Intuition of the Vol Smile

[Magic]

@TheBigShort , were you able to internalize this discussion and come away with a deeper understanding of skew and its implications by now?

I was doing some thinking today and I still don't have a complete intuitive grasp on the smile.

Take the following scenario: I have $28,714 (SPY @ 287.14 as I'm writing) and want to deploy it in a combination of short vol / gamma some passive equity exposure. Intend to hedge option deltas. Looking at the Jun '21 expiration.

Option 1: I short a 30 delta PUT, go long 40 shares and hold the rest in cash (LIBOR @ 2.7% and usually derivative embedded interest is south of that so using 2.5% yield for that portion).

Option 1 cash flows will be as follows:

($11,485.60 SPY * 1.81% Div yield * 73 days)
($375 credit for the short put)
(Div coming out of the shares makes -$31.18 drag on Put PnL 1.81% * 30 shares * 73 days)
($17,228.40 CASH * 2.5% yield * 73 days)
(Unknown return of 70 deltas equity exposure over the period)
----
Returns = $471.54 + 70 deltas

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Option 2: I short a 30 delta CALL, go long 100 shares SPY.

Option 2 cash flows will be as follows:

($28,714 SPY * 1.81% Div yield * 73 days)
($257 credit for the short call)
(Div coming out of shares boosts Call PnL +$31.18)
(Unknown return of 70 deltas equity exposure over the period)
----
Returns = $392.12 + 70 deltas

Basically, the additional PnL from writing the PUT comes from the higher IV because of skew. And this isn't free money or it would be arbed away. We're essentially saying the extra $79.42 from the PUT option is an approximation of the increased hedging costs / risk that is likely to occur because we tend to realize more volatility on down-side movements vs. market appreciation.

Is the above an accurate assessment?

Thanks,
Magic

 

[TheBigShort]

Magic as in Magic Mike? Still waiting for MM #4 to come out!

You will realize most of the pnl where your max gamma is (assuming you are hedging)So if your max gamma is lower than spot and we realize more vol below spot then there should be a higher IV. Hence the reason for the smile.

I think (and I am not to sure, hopefully some of the guys can join in), you can lock in the skew buy trading a ratio spread. So if SPY realized skew is 3 and the implied skew is 5. You can trade a 1 x N ratio spread vega nuetral and lock in a profit (assuming SPY realizes a skew of 3).

But overall the smile is justified. Sometimes it might be to steep or to flat, but it should be there.

As for your strategies I can not comment on that as I would never do those (not saying they are unreasonable, they are just not for my risk profile).
Your two strategies have different payoffs which is another reason why there PnLs are different.
I hope that helps!

 

[Magic]

Haven't heard of Magic Mike; I'll need to check it out!

Thanks for weighing in.. strategies are more a thought exercise for me to understand skew. In theory if hedging is perfect the PnL from the equity exposure should be identical unless I'm missing something. But choosing to sell under spot instead of over it results in gross profits. And skew is the cause of that.. but I am trying to get comfortable with why the market pays more for holding short vol under spot vs. over.

I've heard gamma refered to as the estimated cost / fair value of the hedging required. Short expiry ATM is the most difficult and labor intensive place to hedge so gamma is highest there. So I suppose holding under spot should come with a premium since we're more likely to realize higher there than equidistant strike above spot.

That's a good point with the ratio spreads. I'll need to think about that more. From other things I've read about skew and dispersion trading, skew has gotten very accurately priced in recent years. So maybe it shouldn't factor that much into my thoughts.. unless I had a method to forecast it against what's currently priced. Since it does exist maybe there is benefit in using it to add juice to something like a ratio.

If I have a forecast of dropping spot and I structure with something like a ratio in there, there should be additional gain from the lower strike IV's coming down as they near or surpass ATM all else being equal. Appreciate the food for thought.