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032

Case 032Strategy evaluation and backtestsCore

A strategy has a Sharpe ratio of 1.0 at 12% volatility and a worst drawdown of 8% in two years live. What drawdown should investors expect over ten years, and is a 20% fall in year three evidence it is broken?

1The situation

Seravane Systematic runs a futures strategy targeting 12% annual volatility. Its two-year live record shows a Sharpe ratio of 1.0, so an excess return of about 12% a year, and a worst peak-to-trough fall of 8%. Marketing materials quote the 8% as the strategy's drawdown.

In year three the fund falls 20% from its high. An investor asks whether the strategy has stopped working.

2Your task

Estimate the drawdown a Sharpe 1 strategy should be expected to suffer over ten years, judge whether 20% is outside that range, and say what evidence would really show it is broken.

Quick check

Over ten years, what is the typical worst drawdown for a Sharpe 1 strategy at 12% volatility?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Investors should expect a worst drawdown of around 18% over ten years, and a 20% fall is well inside the normal range. About 34% of simulated ten-year paths for a Sharpe 1 strategy at 12% volatility fall 20% or more. The 8% record reflects a short, lucky window: even over two years the median worst fall is 10.8%. A drawdown alone says little; changes in the signal's behaviour say more.

Step 1Why does a short record understate drawdown?

Think of the worst traffic jam you have sat in. After one month of commuting it might be 40 minutes; after ten years it is probably two hours, not because the roads got worse but because you sampled more days. The maximum drawdown is the worst stretch in the record, so it can only grow as the record lengthens. Seravane's 8% is the worst of two years. Even for those two years it was on the kind side: the median worst fall over two years for this strategy is 10.8%, and about 79% of two-year paths go beyond 8%.

The longer you watch, the deeper the worst fall you will seeTwo years, median10.8%Ten years, median17.8%Ten years, 90th percentile26.1%live record, 8%
For a Sharpe 1 strategy at 12% volatility, the median worst drawdown is 10.8% over two years and 17.8% over ten, with a 90th percentile of 26.1%, so the live 8% sits below even the two-year median.
Step 2What should investors expect over ten years?

Simulate it. Draw 20,000 ten-year paths of weekly returns with a 12% excess return and 12% volatility, and record each path's worst peak-to-trough fall. The median is 17.8%, one path in ten is worse than 26.1%, and one in twenty is worse than 29.2%. In units of annual volatility, the median ten-year drawdown is about 1.5 vols, which is a useful rule to carry: for a Sharpe 1 strategy over a decade, expect the worst fall to be around one and a half times the annual volatility, and plan for twice that. The maximum drawdownThe largest fall from a running peak to a later trough, as a percentage of the peak. It depends on the path and on how long you watch. in the marketing should be replaced by this range.

Worst drawdown over ten years, Sharpe 1 at 12% volatility5%10%15%20%25%30%35%40%Worst peak-to-trough fall in ten years8%: the live recordmedian 17.8%20%: the year-three fall34% of paths fall20% or more
Across 20,000 simulated ten-year paths of a Sharpe 1 strategy at 12% volatility, the median worst drawdown is 17.8%, the live record of 8% sits at the far left, and 34% of paths fall 20% or more.
Step 3Is the 20% fall evidence that the strategy is broken?

Not on its own. A 20% fall is 1.67 annual vols, and 34% of healthy ten-year paths contain one. Hitting a drawdown that roughly a third of working strategies hit cannot tell you this one has stopped working. The test that has power looks inside the returns: has the signal's correlation with next-period returns collapsed, has turnover or slippage jumped, has the strategy started losing in the market conditions it used to win in? A drawdown with an unchanged hit rate and unchanged costs is most likely bad luck; one with a changed signal is evidence.

Two limits belong in the answer. The simulation assumes the Sharpe really is 1.0, but two years of data estimate a Sharpe with a standard error of about 1 over the square root of 2, roughly 0.7, so the true figure could be much lower, and a lower Sharpe means deeper drawdowns. It also assumes normal returns; fat tails and volatility clustering make deep drawdowns more common, not less. Both errors point the same way, so the 18% median is a floor for planning, not a ceiling.

Where candidates lose it

The usual loss is anchoring on the observed 8% and treating it as the strategy's drawdown, then calling 20% a two-and-a-half times breach. A maximum over a short window is a biased, low estimate of what a longer window will show.

The second is the opposite error: declaring that nothing can ever be learned from a drawdown. The right answer separates the size of the fall, which is weak evidence, from changes in how the signal behaves, which is strong evidence.

What the interviewer asks next

  • How long a record would you need to tell a Sharpe 1 strategy from a Sharpe 0.5 one?
  • How does volatility targeting change the drawdown distribution?
  • What drawdown would you set as a stop for this fund, and why?
← Case 031Three assets return 6%, 9% and 12% with volatilities of 8%, 15% and 25%. Long only, at most 50% in any one, target volatility 12%. Write the optimisation problem and find approximate weights.Case 033 →Given twenty days of desk P and L that include one very large loss, compute the 95% historical VaR, the normal VaR and the expected shortfall, and say which the risk committee should see.

Company names and figures are illustrative.

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