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Variance risk premium is a difference between implied and realized volatility. You can think about it as an insurance price against an adverse move in the underlying - institutions (asset managers, hedge fund, pension funds, etc.) want to hedge a risk of a market crash, to that extent they buy option contracts (usually puts), creating a supply-demand imbalance that drive prices of those contracts up.
Those who are willing to accept that risk can act as a supplier and receive a premium for that. Theoretically those contracts are overpriced under no-arbitrage assumptions, so potentially traders could harvest this mispricing by selling any type of option structure, or even naked options.
Short straddle has an advantage of being delta neutral, therefore its value does not change with changes in the underlying (again theoretically for small changes, do not forget about gamma). That leaves us with volatility (short vega) and time (long theta) exposures. To profit from short straddles we need for IV at the moment of selling to be greater than volatility realized over the holding period, which is a definition of VRP.
I backtested 4 variants of selling ATM short straddles strategy on 50 largest single stocks and 6 indices options, spanning all major sectors:
* Single name, unhedged;
* Single name, delta-hedged daily;
* Index, undedged;
* Index, delta-hedged daily.
Contracts were held until expiration for all 4 variants. Here are the returns:
[Returns of 4 strategy variants, commisions and slippage costs applied](https://preview.redd.it/senoq2x40qmh1.png?width=2546&format=png&auto=webp&s=1cd2cf21374af85e15511db2efe342d97883cdff)
||CAGR|Max drawdown|Sharpe|Alpha (regressed)|Beta (regressed)|
|:-|:-|:-|:-|:-|:-|
|Single, unhedged|\-4.7%|\-174%|\-0.15|\-11.6%|0.65|
|Single, delta-hedge|\-0.2%|\-63%|\-0.02|\-3.53%|0.32|
|Index, unhedged|7.1%|\-110%|0.15|\-2.47%|0.91|
|Index, delta-hedge|8.5%|\-45%|0.39|5.98%|0.24|
Results are not great. Only indices made profit, all variants underperformed compared to SPY. Let's interpret the data:
* Single stocks massively underperformed to indices;
* Unhedged variants had significantly larger drawdowns and beta values compared to delta-hedged ones;
* Only delta-hedged index strategy had positive alpha (returns unexplained by overall market returns).
Let's start from the first point. Why did single stock trades have such a bad performance? My take is that VRP is an index phenomenon and either absent or significantly diminished in single stock options. And the reason is simple: institutions are not that afraid of a single stock crash because it's a risk that can be hedged away by diversification. Indices, by their nature, are already diversified, and only risk exposure they bear is market risk, which can only be hedged by negative delta exposure. Puts provide that and in addition they provide convex returns, therefore they are attractive as a hedging mechanism.
Why did unhedged variants lost to delta-hedged ones? Because unhedged short straddles are not a bet on volatility magnitude, but on terminal move in the underlying. Delta hedging allows trader to secure his returns day-by-day. And because VRP is on average positive, returns are too.
Here are some other interesting figures from this research:
[VRP distribution for single names and indices](https://preview.redd.it/hjmj4cjq4qmh1.png?width=2537&format=png&auto=webp&s=3b96d63a927d2ce9a1a59fa2884688b91a0c6600)
||Mean entry IV|Mean RV|Mean VRP|Median VRP|IV > RV|
|:-|:-|:-|:-|:-|:-|
|Single name|29.26|29.22|0.04|1.38|58.6%|
|Index|19.46|18.88|0.58|1.69|65.6%|
Both distributions show high left tails. The premium is positive most of the time and the tail eats into the mean, especially for single names.
[Apha and beta regressed to SPY](https://preview.redd.it/7r9cicwy5qmh1.png?width=2301&format=png&auto=webp&s=5112602863933aae6280b5f5d3e191a80fe97885)
Alpha increases and beta decreases with delta-hedging. We went over this topic above.
[Strategies returns by sector](https://preview.redd.it/bppzr1zj6qmh1.png?width=2520&format=png&auto=webp&s=2a507225f31ff141603073bc282cbebf28c1301a)
Single names actually made money in some sectors. Almost all indices made money. Small cap paid the most.
[Returns series for single names and indices](https://preview.redd.it/91ehg5td7qmh1.png?width=2546&format=png&auto=webp&s=2b1b91a91e5d05a2ee187a2cf90f7624ff7f8e0c)
Returns were fairly stable with expections during 2008, 2020 crises and 2022 bear market and other short periods of underperformance.
[Possible entry indicators](https://preview.redd.it/hhndmrey7qmh1.png?width=2571&format=png&auto=webp&s=80ff6e8cd912e4504a905867068730441221f4fa)
Entries with higher IVR (>60%) had increased returns. Could be viable entry signal.
[Returns correlation to SPY over time](https://preview.redd.it/y1vwd7rc8qmh1.png?width=2520&format=png&auto=webp&s=e1163f2ae64d222c02a5fd3a619e779a8dc0172f)
Mean returns correlation to SPY at 0.22, pushed down by a drop during 2022 bear market. It tends to spike during abnormal market conditions (Lehman, Volmageddon).
Before wrapping up i would like to point out some limitations of this backtest:
* Index sample size is small, only 877 trades compared to 7k+ single name ones. Related to this, index alpha value has t-score of +1.78. Statistical significance should be questioned;
* End-of-day fills and hedges only;
* Only ATM contracts. VRP could be more pronounced in OTM puts, but that would introduce skew dynamics, i wanted to zero in on VRP;
* Fixed one contract. No compounding or margin, which could have improved indices returns even futher.
This is not a trading strategy and not in any way a financial advice. My main goal with this post was to underline misconceptions someone might have when trading short straddles, namely: VRP mainly exists in index products and only delta hedged straddles should be used to harvest VRP, naked straddles are a bet on terminal move in the underlying, not volatility magnitude.
This research would not be possible without the options analytics/backtesting platform i have created. I'm releasing it in free beta for anyone interested in doing similar research for themselves. Link in bio.