tag:blogger.com,1999:blog-7366878066073177705.post5049772925003688753..comments2021-04-15T09:22:12.549+01:00Comments on The Psy-Fi Blog: Regression to the Mean: Of Nazis and Investment Analysistimarrhttp://www.blogger.com/profile/06254802085744425067noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-7366878066073177705.post-60335557682437848952009-05-10T16:50:00.000+01:002009-05-10T16:50:00.000+01:00I'm afraid that you've chosen an unfortunate (way ...I'm afraid that you've chosen an unfortunate (way to present the coin-tossing) example when explaining "regression to the mean":<br /><br />``Think about tossing a coin ten times. On average you’ll get five heads and five tails. If last time you got ten heads next time you’re more likely to approach the average value or regress to the mean. It’s just probability.''<br /><br />Someone who is not familiar with the concept of independence (or, lack of correlation) of events may, very wrongly, conclude that if you get ten heads in a row then it is more likely to get tails in the next toss (or, e.g., to get more tails than heads in the next ten tosses). This of course cannot be the case if one assumes, as one typically does when evoking the coin-tossing example, that the coin is fair and the tosses are independent of each other. One non-technical way to explain it is that, when the eleventh coin toss happens, the coin ``doesn't know'' that ten heads in a row have just happened.<br /><br />What you say is correct: the expected number of heads-per-coin-toss is (always!) 0.5, and hence if the current average is 1-head-per-toss (ten heads in a row) then the expected average after twenty tosses (given that the first ten were all heads) is 0.75 = (10+10*0.5)/20: that is a ``reversion to mean'' from 1 to 0.75 (towards the mean of 0.5). And that, as you say, is ``just probability''.<br /><br />The way you formulated your (pithy) paragraph, however, might confuse some to believe that the ``magic of regression to the mean'' makes the coin more likely to yield tails after a long streak of heads. It doesn't, and it's not magic: indeed, it's ``just'' probability.<br /><br />Sorry for being picky about this, but it's worth appreciating the significant difference between the reversion to the mean in the coin tossing example and in the financial markets. While the coin doesn't know what happened to it in the previous ten tosses, the markets do know! In other words, the action of a market today is not independent of its action in the last ten days. It's not just probability that makes markets ``revert to the mean'': it's economics and psychology that do (too)! Another difference between investing and gambling in a casino. <br /><br />LostInMidlandsUnknownhttps://www.blogger.com/profile/03579536889235028961noreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-48217283917223639482009-04-07T20:14:00.000+01:002009-04-07T20:14:00.000+01:00Hi uchinadiGlad you enjoy it. All feedback is wel...Hi uchinadi<BR/><BR/>Glad you enjoy it. All feedback is welcome, it's difficult to know at what level to pitch posts. Don't want to be too technical nor too simple.<BR/><BR/>Your comments are all true. Perhaps shares are the least worst option a lot of the time. At least they ought to roughly track global growth (assuming we ever get any again!)<BR/><BR/>Even mutual funds with their excessive fees would normally provide better returns than cash in a bank account so we perhaps shouldn't be too critical of their misuse of stats. The best possible bad option, maybe?<BR/><BR/>timarrtimarrhttps://www.blogger.com/profile/06254802085744425067noreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-43503769449568894932009-04-06T17:18:00.000+01:002009-04-06T17:18:00.000+01:00Statistics are such a powerful tool, and as you me...Statistics are such a powerful tool, and as you mention, so misused! <BR/>The power of statistics are both in comparing similar sets, and in looking back at the progress of a series of values. It is distinctly not of any use in predicting where a series of values is likely to head, unless the series of values has been correctly profiled and characterized as being of a particular and known distribution.<BR/><BR/>In particular, the returns on the stock market, do not follow any such known distribution. That the mean over a century has been 12% will be a result of a multitude of inputs such as world population, industrial output, wars, global taxation, and a myriad others... There's no guarantee that the 21st century will exhibit the same pattern, and in fact, given that massive shifts in population and global trade patterns occurring in the last decade or two, chances are that it will be radically different.<BR/><BR/>As an aside, it is galling that finance professionals such as pension funds use backward looking statistics to project future returns, when a large percentage of their clients are not aware of the unsuitability of these statistic return expectations.<BR/><BR/>Yours, and very grateful for your outstanding blog!uchinadinoreply@blogger.com