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Calculating Delta Across Options

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bginburg
Posts: 13
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(@bginburg)
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Thanks for all the guidance between the blog posts and forum - they have been instrumental tools in expanding my knowledge when trading puts!

One question in how to calculate delta across positions.  Currently, I target a 5 delta when selling puts.  If/when that delta declines ahead of expiry, I usually sell another option.  For example, when the first option drops from a 5 delta to 1 delta, I might sell another put at a 4 delta.  Is it fair to add the two contract deltas to be 5 delta total, or should it be averaged?

How does this work if selling puts across different multipliers but within the same underlier, like ES/MES?  Would it be Multiplier x Delta divided by total so [(50 x ES Delta) + (5 x MES Delta)]/55?

Trying to figure out how to measure my risk as with my portfolio, I probably will be trading a mix of ES/MES puts to get to target leverage.

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nobatmanjokes
Posts: 91
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Generally portfolio delta is multiplied by the relevant multiplier to calculate delta to adjust for scale and number of contracts. So a 5 delta option really says 0.05 and would be 5 delta SPX, 2.5 delta ES, 0.5 delta XSP and 0.25 delta MES. Multiply by the respective number of contracts as well then add.

I am not so strict on delta myself even if I do something generally like what you’re doing. Sometimes I’m below 5 and sometimes I’m around it.

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bginburg
(@bginburg)
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Posts: 13

@nobatmanjokes appreciate the feedback and that all definitely makes sense. I think where I struggle with portfolio delta is if I sell 2 puts at a 5 delta, my risk of those options finishing ITM hasn’t doubled despite the portfolio delta being twice that of the single contract.

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nobatmanjokes
(@nobatmanjokes)
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@bginburg that’s where you can “normalize” it back to the number of contracts you are trying to sell to get portfolio risk. With one type of contract it’s trivial just average the deltas. With mixes you have to scale. So one ES and and two MES is the same as “1.2 ES”.

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bginburg
(@bginburg)
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Posts: 13

@nobatmanjokes so the math before of [(50 x ES Delta) + (5 x MES Delta)] / 55 if selling one of each. It can then scale if I’m selling more of either of the contracts accordingly.

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earlyretirementnow.com
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You can certainly calculate the weighted average Delta with the formula you used. You could also compute the total Delta as 50xESdelta+5xMESdelta (i.e., without dividing by 50xES+5xMES) to gauge the total portfolio exposure, i.e., how many $ your portfolio will move with each ES or SPX point.

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nobatmanjokes
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Don’t forget that two portfolios with the same weighted average delta could behave quite differently. A portfolio with one ES put at 1 delta and one at 9 delta isn’t the same as a portfolio with 2x5 delta!

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bginburg
Posts: 13
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(@bginburg)
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Thanks both of you, this has been very helpful!  Agree completely on the how same weighted average delta isn't the same - trying to figure out an appropriate framework for me to estimate risk on my trades as I get closer to expiry and underlying price changes.

Real world examples - 

  • I'm using $6500 portfolio until I get a good handle, trading MES.  Figure its low risk and once I have my confidence, can put more money behind it
  • I typically sell 1 contract on Fridays for following week expiry, targeting a 5 delta.  I figure this starts me at 3.25x leverage
  • If market moves in my favor and as I approach expiry, I look to sell additional contracts.  If they don't, I hold with the one contract during the week
    • I stopped closing out the contract because I typically wait until the delta has fallen to .01 or .02 before selling another contract.  It also costs me $0.47 commissions to close it out, which eats into the returns.
  • Weekly example:
    • On 6/18, I sold a 4000 put at ~5 delta
    • On 6/22, that 4000 put had dropped to around a 2 delta, so I sold a 4030 put that was around a 2-3 delta
    • Today, both those put deltas were nominal (.001 and .002) so I sold a 4205 put around a 5 delta

I know I have more risk than I did with just the 4000 put, but to me, that is primarily driven by leverage (I am more like 9.8x levered vs. 3.25x since I am holding 3 contracts).  The risk I have as it relates to options moving ITM is much less and I would say is still around that 5% overall given the combined delta across all 3 contracts.  Is that a fair way to look at it or should I be thinking about it differently?

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