similar variation with 8 delta short strikes.

  • P&L / Trade vs Risk (stop loss):
  • Trades managed with larger risk / stops (i.e. 300% or NA) generated greater returns per trade than those managed with lower risk. With larger stops, you give the market more "room to run" inside the structure of the Iron Condor.

  • Win % vs Short Delta:
  • As the delta of the short strike decreases, Win % increases. For example, a variation with an 8 delta short strike would tend to have a higher win rate than a similar variation with a 12 delta short strike.

  • Win % vs Risk (stop loss):
  • The Win % is strongly correlated with Risk / stop level. Higher stop loss levels (i.e. 300% or NA) are associated with higher Win % numbers.

  • Win % vs Reward (profit target):
  • The Win % is negatively correlated with Reward / profit target. Variations with lower profit targets (i.e. 50%) have higher Win % numbers than variations with higher profit targets.

  • Largest Loss vs Wing Width:
  • This one is less obvious due to the way I measured Largest Loss. The larger the Wing Width, the smaller the Largest Loss. Fore example, a variation with a Wing Width of 75 would tend to have smaller losses (in terms of % of max risk) than a similar variation with 25 point wings.

  • Largest Loss vs Short Delta:
  • Again, this is less obvious due to the way I recorded Largest Loss. The larger the Short Delta, the larger the Largest Loss. A variation with short strikes at 8 delta would tend to have smaller losses (in terms of % of max risk) than a similar variation with short strikes at 20 delta.

  • Largest Loss vs Risk (stop loss):
  • The larger the Risk / stop loss, the larger the Largest Loss. For example, a variation with a 300% stop would tend to have larger losses than a similar variation with a 100% stop loss.

  • P&L / Day vs Short Delta:
  • The smaller the short strike delta, the smaller the P&L per Day. For example, a variation with short deltas at 8 would then to generate less profit per day than a similar variation with shorts at 20 delta.

  • P&L / Day vs Reward (profit target):
  • The lower the Reward / profit target, the higher the P&L per Day. For example, a variation with a profit target of 50% would tend to generate more profit per day than a similar variation with a profit target of 75%.

I'm not sure there is anything too surprising in the above correlations. Most of us would have assumed that these relationships existed, but it's nice to quantify the correlations. Also note what did not show much of a correlation:

  • DTE: no significant correlation with Win%, Largest Loss, or P&L / Day
  • Wing Width: no significant correlation with P&L / Trade, Win %, or P&L / Day
  • Type: very minimal correlation between P&L / Day and the ST initial starting structure
  • Risk (stop loss): minimal correlation between P&L / Day and stop loss level, with a larger stop generating slightly more P&L / day
  • Reward (profit target): no significant correlation with P&L / Trade, or Largest Loss


2. Metrics Influencing Equity Curve Shape
Now let's move on to bullet 2 in the list above...the result metrics that most influence equity curve shape. This again shouldn't be a big surprise. A variation with a high Win % and low Largest Loss will have the smoothest equity curve. A variation with a low Win % will be more "jagged", with the size of the drops being related to the Largest Loss number.

Let's now find some examples of variations with smooth equity curves. We need variations with a high Win% and low Largest Loss number.

A high Win % is correlated with low deltas, high risk / stops, and low reward / profit targets. An example would be an Iron Condor with 8 delta shorts, a stop at 300% or NA, and a profit target of 50%.

A small Largest Loss number is correlated with large wing widths, low deltas, and low risk / stops. The last one is at odds with our Win % requirements. An example of a variation that meets this requirement would be an Iron Condor with 75 point wings, 8 delta shorts, and a stop at 100%.

For the smoothest equity curve, we should be looking at Iron Condors with 50 to 75 point wings, 8 to 12 delta shorts, stops in the 200% to 300% range, and a profit target of 50%.

We'll look at bullets three, and possibly four, in the next article. Also, my plan is to try to close out this Iron Condor series by the end of the year, and move on to other analysis...if all goes well.


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Sunday, October 29, 2017

Broken Wing Butterfly Price and Volatility - CDN

In the last two posts (RTT and 60/40/20), we looked at how implied volatility (IV) and price of the option strikes in two broken wing butterfly (BWB) strategies changed with time. In this post, we'll look at another BWB strategy, the centered delta neutral (CDN) BWB. In this strategy, the short put options are at-the-money (ATM), the lower long is at least 100 points below the market, and the upper long is positioned to create a delta neutral structure. An SPX January 2018 expiration CDN is modeled below.

(click to enlarge)

As in the last two articles, we'll use five option chains in our analysis. The options chains we'll use expire on:
  • 03-Nov-2017 (7 DTE)
  • 10-Nov-2017 (14 DTE)
  • 17-Nov-2017 (20 DTE)
  • 15-Dec-2017 (48 DTE)
  • 19-Jan-2018 (83 DTE)
In the chart below, these five SPX options chains are plotted in terms of IV. In addition, the three strikes of our CDN along with the current market are marked with vertical lines.

(click to enlarge)

If the market conditions don't change, what can we expect? As time progresses in this trade, we expect the IV of the lower long ("Long 1" - blue vertical line) to increase from approximately 12.5% to 16+%. Notice how the different expirations move up the blue vertical line ("Long 1") as DTE decrease. The center strike ("Short" - red vertical line), behaves differently, with the IV dropping from approximately 9% to about 6%. The IV of the upper long ("Long 2") behaves similar to "Long 1" and increases from approximately 8% to about 12%.

So what happens with the price of these put options as DTE decrease? They all lose value with time...not a surprise! The options at-the-money (ATM) lose the most...again, not a surprise. The upper longs in-the-money (ITM) lose the least. Similar to the IV chart above, the strikes of our CDN along with the current market price are marked with vertical lines.

(click to enlarge)

As we did with the last two BWB strategies, we'll use the Black-Scholes model to simulate how the prices of our CDN strikes change with DTE. For a given strike, we use the actual IVs from our options chains as inputs to the Black-Scholes model.

For the lower long strike of our CDN, the 2470 strike, we have IVs at 7 DTE, 14 DTE, 20 DTE, 48 DTE, and 83 DTE. At 83 DTE the IV of the 2470 strike is 12.6%, and at 7 DTE the IV of the 2470 strike is 16.1%. The chart below shows how the price of the 2470 strike decays with variable IV (changing from 12.6% to 16.1%), with fixed IV of 12.6%, and with fixed IV of 16.1%. The variable IV (purple line) is closer to how this option price will actually decay.

(click to enlarge)

The theoretical decay of the center short strike is shown in the chart below.

(click to enlarge)

Finally, the theoretical decay of the upper long strike is shown in the next chart.

(click to enlarge)

In ThinkOrSwim (TOS), using four 20 day steps, we can see how the price of the CDN changes with time. This is shown in the image below. We can see that if the market did not move, and if the IV stayed constant, we would expect the price to increase to expiration.

(click to enlarge)

Using the theoretical Black-Scholes option prices from the analysis above, we can model the CDN price by DTE. Assuming the market and IV remain constant, the Black-Scholes model shows the CDN price change by DTE in the chart below.

(click to enlarge)

Neither the TOS Bjerksund-Stensland model nor the Black-Scholes model reflect what will actually happen with this trade, even if both the SPX and IV remained constant. These models do provide a view of the general trend of price change with DTE, which can be useful when evaluating your actual trades.

This is all for now for BWB, but in the future we'll look more at how initial conditions impact the outcome of these trades.


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