Chapter 6: Risk Management¶
Control portfolio risk to survive and thrive.
Why Risk Management?¶
"Rule #1: Never lose money. Rule #2: Never forget rule #1." - Warren Buffett
Even the best signals fail sometimes. Risk management:
- Limits losses during drawdowns
- Ensures survival through bad periods
- Enables consistent compounding
Types of Risk¶
Market Risk¶
Exposure to overall market movements:
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signal beta:
stock_ret = ret(prices, 1)
market_ret = ret(market, 1)
beta = rolling_cov(stock_ret, market_ret, 60) / rolling_var(market_ret, 60)
emit beta
Specific Risk¶
Risk unique to individual securities:
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signal idio_risk:
// Risk unexplained by market
residual = stock_returns - beta * market_returns
idio_vol = rolling_std(residual, 60)
emit idio_vol
Factor Risk¶
Exposure to common factors (size, value, momentum):
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// Monitor factor exposures
factor_exposure:
market_beta: [0.9, 1.1] // Target range
size: [-0.1, 0.1] // Neutral
value: [0.0, 0.3] // Slight tilt
Concentration Risk¶
Too much exposure to single positions/sectors:
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constraints:
max_position = 0.03 // No more than 3% per stock
max_sector = 0.20 // No more than 20% per sector
Position-Level Risk¶
Position Sizing¶
Limit exposure to individual stocks:
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portfolio main:
weights = rank(signal).long_short(
top = 0.2,
bottom = 0.2,
cap = 0.03 // Max 3% per position
)
Volatility-Based Sizing¶
Allocate less to volatile stocks:
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signal vol_adjusted_weights:
raw_weight = rank(signal) / count(signal)
vol = rolling_std(ret(prices, 1), 60) * sqrt(252)
inv_vol = 1 / vol
adjusted = raw_weight * inv_vol
emit adjusted / sum(adjusted) // Normalize
Portfolio-Level Risk¶
Gross Exposure¶
Total absolute exposure:
Net Exposure¶
Directional market exposure:
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constraints:
net_exposure = 0.0 // Dollar neutral
// or
net_exposure: [-0.1, 0.1] // Small range
Sector Constraints¶
Limit sector concentration:
Turnover Control¶
Limit trading activity:
Volatility Targeting¶
Fixed Volatility Target¶
Scale positions to target volatility:
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portfolio vol_targeted:
raw_weights = rank(signal).long_short(top=0.2, bottom=0.2)
// Target 10% annual volatility
vol_target = 0.10
current_vol = portfolio_volatility(raw_weights)
scale = vol_target / current_vol
weights = raw_weights * scale
backtest from 2015-01-01 to 2024-12-31
Dynamic Scaling¶
Reduce exposure in high volatility environments:
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signal vol_scale:
current_vol = rolling_std(ret(market, 1), 20) * sqrt(252)
target_vol = 0.15
scale = clip(target_vol / current_vol, 0.5, 1.5)
emit scale
portfolio adaptive:
base_weights = rank(signal).long_short(top=0.2, bottom=0.2)
weights = base_weights * vol_scale
Drawdown Management¶
Maximum Drawdown Monitoring¶
Track underwater periods:
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signal drawdown:
peak = rolling_max(portfolio_value, 252)
dd = (portfolio_value - peak) / peak
emit dd
Drawdown-Based Deleveraging¶
Reduce exposure during drawdowns:
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signal dd_scale:
drawdown = current_drawdown
// Scale down as drawdown increases
scale = where(drawdown > -0.05, 1.0,
where(drawdown > -0.10, 0.75,
where(drawdown > -0.15, 0.50, 0.25)))
emit scale
Risk Metrics¶
Value at Risk (VaR)¶
Maximum expected loss at confidence level:
For a portfolio with 10% annual vol:
Conditional VaR (CVaR)¶
Expected loss given VaR breach:
Tracking Error¶
Volatility of returns vs benchmark:
Complete Risk Framework¶
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data:
source = "prices_fundamentals.parquet"
format = parquet
// Signals
signal momentum:
emit neutralize(zscore(ret(prices, 60)), by=sectors)
signal value:
emit neutralize(zscore(book_to_market), by=sectors)
signal combined:
emit 0.5 * momentum + 0.5 * value
// Volatility regime
signal vol_regime:
market_vol = rolling_std(ret(market, 1), 20) * sqrt(252)
long_vol = rolling_std(ret(market, 1), 60) * sqrt(252)
high_vol = market_vol > long_vol * 1.3
emit high_vol
// Risk-aware portfolio
portfolio risk_managed:
// Base weights
base_weights = rank(combined).long_short(
top = 0.2,
bottom = 0.2,
cap = 0.03
)
// Scale down in high vol regime
vol_scale = where(vol_regime, 0.7, 1.0)
weights = base_weights * vol_scale
constraints:
// Exposure limits
gross_exposure = 2.0
net_exposure: [-0.1, 0.1]
// Concentration limits
max_position = 0.03
max_sector = 0.20
// Factor limits
beta: [0.8, 1.2]
// Turnover
max_turnover = 0.25
// Risk limit
max_volatility = 0.12 // 12% target vol
costs = tc.bps(10)
backtest rebal=21 from 2015-01-01 to 2024-12-31
Risk Monitoring in Production¶
Key Metrics to Monitor¶
| Metric | Frequency | Alert Level |
|---|---|---|
| Daily P&L | Daily | >2% loss |
| Drawdown | Daily | >10% |
| Volatility | Daily | >1.5x target |
| Gross Exposure | Intraday | Outside limits |
| Factor Exposure | Daily | Outside limits |
Alert Configuration¶
YAML
alerts:
- name: "Drawdown Alert"
condition: drawdown > 0.10
action: notify
- name: "Circuit Breaker"
condition: daily_loss > 0.03
action: halt_trading
Risk Budgeting¶
Equal Risk Contribution¶
Each position contributes equally to risk:
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portfolio risk_parity:
// Weight inversely to volatility
vol = rolling_std(ret(prices, 1), 60)
inv_vol = 1 / vol
weights = inv_vol / sum(inv_vol)
Factor Risk Budgeting¶
Allocate risk to factors:
Best Practices¶
1. Start Conservative¶
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// Start
max_position = 0.02
gross_exposure = 1.5
// Increase over time as confidence grows
max_position = 0.03
gross_exposure = 2.0
2. Multiple Defense Layers¶
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// Layer 1: Position limits
cap = 0.03
// Layer 2: Sector limits
max_sector = 0.20
// Layer 3: Volatility targeting
max_volatility = 0.12
// Layer 4: Drawdown circuit breaker
max_daily_loss = 0.03
3. Stress Testing¶
Test against historical crises: - 2008 Financial Crisis - 2020 COVID Crash - 2022 Rate Hikes
4. Know Your Limits¶
Define maximum acceptable: - Daily loss: 3% - Monthly loss: 10% - Maximum drawdown: 20%
Exercises¶
- Add position and sector constraints to a strategy
- Implement volatility targeting
- Create a drawdown-based scaling mechanism
- Monitor factor exposures
Next Chapter¶
Continue to Chapter 7: Going to Production to learn about deploying live trading systems.