Left Tail Hedging with Volga

6 min read

Volga is a fancy-sounding but easy-to-grasp attribute of options. An option’s price is based, among other things, on implied volatility (IV). For S&P 500 options, this would be VIX. When VIX goes up, all other things held constant, so does an S&P 500’s option’s value. Volga describes the rate at which an option’s price changes with regard to IV. A low volga value may mean that VIX going from 20 to 21 yields a $0.10 increase in an option’s price while a high volga value may mean that the same change yields a $1.00 increase.

Farther out-of-the-money (OTM) positions tend to have greater amounts of volga relative to positions that are closer to the money. If you ever found yourself selling $.80 to $1.00 far OTM positions on SPX only to have the positions be 3x losers in short order despite still being comfortably OTM, this is in part due to volga exacerbating small upward VIX moves.

Can we amplify this effect and use it to our advantage? It turns out that 90 DTE 30% OTM puts tend to be a decent, simple vehicle to get elevated exposure to volga. Go long to get long volga, go short to get short volga. The trade would go something to the effect of: open a 90 DTE 30% OTM long SPX put, hold for 30 days so as to minimize the impacts of theta decay, then roll to a new position next month. When VIX inevitably spikes and a basic short theta strategy begins to suffer, the long puts with high volga explode in value and allow the portfolio to remain solvent.

I did a study on this exact trade and, with permission from the client, published the results. My interpretation of the results is that the trade is indeed effective at hedging rapid downward market moves. However, as with any “open a position once a month and roll” strategies, it’s subject to a material amount of timing luck.

Also, we now have the s1 signal – a daily trade signal for S&P 500 put options that has historically outperformed buy/hold. Historical s1 research suggests that it’s optimal to open most short-put positions on days when the s1 signal is “True.” However, I have not explored the reverse – opening long puts when the signal is “False.”

I’d like to revisit the original trade idea, mitigate the timing luck, and explore the performance of the s1 signal against a “market agnostic” daily-entry approach.

In this post we’ll take a look at the backtest results of opening one SPX long put 90 DTE position each trading day from Jan 3 2007 through Jan 31 2021, exiting after holding for 30 days, and see if there are any discernible trends. Backtest duration is limited due to availability of historical data from Cboe.

We will also explore the performance of the s1 signal. The s1 signal is a boolean (TRUE / FALSE) daily indicator for trading put options on the S&P 500 that has historically outperformed buy/hold with regard to both risk-adjusted and total return. s1 is based on data from Cboe and S&P Global.

The strategies will be compared against the following benchmark(s):

• SPY buy/hold (total return) | 100% allocation, no leverage
• A “market-agnostic” daily-entry long-put strategy

There are 3 backtests in this study evaluating over 7,400 SPX long put 90 DTE trades.

Let’s dive in!

Summary

A market-agnostic daily SPX long put 90 DTE 30% OTM strategy that’s rolled after holding for 30 days did a reasonable job mitigating sudden left-tail events.

The s1 signal yielded a material improvement over the “market-agnostic” strat, requiring 86% less capital to fund the same hedge over the same duration while maintaining comparable hedge effectiveness.

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Methodology

Strategy Details

• Symbol: SPX
• Strategy: Long Put
• Days Till Expiration: 90 DTE +/- 17, closest to 90
• Start Date: 2007-01-03
• End Date: 2022-01-31
• Positions opened per trade: 1
• Entry Days: daily; when s1 = True; when s1 = False
• Entry Signal: s1 signal
• Timing 3:46pm ET
• Strike Short Leg: N/A
• Strike Long Leg: 30% OTM +/- 500 bps, closest to 30%
• Exit Logic: whichever occurs first
  • Exit Profit Target: N/A
  • Exit DTE: N/A
  • Exit Hold Days: 30
  • 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
• Margin requirement for short CALENDAR SPREAD positions is 20% of the short option (short option expires after the long option)
• Margin requirement for long CALENDAR SPREAD positions is the net cost of the spread (short option expires before the long option)
• Early assignment never occurs
• There is ample liquidity at all times

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 1.32 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 $1000 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 $1000 increments such that max drawdown is between 80-100%, closest to 100%, of max drawdown target.
• For comprehensive details, visit the methodology page

Results

Starting Capital and Leverage

Hindsight bias was used to minimize starting capital [by maximizing max drawdown and normalizing to negative 99%] for each strategy. This allows a “best case” scenario for depicting the option strategy performance.

s1 = False outperformed daily entry and s1 = True with regard to capital needed to implement the hedge. In fact, the s1 = False strat required 86% less capital (!) to execute the same strategy.

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.”

Win Rate

s1 = False outperformed daily entry and s1 = True with regard to win rate.

s1 = False won 26% more trades vs daily entry.

Profit / Loss

The strategies themselves are net negative. This is expected for most hedges. Generally speaking, a trader pays a hedge cost, whether implied (opportunity cost) or explicit (actual cost), with the intent of generating results superior to (or different from) a benchmark that are not achievable without a hedge.

Long option strategies operated as a hedge 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.

What’s notable is that the total P/L at the conclusion of the backtest is NOT negative 99% for the s1 = False strat. In fact, over 70% of the capital allocated to the hedge is still available. Given that all the strats are normalized for a 99% max drawdown, this clearly isn’t a smooth P/L curve, which is a good for a hedge of this nature.

Performance

Risk Management

Overall

The high-volga strategies demonstrated returns commensurate with the portfolio’s volga exposure.

Discussion

The discussion section will be kept brief since the notable observations were mentioned in the respective sections above.

The daily SPX Long Put 90 DTE 30% OTM hold-for-30-days strategy provides a decent hedge against left tail events, roughly breaking even on lifetime cost to implement, around the Feb/March 2020 market volatility event. More succinctly, long volga can be an effective left-tail hedge.

Applying the s1 signal to the strategy, opening long put positions only when s1 = False, reduced the hedge cost by 86% while matching the magnitude (degree) of hedge when it’s needed most.

Financial market edges and arbitrage plays are often tiny and require large amounts of leverage to meaningfully monetize. To reduce the cost of a hedge by 5% or even 20% may not be compelling or significant enough to give it much thought or consideration.

“What is the variance between backtest results and actual results,” you might ask. I generally set expectations at +/- 20% as a worst-case scenario, mostly attributable to lack of intra-day and intra-minute data, early-assignment assumptions where applicable, and variance in trading fees over the backtest duration. If a backtest suggests CAGR is 10%, I would say real world is between 8-12%.

To have an 86% reduction in hedge cost while maintaining the same degree of effectiveness is something that is worth exploring in practice.

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