Sizing a Thin Edge With Fat Tails
A systematic trader has 800 trades of history: 58% winners, average win 0.90R, average loss 1.00R. Maximum historical drawdown is 14R. The account is $2.0m. The trader proposes risking 4% of equity per trade, arguing that the win rate is high and the equity curve has been smooth. In the last two months, however, three losing trades gap-filled over a weekend to 2.1R, 2.4R and 2.6R rather than stopping at 1.0R, and correlations across open positions have risen because the trader is now running six positions in the same sector.
1. Compute the expectancy and the Kelly-implied risk fraction from the 800-trade record. Then show why 4% is not supported once the tail behavior is included.
Read the worked answer
Base-case expectancy: E = 0.58(0.90) − 0.42(1.00) = 0.522 − 0.420 = +0.102R per trade
An edge of 0.10R is real but thin - roughly a 10-cent return per dollar risked.
Kelly fraction for a binary payoff with win b = 0.90, p = 0.58: f* = p − q/b = 0.58 − 0.42/0.90 = 0.58 − 0.4667 = 0.113R, i.e. full Kelly would risk ~11.3% of equity per trade if the payoff distribution were as assumed.
Why that number is not usable here:
- The loss assumption is violated. Replace the 1.0R loss with the observed tail. If the average loss becomes 1.3R (a reasonable blend of the 800-trade record and the recent gaps): E = 0.58(0.90) − 0.42(1.30) = 0.522 − 0.546 = −0.024R. The edge flips negative. A strategy whose sign depends on the loss assumption must be sized to the bad assumption, not the good one.
- Kelly is logarithmic and brutal about estimation error. f* is a maximum of an expected log-growth function; risk above f* lowers long-run growth and below f* lowers it only mildly. With a 0.10R edge estimated from a finite sample, the confidence interval around f* is wide enough that half-Kelly or less is the defensible operating point. Full Kelly on an estimated edge is effectively an all-in bet on the estimate.
- Drawdown arithmetic. 14R maximum drawdown at 4% risk per trade = 14 × 4% = 56% of equity - and that is the historical worst case, drawn from a period before the gaps appeared and before the book became a single sector. A 56% drawdown requires a 127% gain to recover.
- Correlation. Six same-sector positions at 4% each is not six 4% bets; in a correlated selloff it behaves like one ~20%+ bet. Position-level risk limits do not control portfolio risk here.
2. State the risk setting you would authorize, the reasoning behind it, and the specific conditions under which it could be raised.
Read the worked answer
Authorized setting: 1.0–1.25% of equity per trade, with a portfolio heat cap of 5%.
Reasoning:
- At 1.25%, base-case expectancy is ~13 bp of equity per trade; with the 1.3R tail assumption it is ~−3 bp, i.e. roughly breakeven rather than ruinous. The position is small enough that a mis-estimated edge is a cost, not an extinction event.
- Historical 14R drawdown becomes 14 × 1.25% = 17.5%, which is recoverable (a 21% gain) and inside typical risk tolerance.
- Worst single gap of 2.6R at 1.25% is 3.25% of equity - survivable in a single event.
- 1.25% sits at roughly one-ninth to one-tenth of the estimated Kelly fraction, comfortably in the fractional-Kelly range appropriate to an uncertain edge.
Portfolio-level rules that matter more than the per-trade number:
- Cap aggregate heat (sum of open risk) at 5% of equity.
- Cap sector concentration: no more than 2 simultaneous positions in the same sector, or apply a correlation haircut that reduces each position to 0.75% when the six-position cluster is present.
- Stress the book to a 2.5R average loss on all open positions at once, and require survival with less than a 25% drawdown.
Conditions to raise toward 2–3%: a full market cycle of out-of-sample trading with realized average loss within 1.05R of the model, no gaps beyond 1.5R in the trailing 200 trades, documented stable expectancy, and a portfolio heat report showing the book is not a single factor. Absent any of those, the 1.25% stands. The trader's 'smooth equity curve' is not a condition - smoothness is the observation that most provoked the current problem.