tag:blogger.com,1999:blog-9959776.comments2019-08-20T08:19:33.521+01:00James' Empty BlogJames Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.comBlogger11620125tag:blogger.com,1999:blog-9959776.post-71369001321276266002019-07-18T04:00:03.453+01:002019-07-18T04:00:03.453+01:00And what are the odds of that? And what are the odds of that? David B. Bensonhttps://www.blogger.com/profile/15914145623997712113noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-44199213945715398162019-07-14T13:26:48.725+01:002019-07-14T13:26:48.725+01:00Don't expect to see either in my lifetime. But...Don't expect to see either in my lifetime. But I don't expect brexit either :-)James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-18210344345594118432019-07-14T12:16:32.229+01:002019-07-14T12:16:32.229+01:00What are the odds that Scotland leaves the union b...What are the odds that Scotland leaves the union before Northern Ireland? David B. Bensonhttps://www.blogger.com/profile/15914145623997712113noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-9694478133956995762019-07-12T11:53:24.866+01:002019-07-12T11:53:24.866+01:00I can think of no sound worse than a french horn p...I can think of no sound worse than a french horn played badly. <br /><br />Even poorly.David B. Bensonhttps://www.blogger.com/profile/15914145623997712113noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-55175996271606894762019-07-08T11:30:21.438+01:002019-07-08T11:30:21.438+01:00"But I still feel fortunate for not being a b..."But I still feel fortunate for not being a bad french horn player."<br /><br />Not as fortunate as I feel for not being married to one :-)James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-68462292935397053612019-06-19T16:58:53.008+01:002019-06-19T16:58:53.008+01:00Conservative party members. That's about 150,...Conservative party members. That's about 150,000 people mostly of the same elderly white male demographic who, in the USA, voted overwhelmingly for Donald Trump. And who now, by their power to deselect Tory MPs, have the final say on Brexit.Andy Mitchellhttps://www.blogger.com/profile/14975141756383175819noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-82378624711062788002019-06-19T04:27:11.851+01:002019-06-19T04:27:11.851+01:00Best argument for dissolution of the union I have ...Best argument for dissolution of the union I have seen. Presume they dont mind a hard border with Scotland either.PhilScaddenhttps://www.blogger.com/profile/05937238628676275303noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-22966956760851257422019-06-18T19:17:28.162+01:002019-06-18T19:17:28.162+01:00they say two types of people voted Brexit in NI - ...they say two types of people voted Brexit in NI - thick unionists and clever republicans Tadaaahttps://www.blogger.com/profile/07736188830660481871noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-72106931543092071482019-06-14T11:50:34.752+01:002019-06-14T11:50:34.752+01:00And how many olympic/world champs medals?
I agree...And how many olympic/world champs medals?<br /><br />I agree the women are likely to get more in the next few years...James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-91598950471633876792019-06-14T11:47:38.116+01:002019-06-14T11:47:38.116+01:00Lovely post! The swim and cycle were fantastic fun...Lovely post! The swim and cycle were fantastic fun. The run, though, quite horrible. But James says the last 10km of a marathon is also horrible, so maybe it is painful even for those who are able to run...<br /><br />But also..<br /><br />ROFL! <br />It's a tough life for them wimmins creatures.<br />How much does it take for women to be ACTUALLY "better than the men"?<br /><br />In this event: <br />GBR wimmins - 1st,3rd,5th,7th,9th,15th / 28<br />GBR mans - 13th,15th,35th,44th / 47<br /><br />And yet it's still just a "probably better" :?<br />juleshttps://www.blogger.com/profile/02591920483149775255noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-17188813963465080532019-06-14T11:10:34.071+01:002019-06-14T11:10:34.071+01:00Magnificent effort! BravoMagnificent effort! Bravosylashttps://www.blogger.com/profile/10594421176931832170noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-79973232257808448842019-06-09T04:44:45.531+01:002019-06-09T04:44:45.531+01:00Without stating probabilities the chance of a rece...Without stating probabilities the chance of a recession has dramatically increased. David B. Bensonhttps://www.blogger.com/profile/15914145623997712113noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-79887210739740520622019-06-07T05:19:45.152+01:002019-06-07T05:19:45.152+01:00JA,
If at all possible, teach me further father, ...JA,<br /><br />If at all possible, teach me further father, in your follow on post.<br /><br />I think I have it coded but need a bit more time and/or help (I say time because I will have to modify two pieces of code, one is done (hopefully), the other takes the binary output from the 1st to generate the statistics (I thought it would run as is, but not so lucky for now).<br /><br />TIA :)Everett F Sargenthttps://www.blogger.com/profile/00201577558036010680noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-23964760487564836262019-06-06T19:24:59.728+01:002019-06-06T19:24:59.728+01:00We have a winner :-) Guessing as to Unknown's ...We have a winner :-) Guessing as to Unknown's identity, I'm not surprised....James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-1778670316845130832019-06-06T15:56:25.259+01:002019-06-06T15:56:25.259+01:00Well, that explains why maths grads can make so mu...Well, that explains why maths grads can make so much money playing with the Black-Scholes equation in the city. Those who can't, give financial advice.<br /><br />Multiple reinvestments are a random walk in log-space, since returns are multiplicative. So typical returns are (roughly) the logarithmic mean of the investment. But exp(0.5*[log(1+0.58) + log(1-0.48)]) ~ 0.9, so typical losses are 10% per reinvestment for strategy E. The probability distribution in log space is a Gaussian with a mean that decreases 10% with each reinvestment. So most investors will lose about 10% per year as they reinvest in E.<br /><br />Mean returns (i.e. expected returns) are just the usual arithmetic mean, so 'on average' investors gain 5% per reinvestment for strategy E.<br /><br />Basically the reason this happens is that the distribution of returns (not log returns) is extremely skewed, so most investors lose money, but a few lucky ones (in the tail) win big-time. <br /><br />Still better than a casino (since expected returns still positive) and people seem to like those...<br />Unknownhttps://www.blogger.com/profile/12207321632374481100noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-20974277772222975612019-06-06T14:08:49.519+01:002019-06-06T14:08:49.519+01:005 years was silly (I made that up myself to give a...5 years was silly (I made that up myself to give a concrete time frame). I have now changed it to 1 year in the post.<br /><br />Everett is just about there. Using logarithms helps (IMO). Will expand in longer post (but you can add comments in the meantime).<br />James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-87463048194925023592019-06-06T13:36:07.328+01:002019-06-06T13:36:07.328+01:00Yes binomial!
A 1D Ransom Walk even (likelihoods ...Yes binomial!<br /><br />A 1D Ransom Walk even (likelihoods all p=0.5). For large n (steps) the walk itself is Gaussian and via the LLN/CLT (I'm prettey sure it is the LLN more so than the CLT) it is exactly Gaussian.<br /><br />I almost have the code to do this now (need to track not just the walk but also the percentages for each heads or tails step in a separate co-array).<br /><br />I think the bottom line is this (asymptotically) ... <br /><br />A: 50% chance of either +11% or -7% (1.11,0.93, 1.11*0.93=1.0323, mean compounding)<br />B: 50% chance of either +17% or -10% (1.17*0.9=1.053)<br />C: 50% chance of either +25% or -16% (1.25*0.84=1.05)<br />D: 50% chance of either +37% or -27% (1.37*0.73=1.0001)<br />E: 50% chance of either +58% or -48%" (1.58*0.48=0.9216)<br /><br />B has the highest mean compounding rate of 1.053 (corresponding to a random walk ending where it starts (at zero). There are only odd or even steps (odd contains zero even contains either -1 or 1 (the steps closest to zero, which for large n is still Gaussian)).<br /><br />None of the five are a double or nothing propositions, so the remaining amounts can never truly go to zero (within the limits of machine precision).<br /><br />I would agree with WMC though, if I'm correct about the above, as 1.053 is only about 1%/year, it would be worth it if I were Philip J. Fry though (who paid for the 1000 year electricity bill though).Everett F Sargenthttps://www.blogger.com/profile/00201577558036010680noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-48563160346675023262019-06-06T12:21:33.788+01:002019-06-06T12:21:33.788+01:00>I bet it's got a name that I once knew.
B...>I bet it's got a name that I once knew.<br /><br />Binomial?crandleshttps://www.blogger.com/profile/15181530527401007161noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-29530127223020574882019-06-06T12:19:12.297+01:002019-06-06T12:19:12.297+01:00>"Yes that's true in expectation. What...>"Yes that's true in expectation. What about the distribution?"<br /><br />Yes, it is huge. With odd number of periods looks like 50% chance of loss. Even numbers more variable but your examples give 75% chance and 62.3% chances of loss. But so what? I said "you have to be a risk seeker to prefer E to D". A risk seeker is a thill seeker who likes the wild distribution. It doesn't look like a skewed distribution problem.<br /><br />>"no logical reason to have a different answer in 2019 vs 2024"<br />Whether you want your money out in 2024 or 2029 or 2034 or whether you might change your plans about when you want the money out, may well play a role in how you choose to invest. Other questions in the questionnaire deal with that. You are just considering repeating the period to get to longer periods, it may not quite work like that but it doesn't seem an unreasonable first approximation and trying to do better is going to add complexity to the question and make it more difficult to easily give an answer.crandleshttps://www.blogger.com/profile/15181530527401007161noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-31788706734452152092019-06-06T12:08:36.464+01:002019-06-06T12:08:36.464+01:00Ah, interesting. The distribution (which I did exp...Ah, interesting. The distribution (which I did experimentally for case E, but which I presume is the same but for scaling for other cases; does case A... hmmm, appears to have the same peak as E, I wasn't expecting that) is sparse and bunched off towards the origin. I bet it's got a name that I once knew.William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-75364071665716801472019-06-06T11:33:54.663+01:002019-06-06T11:33:54.663+01:00D'oh that last post is full of errors. I forgo...D'oh that last post is full of errors. I forgot to divide -249995 by 20 and as it is a 95 CI I should have written 2.5-97.5% ranges not 5-95. Hope these errors don't distract too much.crandleshttps://www.blogger.com/profile/15181530527401007161noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-40294922370899104932019-06-06T10:47:01.512+01:002019-06-06T10:47:01.512+01:00Yes that's true in expectation. What about the...Yes that's true in expectation. What about the distribution?<br /><br />My assumption is that the question must be considered to be time-invariant, there is no logical reason to have a different answer in 2019 vs 2024. I'm thinking of this essentially from a mathematical rather than real-life perspective.James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-46754485133325677402019-06-06T10:24:12.946+01:002019-06-06T10:24:12.946+01:00You didn't say how many consecutive 5 years yo...You didn't say how many consecutive 5 years you intended at first. If there's only one period, then the expected return rises from 2% for A to 5% for E, but at the cost of increased risk. The risk-averse choice is A. None of the choices seem appealling, I'd rather invest my money myself thanks :-)<br /><br />I didn't think about iterating it, because I kinda hoped that it would be "the same". And... it is. Your expected return for case E is just (1.05)^n. Your max gain becomes large and you max loss is most of your money, though.William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-81518547397075947332019-06-06T07:54:46.202+01:002019-06-06T07:54:46.202+01:00Ok, a hint.
What will the outcomes be after say 1...Ok, a hint.<br /><br />What will the outcomes be after say 10 years of plan E? (ie 2 consecutive 5 year periods as above)<br />After 50 years?<br /><br />The first you can do by direct calculation, the latter may be easiest with some random sampling.James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-7478781761853684502019-06-06T01:23:27.698+01:002019-06-06T01:23:27.698+01:00Well you are the expert and if you say my example ...Well you are the expert and if you say my example is not valid, you are almost certain to be correct. Yes I accept that there is at least an error in the auxiliary hypotheses and that may well make it a bad example to use. However, does this really matter if no-one knows about the 1 in 1,000,000 chance?<br /><br /><br />Re "the CIs do not have correct coverage under repeated experimentation".<br /><br />My 1 in 1000000 chance is well outside a 5%-95% range. If the experiment is take the mean of 20 numbers drawn from this distribution, then 1 in a 1,000,000 chance coming up is a rare case well outside the 5-95 range. Does it matter to the CI whether whether the 1 in a 1,000,000 chance has value of -250,000 or +100,000? I don't see that the CI is changed much if at all whether you repeat the experiment 100 times, 10,000 times or 10,000,000 times.<br /><br />If the experiment is take the mean of 10,000,000 numbers drawn from this distribution and this is repeated 10,000,000 times then the CI will be centred near 0 and and I accept that here the 0.1-0.4 range does not have correct coverage under repeated experimentation. In that case fair enough, but this wasn't what I was intending.<br /><br />Maybe this quibble is my fault that I didn't adequately explain my example was finding the mean of just 20 numbers drawn from this distribution. (Or more likely I am still wrong maybe in more different ways.) <br /><br />Yes the distribution is still not gaussian, there is a small very low probability peak near -249,995, but this seems such a small divergence from the gaussian assumption that I am inclined to try to dismiss it as a rather trivial error in the auxiliary hypotheses. Maybe I shouldn't get away with that?<br />crandleshttps://www.blogger.com/profile/15181530527401007161noreply@blogger.com