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Salil Mehta

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  • Statistics Topics [View instapost]
    Hi and thanks much Mr. Bear, How are you doing? I have stayed neutral in the markets since the end of February and am content with that! There will be a good short ahead though (eventually in bonds) if you can wait for the right signal.

    Meanwhile I have put together some interesting peer-reviewed research (liquidity risk for the Society of Actuaries, and Federal Reserve forecasting statistics for a leading academic review- this latter one is a topic you seem to be into), and a Kids' Statistics internet-playground, both of which have taken up considerable time recently.

    P.S.- BRK shares have now fallen back to below the S&P YTD, on market value basis. Where's that massive outperformance some wrong-headed critics/believers said is returning? ;)
    Jun 18 06:09 PM | Likes Like |Link to Comment
  • Statistics Topics [View instapost]
    Thanks much Market Map. Hope all is well with you, this busy summer!
    Jun 17 04:02 PM | Likes Like |Link to Comment
  • Being Good, Until One's Not [View article]
    Heavy abusive, denigrating, and negative comments are being deleted. They are not welcome.
    Apr 25 08:17 AM | Likes Like |Link to Comment
  • Forever Elusive Alpha [View article]
    So had some media also interested in my views on reconciling to the same article mentioned. My research varies from it, but not in ways that can be reconciled. And it adds more clarity on where we are today with the data.

    You might like also just some raw BRK data, which you can see on this link from the Statistical Ideas web portal:

    There are no statistics nor econometric analysis on the link immediately above. Just raw data, which one can see and download. Also note that the data is illustrated against the S&P per the initial pages of the annual report. If one were instead to use other equity benchmark indices, then for some periods of time they would show marginally different results. The bottom line is that BRK's performance has certainly been slipping from the lofty levels (by a statistically large amount that can not be explained by luck), and not just over the past five years, but for much of this millennium.

    It wouldn't be difficult to find that research as well.
    Apr 25 12:07 AM | Likes Like |Link to Comment
  • Being Good, Until One's Not [View article]
    Thanks much Albertasunwapta. I should just note that I am studying the probability related to ordinary investors, and integrated (though in the link on the article it states other comparisons to BRK are imprecise) the data and comments provided in BRK's report so that one can get better quantitative tools to assess these comments in the future. Feel free to see more on the underlying research on my blog

    This weekend it was one of the most read and shared research in the news.
    Apr 7 08:17 AM | Likes Like |Link to Comment
  • Being Good, Until One's Not [View article]
    Thanks much acm_acm. Not much time to write today as I am busy. Yes and they're not any better, when they're old and weak (as can be seen by a few of the zanies on this commenting thread).
    Apr 4 09:09 AM | Likes Like |Link to Comment
  • Being Good, Until One's Not [View article]
    If frogs just want to stay in suddenly boiling water, then they should.
    Apr 3 06:13 PM | Likes Like |Link to Comment
  • Being Good, Until One's Not [View article]
    Here is an extreme example, if we state flipping a coin and having it land on heads 100% of the time suggests skill, then 25% of people can still do this after 2 flips, however well less than 1/2% can do this after 50 flips. On the other hand, if we reduce the requirement to stating that landing on heads 54% of the time suggests skill, then still 25% of people can do this after 50 flips. Hence the requirements are more strict at the short-end of the experiment number of trials, and there could even be a blend of a slightly greater portion of people demonstrating skill at this short-end if the performance requirements are strengthened but not by enough.

    Now to just see an extreme illustration of how the requirement to demonstrate skill rises as the number of trials is reduced, see this illustration at the bottom of this link ( concerning a fair coin flip (so now completely unhinged from empirical stock market analysis). We see the probability of flipping this 50/50 coin consistently with one outcome (e.g., heads) is inversely proportional to the number of chained attempts (and greatly reduces well under 1/2% if done over 50 times). Notice the small jaggedness in the red line, due to the discrete approximation error with the number of coin flips.
    Apr 3 09:49 AM | Likes Like |Link to Comment
  • Being Good, Until One's Not [View article]
    Thanks much Sal's Dad. Buffett's overperformance was 38 of 48 years, or a 79% rate. No one has issues with that statement.

    It's corollary is: Buffett's underperformance was 10 of 48 years, or 21%. They force us to use these summary bullets, which is annoying for you as it is for me.

    A 21% underperformance rate is good. What's stated is that it is expected that he will experience continued underperformance rate at this same (good) 21% rate in the future.

    Your final comment piques my interest since I have studied Tufte's work and recommend it to my students as some, among many, best-practice examples. I find often that people either really find my charts great and clear, or they tend to have different stylistic tastes (which is generally more personal and not a reflection of the original quality). I do think that often people should still be able to learn the material, even if presented in a less preferable way for their own interests (while Tufte is great, no one person's style works best for everyone). I take feedback like this seriously through, so please let me know exactly what you liked or would see differently.

    Send it as a public response, or shoot me a personal e-mail.
    Apr 2 09:39 PM | Likes Like |Link to Comment
  • Being Good, Until One's Not [View article]
    The chart in the note shows that in the five years of 1995-1999, Buffet outperformed the S&P 500 4 of the 5 years. That's 80%. And 80% is just higher than his current 79% career average.

    The S&P is the benchmark, not momentum stocks. And rising markets (S&P 500) does not excuse underperformance (using 1995-1999, or 1984-1988 as examples). Any astute analyst should be able to connect the dots and not use Buffett's underperformance as a contra-indicator for relative performance. That's confounding and below the level expected of Seeking Alpha.

    If someone has issues with the S&P 500 (or some other sector of market) being frothy, then just sell the market short. Buffett goes down if the market crashes. So does your portfolio. Else this aggressive idea that people are magically owed good performance since the S&P 500 has had it good is getting tiring.
    Apr 2 08:14 PM | Likes Like |Link to Comment
  • Being Good, Until One's Not [View article]
    Thanks much Illuminati Investments. Not sure if you read one of my three summary bullets at the top of the note (in fact, why should any religious BRK investors ever consider anything other than dogmatic views):
    "Still, if statistical mean-reversion has anything to say about market patterns, then Buffett should experience continued underperformance at the same good rate in the future."
    Even Michael Jordan misses some shots at the hoop, just at a good (lower) rate, and every once in a small while can have a small negative streak. Doubt that when a lengthy career shows sign of fatigue, (A) whether you can pick that up, (B) if so, know what that can portend about the future, and (C) understand that there is a rich battery of probability and statistics modeling that can be explored on skill versus luck risk decomposition, which goes beyond any one senior investing legend and his cult of followers.
    Apr 2 07:34 PM | Likes Like |Link to Comment
  • Forever Elusive Alpha [View article]
    Anyone who liked this article is going to like this one:
    Apr 2 05:06 PM | Likes Like |Link to Comment
  • Being Good, Until One's Not [View article]
    So in terms of these coin tossing probabilities, we can give Buffett the benefit of the doubt and suggest his overall performance is similar to that from an unfair coin that lands on heads 79% of the time (reflecting the ratio of Buffett's 38 out of 48 years of outperformance). The probability of such an unfair coin landing on heads at least 38 times out of 48 flips is 57%. This is simply the combination of choosing n=38 from 48, multiplied by 79%^n, multiplied by (100%-79%)^(48-n). Then we sum this for n=38, to 48.

    So now the chance of seeing the 5 year "abberative" streak, of at least 4 losses in 5 years (either at the start or the conclusion of the 48-year pattern) would come to roughly 3%. This can be solved at least two general ways, using both a combinatorial mathematics estimate and another with a difference in means estimate (or a t-distribution test). The bottom line is that we can best explain the pattern with an unfair coin analogy, and even then it is rare to see such a dichotomous drop-off at one end to be simply a normal (non-significant) continuation of the other 43-trial period.

    There are also multiple other ways to look at this, and some are not so meaningful. What would lose statistical credibility, for example, is if one were to go above and beyond these paragraphs, and suggesting there is one pattern completely "flanked" by a different pattern.
    Apr 2 01:34 PM | Likes Like |Link to Comment
  • Being Good, Until One's Not [View article]
    Thanks much gunka for thinking through this, but your overall statement is unfortunate. The difference you refer to, by taking one good year from further back in time (2008) and appending it to the set. That also further makes my point that the performance has deteriorated recently.

    Still, mixing now over 6 years, as you suggest, you get a monthly overperformance of 0.3% (continuous rate). Less than the 0.8% that show outperformance by skill given the stock dispersion opportunities that were offered over this time! A haphazard investor is more likely to achieve a 0.3% outperformance over 6 years, then would have occured by a skilled investor.
    Apr 1 02:19 PM | 1 Like Like |Link to Comment
  • Being Good, Until One's Not [View article]
    Thanks much thenoffya for the good questions. Please read more of my blog writings and let me know what you think.

    I did mention in a couple of my blog notes that Buffett's overall outperformance is statistically significant, and he's of course in a small fraction of people in his decade of investment experience to get there since the odds stiffen over the long haul. To see this up close, see the levels at 47 years of the [“The Forever Elusive α” (Statistical Ideas)] chart on this link:

    For fun, and this deviates from the probabilistic pattern I show above that has deteriorated, here is the probability of getting at least 38 heads out of 48 flips:

    Unfair coin weighted to land on heads 25% of the time: 0% (0.0 even in bps)
    Fair coin weighted to land on heads 50% of the time: 0% (0.3 in bps to be precise)
    Unfair coin weighted to land on heads 2/3 of the time: 4%
    Unfair coin weighted to land on heads 75% of the time: 32%
    Apr 1 01:13 PM | Likes Like |Link to Comment