Daily Break Even

TheBigShort

TheBigShort

Considering the formula for the daily break even as Iv/16 where 16 is Sqrt(252).

This tells us the the 1 day SD and it also tells us where our break even point is.
But the straddle price for a 1 day option is .79*SD move.

This would mean that our break even is not the SD but rather the mean? Can someone clarify this for me?

I looked at the actual break even formula under BS sqrt(2*gamma/theta) and the numbers coming out are much closer to .79*SD rather than the SD. Here is real time example.

SPX = 2824
SPX March22 Straddle = 18.50
IV = 13
Daily $ SD = 13/16 * 2824 = $22.95
Mean Move = $22.95*.79 = 18.15 =~ Straddle Px
Daily $ Break Even (using BS) = sqrt(2 * theta/gamma) = sqrt(7.8/.02) =~ 19.75
cboe.PNG

On a side note here is a statement from a Bloomberg Presentation.
vols.PNG

I thought both paths realize 16% volatility. In my head, scenario 1 we get (16 vol *5)/5 = 16.
In scenario 2, I get
(0*4 + 80)/5 = 16 vol.
 
For your first question: Why would the breakeven of a straddle be the implied 1SD move from the IV? The expiration breakeven for a straddle is purely determined by the price of the straddle. Say the stock price is 100 and straddle is 20. The expiration breakeven range for the short straddle would be (80,120). Any point prior to expiration would have a similar breakeven range.

For your second question:
Variance is the mean of the squares of daily returns (assuming the mean return is 0%). So in scenario 1 the vol is 0.01*16, and in scenario 2 it's 0.022*16.
 
oldmonk said:
Why would the breakeven of a straddle be the implied 1SD move from the IV?
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I have read this countless of times by reputable posters, it's even in Sinclairs book and Natenburgs (IV/16 = daily break even) which is why I am confused.

Here is ours truly @Martinghoul explaining it a few times.
"If IV is in %, your daily breakeven is (IV*S)/sqrt(252)."

"1) you have bought a call w/IV of X.
2) on a given day I you delta hedged, such that you bought some quantity at price P1I and sold at price P2I for a PNL of ZI; ZI is a measure of realised variance/volatility/etc that you've "locked in" for the day.
3) if ZI is equal to X*sqrt(T) (where T is time to expiry), congrats, you have broken even. That's why this X*sqrt(T) quantity is known as your "daily breakeven". If ZI is less than the daily breakeven, you didn't do so well on the day and vice versa.
4) Lather, rinse, repeat, until expiration
5) At the end your PNL is the sum total of all the ZIs over the course of the procedure. If that number is greater than the premium you paid, congrats! Otherwise, not so lucky."


oldmonk said:
Variance is the mean of the squares of daily returns (assuming the mean return is 0%). So in scenario 1 the vol is 0.01*16, and in scenario 2 it's 0.022*16.
More...
Thanks for the clarification
 
I thought you meant the breakeven of a straddle without any delta hedging. If you're continuously delta hedged, you'd break even as long as the IV stays below the IV you sold the straddle at. Discrete delta hedging would complicate things a bit, but I imagine that's where the notion of the 1SD move comes from.
 
Isn't daily breakeven is same as daily average move, which is same as straddle price?

Average move = Sigma * stock price/20.

In your example = 0.1316 * 2824 /20 = $18.58
 
oldmonk said:
If you're continuously delta hedged, you'd break even as long as the IV stays below the IV you sold the straddle at.
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This was what I was looking for. Thanks oldmonk.
srinir said:
Isn't daily breakeven is same as daily average move, which is same as straddle price?
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I believe they are different. Old Monk explained. Daily break even is roughly IV/16 assuming you are delta hedging. The straddle px is the terminal break even or the average move assuming no delta hedging.
 
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