{"id":1227,"date":"2014-02-07T01:19:26","date_gmt":"2014-02-07T06:19:26","guid":{"rendered":"http:\/\/www.holypotato.net\/?p=1227"},"modified":"2014-06-07T13:07:47","modified_gmt":"2014-06-07T18:07:47","slug":"the-cone-of-probability","status":"publish","type":"post","link":"https:\/\/www.holypotato.net\/?p=1227","title":{"rendered":"The Cone of Probability"},"content":{"rendered":"<p>[Update: this post appears in the <a href=\"http:\/\/www.controlyourcash.com\/2014\/02\/17\/carnival-of-wealth-dollars-to-dollars-edition\/\">Carnival of Wealth, Dollars to Dollars Edition<\/a>]<\/p>\n<p>Here is how many people plan for retirement (and many similar activities that involve projections): come up with reasonable estimates of the relevant parameters. Plug it into an online calculator or spreadsheet to do the math. Have a cookie.<\/p>\n<p>Yet you really can&#8217;t just say that the average investment return is 6%, your average spending needs are $40k\/yr and inflation will hit 2%, plug that into a spreadsheet, and call your financial planning exercise completed. That might be your expected, most likely outcome and an excellent start. You can plot it for a nice, smooth exponential growth trajectory like this:<\/p>\n<p><img src=\/wp-content\/course_correction4_plan.png width=\"640\" \/><\/p>\n<p>A very comforting graph: continually saving money, making steady returns, you move smoothly towards your retirement goal. While your future might have a good chance of looking <em>something <\/em>like that, it&#8217;s highly unlikely to be <em>precisely <\/em>like that. There&#8217;s a whole range of possible outcomes. So we don&#8217;t want to just plot the course that&#8217;s going to get us there. Take a few minutes and add a &#8220;95%<sup>1<\/sup> best case&#8221; and &#8220;95% worst case&#8221; projection. How would those scenarios affect your plans?<br \/>\n<script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script> <!-- 468x60, created 7\/4\/08 --><br \/>\n<ins class=\"adsbygoogle\" style=\"display:inline-block;width:468px;height:60px\" data-ad-client=\"ca-pub-1468596978203595\" data-ad-slot=\"4685444840\"><\/ins><br \/>\n<script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/p>\n<p><img src=\/wp-content\/course_correction4_bounds.png width=\"640\" \/><\/p>\n<p>That&#8217;s a fair bit better: you have some idea of the range of future outcomes, and may even be able to say how those might compare to what you&#8217;re willing to accept, and set some limits and guidelines for your future course corrections. Maybe if by year 5 you&#8217;re closer to the bottom line than the middle one, you&#8217;ll increase your savings rate to compensate. But even that is not really capturing the uncertainty and more importantly the variability ahead. There&#8217;s a big <strong>cloud of probability<\/strong> around the outcomes, and this is just a small, simplified part of a projection to retirement. <\/p>\n<p><img src=\/wp-content\/course_correction4_probcloud.png width=\"640\" \/><\/p>\n<p>Maybe describing it as a <strong>cone of probability<\/strong> is a better way of putting it. This helps visualize all the uncertainty that we face going into the future. Note that I made the bottom edge creep up over time; this works with some recent posts by <a href=\"http:\/\/www.michaeljamesonmoney.com\/2013\/12\/do-stocks-become-more-or-less-risky.html\">Michael James about stocks becoming less risky over time.<\/a> Next year the market could be down 50% in a repeat of 2008, but 30 years from now it&#8217;s very likely that the market will be up. Up less than your projected 6% real return perhaps, which could be a challenge to your initial plan, but up nonetheless. <\/p>\n<p>Because the future is so inherently uncertain, I generally tell people with a lot of future ahead of them to not sweat the fine details: tweaking your asset allocation to the last half a percent really won&#8217;t matter when you can only guess at future returns to plus or minus 5% CAGR over 30 years. Control what you can (keep fees low, save some decent amount of your income, start early, don&#8217;t panic), and be prepared to be surprised and <a href=\"https:\/\/www.holypotato.net\/?p=1215\">make adjustments<\/a>. Get started in approximately the right direction, try to keep moving in the right direction through an iterative process, and try not to fear the uncertainty. Uncertainty is a fact of life. The future will &#8212; at best &#8212; only look approximately like how we imagine it will. <\/p>\n<p>That&#8217;s a tough, uncomfortable concept for many. <em>We demand rigidly defined areas of doubt and uncertainty!<\/em> The <a href=\"http:\/\/en.wikipedia.org\/wiki\/Fear#Fear_of_the_unknown\">unknown is scary<\/a> and foreign and weird, and people just don&#8217;t like the unknown; uncertainty looks a lot like that with some kind of math mixed in (which is frightening and uncomfortable in its own right). As terrifying as this is going to sound: you can&#8217;t hide from uncertainty. That&#8217;s just the nature of life (and if it was less uncertain it would be <em>boring<\/em>). <\/p>\n<p>A plan that includes a big cone of probability and uncertainty may actually be more useful than one that pretends there is no uncertainty in the future, though the single line, ever-upwards trajectory was a lot more appealing to our baser selves.<\/p>\n<p><em>Podcast podcast podcast! <\/em>In case you missed it, <a href=\"http:\/\/www.becausemoney.ca\/borrowing-money-isnt-sacred-right-canadian-math\/\">we talked about these issues (and I unveiled these terrible excel\/photoshop hybrids) in the because money podcast earlier in January<\/a>.<br \/>\n<script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script> <!-- 468x60, created 7\/4\/08 --><br \/>\n<ins class=\"adsbygoogle\" style=\"display:inline-block;width:468px;height:60px\" data-ad-client=\"ca-pub-1468596978203595\" data-ad-slot=\"4685444840\"><\/ins><br \/>\n<script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/p>\n<p><small>Footnote: pardon me for using photoshop to make the probability clouds. I should have used MATlab or something with an actual Monte Carlo simulation, but I don&#8217;t actually have it on any of my current computers &#8212; I&#8217;d have to go fire up my ancient Pentium 3 system as it&#8217;s the only one left in the house that still has MATlab and Maple. The consequence is that the clouds are not particularly accurate, and aren&#8217;t as much like cones as I would have liked. Hopefully the visual still works for you.<\/p>\n<p>1 &#8211; By which I mean in a stats sense your 95% confidence interval &#8212; or in a more plain language sense &#8212; aside from a few extreme cases, the range your results will most likely fall within.<br \/>\n<\/small><\/p>\n","protected":false},"excerpt":{"rendered":"<p>[Update: this post appears in the Carnival of Wealth, Dollars to Dollars Edition] Here is how many people plan for retirement (and many similar activities that involve projections): come up with reasonable estimates of the relevant parameters. Plug it into an online calculator or spreadsheet to do the math. Have a cookie. Yet you really [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"_links":{"self":[{"href":"https:\/\/www.holypotato.net\/index.php?rest_route=\/wp\/v2\/posts\/1227"}],"collection":[{"href":"https:\/\/www.holypotato.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.holypotato.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.holypotato.net\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.holypotato.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1227"}],"version-history":[{"count":0,"href":"https:\/\/www.holypotato.net\/index.php?rest_route=\/wp\/v2\/posts\/1227\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.holypotato.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1227"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.holypotato.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1227"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.holypotato.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1227"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}