# Similar Sharpe Ratios Hide Severe Loss Tails and Distort Position Sizing > Loss tails of a put-selling index, the US stock market, the momentum factor and fourteen hedge fund strategy indices against a normal model, 1926 to 2026. The put-seller came within 0.09 of the market's Sharpe ratio, yet its worst 5% of months ran 1.50 times deeper than the normal forecast. At the same 10% volatility, drawdowns ranged from 15% to 60%. 13 pages, 11 direct sources. Published: 2026-09-29 Publisher: BlackRidge (https://blckridge.com/) Canonical: https://blckridge.com/research/asymmetric-tail-risk-20260929/ PDF: https://blckridge.com/research/asymmetric-tail-risk-20260929/asymmetric-tail-risk-20260929-en.pdf --- # Similar Sharpe ratios hide severe loss tails and distort position sizing We compare the loss tails of a put-selling index, the US stock market, the momentum factor and fourteen hedge fund strategy indices with what a normal model predicts. Equal volatility hid up to a fourfold difference in drawdown. Expected shortfall describes the tail better, but estimated from one history it did not beat volatility sizing on average out of sample. ## Put-sellers and the market earned similar Sharpe ratios, yet the put-seller's bad months fell 1.50 times deeper than normal models predict The put-selling index comes within 0.09 of the stock market's Sharpe ratio [02] . The symmetry fails in the tail: during the worst 5% of months, the strategy's average loss hits 1.50 times the normal model's prediction (against 1.18 for the market). Because most hedge fund indices share this negative skew, volatility and Sharpe ratios are the wrong inputs for sizing leveraged positions [04] . Size on the loss tail and a drawdown limit, treating the tail estimate as uncertain. ## 105 days fell more than four standard deviations. A normal model expects one. Parametric 95% VaR stops at 1.645 standard deviations. It says absolutely nothing about how far beyond that mark the losses go. In the middle of the distribution the normal model is too pessimistic, yet in the far tail it becomes absurdly optimistic [01] . Count of daily market losses exceeding standard deviation thresholds, 1 July 1926 to 31 August 2026, US market data [01] . Loss threshold in standard deviations ## The put-seller came within 0.09 of the market's Sharpe ratio and lost 5.9 standard deviations in one month. The index collects option premium month after month and gives it back in a few short months [02] . Its volatility runs at two thirds of the US market's [01] . That lower variance flatters the Sharpe ratio. Growth of 1 dollar, log scale, monthly, February 2007 to August 2026 [01] [02] . - Measure - Put-selling index - US stock market - Return a year - 7.1% - 11.1% - Volatility a year - 10.7% - 15.9% - Sharpe ratio - 0.56 - 0.65 - Skewness - −1.67 - −0.51 - Excess kurtosis - 7.1 - 1.0 - Normal 95% VaR, a month - −4.47% - −6.55% - Realised CVaR, a month - −8.66% - −10.03% - Normal expected shortfall, a month - −5.77% - −8.47% - Worst month - −17.7% - −17.1% - Largest drawdown - −32.7% - −50.3% - Months under water - 30 mo - 52 mo ## Ten of fourteen hedge fund strategies have a negative skew, and their tails run up to 1.53 times the normal forecast Arbitrage strategies take small steady gains and pay in rare large losses. Their Sharpe ratios often look best, but for the arbitrage strategies part of the steady return is payment for carrying the left tail [09] . The more negative the skew, the further the realised tail exceeds the normal forecast, driving a correlation of -0.85 across indices [04] . - Strategy - Skewness - Excess kurtosis - Normal expected shortfall - Realised CVaR - Ratio - Fixed income arbitrage - −4.85 - 47.1 - −2.10% - −3.22% - 1.53 - Convertible arbitrage - −2.65 - 23.5 - −2.72% - −3.43% - 1.26 - Multi-strategy - −1.90 - 10.1 - −2.14% - −3.03% - 1.42 - Merger arbitrage - −1.42 - 12.0 - −1.69% - −2.19% - 1.30 - Event driven - −1.38 - 7.5 - −3.51% - −4.46% - 1.27 - Distressed securities - −1.18 - 3.7 - −3.39% - −4.75% - 1.40 - Fund of funds - −0.80 - 4.6 - −2.74% - −3.54% - 1.29 - All strategies (composite) - −0.73 - 3.6 - −3.50% - −4.46% - 1.27 - Emerging markets - −0.72 - 3.9 - −6.97% - −8.50% - 1.22 - Equity long bias - −0.61 - 1.8 - −5.87% - −7.07% - 1.20 - Equity market neutral - 0.01 - 1.8 - −1.26% - −1.45% - 1.15 - Technology sector - 0.53 - 3.1 - −6.80% - −7.02% - 1.03 - Global macro - 0.57 - 1.2 - −2.73% - −2.50% - 0.92 - Equity long/short - 0.67 - 4.6 - −3.25% - −3.41% - 1.05 ## Momentum has been under its 2008 peak for 213 months. The put-seller needed 30. Volatility and the Sharpe ratio have no time dimension. Months spent below the high-water mark decide whether investors stay. That duration dictates whether a leveraged book survives margin calls [01] [02] . Drawdown from previous peak, %, monthly, February 2007 to August 2026 [02] [01] . ## Momentum showed a Sharpe ratio of 0.85 just before losing 49% in three months The trailing record looked perfectly calm, with volatility at an ordinary 14.2% in February 2009 [01] . The crash came when the market rebounded after the fall. Daniel and Moskowitz document this pattern [10] . Momentum factor drawdown from previous peak, %, monthly, January 1927 to August 2026 [01] . ## At three times leverage the put-seller fell 76% and needed a 321% gain to recover Leverage scales the annual return roughly linearly. The gain needed to get back grows much faster than the initial loss. At 1x leverage the index needed a 48% gain to recover and at 3x it needed 321%, while the months spent under water rose only from 30 to 46 [02] . Drawdown from previous peak, %, levered put-selling index, monthly, 2007-2026 [02] . - Leverage - Return a year - Largest drawdown - Gain needed to recover - Months under water - 1.0× - 7.1% - −32.7% - +48% - 30 mo - 1.5× - 9.5% - −46.2% - +86% - 31 mo - 2.0× - 11.6% - −57.9% - +138% - 35 mo - 3.0× - 14.4% - −76.3% - +321% - 46 mo ## At the same 10% volatility, drawdowns ran from 15% to 60% Equal volatility budgets gave fixed income arbitrage four times the drawdown of global macro. A 20% drawdown limit would have allowed fixed income arbitrage just 0.30 of its volatility-based leverage. Global macro could have taken 1.30. Estimated on 1997-2011 and applied to 2011-2026, CVaR sizing lowered the drawdown for 10 of 14 indices but left the average almost unchanged [04] . ## The put-seller's CVaR estimate swung from -9.2% to -6.1% when October 2008 left the window CVaR describes the left tail better than VaR, yet it demands a lot of data. A ten-year rolling window leaves you looking at a handful of extreme months [11] . The realised tail proved worse than the normal forecast in all 116 windows we checked, and dropping the 2008 crash shifted the severity estimate by a third [02] . rolling ten-year 95% CVaR and normal expected shortfall, % a month, windows ending January 2017 to August 2026, [02] ## The put-seller's three-year Sharpe ratio is higher than in 87.5% of months since 2010 while VIX sits below its median Calm markets routinely pay insurance sellers, with VIX closing above the subsequent realised volatility on 85.2% of days [03] . This volatility premium makes their record look best exactly when the stored-up tail is least visible [02] . We saw the same setup when VIX traded at 16.23 at the end of June 2007. Trailing 36-month Sharpe ratio, monthly, January 2010 to August 2026 [02] [01] . ## Standard risk models severely understate the loss tail in leveraged and short-volatility strategies. Standard risk metrics routinely disguise the structural downside of short-volatility payoffs. Prudent capital allocation demands assessing historical drawdowns instead of trusting a normal model built around a 1.08% daily standard deviation. - Measure - What it shows - Value - Extreme tail days - Count of daily losses far outside normal distribution limits - Put-writing shortfall ratio - Ratio of realised extreme losses against normal model predictions - 1.50 - Negative skewness strategies - Count of hedge fund indices exhibiting asymmetric downside risk - 10 / 14 - Momentum drawdown duration - Months spent failing to recover the previous market peak - 213 mo - Levered recovery requirement - Return required to break even following the maximum trough - +321% - Volatility targeted drawdowns - Range of maximum losses across strategies scaled to identical volatility - 15–60% Never allocate capital to a leveraged strategy without examining its loss tail and the duration of its worst drawdown. Demand to see exactly how the proposed position size would have behaved through that entire historical trough. ## Selected sources This report is research rather than investment advice. Index returns stand gross of fees, costs and taxes, and the hedge fund indices run entirely on self-reported data. Past market tails do not bound future ones. ## Keep up with the research. Choose optional research updates, or learn how the account structure works. ## Independent research, introductions clearly defined. BlackRidge is an independent research bureau introducing private investors to quantitative traders through multiple strategy providers. We publish quantitative research. Investors access strategies through PAMM accounts at the broker. We are not a fund or broker and never hold client money. Your funds stay at the broker. The account is opened in your own name. BlackRidge never receives, holds, or has withdrawal rights over client capital. No fee on your profits. 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Past performance does not indicate future results. ## Sources - [01] [Kenneth French Data Library](https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). We pull daily and monthly US market and risk-free returns from July 1926 to August 2026, alongside the momentum factor since 1927. - [02] [Cboe S&P 500 PutWrite Index](https://www.cboe.com/us/indices/dashboard/put). Daily levels and monthly data from February 2007 track a strategy of selling at-the-money S&P 500 puts collateralised by Treasury bills. - [03] [Cboe VIX historical data](https://www.cboe.com/en/tradable-products/vix/vix-historical-data/). Daily closing values since 1990 let us track expected market volatility. - [04] [BarclayHedge hedge fund indices](https://portal.barclayhedge.com/cgi-bin/indices/displayIndices.cgi?indexID=hf). Fourteen strategy indices from 1997 to 2026 provide the monthly return history for hedge funds. - [05] [Basel Committee on Banking Supervision, Minimum capital requirements for market risk (January 2019)](https://www.bis.org/bcbs/publ/d457.htm). This regulatory text forces the shift from a 99% VaR to a 97.5% expected shortfall. - [06] [European Commission, temporary adjustments to Basel III market risk rules (4 June 2026)](https://finance.ec.europa.eu/publications/commission-adopts-temporary-adjustments-basel-iii-market-risk-rules-safeguard-eu-banks_en). These adjustments alter the new market risk framework applying from 1 January 2027. - [07] [Artzner, Delbaen, Eber and Heath, Coherent Measures of Risk (1999)](https://people.math.ethz.ch/~delbaen/ftp/preprints/CoherentMF.pdf). The authors prove VaR lacks subadditivity, meaning it can mechanically penalise portfolio diversification. - [08] [Rockafellar and Uryasev, Optimization of Conditional Value-at-Risk (2000)](https://doi.org/10.21314/JOR.2000.038). Portfolio construction can optimise directly for CVaR instead of variance. - [09] [Agarwal and Naik, Risks and Portfolio Decisions Involving Hedge Funds (2004)](https://academic.oup.com/rfs/article-abstract/17/1/63/1564388). Many equity hedge fund strategies hold option-like left-tail payoffs that mean-variance analysis completely ignores. - [10] [Daniel and Moskowitz, Momentum Crashes (2016)](https://www.sciencedirect.com/science/article/pii/S0304405X16301490). Momentum strategies suffer severe crashes in panic states after market declines, hitting exactly when the market rebounds. - [11] [Yamai and Yoshiba, Value-at-risk versus expected shortfall: A practical perspective (2005)](https://www.sciencedirect.com/science/article/abs/pii/S0378426604001499). Expected shortfall requires much larger data samples than VaR to achieve the same estimation accuracy. --- ## Citation context The put-selling index comes within 0.09 of the stock market's Sharpe ratio. In the worst 5% of months, its average loss is 1.50 times the normal model's prediction, against 1.18 for the market. At the same 10% volatility, drawdowns ranged from 15% to 60%. Sample and method: loss tails of a put-selling index, the US stock market, the momentum factor and fourteen hedge fund strategy indices, 1926 to 2026. Limits: the CVaR figure rests on just 11 worst months and is inherently noisy. Out of sample, CVaR sizing did not beat volatility sizing on average. Primary input: [Cboe S&P 500 PutWrite Index](https://www.cboe.com/us/indices/dashboard/put). Stable permalink: [https://blckridge.com/research/asymmetric-tail-risk-20260929/#citation-context](https://blckridge.com/research/asymmetric-tail-risk-20260929/#citation-context). ## Read next - [Historical Covariance Forecasts Underestimate Stress Risk by a Factor of 1.6](/research/covariance-estimation-error-20260929/). The companion study uses daily US industry data to examine covariance forecast errors during stress, a different risk question from monthly CVaR.