{"id":232738,"date":"2025-10-15T10:57:12","date_gmt":"2025-10-15T14:57:12","guid":{"rendered":"https:\/\/ibkrcampus.com\/campus\/?p=232738"},"modified":"2025-10-16T04:31:49","modified_gmt":"2025-10-16T08:31:49","slug":"why-you-cant-tell-if-your-strategy-stopped-working-statistically-speaking","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/why-you-cant-tell-if-your-strategy-stopped-working-statistically-speaking\/","title":{"rendered":"Why You Can&#8217;t Tell if Your Strategy &#8220;Stopped Working&#8221; (Statistically Speaking)"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><em>The article &#8220;Why You Can&#8217;t Tell if Your Strategy &#8220;Stopped Working&#8221; (Statistically Speaking)&#8221; was originally posted on <a href=\"https:\/\/robotwealth.com\/why-you-cant-tell-if-your-strategy-stopped-working-statistically-speaking\/\">Robot Wealth<\/a> blog.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Traders love the illusion of precision. A few bad weeks go by, and you think, \u201cLet\u2019s run a t-test and see if the strategy stopped working.\u201d It sounds rigorous. It isn\u2019t.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Imagine a strategy that, in truth, earns 10% per year with 20% volatility \u2013 roughly the S&amp;P\u2019s long-term profile. We\u2019ll simulate five years of daily returns, about 1,260 observations, from a geometric Brownian motion with those parameters.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now the world changes. For the next month, 21 trading days, the strategy\u2019s expected return drops to zero, but volatility stays at 20%.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We\u2019d like to detect that change. The question:&nbsp;<em>Can you statistically prove the edge is gone?<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A t-test compares these two samples (before and after) and asks if their means differ significantly.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Five years of data vs. one month.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">That\u2019s n\u2081 \u2248 1260 vs. n\u2082 \u2248 21.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Noise \u2248 20% \/ \u221a252 \u2248 1.26% daily.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The expected daily drift for 10% annual return is just 0.10 \/ 252 \u2248 0.04% per day. That\u2019s our signal. The noise is thirty times larger. In other words, your daily Sharpe ratio is 0.04 \/ 1.26 \u2248 0.03,&nbsp;<strong><em>an astronomically low signal-to-noise ratio<\/em><\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So even if the edge disappeared entirely, you\u2019d barely notice in a month.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">From the simulation:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td><strong>Test<\/strong><\/td><td><strong>p-value<\/strong><\/td><td><strong>Interpretation<\/strong><\/td><\/tr><\/thead><tbody><tr><td>Welch t-test<\/td><td>0.12<\/td><td>Not significant<\/td><\/tr><tr><td>Kolmogorov Smirnov test<\/td><td>0.37<\/td><td>Not significant (even worse)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The t-test finds nothing. The KS test, which looks at the whole distribution, not just the mean, finds&nbsp;<em>even less<\/em>. The supposed \u201ccollapse in performance\u201d doesn\u2019t even register as a blip in the statistics.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">That\u2019s the problem: volatility dominates everything. The mean shift you\u2019re trying to detect (0.04%\/day) is microscopic relative to the daily noise (\u00b11%). Twenty-one days is simply not enough data to estimate a mean that small with any precision.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The t-stat came out around&nbsp;<strong>\u20131.6<\/strong>, roughly a 12% chance under the null of equal means. Even if you doubled the sample size \u2013 two months of underperformance \u2013 the p-value would still hover around 0.06. You\u2019d need a&nbsp;<strong>multi-month drought<\/strong>&nbsp;before statistics would admit the obvious.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The funny part: in that same run, the \u201cdead\u201d strategy\u2019s one-month realised return was +7.5%.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">That\u2019s right. A zero-drift month beat 93% of all months during the prior five years of positive-drift data.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Why?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A 20% annual volatility means roughly 5.8% standard deviation per month.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Even with zero drift, one standard deviation up is +5.8%, and 1.3\u03c3 is +7.5%. That happens 10% of the time purely by chance.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Meanwhile, in the \u201cgood\u201d regime (10% annual drift), the expected monthly gain is only +0.8%. A +7.5% outlier month easily beats the vast majority of historical months.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, you end up with a bizarre headline:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>\u201cOur strategy just lost its edge, but had its second-best month ever.\u201d<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Noise does that.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To see if the phenomenon was a fluke, I ran 3,000 simulations of the same setup.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Across runs:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The median one-month return (true zero drift) was roughly \u20130.06%, but the 90th percentile was +7.4%.<\/li>\n\n\n\n<li>In half of all runs, the zero-drift month beat 45% of all historical months.<\/li>\n\n\n\n<li>In 16% of runs, it beat more than 80% of the prior months.<\/li>\n\n\n\n<li>In 7.5% of runs, it beat more than 90%.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">So, one in every thirteen \u201cdead\u201d months looks like a top-decile success. Statistically, that\u2019s unremarkable. Psychologically, it\u2019s devastating \u2013 because you\u2019ll tell yourself the system recovered, tweak nothing, and (probably) then spend the next quarter losing money.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Some traders, knowing the t-test\u2019s weakness, pivot to \u201cnon-parametric\u201d tests like the Kolmogorov-Smirnov. It compares the cumulative distributions directly, not the means. Surely that\u2019s more robust?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">No.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When two normal distributions differ only slightly in mean but have the same variance, the KS test has&nbsp;<em>less<\/em>&nbsp;power than the t-test. It\u2019s designed to catch shape differences \u2013 fat tails, variance shifts, asymmetry \u2013 not small mean drifts. With n\u2082 = 21, it\u2019s practically blind.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In our case, the KS p-value was 0.37. The test confidently says \u201cnothing to see here.\u201d It\u2019s technically correct.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here\u2019s the deeper problem. The tools we use, t-tests, p-values, Sharpe ratios, were designed for large-sample, low-noise situations. Financial returns are the opposite: small signals, fat tails, short samples.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When you apply a test that needs thousands of points to reject the null at 95% confidence, you\u2019ll never detect regime shifts in real time. The market will move on long before the statistic does.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A five-year window may&nbsp;<em>contain<\/em>&nbsp;your \u201ctrue\u201d performance, but it\u2019s useless for diagnosing the present. A one-month drought tells you nothing. A three-month one tells you almost nothing.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The conclusion isn\u2019t that tests are bad\u2014it\u2019s that the&nbsp;<em>problem<\/em>&nbsp;is mis-specified. The null hypothesis \u201cmean return hasn\u2019t changed\u201d is almost never the right one. Markets evolve, but slowly and noisily. No binary test will save you.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Practical Interpretation<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When a strategy underperforms for a few weeks, you face two equally dangerous errors:<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Type I error<\/strong>&nbsp;\u2013 You think it\u2019s dead when it\u2019s just noise. You abandon a still-valid edge.<\/li>\n\n\n\n<li><strong>Type II error<\/strong>&nbsp;\u2013 You think it\u2019s noise when it\u2019s actually dead. You keep bleeding capital.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Classical statistics tries to balance those. Trading doesn\u2019t care. You\u2019re asymmetric: Type II errors cost you more because capital decays geometrically, not linearly.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, the sensible response isn\u2019t to chase significance but to&nbsp;<strong>control exposure<\/strong>. Cut risk when the environment looks hostile, but don\u2019t fool yourself that a p-value will tell you when to quit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you want to formalise this intuition, think Bayesian: update your belief about the strategy\u2019s drift each day. The posterior distribution will drift toward zero if recent returns are weak, but uncertainty will remain large. The proper decision rule is&nbsp;<em>probabilistic<\/em>, not binary.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Even better, you can encode prior scepticism \u2013 say, most strategies decay over time \u2013 and let data modify that belief. The output isn\u2019t \u201cdead or alive,\u201d but \u201cprobability the drift &gt; 0.\u201d You can then size down continuously rather than panic after a failed t-test.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But that\u2019s another post.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Every quantitative trader eventually learns this the hard way: statistics are lagging indicators. They confirm what you already know, long after it\u2019s actionable.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A strategy doesn\u2019t announce its death with a p-value. It fades, subtly, while your t-statistic wobbles somewhere between 0.5 and 1.2. By the time a 5-year backtest fails a significance test, you\u2019ve lost more in opportunity cost than you saved by being \u201crigorous.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Markets are too noisy for clean statistical detection. The right question isn\u2019t&nbsp;<em>\u201cHas my edge stopped working?\u201d<\/em>&nbsp;but&nbsp;<em>\u201cGiven recent evidence, how much do I trust it now?\u201d<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The answer is always probabilistic, never definitive, which is precisely why trading is hard \u2013 and why so many seek comfort in meaningless tests.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Traders love the illusion of precision. <\/p>\n","protected":false},"author":1673,"featured_media":224910,"comment_status":"open","ping_status":"closed","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[339,338,341],"tags":[11881,4922,20637,5545,4939],"contributors-categories":[13676],"class_list":["post-232738","post","type-post","status-publish","format-standard","has-post-thumbnail","category-data-science","category-ibkr-quant-news","category-quant-development","tag-bayesian-statistics","tag-econometrics","tag-kolmogorov-smirnov-test","tag-sharpe-ratio","tag-statistics","contributors-categories-robot-wealth"],"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.9 (Yoast SEO v27.8) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Why You Can&#8217;t Tell if Your 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