In the lengthy thread regarding "whether markets decline faster than they rise," I did not see any mention of the put/call skew in S&P. It's well documented that, at least since 1987, during most "normal" periods, out-of-the-money puts are rather more expensive than out-of-the-money calls. There are several ways to explain this phenomenon:

1) Markets fall faster than they rise — and options traders know this. Otherwise, arbitraging this difference would be a meal for a lifetime.

2) Market participants perhaps anticipate that the realized volatility during a bear market is greater than a bull market. However, the problem with this analysis is one might expect to see an upward sloping volatility yield curve in out-of-the-money puts (during bull markets), and yet that does not usually occur based on my tests. Conversely, right now have a downward sloping yield curve in out of the money calls — which confirms the hypothesis that market participants anticipate slower price rises in the future. [Note to quants: I am not confusing delta, gamma and vega. I'm using options to predict terminal price at expiration.]

3) For most humans, fear of loss is a stronger emotion/motivator than the pleasure of gain (greed). This is well documented in the psychology and behavioral finance literature. Hence, ceterus paribus, capital market participants (who have a net long position) will, as a group, pull their rip cord faster — to flee from risk — than they will embrace the possibility of profit.

4) Lastly, my tests show that, in certain commodities, the exact opposite behavior to S&P occurs. For example, and perhaps due to the inelasticity of demand for grains, more-often-than-not one sees a call/put skew on the call side. Every so often, after a quiet "normal" period, one does indeed find an upward acceleration in price change correctly predicted by the put/call skew. Once suppy/demand is normalized, the (inevitable) ensuing bear market is much slower. These are generalizations of course, but I've found them to be true over the years. Bottom line: Market participants anticipate that stocks do indeed decline faster than they rise. The options market is priced for this outcome. And if it were not true, you could arbitrage the put/call skew.





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11 Comments so far

  1. Russell Sears on October 31, 2008 11:08 am

    To back this up with historical results, I tested the number of “surprise large moves”. A “surprise large move” was defined as prior 10 trading days no 30 point absolute close to close change of the S&P index occurred and that day a 30 pt absolute change occurred.
    In the last 10 years there were 37 such “surprise” moves 23 negative and 14 positive.

    The number of such moves occurring was fairly resilient to the size of points needed to incur a large move. For example a 20 point move gives fewer chances to be “surprised” but more days a surprise occurs. And there were 39 such surprises with 26 negative and 13 positive.

    With 5 days prior limit and 30 pts moves: 58 days of surprises and 36/22 neg./pos. surprises.

  2. D. K. Goodwin on October 31, 2008 2:48 pm

    For SPY since 1993, I provide below the root-mean-square of all the UP moves and of all the DOWN moves (in percent), and the statistical uncertainties of each number:

    rms of UPS rms of DOWNS
    daily 1.07+-0.06 1.13+-0.07
    weekly 2.08+-0.17 2.20+-0.25
    monthly 3.87+-0.44 4.34+-0.89
    quarterly 7.36+-1.64 5.86+-2.18
    yearly 20.25+-4.67 20.70+-9.6

    On what time scale is it claimed that down moves are systematically bigger than up moves? With 15 years of data, this non-partisan methodology can’t detect anything with statistical significance.

    Thank you to all of you who are getting out of your armchairs and getting your bait into the water.

  3. Rocky Humbert on October 31, 2008 5:08 pm

    To D.K. Goodwin:

    I believe it was Mark Twain who said: “Statistics don’t lie. It’s people who lie with statistics.”

    Are you perhaps making the presumption that the distribution of returns are normal or near-normal? I believe that the proposition is, whatever the distribution, leptokurtosis may be present — and that the far left tail is fatter than the far right tail.

    Mr. Sears’s example demonstrates this simply and eloquently….without the use of terminology favored mostly by electrical engineers ;) [It’s not the average. It’s the outliers!!!]

    Additionally, (although perhaps not statistically significant), it is striking that your daily and weekly “downs” are bigger than your daily and weekly “ups” … in a data sample that excluded the 1987 and 1989 crashes, but which included the largest bull market of the century!

    Despite my disagreement with your methodology I thank you for sharing your analysis with the Speclist.

  4. Russell Sears on October 31, 2008 5:31 pm

    within %
    42 day std Neg freq Pos freq
    0%-50% 490 560
    50%-100% 310 370
    100%-150% 211 199
    150%-200% 118 104
    200%-250% 42 45
    250%-300% 25 23
    300%-350% 7 5
    350%-400% 1 2
    >400% 5 0
    total 1209 1308
    std 0.94% 0.88%

    This frequency table for last 10 years S&P index gives just what you would expect if s&p slowly moves up, but quickly moves down. That is more positives days within narrow range of prior 42 trading days stdev. but more large negative days.

  5. George Parkanyi on October 31, 2008 6:00 pm

    The corollary to this question: Do put options for a given month expire faster than the call option? Cheers, GP

  6. Matt Johnson on October 31, 2008 6:13 pm

    I feel your third point answers the question. People don’t herd in bear runs, as they do in bull runs; they make the market erratic.

  7. D. K. Goodwin on November 1, 2008 9:34 am

    Rocky writes "…It’s people who lie with statistics.”… For the record, let the world know that D. K. Goodwin knows all of the major platitudes and market adages. D. K. Goodwin is not engaged in a pursuit so vulgar as electrical engineering. D. K. Goodwin is aware of outliers, and addressed them in previous posts, having shown that, over the history of SPY, the top N up moves over M days are about as large in magnitude as the top N down moves over M days.

  8. Steve on November 2, 2008 9:07 am

    I have heard people say “Figures lie and liars figure.”

    However the true quote according to Wikipedia is that Benjamin Disraeli first used this phrase and Mark Twain referenced it in one of his writings.

    “Lies, damned lies, and statistics” is part of a phrase attributed to Benjamin Disraeli and popularised in the United States by Mark Twain: “There are three kinds of lies: lies, damned lies, and statistics.” The statement refers to the persuasive power of numbers, the use of statistics to bolster weak arguments, and the tendency of people to disparage statistics that do not support their positions.

    Twain popularized the quote in his book “Chapters from my Autobiography.”


  9. Rocky Humbert on November 2, 2008 9:28 am

    Some corrections/addendums for the record:

    Mark Twain actually said that there are three kinds of lies: “Lies, Damned Lies, and Statistics.” Given D.K.’s self-professed familiarity with platitudes, I wanted to correct myself before he corrected me…especially since my academic training was in electrical engineering.

    And, while on the subject of platitudes:
    George: I believe you have stumbled upon a special case of Murphy’s Law. “Whatever can go wrong will go wrong, and at the worst possible time, in the worst possible way.” Hence, the answer to your question, over time, depends on your portfolio position! Cheers.

  10. Sam Humbert on November 2, 2008 7:22 pm

    Relatedly to your point 4) about upstrike-skews, NNT writes in his “Dynamic Hedging" (Wiley, 1997), pgs 250-251, "Veteran options traders can easily detect if a currency pair is biased. Typically, currencies that are 'parallel' exhibit a symmetrical behavior between sell-offs and rallies. They are the ones where the trading of the currency pair is dominated by flows based on the commercial exchange of products. On the other hand, the currencies that act as investment assets vis-a-vis one another are going to behave in an asymmetrical manner. The German mark against the Italian lira, the Spanish peseta, or the Greek drachma represents such behavior… Some assets like gold, and to a lesser extent the Swiss franc, the German mark, and the yen, will exhibit the mirror image of others, often when they behave exactly as the opposite of a regular asset. They become the recipient of capital flights away from regular investment currencies and equities."

  11. Adrian A. Dragulescu on November 4, 2008 1:29 pm

    I confirm the point made in 4) for electricity markets. Often power generators cannot respond fast enough to increases in demand, and because electricity is non storable, it leads to price spikes. These price spikes on high demand hours are one or even two order of magnitude higher than prices on low demand hours (say during the night hours). To protect against such extreme upward moves, implied volatility of OTM calls trade at a premium to the implied volatility of OTM puts.


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