Pairs Trading by the Numbers: Spreads, Hedge Ratios, Mean-Reversion Tests, Z-Score Signals, Half-Lives, Backtests & Trading Costs

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Put 120 daily closes of two fictional freight companies on a common base of 100, turn them into log returns, write the return correlation out with SUMPRODUCT and measure how far the two lines still drift apart.
• Estimate how many units of Ostrand move with one unit of Halvery, write the intercept as ȳ − b·x̄, build the spread for all 120 days and chart it.
• Regress the daily change of the spread on yesterday's spread, write out the standard error of the slope, look up a critical value in a fictional table and give a verdict – then repeat it on a toy pair that only wanders.
• Measure the spread against its own last 20 days with a rolling mean and σ, turn it into a z-score and label each day as entry, exit, stop or hold.
• Turn the reversion slope θ of six pairs into half-lives, derive a look-back window within limits and a maximum holding period, and flag which pairs pass both the test and the half-life rule.
• Turn the z-scores into a position that remembers yesterday, size both legs from the hedge ratio, book the daily P&L on yesterday's position and chart the cumulative result.
• Subtract trading costs and a fictional borrow fee from the gross result, count the trades, and track the running peak of the net P&L to find the deepest drawdown.
• Estimate the hedge ratio on days 1–80 only, measure how far it drifts on days 81–120, pick the best entry level in-sample with INDEX/MATCH and see how it fares on the days it never saw.