Overview of Quantitative Trading Strategies › From Backtest to Live Trading

The transition from backtest to live trading represents the ultimate test of a quantitative strategy. Several additional considerations arise:

Before risking real capital, run the strategy in a paper trading environment. This stage validates:

• Execution infrastructure works correctly
• Data feeds are reliable and timely
• Order management handles edge cases
• Risk controls trigger appropriately

Paper trading also provides a psychological bridge, allowing you to experience the strategy's behavior in real-time without financial consequence.

Even a profitable strategy can blow up if position sizes are too large. Building on the risk management principles from Part V, key decisions include:

• Capital allocation. How much of total capital to deploy
• Position limits. Maximum size for individual positions
• Sector and factor limits. Concentration limits to ensure diversification
• Drawdown triggers. Conditions for reducing or halting the strategy

The Kelly criterion provides theoretical guidance on optimal bet sizing. The fundamental question Kelly addresses is: given a trading opportunity with known probabilities of winning and losing, what fraction of your capital should you risk to maximize long-term wealth growth? Betting too little leaves money on the table, while betting too much risks catastrophic losses.

The formula can be derived by maximizing the expected logarithm of wealth, which naturally balances return against risk:

$$\begin{aligned} f^* &= \frac{bp - q}{b} && \text{(basic form using edge/odds)} \\ &= \frac{bp - (1-p)}{b} && \text{(substitute } q = 1-p \text{)} \\ &= \frac{p(b+1) - 1}{b} && \text{(simplify)} \end{aligned}$$

Each variable captures a key aspect of the trading opportunity:

• $f^*$: optimal fraction of capital to allocate, the output we seek
• $p$: probability of a winning trade, estimated from historical analysis
• $q$: probability of a losing trade ($1 - p$), the complement of the win probability
• $b$: win/loss ratio (average gain divided by average loss), measuring the payoff structure
• $bp - q$: expected net profit of the trade (the edge), combining probability and magnitude

The formula balances the strategy's edge against the risk of variance:

• The numerator represents the edge: the expected return per unit of risk. A positive edge means the strategy is profitable on average. The larger the edge, the more capital we should allocate.
• The denominator represents the odds: scaling the bet size inversely to the payoff ratio. When wins are much larger than losses (high $b$), we can afford smaller position sizes because each win contributes more. When the win/loss ratio is closer to 1, we need larger positions to capitalize on our edge.

By maximizing the expected logarithm of wealth, this formula determines the position size that yields the highest long-term geometric growth rate, explicitly penalizing volatility to avoid the ruin associated with over-betting. The logarithmic objective naturally incorporates risk aversion because the pain of losing half your wealth outweighs the joy of doubling it.

In practice, most of us use fractional Kelly (e.g., half Kelly) to account for estimation uncertainty. The probabilities and payoff ratios used in the Kelly formula are estimates, and overconfidence in these estimates leads to position sizes that are too large. Using half or quarter Kelly provides a margin of safety against parameter estimation errors.

Live strategies require continuous monitoring. Key metrics to track include:

• Performance versus expectation: Is the strategy performing within backtested parameters?
• Factor exposures: Have risk exposures drifted from intended levels?
• Execution quality: Are fills occurring at expected prices?
• Capacity utilization: Is the strategy experiencing increasing market impact?

Strategies also decay over time as the market learns and adapts. You continuously research new signals and retire strategies that have stopped working.