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Option Strategy: Long Gamma, Short Vega

Volatility is an asset class that trades under different regimes.  During very calm periods with more economic certainty and stability, volatility trades at very low levels.  When corporate earnings become uncertain, GDP growth is unknown, and jobless rates are high, volatility tends to shift and trade at higher levels.  This might seem like an overly simple concept, but it is important to keep in mind at all times when trading options.  The question becomes: are we in a high volatility regime, a medium volatility regime or a low volatility regime?

Volatility entered a higher regime mid-2007.  Are we leaving that regime?

Volatility entered a higher regime mid-2007. Are we leaving that regime?

Historical 30-day volatility has recently hit a low of below 12%.  A volatility of 12% means that we are experiencing daily moves on the S&P 500 of about .75%.  My belief is that this is much too low.  When top economists such as Krugman and Morgan Stanley’s Stephen Roach are placing 40% odds of a double dip global recession by the end of 2010, I find it improbable that we can expect daily moves of less than 1%.  In addition, the historical periods following the great depression’s market bottom and the Japanese asset bubble bottom were ripe with volatility.  For over 7 years after the market bottoms the returns remained turbulent.

Historically, volatility remains high after market bottoms from major market corrections

Historically, volatility remains high after market bottoms from major market corrections

The question is how to profit from the idea of volatility returning to the market when you are generally an option seller and want to take advantage of implied volatility being higher than realized volatility.  The key lies in the tenor of the options.

Options with longer lives have higher implied volatility

Options with longer lives have higher implied volatility

By examining the skew and term structure of implied volatility, you can see that options with longer maturities have higher implied volatilities than options that expire soon.  In addition, we still see a pretty strong skew, meaning that out of the money put options are trading for quite a bit higher implied volatility than at the money put options.  This structure provides a very good way to take advantage of a view that realized volatility will pick up soon while long term volatility will be lower than the ~24% that out of the money put options are trading at.

The strategy is simple:

  1. Purchase a 1 – 3 month put at-the-money which has a high gamma and low vega
  2. Sell a 1 year put 10% or further out of the money which exhibits a high negative vega and low gamma
  3. Delta hedge the overall position with the SPY ETF so that the delta is neutral at the end of each trading day

The purchased short-term put option will make money when the S&P 500 moves more than the expected 16% implied volatility that you purchased it at.  The written 1 year put option out of the money will make money as that long term implied volatility falls, but if you hold it to expiration it will make money as realized volatility comes in less than the 25% implied that you sold it at.  We could ignore the delta-hedging aspect of this position, but it would leave us with directional risk in the markets which we might want to avoid.

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23 Responses

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  1. J.Q. says

    I’d like to see when one is going to lose on this position, and how much (stress-test?). Having short vega doesn’t seem to be a great idea at low levels of implied. One who hates selling naked puts will hate this one too.

  2. SurlyTrader says

    The risks of the trade will depend on the maturity of the options and the ratio that you bought and sold them. At a high level your biggest risk is that implied volatility on the 1 year option increases dramatically. This would only be a mark to market risk though, because if you hold this 1 year written option to maturity and delta hedge it the entire time you will only pay the realized volatility over the term of the option. As long as realized volatility comes in below the 25% that you sold it at, you should have made money.

  3. R.P. says

    As an options newbie, I have found your articles very informative and thank you for taking the time to do this. I am assuming you must continue to roll your atm put if there is no definitive movement? I have a small postion in VXX but I’m concerned that it won’t move as fast as the market. I also have a otm put credit spread on SDS. Since the only greek I have a handle on is Delta, I am hestitant to implement the strategy above, but would be interested in your previous suggestion of itm puts on an index or indexes. Do you still stand by that idea?

  4. SurlyTrader says

    If your question is asking whether I would prefer to buy ITM puts then I would says yes, I still stand by that idea. Buying ITM puts allows you to buy the option with cheaper implied volatility because of the skew. Selling far out of the money puts is a better proposition than selling ATM puts. Sell high implied vol, buy low implied vol. The price is not nearly as important as the implied volatility.

  5. NGB says

    I am also very new in the options world, and according to what I have learned in this blog. Wouldn’t be the same to buy a near term VIX future and then sell a 1 year variance swap? Tha way I would buy low implied and sell high implied volatility, I would capture the same skew effect but with less transaction costs.

  6. SurlyTrader says

    You have the right idea, but I am not sure where you would get the variance swap exposure without being an institution with the ability to trade OTC instruments. Also, when you think of “transaction costs” be sure to understand that more complex instruments (variance swaps) are always created or hedged with more basic instruments. Therefore, when you enter into a variance swap with a bank, the bank replicates the variance swap with options. If the bank instead offloads the risk to a hedge fund, that hedge fund is replicating the swap with options. What I am saying is that the more complex products have the “transaction costs” embedded in their prices. Banks love to sell more complex products because there is a lack of transparency on how much you are paying in transaction costs.

    Bottom line, if you can, always try to implement your strategy with the most basic instruments.

  7. vJD says

    For the European readers: In Germany/Switzerland you can short a variance swap as a private investor: – a very profitable strategy lately!

    The German/Swiss Market is much more developed when it comes to derivatives (e.g. in Frankfurt there is the biggest and most modern Derivatives Exchange of the World, the EUREX).

  8. SurlyTrader says

    Thanks for the information. European private investors are definitely far ahead of the derivatives curve when it comes to instruments available for private investors. I think it might have a lot to do with the litigious nature of the United States… Plus, the financial institutions get around the rules by embedding the more exotic derivatives in insurance contracts ;-) For some reason, that is allowed…

  9. david nichols says

    What would happen if you rebalanced less frequently, such as once a week or even once per month?

  10. SurlyTrader says

    Many investment banks have spent quite a bit of money searching for the perfect re-hedging frequency. I have done my own studies and here is the bottom line: When the market is not trending, it is great to have very wide tolerances. When the market ends up going in a certain direction you either make a ton of money or lose a ton of money. To answer your question, it depends on how volatile the market is and how directional it is. If we had a crystal ball that told us that the market would trade in a very specific range then I would tell you to keep your delta hedging loose. If the market was trending in a certain direction and was very volatile then I would tell you to hedge twice a day. So goes the life of a delta hedger. This answer also depends very strongly on your gamma position, if you have a very large gamma then you would want to be very careful about how you let you tolerance stray.

  11. Uzair says

    @david nichols:

    If you’re long gamma, it serves you to have the market be more volatile and for you to rebalance every time the market moves (beyond some threshold that allows you to recover transaction costs). The caveat is that if you’re holding a vanilla option and the market veers far from the strike, the gamma of the option decreases and you make progressively less money — you want the market to move far from the strike, *but* return to the strike often so that your gamma exposure is maximised.

    If you’re short gamma, you want to rebalance as little as possible and hope the market reverts to the mean (where you’re delta-neutral).

    The story’s different for variance swaps, where you have constant gamma exposure across all spot levels.

  12. SurlyTrader says

    I very much agree with you, but you can structure the short option position to have a more consistent gamma by buying options at different strikes. That is the practical way that you would want to be long gamma and delta hedge the position…unless you really felt that the market was going to whipsaw around a certain level.

  13. scharfy says

    Been lurking for a bit on your blog. Nice work.

    The calendar structures at the time this was written had been daring you to try the above trades for quite some time. For the most part, they bleed you on the gamma, and the vega stays firm. Wasn’t fun. However, in this case, given what happened in the following weeks, and unless the trade was totally mismanaged or struck in an unfortunate manner, would have been a nice winner – at worst a scratch, and a big winner if you were inclined to let the deltas run.

    Your analysis was spot on, but given that you lean a touch towards selling – you may have applied that bias in the trade and cost yourself a bit… but, YES, the front month blew up in short order after this post, so gold star for you.

    I am very struck by your “regime” terminology – as I subscribe to a similar ideology, with different phraseology. I would always browbeat my partner(and myself) gotta be quick on the “tone” changes. you say regime, i say tone.

    Anyway, good stuff. You got a good shout out at VIX and more as I’m sure you know…..

  14. Mourad says

    I realize that this post is a bit old, but it seems as though we are now in a regime similar to the one when this article was originally posted. Couldn’t a similar trade be set up using VIX options? It seems like it could be especially good now with such a steep term structure in the VIX futures. Am I way off base?

  15. SurlyTrader says

    You could use vix options or vix futures to hedge your Vega position in the trade, but I cannot clearly think of a way that you can trade the gamma of the S&P 500. If you bought vix options and delta hedged with vix futures you would be trading the gamma of the VIX. If you are thinking about capturing the gap in the S&P 500 by capturing the gap in the VIX – then yes, they are similar, but not exactly the same. The S&P 500 can have volatility without seeing gaps out in the VIX, iimplied volatility or both. It is also the case that VIX futures are priced much more expensively out on the curve than some S&P 500 options, so capturing that gamma seems cheaper in the S&P option space.

  16. Daniel says

    Great strategy. Thanks for the information.

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