{"id":6770,"date":"2012-04-16T09:44:31","date_gmt":"2012-04-16T08:44:31","guid":{"rendered":"https:\/\/www.portfolioprobe.com\/?p=6770"},"modified":"2012-04-16T09:44:31","modified_gmt":"2012-04-16T08:44:31","slug":"information-flows-like-water","status":"publish","type":"post","link":"https:\/\/www.portfolioprobe.com\/2012\/04\/16\/information-flows-like-water\/","title":{"rendered":"Information flows like water"},"content":{"rendered":"<blockquote><p>Guiding a ship, it takes more than your skill<\/p><\/blockquote>\n<h2>Spark<\/h2>\n<p>David Rowe&#8217;s <strong>Risk<\/strong> column this month is about <a href=\"http:\/\/www.dmrra.com\/publications\/Risk%20Magazine\/201204%20Beware%20of%20Data%20Leverage.pdf\" target=\"_blank\">data leverage<\/a>. The idea is that you are leveraging your data if you are using it to answer questions that are too demanding of information.<\/p>\n<p>The piece reminded me of a talk that Dave gave a few years ago, and he was kind enough to remind me of his terminology.<\/p>\n<p>One of his phrases is &#8220;statistical entropy&#8221;.\u00a0 Very homiletic &#8212; I can envision one or more dissertations written on this topic.<\/p>\n<p>But the image that resonates with me is:<\/p>\n<blockquote><p>Like water, information can never rise higher than its source, and the source is the data you have to work with in the first place.<\/p><\/blockquote>\n<p>In academic statistics the game is almost always:<\/p>\n<ul>\n<li>Given some data, what information can I extract from it?<\/li>\n<\/ul>\n<p>No possibility of data leveraging here.<\/p>\n<p>In the so-called real world the game is much more likely to be:<\/p>\n<ul>\n<li>I have to make a decision, what data do I need to inform that decision?<\/li>\n<\/ul>\n<p>Except that the thought process is often not nearly so clear.\u00a0 In particular it might be more like:<\/p>\n<ul>\n<li>I have to make a decision, what data do we have lying about that inform that decision?<\/li>\n<\/ul>\n<p>And &#8220;none&#8221; is an unacceptable answer.<\/p>\n<h2>Information in finance<\/h2>\n<p>In finance two very common tasks are:<\/p>\n<ul>\n<li>predict expected returns of assets<\/li>\n<li>predict the variance matrix of asset returns<\/li>\n<\/ul>\n<p>Figure 1 is an illustration of the information situation with predicting returns.<\/p>\n<p>Figure 1: Sketch of the informational requirements of predicting returns. <a href=\"https:\/\/www.portfolioprobe.com\/2012\/04\/16\/information-flows-like-water\/infoexpret\/\" rel=\"attachment wp-att-6781\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6781\" title=\"infoexpret\" src=\"https:\/\/www.portfolioprobe.com\/wp-content\/uploads\/2012\/04\/infoexpret.png\" alt=\"\" width=\"512\" height=\"480\" srcset=\"https:\/\/www.portfolioprobe.com\/wp-content\/uploads\/2012\/04\/infoexpret.png 512w, https:\/\/www.portfolioprobe.com\/wp-content\/uploads\/2012\/04\/infoexpret-250x234.png 250w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/a>The amount of information available to predict returns is probably exaggerated in Figure 1.\u00a0 In pretty much any other field of study, it would be deemed impossible to do the prediction.\u00a0 However, the ability to predict even a little bit can be worth billions of dollars.\u00a0 Hence a little more effort tends to be exerted.<\/p>\n<p>Figure 2: Sketch of the informational requirements of predicting the return variance matrix. <a href=\"https:\/\/www.portfolioprobe.com\/2012\/04\/16\/information-flows-like-water\/infovarmat\/\" rel=\"attachment wp-att-6782\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6782\" title=\"infovarmat\" src=\"https:\/\/www.portfolioprobe.com\/wp-content\/uploads\/2012\/04\/infovarmat.png\" alt=\"\" width=\"512\" height=\"480\" srcset=\"https:\/\/www.portfolioprobe.com\/wp-content\/uploads\/2012\/04\/infovarmat.png 512w, https:\/\/www.portfolioprobe.com\/wp-content\/uploads\/2012\/04\/infovarmat-250x234.png 250w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/a><\/p>\n<p>Figure 2 portrays predicting the variance matrix as a much easier task.<\/p>\n<p><a href=\"https:\/\/www.portfolioprobe.com\/2010\/08\/25\/what-the-hell-is-a-variance-matrix\/\">&#8220;What the hell is a variance matrix?&#8221;<\/a> gives reasons why we should be skeptical that we can get reasonable estimates of the variance.<\/p>\n<p>However, <a href=\"https:\/\/www.portfolioprobe.com\/2012\/03\/12\/the-quality-of-variance-matrix-estimation\/\">&#8220;The quality of variance matrix estimation&#8221;<\/a> shows that we can do okay.\u00a0 We can&#8217;t predict the general level of volatility very well.\u00a0 But if we have a portfolio in each hand, then we have a good shot at predicting which one will be more volatile.<\/p>\n<h2>Epilogue<\/h2>\n<blockquote><p>You take the wheel one more time like I showed you<br \/>\nWe&#8217;ve reached the strait once even I could not go through<\/p><\/blockquote>\n<p>from &#8220;We Learned the Sea&#8221; by Dar Williams<br \/>\n<object width=\"520\" height=\"382\" classid=\"clsid:d27cdb6e-ae6d-11cf-96b8-444553540000\" codebase=\"http:\/\/download.macromedia.com\/pub\/shockwave\/cabs\/flash\/swflash.cab#version=6,0,40,0\"><param name=\"allowFullScreen\" value=\"true\" \/><param name=\"allowscriptaccess\" value=\"always\" \/><param name=\"src\" value=\"http:\/\/www.youtube.com\/v\/q2qzcnrXxPI?version=3&amp;hl=en_GB\" \/><param name=\"allowfullscreen\" value=\"true\" \/><embed width=\"520\" height=\"382\" type=\"application\/x-shockwave-flash\" src=\"http:\/\/www.youtube.com\/v\/q2qzcnrXxPI?version=3&amp;hl=en_GB\" allowFullScreen=\"true\" allowscriptaccess=\"always\" allowfullscreen=\"true\" \/><\/object><\/p>\n<h2>Appendix R<\/h2>\n<p>The function that created Figure 2 was:<\/p>\n<pre>function (filename = \"infovarmat.png\")\r\n{\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 if(length(filename)) {\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 png(file=filename, width=512)\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 par(mar=c(4, 4, 1, 1) + .1)\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 }\r\n\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 plot(0, 0, type=\"n\",, xlim=c(0,1), ylim=c(0,1),\r\n                yaxs=\"i\", yaxt=\"n\", xaxt=\"n\", xlab=\"\",\r\n                ylab=\"Information\")\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 polygon(c(.2, .2, .4, .4), c(0, .5, .5, 0),\r\n                col=\"steelblue\", border=NA)\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 polygon(c(.6, .6, .8, .8), c(.75, .5, .5, .75),\r\n                col=\"gold\", border=NA)\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 polygon(c(.6, .6, .8, .8), c(.29, .5, .5, .29),\r\n                col=\"steelblue\", border=NA)\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 axis(1, at=c(.3, .7),\r\n                labels=c(\"Data\", \"Application\"))\r\n\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 if(length(filename)) {\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 dev.off()\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 }\r\n}<\/pre>\n<p><a href=\"http:\/\/feedburner.google.com\/fb\/a\/mailverify?uri=PortfolioProbe&amp;loc=en_US\" target=\"_blank\">Subscribe to the Portfolio Probe blog by Email<\/a><\/p>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>Guiding a ship, it takes more than your skill Spark David Rowe&#8217;s Risk column this month is about data leverage. The idea is that you are leveraging your data if you are using it to answer questions that are too demanding of information. The piece reminded me of a talk that Dave gave a few &hellip; <a href=\"https:\/\/www.portfolioprobe.com\/2012\/04\/16\/information-flows-like-water\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,17],"tags":[240],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/posts\/6770"}],"collection":[{"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/comments?post=6770"}],"version-history":[{"count":0,"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/posts\/6770\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/media?parent=6770"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/categories?post=6770"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/tags?post=6770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}