tag:blogger.com,1999:blog-7366878066073177705.post7848137193646319539..comments2023-02-13T08:37:29.893+00:00Comments on The Psy-Fi Blog: Monte Carlo Simulation or Nuclear Busttimarrhttp://www.blogger.com/profile/06254802085744425067noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-7366878066073177705.post-55088534176792115512010-11-03T13:20:09.242+00:002010-11-03T13:20:09.242+00:00Valuation clearly matters, but market returns are ...Valuation clearly matters, but market returns are definitively not a normal distribution. <br /><br />Compared to a normal distribution, they appear to<br /><br />1) Exhibit high kurtosis - or 'fat tails'. Extreme events are much, much, more common than suggested by a standard distribution.<br />http://en.wikipedia.org/wiki/Kurtosis_risk<br /><br />2) Be heteroskedastic - or exhibit different standard deviations (or variance) at different times.<br />http://www.riskglossary.com/link/heteroskedasticity.htm<br /><br />3) Have negative skew - or the most extreme events are heavily biased to the downside, rather than the upside. Think 'black swans'.<br />http://www.riskmetrics.com/on_the_whiteboard/20090915<br /><br />All 3 of these factors are just a technical way of saying that markets are riskier and harder to predict than anyone thinks. Modelling markets as a normal distribution is a good way to crash your hedge fund.Unknownhttps://www.blogger.com/profile/11394409575254934751noreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-53163386207984215112010-11-02T20:08:10.014+00:002010-11-02T20:08:10.014+00:00Thanks for helping me out, Anonynous.
I will go t...Thanks for helping me out, Anonynous.<br /><br />I will go take a look at that link.<br /><br />RobRob Bennetthttp://arichlife.passionsaving.comnoreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-85583032286824724872010-11-01T15:24:06.042+00:002010-11-01T15:24:06.042+00:00Rob
take a look at John Hussman's work. i thi...Rob<br /><br />take a look at John Hussman's work. i think this is what you are getting at. he has discussed this issue in several of his weekly posts<br />http://www.hussmanfunds.com/wmc/wmc080630.htmAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-36329499527848643942010-10-31T18:42:00.998+00:002010-10-31T18:42:00.998+00:00I am not sure if I understand your comment exactly...<i>I am not sure if I understand your comment exactly</i><br /><br />I'll try to explain a bit more carefully what I am getting at, Jim.<br /><br />If the market were efficient, stocks would always be priced properly and the most likely return each year would be 6.5 percent real (the average long-term return). We would expect returns to fall in a normal distribution with 6.5 the mid-point.<br /><br />As Tim point out, returns do NOT fall in a normal distribution around 6.5.<br /><br />But we now know that the market is NOT efficient. Thus, it was always an unrealistic expectation to think that returns would fall in a normal distribution around 6.5 percent real. What returns should be doing is falling in a normal distribution around the mid-point return for each valuation level as predicted by a regression analysis of the historical data.<br /><br />For example, the most likely annualized 10-year return at the valuation level that applied in 1982 was 15 percent real. The most likely annualized 10-year return at the valuation level that applied in 2000 was a negative 1 percent real.<br /><br />It obviously is not realistic to expect returns to fall in a normal distribution when the valuation starting points differ by so much. What we should be checking is whether the deviations from the most likely 10-year return fall in a normal pattern or not.<br /><br />If the annualized 10-year return starting from 1982 was 13 percent real, that's 2 points less than the most likely number (as predicted by a valuations-based analysis). If the annualized 10-year return starting from 2000 was a positive 1 percent real, that's 2 points better than the most likely number (as predicted by a valuations-based analysis). Those two results (if they had been real and not hypotheticals that I am putting forward here only for discussion purposes) would balance each other out and you would have a normal distribution around the most likely valuation-adjusted result.<br /><br />I do not know whether results fall in a normal pattern or not. I do not know whether anyone has ever checked this. I think it would be a good thing for someone to check (I do not have the statistics skills to do the job). It would make sense to me for valuation-adjusted numbers to fall in a normal distribution whereas I am not able to see how non-valuation-adjusted returns could do so. <br /><br />I am not surprised that the non-valuation-adjusted returns do not fall in a normal distribution pattern. I do not think that we ever should have expected them to do so. I tend to think that the only reason why anyone ever saw that as a realistic possibility is that there was once a large number of people who believed in the Efficient Market Theory.<br /><br />Thanks for your recommendation of the "The Misbehavior of Markets" book. That one is on my list. I don't know whether it addresses this question or not. I hope that somewhere down the line I will be able to hook up with some statistics-minded person who will be able to check this out for me (and for any others interested in this particular aspect of the question). I personally find it a fascinating little puzzle.<br /><br />RobRob Bennetthttp://arichlife.passionsaving.comnoreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-60837612789085554862010-10-31T13:16:13.885+00:002010-10-31T13:16:13.885+00:00Rob,
I am not sure if I understand your comment e...Rob,<br /><br />I am not sure if I understand your comment exactly but may I suggest "The (Mis)behavior of Markets" by the late Benoit Mandelbrot. He lays out the case against such distributions fairly well.<br /><br />Best,<br />JimJimhttps://www.blogger.com/profile/08533222592229072717noreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-29502748572939861772010-10-30T22:32:11.765+01:002010-10-30T22:32:11.765+01:00Contrary to academic orthodoxy, the distribution o...<i>Contrary to academic orthodoxy, the distribution of U.S. stock market returns is far from normal.”</i><br /><br />My guess is that this conclusion is based on an analysis that does not adjust for valuations. It was probably either done before the Efficient Market Theory was discredited or it was done by someone who still has a lingering belief on the Efficient Market Theory.<br /><br />We should NOT expect returns to fall in a normal distribution now that we know that valuations affect long-term returns. But we SHOULD expect returns to fall in a normal distribution around the return predicted by a valuation-informed analysis.<br /><br />If you know of any research showing that returns do not fall in a normal distribution around the return predicted by a valuation-informed analysis, I would be grateful if you would let me know about it, Tim.<br /><br />RobRob Bennetthttp://arichlife.passionsaving.comnoreply@blogger.com