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Moderators of Daily Follow-through MR: Implied Volatility vs Historical Volatility

August 25, 2009

Before getting into this topic I recommend some background reading as I will be delving quickly into results:

This recent article by Bill Luby inspired me to take a look at the linkage between implied and historical volatility with relevance to short-term trading.  It contains links to previous articles on the topic can be found on the blog site VIX and More: http://vixandmore.blogspot.com/2009/08/gap-between-vix-and-realized-volatility.html

For another very good article with relevant background reading that helped further clarify my theories on the topic, Jared Woodward of Condor Options discusses how to create a trading system using historical vs implied volatility:  http://www.condoroptions.com/index.php/volatility/historical-and-implied-volatility-crossovers/

To summarize their results, when implied volatility (IV) is greater than historical volatility (HV) the market tends to outperform and vice versa. Note to readers: to avoid any confusion this post is not about “realized volatility” because i do not lag the values of the VIX to see how it forecasted historical volatility. All I have done is to subtract current 30-day  historical volatility from current implied volatility via the VIX  .  Here is a quick test of S&P500 returns under different IV-HV regimes going back 3000 bars (days). Again the standard  method for my testing uses a 1-year lookback to calculate percentiles :

  Implied Volatility vs Historical Volatility Regimes (IV minus HV)
  and next day SPY returns        
            % positive avg daily
  CAGR StDev Sharpe R-squared DVR  days return
Below Median

-(2.77%)

15.30%

-0.18

0.2

-0.04

50.70%

-0.01%

Above Median

3.37%

16.30%

0.21

0.28

0.06

54.30%

0.04%

75th Percentile

2.83%

13.00%

0.22

0.46

0.10

55.41%

0.06%

25th Percentile

-(1.32%)

12.20%

-0.11

0.003

0.000

51.43%

-0.01%

The conclusion is fairly obvious- returns the next day for the SPY (P&P500)  risk-adjusted are higher when implied volatility is higher than historical volatility. The significance of this division, is that half the time, returns are expected to be negative under low IV/HV regimes, and thus this variable is a significant indicator to pay attention to. Based on the finance research  the theory is that implied volatility should subsumes the information contained in historical volatility because it is forward-looking. However, implied volatility is not highly accurate and can be volatile, thus comparing it to historical volatility should provide  a smoother basis for judgement. The residual difference between IV and HV should be more accurate in explaining future returns than historic volatility or implied volatility. Since volatility is  expected to be predictably cyclic,  high residual vol should be followed by lower future vol and vice versa. But what about the impact on mean-reversion strategies? Does high IV vs HV forecast higher or lower returns to a mean-reversion strategy? Lets consider how daily follow-through MR performs under different IV-HV regimes. The same time period and methodology was used as the first test:

  Implied Volatility and Historical Volatility Regimes (IV minus HV) 
  and Daily Follow-Through MR returns on SPY (last 3000 bars)
            % positive avg daily
  CAGR StDev Sharpe R-squared DVR  days return
Baseline Daily FT MR 10.10% 22% 0.45 51% 0.2295 51% 0.05%
Below Median -(1.10%) 15.00% -0.075 11% -0.0082 49.90% 0.00%
Above Median 11.90% 16.30% 0.73 66% 0.4818 52.40% 0.10%
75th Percentile 9.00% 13.00% 0.687 90% 0.6183 54.40% 0.15%
25th Percentile 3.00% 12.20% 0.245 30% 0.074 51.70% 0.06%

Looking at this we see a huge difference in the performance of mean-reversion in different residual volatility regimes (IV-HV). Results are superior to looking at historical volatility in isolation. In fact, when the difference between IV and HV is above the median, daily follow through MR was actually higher returning on both an absolute and risk adjusted basis than the baseline strategy. Thus, you could make greater  returns and much less risk and be in the market roughly 50% of the time. That is a huge improvement. The best risk/reward was to trade daily follow-through when IV-HV was in the 75th percentile as it had the highest measure of DVR (R-squared of the equity curve times the sharpe ratio). In this case, your equity curve was straight as an arrow, and you made 90% of the baseline strategy returns in 25% of the time. Money was lost investing in daily follow-through when IV-HV was below the median. Furthermore, the equity curve was terrible with an R-squared of  11%. You would have been better off simply shorting the market in this scenario on an absolute and risk adjusted basis. There are of couse better strategies to take advantage of this, but i will save that for later.

Conclusion: IV-HV  is a very signficant moderator of mean-reversion returns and should be considered when deciding to continue using daily follow-through MR within certain regimes. The explanation for this phenomenon i will leave for   the volatility experts such as Condor Options, or Bill Luby to consider more thoroughly. My take is that IV-HV is a good forecast of future choppiness because it is essentially a reasonable forecast of future volatility. Choppiness is essential for mean-reversion strategies to be effective.

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18 Comments leave one →
  1. toptick permalink
    August 26, 2009 2:16 pm

    Outstanding. Thanks!

    I’m curious about a couple of numbers — perhaps I misinterpret. If the below-median MR CAGR is -1.10 and the above median is 11.90, shouldn’t the baseline be closer to the average of those two, like 5 instead of 10.10? (I.e., I’m thinking of the baseline as being composed of both the half of cases that are above and the half that are below median.)

    • david varadi permalink*
      August 26, 2009 2:57 pm

      actually it just means that all the returns occur on one side of the distribution—under the baseline scenario that is why the standard deviation is higher because half the time you chop around without making money. thanks for the kind words top

      dv

  2. August 26, 2009 8:55 pm

    David, you wrote “All I have done is to subtract current 30-day historical volatility from current implied volatility via the VIX.”

    What are you using for the current 30-day historical volatility?

    Again, this is a great freaking series of posts. I have written in several places that my MR strategies would work better during higher volatility, but this quantification of that is really really excellent. Even better is it makes trading a MR strategy less worrisome when trying to answer, “When will it stop working?” At least we now have part of the answer to that question.

    • david varadi permalink*
      August 26, 2009 11:09 pm

      for 30-day historical i simply take the standard deviation of 30 day returns and multiply that number by the square root of 252 and multiply that number by 100–to scale it up to the vix. thanks for the kind words wood…just trying to solve this crazy market puzzle one brick at a time.

  3. John permalink
    August 26, 2009 10:12 pm

    Brilliant work David! You are quickly becoming my favorite blog!!!

    • david varadi permalink*
      August 26, 2009 11:10 pm

      thanks john, i am just trying to add to all the great work out there that a lot of my peers have already done.
      dv

  4. kostas permalink
    August 28, 2009 12:05 am

    Hi DV, in your answering Woodshedder’s question I am not clear what the steps are–is the following the correct recipe?
    1. create an SP-500 price rate of change series with a period of 30 days
    2. Take the st. dev (period 1) of #1
    3. Multiply #2 by (252^.5)*100
    For 8/17 this value on the SPX would be around 15.07–am I right?

    Terrific post!
    K

  5. kostas permalink
    August 28, 2009 12:09 am

    Or, it dawned on me that the formula could be rather this one:
    1. create an SP-500 price rate of change series with a period of 1 days
    2. Take the st. dev (period 30) of #1
    3. Multiply #2 by (252^.5)*100
    Then only on 8/17 this value on the SPX would be around 15.07–am I right this time?
    K

    • david varadi permalink*
      August 28, 2009 12:37 am

      kostas, the standard deviation is of the 30 days worth of 1-day ROCs, so the return today, yesterday, previous day etc etc. That is then rescaled to annualized SD by multiplying by 252^.5 it is then grossed up by 100 to match the vix……..i haven’t checked but that value sounds about right. thanks for the kind words

      dv

      • kostas permalink
        August 28, 2009 9:42 am

        That’s what I thought, David (second alternative). I have played around with the numbers and there appear to be some interested and stronger results if one uses a 2-d ROC instead. Check it out!
        K

  6. Anon permalink
    August 28, 2009 9:48 am

    Kostas, try your original 30 day ROC, and look at it over a few years at a time.

    Here is one problem I am having though. If we go back 20 years or so on the SPX, the HV calculation doesn’t work as well because the SPX gets cheaper, while the HV calculation is still multiplied by 100. Maybe I am doing something wrong?

  7. toptick permalink
    August 28, 2009 11:17 am

    Wood, sounds like you might be using dollar changes instead of percent changes for input to stddev? Price level of SPY/SPX shouldn’t matter — historically, IV (measured by VIX) averages a little above the HV.

    I use stddev of log returns out of habit (at daily scale it doesn’t make much difference, but at larger scales – monthly, annual – return distributions should look log-normal). I’d be suspicious of improvements from using 2-day ROC, as that will be approximately the same as multiplying the 1-day ROC stddev by 1.44 (2^.5)

    DV, I thought I’d see an improvement by ranking the ratio (IV / HV) instead of the difference (IV – HV), but the difference seems to gives better statistical significance.

    Thanks to all contributors here!

  8. September 18, 2009 7:28 am

    Has anybody managed to replicate these results?

    I seem to come pretty close on the general MR over the past 3000 bars of SPY. However, the IV-HV filter makes things worse in my analysis.

    I am assuming that when comparing IV-HV versus “median” or “75th percentile”, this is the median and 75th percentile of the same 3000 bars we are analyzing, which introduces lookback bias – however, I wouldn’t be surprised if the distribution of IV-HV is relatively similar over entire market cycles, so perhaps the bias isn’t that great. Or are the percentiles taken from some other set of data?

    DV – do you have an Excel sheet of your study so we could compare?

  9. toptick permalink
    September 18, 2009 10:39 am

    JS,

    I understood the IV-HV ranks were taken over the trailing 250 days.

    Taking a different approach, I got results similar enough to support the thesis. I looked at it with finer granularity, and found that the positive returns to mean reversion are bimodal: the highest IV-HV ranks provided the best MR returns, but the lowest worked pretty well, too. It was the middle ranks that faired poorly. Dividing IV-HV into quartiles, for 1998-2009, I got cumulative arithmetic returns of

    1     54
    2    -55
    3     28
    4    114
    

    The 4th quartile returns are consistent through the test period (R^2 93), but not so much before.

  10. March 16, 2014 10:24 pm

    Thanks , I’ve just been searching for information about this
    subject for ages and yours is the best I’ve came
    upon so far. However, what concerning the conclusion?
    Are you positive concerning the supply?

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