Free lesson · Quant strategy development

01 / Start with a source of return

Open interactive lesson Practice calculations Explore labs

Start with the idea

An edge is a conditional comparison, not just a positive average during a rising market. Specify the baseline and ask what additional information changes the distribution of returns, over which holding period and for which executable instrument.

Symbols, units & horizon

α(x,h): conditional excess return relative to the chosen baseline
Xₜ=x: observed feature condition
Rₜ,ₜ₊ₕ: return over horizon h
E: expectation under the estimated model
α̂: estimated edge, not a known quantity
c_all-in: spread, fees, impact, borrow and financing in return units
e_net: estimated net edge, using a baseline matched to the trade

When and why to use this

Use an economic hypothesis to choose features and rejection tests before optimising. It helps distinguish compensation for risk from forecasting information and from accidental sample fit.

An edge is a conditional expected net payoff, estimated with uncertainty. A rule that bought before past rallies is a description; a research hypothesis explains why that information should change future executable returns. Start with the mechanism, the counterparties, and the reason competition has not already removed the opportunity.

α (x, h) = 𝔼 [R_{t, t + h} | X_{t} = x] - 𝔼 [R_{t, t + h}], e_{net} = \hat{α} - c_{a l l i n}

Algebra and arithmetic

Separate baseline, conditional return and costs

Let conditional mean be m(x) and baseline mean be m₀. Define incremental alpha as $α = m (x) - m_{0}$ ; equivalently $m (x) = m_{0} + α$ .
An incremental after-cost advantage is $e = \hat{α} - c$ . A total expected net holding return is instead $m_{0} + \hat{α} - c$ . Keep the comparison consistent.

Work it by hand

Conditional mean 18 bp, baseline 8 bp, additional cost 4 bp: incremental net advantage=6 bp; total expected net holding return=14 bp.

X is information available at decision time and h is the holding horizon. Here alpha denotes incremental conditional return relative to an unconditional baseline; factor-model alpha is a related but different definition. Both expected return and cost are uncertain. A signal predicting a 2 bp midprice move has no usable edge if executing and closing it costs 5 bp.

Possible source	Economic story to test	Failure mechanism
Risk premium	Compensation for bearing losses in states investors dislike	Mistaking crash exposure for repeatable skill
Behavioural or slow information	Underreaction, forced selling, delayed attention	Signal becomes public, crowded or faster to exploit
Structural flow	Index changes, institutional rebalances, funding constraints	Mechanism is anticipated or rule changes
Relative value	Related claims diverge beyond carrying and hedging costs	Relationship breaks or financing disappears
Liquidity provision	Earn compensation for immediacy and inventory risk	Adverse selection, queue competition, jumps

Write the strongest simple alternative explanation: market beta, carry, sample selection, a data revision, or one exceptional event.
Specify which observation would disprove the mechanism. A thesis with no possible rejection criterion cannot be tested.
Identify the natural horizon. A quarterly earnings thesis and a five-second order-book signal need different data, cost and execution models.
Benchmark against no-trade, a relevant passive exposure, and a simple rule with fewer parameters.

Research sources, review dates and limitations

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

def net_edge(conditional_expected_return, baseline_expected_return, all_in_cost):
    """All inputs are same-horizon decimal returns under a matched benchmark."""
    alpha = conditional_expected_return-baseline_expected_return
    return alpha, alpha-all_in_cost

print(net_edge(.002, .0005, .0008))  # .0015 gross, .0007 net

Continue learning

Quant Strategy Development — all lessons

Quantitative finance and development glossary · Python resources and libraries · Research sources and limitations