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Do Black Swans Negate Option Premiums?

Volatility arbitrage generally refers to trading strategies that capture the spread between implied  volatility (forecasted by option prices) and realized volatility (what volatility actually ends up being).  The spread between these two volatilities can be captured by selling options (calls and puts) and delta-hedging the options by buying stock or futures contracts.  This strategy effectively neutralizes the portfolio’s exposure to movement in the underlying stock while leaving the option seller exposed to the volatility of the underlying.  If the volatility of the stock between the time that the option is sold and the time the option expires is higher than the implied volatility at the time that the option was sold, then the option seller loses.

If you are scratching your head in utter confusion, do not worry.  I will continue to delve into this topic with examples and pictures so that we can all  grasp the basics.  The general idea for the strategy is that options inherently trade at an implied volatility that is higher than realized volatility on average. Some academics (Nassim Taleb) believe that options trade at a higher implied volatility because Black-Scholes assumes a normal, bell shaped, distribution in stock returns.  We can all agree that stock returns are anything but normal after going through the extreme volatility of 2008.  In fact, during the 4th quarter of 2008 the S&P 500 had moves in excess of +/-5% during 25% of the trading days. If we assume that the S&P 500 has a long-term standard deviation of 20% on average, then a 5% daily move is in excess of 4 standard deviations.  In a nutshell, equity markets are fat-tailed, meaning that observations that are far away from the mean happen much more frequently than a normal distribution can account for.  Nassim Taleb would argue that these “Black Swan” events more than wipe out the small profits from selling options.


The number of daily returns larger than +/- 8% shows the Fat Tailed nature of S&P 500 Returns

The number of daily returns larger than +/- 8% shows the Fat Tailed nature of S&P 500 Returns

The truth is somewhere inbetween.  It is true that massive dislocations in the markets can wipe out many months or even years of gains from selling implied volatility, but on average selling volatility has been a winning strategy even after taking into account large losses from 2008 or even  20%+ crashes much like the 1987 Black Monday.  In fact, within his academic research study, Oleg Bondarenko found that it would take 1.3 October 1987 crashes every year for ATM put buyers to break even.


Until Recently, Implied Volatility has been significantly higher than Realized Volatility

Until Recently, Implied Volatility has been significantly higher than Realized Volatility

Since 1990, the average Gap between Implied and Realized volatility has been 4.2%

Since 1990, the Average Gap between1-Month Implied and Realized Volatility has been 4.2%

Nassim Taleb is right in suggesting that large outlier events occur in the markets more frequently than many people account for, but I think that he is wrong in asserting that put options are mispriced to the benefit of the option buyer.  Two decades of data with the 1 in 20 year event (2008) included, show that being an option seller was much more lucrative than being an option buyer.  The Standard & Poor’s Volatility Arbitrage index shows this fact even more clearly when looking at its historical results.  The index replicates a variance swap in which the investor sells implied volatility and purchases realized volatility.  Over the course of the 20 years, the index exhibited strong positive returns with very little standard deviation when ignoring the large draw down in 2008.


S&P Volatility Arbitrage Index - Steady upward slope until 2008

S&P Volatility Arbitrage Index - Steady upward slope until 2008

An interesting comparison is that between the S&P 500 total return index and the Volatility Arbitrage index.  Most people believe that being long the equity markets is best way to put your money to work over the long haul, but I disagree.  I would much rather sell option implied volatility rather than ride out the bucking bull and bear markets that are prolific in the S&P 500 stock returns.  Yeah, you might have a draw down of over 30% from selling options like you would have during 2008, but the vast majority of the time you are collecting hefty premiums with little volatility.  That sounds like a winning trade to me.


A leveraged vol arbitrage trade looks much more appealing than the S&P 500

A leveraged vol arbitrage trade looks much more appealing than the S&P 500

For those who are a little more fearful about selling options and delta hedging them outright, why not sell some call options on the stocks you do own as I previously suggested.  That way you are selling option implied volatility and reducing the standard deviation of your equity positions.

This information also gives you a better framework when using options as a tactical bet.  The next time you read an “investment” newsletter that tells you to buy options on such and such stock to take advantage of a huge potential move in the underlying, remind yourself that not only does that author need to get the timing and direction of the bet right, but he/she is fighting the law of averages by buying implied volatility.

Volatility selling on the S&P 500 can look even more attractive if you also hedge your dollar exposure into a strong foreign currency such as the Norwegian Kroner, Candian Dollar or Australian Dollar.

Be aware of your investments and if you get stuck in a rut, remember that researching total bankruptcy information can be the safest way to get back on your feet and can offer a second chance at rebuilding your finances. Always get the professional and trusting advice before you make your final investing decision



Why are Put Options So Expensive Oleg Bondarenko May 2004

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12 Responses

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  1. Steffen says

    “Oleg Bondarenko found that it would take 1.3 October 1987 crashes every year for ATM put buyers to break even.”

    Do you’ve got a source/link for this?

  2. SurlyTrader says

    The title of the research paper is “Why are Put Options So Expensive?” from May 2004. I have attached the pdf at the bottom of the post and you can find the statement in the introduction with supporting analysis throughout the piece.

  3. adrien Sassi says

    Good article.

    I think you rightly expose Taleb’s thinking on the following points:
    – Stock Market returns are characterized by Fat Tails, and thus flollow an underlying power law.
    – Hence, sigma is an overvalued indicator that cannot be trusted. It misses those extraordinary fat tails and the returns/loss they entail.

    Though, I do not fully agree to the second part of your analysis as I think you miss Taleb’s point.
    – A Black Swan Event is by definition unexpected. The best we can do is hedge against those events. When Taleb says one shall be long on options, it is only a matter of the capped loss they provide (even if the payoff may be lower than selling options). You may make less money than in shorting implied volatility, but you are hedged against a potential Black Swan. You’re saying Taleb being wrong does not make sense at that particular point, as you’re target is different.

    “Nassim Taleb is right in suggesting that large outlier events occur in the markets more frequently than many people account for, but I think that he is wrong in asserting that put options are mis-priced to the benefit of the option buyer.”
    Being long provides a good return and hedges you against risk by capping your loss. It is almost a head you lose, tail I win situation. That’s the only reason why Taleb says they are overpriced.

    But that point, I think you understand.
    – Then, you bring up Boudarengo’s work and I am starting to think you missed the Black Swan’s point.The Black swan is on its whole about Statistical regress fallacy: our belief that the structure of probability can be derived from data.Historical data, as the one you bring up to illustrate your point, as one problem. It’s historical.Time series analysis is irrelevant in the estimation of Black Swans.
    Does the fact that over the stock market’s lifespan the gap between realized and implied volatility was prone to option shorting mean that no event could come and erase all this gains? If you think so, prepare for thanksgiving, you are a sitting turkey victim of confirmation bias.
    Briefly, I agree with your analysis, but not with your conclusion.
    Options, if well used, are a cash machine. Because mainly markets are inefficient. I however do not concur with your criticism of Taleb’s “only go long on options” argument. Going long is the only viable way to hedge against Black Swans, because of capped losses.

  4. SurlyTrader says

    I am glad you enjoyed the article and that it invoked a strong response.

    Your points are valid, but I think you might be misinterpreting my conclusion. There *could* be an event that occurs in the markets some day in the future that no person could possibly conceive of. That event could wipe you out as an option seller and the bankruptcy bell will ring. Had you purchased put options you would be touted as the hero and have your face on Trader magazine instead of John Paulson’s. Nassim Taleb purchased his put options repeatedly, and in 2008 they finally paid off. The problem is that I bet that fund will be his first and last successful foray into money management.

    I guess I kind of liken it to locking oneself up in his/her house to protect against unknown mortal dangers – I could get hit by a bus, get in a car accident, fall off a building, or get eaten by a rabid dinosaur (Black Swan). Unfortunately, by locking myself up in the house I cannot make a living. I leave all of the profits to the people who seem to ignore the risk of imminent mortal danger.

    When you state “Options, if well used, are a cash machine” I think you agree with my sentiment. I think that where we slightly disagree is in our use of Taleb’s Black Swan. In my opinion, it’s a neat academic idea and there is truth in many of his assertions. From a practical sense, when playing the stock market game on a repeated basis, I think it is misleading.

  5. Adrien Sassi says

    I agree, and developped my answer on SA.


  6. George says

    I really enjoyed this article. I think it comes back to the fact that most of the time do those premiums collected off-set the one time volatility event? I would never consistently sell 15 Delta’s because eventually you could end up in the poor house with a volatility event.

  7. Ryo says

    Sweet, thanks for all the good info. For a newbie like me anything that goes into more detail is always helpful.

  8. lionel says

    Fat tail returns is a fact that is well-known and accepted in the academic community and even among quants long ago. Nassim Taleb only popularised the concept to laymen recently. I’m not sure why you keep mentioning him. It’s like talking about Einstein’s theory of relativity and attributing it to Carl Sagan.

  9. como emagrecer rapido says

    Have you ever thought about publishing an ebook or guest authoring
    on other blogs? I have a blog based upon on the same ideas you discuss and would love to have you
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  10. SurlyTrader says

    I think that the book I just published is a starting point. Any other ideas?

Continuing the Discussion

  1. The Value of Stock Replacement Strategies | SurlyTrader linked to this post on November 2, 2010

    […] First, let me say that I am tired of hearing and reading about fat tails.  I really liked Nassim Taleb’s Fooled By Randomness, but when Black Swan became a hit, the meme became overwhelming.  The book, along with the 2008 crash, gave everyone the full and utter knowledge about how fat tails happen often and how you would be stupid to believe otherwise.  When you talk about selling options, you often get harassed by those who know the truth.  I say bullocks and read through this link first if you want to argue about it. […]

  2. The Relationship Between Returns and Volatility | iBC_FN | iBankCoin Financial News linked to this post on February 13, 2013

    […] “Do returns dictate volatility or does volatility dictate returns?  It might seem like a silly question, but one that is worth spending a bit of time on.  If market returns actually followed normal distributions, then we might expect that there are as many up days as down days and upside deviation equals downside deviation.  Unfortunately, the distribution of returns is rather non-normal with a larger number of negative returns and a lot of small positive returns.  You can read about option pricing and equity return distributions at a popular old post, “Do Black Swans Negate Option Premiums“. […]

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