# Distributional Edge vs Carry

The problem with buying "low" and selling "high"

I had a recent discussion with a younger trader. His strategy was to sell options when IV was in the 100th percentile.

What are some problems with this?

- That 100th percentile depends on your lookback window and the relevance of that window is I don’t know, arbitrary. The historical distribution of IV does not need to have any relevance with respect to qualitative information you have today. Exhibit A: GME.
- Any day when vol goes up after a 100th percentile IV day is just another 100th percentile IV day. The next day given, that you just hit 100th percentile yesterday, just doesn’t care that yesterday was a “top” compared to the days that preceded it.
- But the biggest issue here is that selling a “high” number that you know will go down looks like distributional edge. What goes up must come down right?

**High <> expensive**

If something is high and you expect it to go down, there must be a countervailing force which drives the price being “high”. That’s the carry. We don’t want to sell things that are just “high”. We want to sell expensive.

So if a price is “high” we must ask: *“Is it high enough relative to the carry?”*

Let’s examine this idea in a few contexts.

**Volatility**

If you sell vol at 150% and that implies a $50 straddle, it won’t matter if vol goes down to 25% if the stock gaps down $75. This is well understood already. Everyone knows vol comes down after earnings. But the p/l driver is the carry — the size of the earnings move.

**Real Estate**

Everyone and their grandma has seen the low cap rates in the Bay Area for the past decade. But the cap rates are so low because the carry is high…the annual appreciation. (One of my suspicions is that low cap rate properties are actually relatively underpriced. Any donkey can pull up mashvisor.com and see what screens as value. It takes more effort to find reliable drivers of growth to earn carry in “expensive” markets)

**Stocks**

Earnings are the carry and the P/E is the directional trade. Yes, a 100 P/E stock is going to eventually have a lower P/E. Yay, directional edge!

But what about the carry? Earnings growth.

If earnings grow 100% per year, in 3 years that stock is 12.5 P/E if the stock price doesn’t move. How about stocks that look like they have distributional edge if we buy them on the “low” end? We have a name for those — “value traps”. The tailwind of valuation is battling the headwind of earnings deterioration.

**Implied Parameters Do Not Vary As Widely As Reality**

Going back to the options example. if you sell “high” IV remember IV will rarely get higher than the range of RV because the market sets point spreads to imply mean reversion. If near term volatility explodes from 30% to 100% the market does not extrapolate this throughout the term structure.

So if you are short high IV expect negative carry. If a stock is typically 30% vol and realized shoots to 100% don’t expect IV to keep pace. You might find yourself shorting IV at the 100th percentile at say 85% vol while the stock moves 7% per day (about 112% annualized).

This dynamic holds when vol gets very low as well. Vet option traders expect to choke when they buy IV at-all-time lows. Wow, I can buy SPX weeklies for 7%! Too bad, it’s so quiet I can’t even tell if the market is open.

**Path**

The big question is the speed of convergence.

If you are short that $50 straddle at 150% vol and the next day the stock is down $25, but vol halves you can hedge your negative gamma, cover some short options and win. But if you gap down $75 you lose no matter what vol does.

Profitability depend on how the speed and shape of the implied parameters (IV, P/E, cap rate) cross the carry parameters (RV, earnings, rent).

**Conclusion: No Easy Trades**

If IV got so high as to exceed any point on a vol cone maybe then you’d have an easy trade. Your directional tailwind (IV will probably decline) and your carry can both win. Good luck finding that.

Keep in mind:

- Carry is the compensation for betting against mean reversion
- Carry is the cost of betting on mean reversion

Finally, a half-joke rule I’ve had with traders I’ve worked with:

When you do your vol sorts, you sell the second highest vol on the board. You always buy the highest. This is not advice.

If the directional tailwind vs carry frontier sounds familiar it’s because I’ve talked about it before. It’s my version of EMH…*The “No Easy Trades Principle”*