tag:blogger.com,1999:blog-35364652.post6641714432704666214..comments2022-10-03T06:16:28.617-04:00Comments on Quantitative Trading: Universal PortfoliosErnie Chanhttp://www.blogger.com/profile/02747099358519893177noreply@blogger.comBlogger21125tag:blogger.com,1999:blog-35364652.post-89339840763688380242016-10-21T11:01:48.153-04:002016-10-21T11:01:48.153-04:00Universal portfolio scheme by Cover would *not* re...Universal portfolio scheme by Cover would *not* recommend that the allocation be set to just trading the "best" stock at 100%. It just gives the highest weight to this allocation scheme, but all other less profitable schemes also get their weights based on how profitable they were.<br /><br />ErnieErnie Chanhttps://www.blogger.com/profile/02747099358519893177noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-74409154214160536102016-10-21T09:22:19.943-04:002016-10-21T09:22:19.943-04:00the question is "rebalance to what?"
Ri...the question is "rebalance to what?"<br /><br />Right, and it seems in some simplified way that if you consider the "universe" of investable securities to be be 2 "stocks", A & B, that the rebalancing question immediately boils down to a very simple answer: Own ALL of the highest performing stock since inception. Owning any positive percentage of the lesser performing stock be definition results in lower total wealth.<br /><br />Abstracting this idea "outward" to include all/any securities, and any time period of arbitrary length, it seems this argument holds of owning 100% of the best performing security, all other allocations result in lower total wealth. eg: Cover's Universal Portfolio theory seems to be a sort of ultimate pathological trend following system. <br /><br />The only question seems to be "when" to choose as your start date. It seems at different points such as the 90's you would have owned nothing but AOL, and perhaps Priceline or Amazon recently.<br /><br />To me, this has a whiff of Kelly "overbetting" which inevitably leads to ruin, especially if you have chosen to leverage something like the 12.5X (full Kelly bet) as stated in another post. (Overbetting is something that I believe that a competitive society compels its institutions to engage in, and leads to virtually all financial catastrophes, such as Tulip-mania, 2008 housing collapse, etc. Personally believe the 2008 bailouts have "institutionalized" overbetting in the US financial system.)<br /><br />I guess I am having a hard time rationalizing Cover's Universal Portfolios, which seems to have a pathological 100% single security solution, and Kelly criterion, which NEVER has a 100% allocation when there is ANY positive chance of loss.<br /><br /><br /><br />IHateToBurstYourBubblehttps://www.blogger.com/profile/01660687201024720176noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-30261397986645001862016-10-21T08:31:49.870-04:002016-10-21T08:31:49.870-04:00Hi,
The daily rebalancing indeed has a mean revers...Hi,<br />The daily rebalancing indeed has a mean reversion character, as the IBM/MSFT example shows.<br />However, the question is "rebalance to what?" It is rebalancing to an allocation scheme that is constantly changing, and giving more weights to the most profitable allocation in the past. So the allocation scheme itself has a momentum/trending character, but that happens on a slower time scale. <br /><br />This is actually quite generic in the financial markets: mean reversion can happen in a very short time scale, even milliseconds, but momentum can take weeks. Both can happen simultaneously, but at different time scales.<br />ErnieErnie Chanhttps://www.blogger.com/profile/02747099358519893177noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-50493111815680490552016-10-21T08:19:18.848-04:002016-10-21T08:19:18.848-04:00This seems contradictory to me. At first it sound...This seems contradictory to me. At first it sounds like a mean reversion strategy:<br /><br />"if you own IBM and MSFT, and IBM went up after one day whereas MSFT went down, you should sell some IBM and use the capital to buy some more MSFT"<br /><br />eg: if something goes down (relative to the avg stock in the port), buy more. if it goes up relatively, sell it.<br /><br />But later, there is this:<br /><br />"try all possible initial allocations, and calculate the hypothetical net worth of the resulting portfolio. Use these hypothetical net worth as weights (after normalizing them by the sum of all net worth), and compute a weighted-average percent allocation. Finally, adopt this weighted average allocation as the new desired allocation and rebalance the portfolio accordingly."<br /><br />The easiest hypothetical portfolios to calculate are where each respective stock, except for 1, is 0% and then 1 stock is all that is held. eg: 100%<br /><br />If this is the criteria for evaluating and re-balancing, the strategy is simple: Buy the stock that has had the largest percent gain since the beginning date of the evaluation as your only holding. Simply hold 100% of your portfolio in the stock that has gone up the most. Re-balancing only happens when another stock has a larger percent gain in the period.<br /><br />I am confused by the seeming contradictory nature of Kelly-criterion betting, which maximizes geometric returns, which seems congruent with the above scheme (eg: "trend following" and "averaging up"), and the seeming opposite idea of mean reversion, or averaging down, which seems parallel to your IBM/MSFT example, as well as the "Shannons Demon" example on page 203 of "Fortune's Formula", where Shannon seems to indicate a geometric random walk can be exploited in a mean reversion scheme of money management.<br /><br />Hoping you might clarify..IHateToBurstYourBubblehttps://www.blogger.com/profile/01660687201024720176noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-57589174497849825642014-12-24T08:45:18.084-05:002014-12-24T08:45:18.084-05:00Hi M,
Thanks for the link.
Yes, there are various...Hi M,<br />Thanks for the link.<br /><br />Yes, there are various authors who claim they can construct optimal trading strategies that can overcome transaction costs. Unfortunately, I have never been able to verified their results out-of-sample using a representative universe of instruments.<br />ErnieErnie Chanhttps://www.blogger.com/profile/02747099358519893177noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-7608827920490380452014-12-24T07:46:17.490-05:002014-12-24T07:46:17.490-05:00Thanks for sharing this. I'm looking into this...Thanks for sharing this. I'm looking into this uni portfolios concept and I recently found this nice paper titled 'Universal Semi-Constant Rebalanced Portfolios'. I'm still behind on understanding their algorithm, but they seem to have figured out the optimal formula with transaction costs included. https://ais.ku.edu.tr/AR/SKOZAT200920__manuscript_fin_revised.pdfMhttps://www.blogger.com/profile/13278406145594006582noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-9341822015385373912014-02-18T02:59:12.833-05:002014-02-18T02:59:12.833-05:00In a 2004 paper "Can We Learn to Beat the Bes...In a 2004 paper "Can We Learn to Beat the Best Stock" it showed that although the optimal re-balance vector hindsight beats the best stock, when running the Universal portfolio algo by cover it really don't get near the best stock. Surely not in the short term of 3-4 years as their dataset contains. The dataset used in cover original paper is also very very biased. Rannoreply@blogger.comtag:blogger.com,1999:blog-35364652.post-76163645467531152172010-08-12T08:49:22.958-04:002010-08-12T08:49:22.958-04:00Dear Ernest,
Having read your blog a little more ...Dear Ernest,<br /><br />Having read your blog a little more and discovered that it's actually quite easy to add comments, I thought I would! <br /><br />As part of my philosophy of `learning by doing', I coded up a simple example of volatility pumping based on a paper from yats.com. This of course is a prelude to Cover's Universal Portfolios. The MATLAB code is available from the MATHWORKS website under <br /><a href="http://www.mathworks.com/matlabcentral/fileexchange/28427-example-of-volatility-pumping" rel="nofollow">example-of-volatility-pumping</a> and contains references.<br /><br />I am happy to receive comments / bug suggestions.<br /><br />Best,<br /><br />-edUnknownhttps://www.blogger.com/profile/08083616296803773674noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-3740495547157580612010-06-17T02:28:42.913-04:002010-06-17T02:28:42.913-04:00> this scheme is supposed to work even if the s...> this scheme is supposed to work even if the stock prices are totally random<br /><br />Well, that is definitely to good to be true..Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-35364652.post-11611927338478071922009-12-13T09:20:49.304-05:002009-12-13T09:20:49.304-05:00Hi Kirill,
Yes, your link works... thanks!
ErnieHi Kirill,<br />Yes, your link works... thanks!<br />ErnieErnie Chanhttps://www.blogger.com/profile/02747099358519893177noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-5668438716239606972009-12-07T13:28:10.312-05:002009-12-07T13:28:10.312-05:00Ernie,
the paper that your are referring to is a...Ernie, <br /><br />the paper that your are referring to is available at the Stanford's web site. The hyperlink should start with "www" instead of "itg": <br /><br /><br />http://www.stanford.edu/~cover/papers/universal_portfolios.pdf<br /><br />Thanks, <br />KirillKirillnoreply@blogger.comtag:blogger.com,1999:blog-35364652.post-91934778220728411982009-07-29T19:51:16.282-04:002009-07-29T19:51:16.282-04:00sorry... that was one particular paper. here'...sorry... that was one particular paper. here's the larger list: http://www.stanford.edu/~cover/portfolio-theory.htmlUnknownhttps://www.blogger.com/profile/01886074026063358802noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-29252374877626521242009-07-29T19:50:06.031-04:002009-07-29T19:50:06.031-04:00Prof. Cover's papers on portfolio theory are p...Prof. Cover's papers on portfolio theory are posted at http://www.stanford.edu/~cover/papers/paper93.pdfUnknownhttps://www.blogger.com/profile/01886074026063358802noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-8211898438029200362009-07-22T10:00:37.891-04:002009-07-22T10:00:37.891-04:00Anonymous,
If one is to use UP for reallocation, o...Anonymous,<br />If one is to use UP for reallocation, one has to know the history of returns of the various instruments. The latest returns alone are not sufficient.<br /><br />If one, however, assumes that the allocation is fairly constant, then one should make sure that their percentages in the portfolio are constant. In your example, you need to use cash to buy ETF A and B so that they return to 25% of equity.<br /><br />ErnieErnie Chanhttps://www.blogger.com/profile/02747099358519893177noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-8338668830063132732009-07-21T13:24:47.774-04:002009-07-21T13:24:47.774-04:00Mr. Chan -
Have you tried this concept with the 3...Mr. Chan -<br /><br />Have you tried this concept with the 3x (Direxion or other) funds? Also, if we start with the following:<br /><br />ETF A - $5000<br />ETF B - $5000<br />Cash - $10,000<br /><br />and both ETF A and ETF B lose value over time, say both drop to:<br /><br />ETF A - $3000<br />ETF B - $2000<br />Cash - $10,000<br /><br />How should one rebalance?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-35364652.post-10474870607752669632009-06-01T15:36:05.159-04:002009-06-01T15:36:05.159-04:00Hi Anonymous,
Thank you for the heads-up on the ne...Hi Anonymous,<br />Thank you for the heads-up on the new article on Universal Portfolio. I will see if I have time to read such heavily mathematical article. My past experience has been that the more mathematical an article is, the less likely it will actually be a profitable strategy.<br />ErnieErnie Chanhttps://www.blogger.com/profile/02747099358519893177noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-54897057773127322752009-06-01T12:54:13.597-04:002009-06-01T12:54:13.597-04:00Hi Ernie,
Dokuchaev and Savkin have published an i...Hi Ernie,<br />Dokuchaev and Savkin have published an improved version of Cover's Ultimate Portfolio theory (in the journal: Insurance:Mathematics and Economics 34 (2004) 409 - 419). Are you able to decode from the heavy maths what their modified version entails?I could not follow the maths..Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-35364652.post-86111880940946555052007-06-17T17:17:00.000-04:002007-06-17T17:17:00.000-04:00Dear Anonymous,Certainly using futures will reduce...Dear Anonymous,<BR/>Certainly using futures will reduce transaction cost, which is the main reason why this strategy didn't work well for stocks or ETF's. I will post the results on futures here when I get around to doing the calculations.<BR/><BR/>I have tried rebalancing at different time period -- the results are not significantly different.<BR/><BR/>Thanks for your suggestions!<BR/>ErnieErnie Chanhttps://www.blogger.com/profile/02747099358519893177noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-66389913671250399792007-06-17T15:35:00.000-04:002007-06-17T15:35:00.000-04:00Hi,Why did you use ETFs as opposed to futures on i...Hi,<BR/><BR/>Why did you use ETFs as opposed to futures on indexes, commodities and interest rates, which would eliminate issues with suvivorship, allow for more volatility with higher leverage and lower transaction costs? Also, did you try different time periods for portfolio rebalancing such as weekly or monthly? Would rebalancing using these time periods provide some benefits?<BR/><BR/>Thanks!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-35364652.post-80842635202335309802007-01-08T17:26:00.000-05:002007-01-08T17:26:00.000-05:00It seems that either Prof. Cover has removed his r...It seems that either Prof. Cover has removed his reprint from public access, or the Stanford server is down. You can read other similar papers by googling Universal Portfolios. -ErnieErnie Chanhttps://www.blogger.com/profile/02747099358519893177noreply@blogger.comtag:blogger.com,1999:blog-35364652.post-26952921742206290282007-01-08T17:20:00.000-05:002007-01-08T17:20:00.000-05:00interesting, I'm getting a 404 error when trying t...interesting, I'm getting a 404 error when trying to view the paper :(Anonymousnoreply@blogger.com