1. Skew distorts hedge ratios

   Imagine a $100 stock that has a $7.50 0DTE straddle on earnings day

   • The balanced case: stock is 50/50 to move up or down $7.50
   • The skewed case: stock is 75% to go up $5, 25% to go down $15

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2. A straddle (ie MAD) understates risk in the presence of skew

If the straddle or MAD is $7.50, then as we established earlier that maps to a volatility of 9.375%.

Balanced case

The stock dropping $15 is impossible (we set up a binary). The $10 put is worthless.

Now relax the binary. The balanced stock dropping $15 is a 1.6 standard deviation move.

[The z-score: -15%/9.375% = -1.6]

The probability of that is 5.5%

![Untitled](<https://prod-files-secure.s3.us-west-2.amazonaws.com/0cf10c00-9599-48d1-b309-4bb16acbc805/243fc0c3-d3cf-4744-a3b7-ee2acea34300/Untitled.png>)

The 90-strike put has some value now. Plugging into an [option calculator](<https://www.optionseducation.org/toolsoptionquotes/optionscalculator>) with 1 day to expiry and 148% annualized vol I get a value of **$.29**

**Skewed case**

In the skewed case, remember we can’t see the skew. We still just see the $7.50 straddle and if we use the vol implied from that we will think the option is worth $.29.

But we stipulated that the hidden binary distribution has a 25% chance of the stock dropping to $85 giving that put a true value of **$1.25** (25% x $5)

This is concerning even if you don’t trade options but use the straddles to imply a standard deviation, perhaps for vol-weighted position sizing.

For the same straddle value the balanced stock with the lognormal distribution (remember we relaxed the binary condition) had a 5.5% chance of dropping $15 but the binary skewed stock had a 25% chance.

***But both stocks had the same straddle price!***