ml4t Risk Metrics
A strategy with Sharpe 1.5 and max drawdown -55% will get shut down before it recovers. Reporting returns without drawdowns, tail risk, and duration metrics hides the path dependency that determines whether a strategy survives.
The Problem
Sharpe ratio is the default performance metric, but it treats upside and downside volatility equally and says nothing about tail losses. A strategy can have a high Sharpe while hiding a -40% drawdown that takes 18 months to recover. Fund managers and allocators care about max drawdown, time underwater, and worst-case losses - because those determine whether the strategy (and the fund) survives. Always report drawdown alongside return metrics.
The Pattern
WRONG
import numpy as np
returns = strategy_returns # daily
sharpe = returns.mean() / returns.std() * np.sqrt(252)
print(f"Sharpe: {sharpe:.2f}") # Looks great - ships it
CORRECT
import numpy as np
from scipy.stats import norm
returns = strategy_returns # daily, numpy array
# Return metrics
sharpe = returns.mean() / returns.std() * np.sqrt(252)
downside = np.minimum(returns, 0) # All returns: negative kept, positive → 0
sortino = returns.mean() / np.sqrt((downside ** 2).mean()) * np.sqrt(252)
# Drawdown
cumulative = np.cumprod(1 + returns)
running_max = np.maximum.accumulate(cumulative)
drawdown = (cumulative - running_max) / running_max
max_dd = drawdown.min()
calmar = (returns.mean() * 252) / abs(max_dd)
# Tail risk (95% confidence)
var_95 = np.percentile(returns, 5)
cvar_95 = returns[returns <= var_95].mean()
print(f"Sharpe: {sharpe:.2f} | Sortino: {sortino:.2f} | Calmar: {calmar:.2f}")
print(f"Max DD: {max_dd:.1%} | VaR(95): {var_95:.1%} | CVaR(95): {cvar_95:.1%}")
Metric Reference
| Metric | Formula | Measures |
|---|---|---|
| Sharpe | mean(r) / std(r) * sqrt(252) | Risk-adjusted return |
| Sortino | mean(r) / sqrt(E[min(r,0)^2]) * sqrt(252) | Downside-adjusted return |
| Max drawdown | max peak-to-trough decline | Worst cumulative loss |
| Calmar | ann_return / |max_dd| | Return per unit of drawdown |
| VaR(95%) | 5th percentile of returns | Daily loss threshold |
| CVaR(95%) | mean of returns below VaR | Expected loss in tail |
Parametric vs Historical VaR
# Historical: uses actual distribution (captures fat tails)
var_hist = np.percentile(returns, 5)
# Parametric: assumes normal (underestimates tails)
var_param = returns.mean() + norm.ppf(0.05) * returns.std()
# Always prefer historical unless you need scenario-based VaR
Guardrails
- Never report Sharpe alone - always include max drawdown and Calmar at minimum
- VaR underestimates tail risk by design - pair it with CVaR (Expected Shortfall)
- Historical VaR assumes the past contains the worst case - it does not
- Annualize consistently: multiply mean by 252, std by sqrt(252) for daily data
- Monitor current drawdown in real time, not just historical max
Production Implementation
ml4t-diagnostic provides validated risk computation:
from ml4t.diagnostic.api import PortfolioAnalysis
pa = PortfolioAnalysis(returns=strategy_returns, benchmark=benchmark_returns)
metrics = pa.compute_summary_stats()
report = metrics.summary() # Sharpe, Sortino, max_dd, Calmar, VaR, CVaR, etc.
Checklist
- Sharpe, Sortino, and Calmar all reported (not Sharpe alone)
- Max drawdown and drawdown duration computed
- CVaR computed alongside VaR for tail risk
- Metrics annualized consistently (daily * sqrt(252))
- Current drawdown monitored in live systems (not just historical max)