14.8 Risk limits and drawdown control · M14 Portfolio and going live

Motivation

Sizing each trade correctly (M03) does not size the book. Limits at two levels, plus a rule for drawdowns, keep a sequence of individually reasonable trades from producing an unreasonable loss.

14.8.1Position and portfolio limits#

Position-level limits

Risk per trade. Fixed fractional: shares $= fE/(P_{entry} - P_{stop})$ where $E$ is equity and $f$ the fraction risked (M03; beginners commonly use 0.25–1%).
Notional cap per name (e.g. ≤ 20% of equity for swing trades), because a stop does not protect against gaps: an overnight gap through the stop turns a 1R loss into several R.
Liquidity cap: position ≤ a small fraction of average daily traded value (M05), so exits do not move the price.
Event rule: reduce or close before results, policy meetings or index rebalancing if the setup's statistics were not estimated over such events.

Portfolio-level limits

Open risk ("heat"): $\sum_i f_i \le H$ . If every stop is hit together (correlation 1), the loss is $H$ . With 5 positions at 1% each, $H = 5\%$ .
Gross and net exposure, and beta-adjusted net exposure to the Nifty.
Sector/factor concentration: e.g. ≤ 2 positions per sector.
Stress loss: portfolio loss under a scenario (Nifty −10% gap, correlations to 1) ≤ a stated fraction of equity.

14.8.2Loss limits#

Loss limits A maximum daily loss (e.g. 2–3R) and weekly loss (e.g. 5–6R) stop trading for the period once hit. Their statistical role: after a cluster of losses, either the market regime has changed (the setup's distribution no longer applies) or the trader's decision quality has deteriorated (tilt; 14.9). Neither can be diagnosed in real time. Calibrate the limit so that it is rarely hit by chance: with 4 trades a day and a 60% loss rate, $P(\ge 3 \text{ losses}) = 0.475$ , so a "3 losses" daily stop would bind every other day and is too tight; with 6 trades a day, $P(\ge 4) = 0.544$ . Set limits from the empirical distribution of daily R outcomes in your backtest (e.g. its 95th–99th percentile of daily loss), not from round numbers.

14.8.3Drawdown control#

Proposition 14.14A drawdown bound by cushion-proportional exposure

Let $W_t$ be wealth, $M_t = \max_{s\le t}W_s$ the running maximum, and fix $d \in (0,1)$ . Define the cushion $C_t = W_t - (1-d)M_t$ and hold risky exposure (in rupees) $m\,C_t$ with $m > 0$ . If the risky asset's price path is continuous, then $W_t > (1-d)M_t$ for all $t$ : drawdown never reaches $d$ .

Proof

$dW_t = mC_t\,dR_t$ , where $dR_t$ is the risky asset's return, and $dC_t = dW_t - (1-d)dM_t$ . On any interval where $M$ is constant, $dC_t = mC_t\,dR_t$ , so $C$ is a stochastic exponential, $C_t = C_s\,\mathcal E(mR)_{s,t}$ , which is strictly positive when $C_s > 0$ and paths are continuous. $M$ increases only when $W_t = M_t$ , at which point $C_t = dM_t > 0$ . Starting from $C_0 = dW_0 > 0$ , $C$ stays positive.∎

This is the idea of Grossman & Zhou ("Optimal Investment Strategies for Controlling Drawdowns", Mathematical Finance 3(3), 1993) and of CPPI. In discrete time with gaps, a single return $R < -1/m$ makes the cushion negative, so choose $m < 1/|\text{worst plausible gap}|$ . With $d = 10\%$ and $m = 5$ , exposure is 50% of wealth at a new high and falls to zero as the drawdown approaches 10%; a 20% gap would take the cushion to exactly zero (a 10% drawdown) and any larger gap would breach the floor.

A practical drawdown rule in the spirit of 14.14 for discretionary traders: at a 5% drawdown from peak equity, halve $f$ ; at 10%, stop live trading and return to paper until the review (14.10) is complete; restore size in steps as equity recovers. This sacrifices expected growth for a bound on the worst case, which, by M03's fractional-Kelly analysis, costs much less growth than it saves in ruin probability.