# SPY Long Put 90 DTE 10% and 30% OTM Tail Hedging

From time to time clients authorize publication of their thesis, trade mechanics and backtest results. This is one such publication. I received compensation to perform this backtest. No discounts or “perks” were offered in return for authorization to publish.

The thesis behind this study starts with a tail-hedging publication from fellow quant researcher Corey Hoffstein.

**Sidebar**: the methodology in Corey’s research uses “a quadratic curve to log-moneyness and implied total variance for each quoted maturity.” That’s a fancy way of saying: “uses a model to generate theoretical pricing,” which is then backtested. The methodology here at spintwig is entirely empirical; no theoretical data is used. There are tradeoffs between each approach but they should yield results in the same ballpark.

Namely, Corey’s work explores hedges comprised of different volga (the rate of change of vega, also referred to as vomma) characteristics and goes on to suggest that a far OTM long put doesn’t have to become ITM for it to be a successful tail hedge. Rather, the repricing of risk alone can be used to successfully tail hedge.

In practice, the comparison is between buying 90 DTE 10% OTM puts, rolled at 60 DTE (lower volga, tends to require going ITM to effectively hedge) and buying 90 DTE 30% OTM puts, rolled at 60 DTE (higher volga, tends to benefit from repricing of risk to effectively hedge). Said another way, put options can serve as insurance based on damage *assessed* (position goes ITM) as well as damage *perceived* (position appreciates materially).

My client wanted to confirm whether long 90 DTE 30% OTM puts indeed offered a comparable or better hedge than 90 DTE 10% OTM for a lower or similar cost.

Over the span of a few months, our research eventually lead to us empirically replicating Corey’s work and performing SPY long put 90 DTE 10% and 30% OTM backtests.

**Sidebar 2:** because the two backtests were performed roughly 3 months apart and on different tickers (SPY for 30% OTM and SPX for 10% OTM), there won’t be an exact 1:1 comparison. However, since this study is about strategy performance during left-tail events, we can focus on the respective time periods and performance characteristics. Also, any dollar amounts associated with the 10% OTM strategy can be divided by 10 to get an approximate 1:1.

In this post we’ll take a look at the backtest results of opening one SPY long put 90 DTE 10% and 30% OTM position each month and rolling when DTE = 60.

There are 2 backtests in this study evaluating over 300 SPY long put 90 DTE 10% and 30% OTM trades.

Let’s dive in!

Contents

## Summary

Systematically opening one SPY long put 90 DTE 10% or 30% OTM position each month and rolling at 60 DTE is a left-tail hedging tactic.

The 30% OTM strategy offered a greater return during the Feb/March crash than the 10% OTM strategy.

## Methodology

### Strategy Details

#### 30% OTM

- Symbol: SPY
- Strategy: Long Put
- Days Till Expiration: 90 DTE +/- 17, closest to 90
- Start Date: 2007-01-03
- End Date: 2020-08-28
- Positions opened per trade: 1
- Entry Days: roll
- Entry Signal: N/A
- Timing 3:46pm ET
- Strike Short Leg: 30% OTM +/- 500 bps, closest to 30%
- Strike Long Leg: N/A
- Exit Logic: whichever occurs first
- Exit Profit Target: N/A
- Exit DTE: 60
- Exit Hold Days: N/A
- Exit Stop Loss: N/A
- Exit Signal: N/A

- Max Margin Utilization Target (short option strats only): N/A
- Max Drawdown Target: 99% | account value shall not go negative

#### 10% OTM

- Symbol: SPX
- Strategy: Long Put
- Days Till Expiration: 90 DTE +/- 17, closest to 90
- Start Date: 2007-01-03
- End Date: 2021-01-04
- Positions opened per trade: 1
- Entry Days: roll
- Entry Signal: N/A
- Timing 3:46pm ET
- Strike Short Leg: 10% OTM +/- 100 bps, closest to 10%
- Strike Long Leg: N/A
- Exit Logic: whichever occurs first
- Exit Profit Target: N/A
- Exit DTE: 60
- Exit Hold Days: N/A
- Exit Stop Loss: N/A
- Exit Signal: N/A

- Max Margin Utilization Target (short option strats only): N/A
- Max Drawdown Target: 99% | account value shall not go negative

### Assumptions

- Margin requirements are always satisfied
- Margin calls never occur
- Margin requirement for short CALL and PUT positions is 20% of notional
- Margin requirement for short STRADDLE and STRANGLE positions is 20% of the larger strike
- Margin requirement for short VERTICAL SPREAD positions is the difference between the strikes
- Early assignment never occurs

### Mechanics

- Prices are in USD
- Prices are nominal (not adjusted for inflation)
- Margin collateral is invested in 3mo US treasuries and earns interest daily
- Assignment P/L is calculated by closing the ITM position at 3:46pm ET the day of expiration / position exit
- Commission to open, close early, or expire ITM is 0.35 USD per contract
- Commission to expire worthless is 0.00 USD per contract
- Commission to open or close non-option positions, if applicable, is 0.00 USD
- Slippage is calculated according to the slippage table
- Starting capital for short option backtests is adjusted in $100 increments such that max margin utilization is between 80-100%, closest to 100%, of max margin utilization target.
- Starting capital for long option backtests is adjusted in $100 increments such that max drawdown is between 80-100%, closest to 100%, of max drawdown target.

## Results

### Starting Capital and Leverage

Long option strategies aren’t traded on margin (not to be confused with generating a margin loan to purchase an option). Thus, margin stats are all “N/A.”

Hindsight bias was used to realize the max drawdown target for each strategy. In this scenario, the max drawdown target was 99% per the “Strategy Details” section above.

Keep in mind that the 10% OTM strategy uses SPX, so any reference to an absolute value (i.e. a dollar amount) can be divided by 10 to approximate a 1:1 comparison against the SPY strategy.

So far we see that opening a 90 DTE position each month and rolling at 60DTE is ~ 5.5x more expensive when using 10% OTM positions vs 30% OTM positions.

Let’s see how they perform.

### Win Rate

There were roughly the same amount of trades in each strategy. However, the 10% OTM strategy experienced roughly twice as many wins.

A win is defined as selling a long put for a profit at 60DTE.

### Profit / Loss

The strategies themselves are net negative. Said another way, these hedges cost money to implement and maintain.

What’s interesting here is that the total P/L at the time of backtest end for the 30% OTM strategy is NOT -99%.

Keep in mind that each strategy’s starting capital was selected using hindsight bias in order to realize a max drawdown value of 99%.

Long option strategies that end at -99% typically decay in a relatively smooth fashion until the account reaches $0 or is otherwise is unable to support the purchase of another option contract. Something different happened with the 30% OTM strategy.

### Performance

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### Risk Management

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### Overall

The proprietary strategies demonstrated returns commensurate with the portfolio’s vomma exposure.

## Discussion

This research was an exploration in [left] tail hedging.

As we can see, the 30% OTM strategy offered a significantly improved hedge for roughly the same cost as the 10% OTM strategy.

As shown by the math in the risk management section above, the cost to implement a ~100% hedge isn’t terribly expensive.

Perhaps what’s more surprising is how little the 10% OTM long put protected the portfolio in Feb/March. Admittedly there is a bit of timing luck at play. Nevertheless, the original thesis appears to be supported: having a greater amount of long vomma can help tail hedge more effectively than being long a smaller amount of vomma.

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ANDREW DURRETT

February 27, 2021 @ 3:23 pm

It always feel wrong to me to compare the performance of bearish options plays to the long underlying. I’d rather see performance vs shorting the underlying, or buying the inverse etf if available.

The question this doesn’t answer is – If we want to hedge against SPY would it be better to do it directly or through long puts.

spintwig.com

February 28, 2021 @ 10:51 pm

Makes sense. I this scenario the client was seeking to overlay the hedge against long SPY to see the relative degree of inverse movement.

That is indeed a good question. It depends on what the hedge is allowing one accomplish that can’t be done without it.

Strider

March 3, 2021 @ 8:32 am

Hello! I’m the client who requested the study. Thanks for the comment Andrew. I think I’ll follow through on your suggestions and compare your ideas to continuous put buying. If I’m right and Spintwig can comment as well, shorting SPY during a crisis would require timing and skill (which I don’t possess!). The returns of shorting SPY continuously….well they’re negative but maybe there is something there.

IIRC hedge funds run a long short strategy where they position themselves net long stocks but short the index in a 1.3 to 1 ration (the 130/30 fund style). Leveraged inverse ETFs face a continuous headwind of losses due to volatility drag but perhaps they could be used as a hedge if the market has a 3 sigma or greater drop or greater.