Subperiod Decomposition of Returns

A volatility-arbitrage strategy shows a ten-year Sharpe of 1.4, computed the standard way from the full daily return series. Split the same ten years into ten one-year chunks and something else appears: 2020 alone contributed a Sharpe-equivalent return so large that removing that single year from the sample drops the remaining nine years' combined Sharpe to 0.3. The full-period statistic is technically correct and almost entirely uninformative about what this strategy does in a normal year, because one abnormal period is doing nearly all the work.

Why one number over the full period can mislead

Sharpe, mean return, and drawdown computed over a full backtest are single summary statistics of the entire path. They treat ten years of data as one draw, giving no visibility into whether performance was smooth and repeatable or concentrated in a handful of episodes. A strategy that's flat-to-losing 90% of the time and makes its entire track record in rare crisis windows is a real and useful thing to know you're funding — a tail-risk hedge, say — but only if the summary statistic doesn't hide that it's what's happening.

Worked example: leave-one-year-out

Same strategy, annual returns (%): 8, 6, 4, −3, 7, 5, 210 (2020), 9, 3, 6. Full-sample mean: $(8+6+4-3+7+5+210+9+3+6)/10 = 25.5\%$, and the full daily-path Sharpe computes to a respectable 1.4, because 2020's gains arrived gradually over several volatile months rather than in one jump.

Excluding 2020: mean $(8+6+4-3+7+5+9+3+6)/9 \approx 5.4\%$, with typical annual volatility near 9%. The full daily recomputation on these nine years lands near 0.3. Either way, the number an allocator should expect in a year that isn't a volatility crisis is far below the headline 1.4.

Worked example: rolling-window consistency check

Compute Sharpe on every trailing 24-month window, stepped monthly (roughly 96 overlapping windows). If 70 of those show a Sharpe between 0.8 and 1.6 — a tight band — that's evidence of a repeatable process. If instead the rolling Sharpe ranges from −0.4 to 4.2, with most mass bunched near 0.3 and a handful of windows overlapping the 2020 stretch pulling the tail to 4.2, that's the signature of a strategy dominated by one episode — exactly what a full-sample statistic can't show you.

Notice how the plot changes shape when the parent distribution is skewed rather than symmetric — a single fat tail pulls the mean away from where most probability mass sits. Same mechanism as the vol-arb example: one enormous subperiod can drag the full-sample Sharpe far from what a "typical" period looks like.

What this means in practice

Always report a leave-one-period-out Sharpe alongside the full-sample number, plus a rolling-window chart showing the spread. If a small number of periods account for a large share of return, say so explicitly and characterize what made them special — whether the strategy can catch the next one like it is a much harder question than whether it caught the last one.