A research screen tells you that the average five-day return after a particular event was +0.9% and that 64% of those windows were positive. Both numbers are useless in isolation. The question that gives them meaning is what happened in five-day windows generally, over the same period, in the same universe.
That is the base rate. It is the answer to “what normally happens”, and every conditional figure is only interesting as a difference from it.
Illustrative arithmetic across 15 years of Nifty 500 daily data. Suppose the unconditional five-day window is positive 55% of the time with a mean return of +0.35%, and your event windows are positive 64% of the time with a mean of +0.9%:
| Measure | After the event | Base rate | Lift |
|---|---|---|---|
| Share positive | 64% | 55% | 9 points |
| Mean return | +0.90% | +0.35% | +0.55% |
| Median return | +0.60% | +0.20% | +0.40% |
The 64% shrinks to a nine-point edge. That is still worth investigating, and it is a different claim from the one the raw number appeared to make.
Matching the comparison
A base rate is only a valid reference if it was computed the same way as the conditional figure. Three things have to match.
The period has to match. A base rate drawn from 2003 to 2007 compared against events clustered in 2020 measures the difference between two market regimes.
The universe has to match. Events tend to concentrate in the parts of the market where the underlying activity happens. Bulk deals cluster in smallcaps, so the reference should be the smallcap base rate rather than the Nifty 50 one.
The horizon has to match, including how the window is measured. Five trading days against five calendar days will diverge in a month with several exchange holidays.
Caveats
Indian equity samples over the last two decades carry a positive unconditional drift, so most base rates for “share of positive windows” sit above 50%. Any signal evaluated without that reference will look better than it is, and long-only event studies will look better than short ones by construction.
Base rates move with volatility. In a high-volatility regime the share of positive windows barely changes while the dispersion doubles, which means the same lift is worth far less per unit of risk.
A large lift on few events is still weak. Nine percentage points across 60 events has a standard error near 6 points. Compute the base rate first, then the lift, then the t-statistic on the difference.