tag:blogger.com,1999:blog-4057266811973629846.post90737054926567058..comments2024-07-02T09:17:38.734-04:00Comments on deagol's AAPL model: What is Apple Worth? Part 1: Regarding Large NumbersDaniel Tellohttp://www.blogger.com/profile/18356162909901960817noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-4057266811973629846.post-68138579596187692082012-09-18T14:09:50.986-04:302012-09-18T14:09:50.986-04:30Danie: Awesome explanation. I get it now. You are ...Danie: Awesome explanation. I get it now. You are a great teacher. Your reply made me go back to some topics and read up on things.<br /><br />Thanks very much.<br /><br />Is the Central Limit Theorem and LLN the same or different? Or at least CLT states more than LLN but it does include LLN fully..vkhttps://www.blogger.com/profile/03594605947782015350noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-91738016844277156202012-09-14T18:33:41.767-04:302012-09-14T18:33:41.767-04:30vik, apologies for the late reply.
In finance, wh...vik, apologies for the late reply.<br /><br />In finance, what's referred as <a href="http://en.wikipedia.org/wiki/Mean_reversion_(finance)" rel="nofollow">mean reversion</a> (e.g. how traders use MACDs and Bollinger Bands, also see Siegel's theories on very long term market returns) is quite different from the well defined statistical effect better known as <a href="http://en.wikipedia.org/wiki/Regression_toward_the_mean" rel="nofollow">regression toward the mean</a> (RTM). The finance usage implies negative serial correlations (i.e. extreme outcomes allegedly tend to be followed by <i>opposite extreme</i> outcomes which compensate each other to create a longer-term trend) while the statistical RTM applies under any kind of imperfect (|r|<1) correlation between the events (e.g. intra-subject test/re-test experimental designs), and its maximum effect happens when there is no correlation or complete independence.<br /><br />It so happens that independence is one of the requisites for the LLN to hold. The other condition for the LLN is that the individual events' probability remains constant, which is not required for the RTM concept.<br /><br />In the coin tossing case, since the tosses are independent (zero correlation) then you have 100% RTM. And since the coin odds remain constant, the LLN is also in play. So yes, in this case the equivalent RTM statement would be similar to that of the LLN.<br /><br />But RTM is practically of no use here since the outcome of a coin toss is completely random (nothing worth measuring unless we were trying to identify unfair coins) and yet assessing the outcome involves no error.<br /><br />RTM is important when repeated measurements are made on the same subject or unit of observation and it happens because values are observed with random error. The effect of RTM is compounded by categorizing subjects into groups based on their baseline measurements (i.e. when trying to discern outperformers from underperformers or improvement/decline of such extreme groups): the top performers on an initial measurement are more likely to do worse (as a group) on a subsequent measurement only due to chance (it's more likely that they had scored better than their true measurement due to luck). Similarly, the worse initial performers will tend to do better on a subsequent measurement. It works both ways: the top performers on the second measurement will have done worse initially, and the worst will have done better at first. It doesn't matter if the group as a whole improved or not, the effects are relative to the overall mean. This is the essence of RTM when there's positive correlation (same thing being measured repeatedly) and the expected real underlying values may change between measurements. The LLN can't be assumed at work in such conditions.<br /><br />Sorry for the long, and perhaps somewhat confusing explanation. And no, you're not pestering at all. Grasping these things is quite tricky and there's a lot of muddling and fallacy going on with all this within conventional wisdom. I'm really glad you asked.Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-59892352061963214542012-09-11T16:15:32.322-04:302012-09-11T16:15:32.322-04:30Daniel: OK, got it about the statelessness/lack of...Daniel: OK, got it about the statelessness/lack of memory and independence of these trials.<br /><br />But still Mean reversion and LLN seems to be saying the same thing, don't they? LLN says that over the long term propotion of head will tend towards 50%, the expected value. What will an equivalent mean reversion statement be?<br /><br />May be, that is what you are explaining in the last paragraph above and I am not catching on to the import of that ( though I understand what you are saying there )<br /><br />Sorry for pestering you on this.<br /><br />Thanks.vkhttps://www.blogger.com/profile/03594605947782015350noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-64109413377951287862012-09-09T22:58:41.538-04:302012-09-09T22:58:41.538-04:30vk, what you described is the typical example of a...vk, what you described is the typical example of a <a href="http://en.wikipedia.org/wiki/Gambler%27s_fallacy" rel="nofollow">Gambler's fallacy</a>. No matter how many heads you've gotten in the previous tosses, the next toss will still have a 50% chance of landing heads because these are <i>independent</i> trials, i.e. the coin knows nothing about the previous results.<br /><br />The LLN only says that in the long run, the proportion of heads will tend toward 50%, but this doesn't mean the next toss will try to compensate for previous imbalances. Your 4 heads in 5 tosses will get diluted to nearly nothing after the next 100 tosses, but definitely not on the 6th toss. Even if you get 100 heads in 100 tosses (an extremely unlikely event but not impossible), the 101st toss will still have a 50% chance of landing heads. But after 10 thousand tosses, the heads imbalance will most likely have disappeared, if the coin is fair of course.<br /><br />On the contrary, a persistent deviation in the long run from the 50% expected probability would suggest the next toss would more likely come up heads again (rather than the fallacious notion that tails must be more likely in order to compensate the prior heads preponderance) simply because it would suggest the coin was not fair to begin with.Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-11491260853031907592012-09-09T14:27:00.796-04:302012-09-09T14:27:00.796-04:30I am actually not clear what the essential differe...I am actually not clear what the essential differences are between LL and Mean Reversion. I agree they do not have anything to do with how the talking heads use it but I want to understand it better on its technical merits. If you toss a coin 5 times, if I get 4 heads and a tail, the mean reversion will tell me that the next tosses may tend to be tails since I got lucky in getting the 4 heads. Meaning, that is always possible by chance but that is not expected to continue in the future. That is mean reversion. LLN will say that over the long term my sample result will tend towards the expected value,namely in this case 50%. Did I get that right? They seem to be talking about pretty much the same thing, hence my confusion.vkhttps://www.blogger.com/profile/03594605947782015350noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-32736159490967100862012-08-19T11:13:34.910-04:302012-08-19T11:13:34.910-04:30Java jack...
The valuations of companies such as ...Java jack...<br /><br />The valuations of companies such as Porsche and BMW depended more on their profit dynamics than on market share.<br /><br />I will start worrying about AAPL when I see significant numbers of people abandoning the platform.<br /><br />With the platform being as sticky as it is, I don't foresee that happening any time soon. <br /><br />Although soon in this industry should be measured in a handful of quarters or less!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-2358428589247357512012-08-08T18:33:08.672-04:302012-08-08T18:33:08.672-04:30How are you feeling about the new Android share of...How are you feeling about the new Android share of the cellphone market moving forward? We all know the release of the iphone 5 will help but they've won a big part of the market recently. It worries me. Will tablet iPad sales begin to decline, too, as more people move to the Adroid OS?JavaJackhttps://www.blogger.com/profile/03263943961526019485noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-43199088393666394212012-08-03T23:09:21.971-04:302012-08-03T23:09:21.971-04:30Outstanding. When do we get Part II?Outstanding. When do we get Part II?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-82076933846951179152012-08-02T08:15:14.793-04:302012-08-02T08:15:14.793-04:30Good and interesting article. Always enjoy your p...Good and interesting article. Always enjoy your posts.<br /><br />Apple is an engineering company. And here is the difference between an engineer and a mathematician:<br /><br />Put a naked lady on one side of a room and both an engineer and mathematician on the other side. The engineer says "We'll walk half the distance to her, then stop. Then half the remaining distance, then stop. Then half the remaining again, etc" The mathematician says "Theoretically we'll never reach her". The engineer says "I'll get close enough".<br /><br />Its all about tolerances.Chrisnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-23703726646935521312012-07-26T02:09:53.557-04:302012-07-26T02:09:53.557-04:30A thorough explanation why the nonsense about the ...A thorough explanation why the nonsense about the "law" of great numbers is, well, nonsense. On the other hand almost everything said by the talking heads on Bloomberg (etc.) about Apple is without value and should be e posed as suce, just like you do.<br /><br />Lou MannheimAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-42507365258159528732012-07-25T07:17:44.651-04:302012-07-25T07:17:44.651-04:30Good article. I think I know where you are going ...Good article. I think I know where you are going with this. Let's see Part II!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-27522787180024080252012-07-24T20:56:24.377-04:302012-07-24T20:56:24.377-04:30Very nice.
Remember though that Apple and AAPL ar...Very nice.<br /><br />Remember though that Apple and AAPL are not coins being tossed.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-28434785927562546882012-07-24T18:53:51.044-04:302012-07-24T18:53:51.044-04:30"You wrote all this since the earning report...."You wrote all this since the earning report. Wow!"<br /><br />You must mean the April report, right? lolDaniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-66444257203137332912012-07-24T17:50:36.538-04:302012-07-24T17:50:36.538-04:30Brilliant thoughts, Daniel. You wrote all this sin...Brilliant thoughts, Daniel. You wrote all this since the earning report. Wow! I look forward to part 2.<br /><br />Jack T.JavaJackhttps://www.blogger.com/profile/03263943961526019485noreply@blogger.com