A risk ratio compares the probability of an event in one group with the probability of the same event in a reference group.
A risk ratio, also called relative risk, compares the probability of an event in one group with the probability of the same event in a reference group over a defined period. A risk ratio of 2 means the event probability in the first group is twice the probability in the reference group.
Risk ratio measures relative probability, not dollar loss, causation, or absolute risk. Analysts should report the underlying event rates beside the ratio.
For groups \(A\) and \(B\):
If \(a\) of \(n_A\) observations in Group A and \(c\) of \(n_B\) observations in Group B experience the event:
Group B is the reference group. Reversing the groups produces the reciprocal ratio, so reports should name both numerator and denominator.
| Risk ratio | Interpretation |
|---|---|
| Above 1 | Event probability is higher in Group A than in Group B |
| 1 | Event probabilities are equal in the observed data |
| Between 0 and 1 | Event probability is lower in Group A than in Group B |
| 0 | No events occurred in Group A, subject to sample uncertainty |
| Undefined | Reference-group event probability is zero |
For a negative event such as default, a ratio above 1 indicates greater relative risk. For a positive event such as successful repayment, the same numerical interpretation applies but the business meaning reverses. Define the event before labeling a result favorable or unfavorable.
Assume two comparable loan cohorts are observed for one year:
| Cohort | Defaults | Loans at start | Default risk |
|---|---|---|---|
| Group A | 40 | 1,000 | 4% |
| Group B | 20 | 1,000 | 2% |
Group A’s observed one-year default risk is twice Group B’s. The absolute risk difference is:
Both statements matter. The ratio communicates proportional difference; the percentage-point difference helps estimate additional defaults and financial impact.
This comparison does not prove why Group A defaulted more often. Borrower mix, underwriting period, geography, loan age, economic conditions, data quality, and other factors may explain some or all of the difference.
Suppose an operational event rises from 0.01% to 0.02%. The risk ratio is 2, but the absolute increase is 0.01 percentage point. If another event rises from 10% to 20%, the ratio is also 2, but the absolute and financial consequences may be much larger.
Report at least:
For business decisions, translate probabilities into exposure and severity. Twice the frequency of a negligible event is different from twice the frequency of a catastrophic loss.
Risk ratios can compare:
In credit risk analysis, the ratio can highlight cohort differences, but it does not replace exposure-at-default, loss-given-default, expected-loss, or concentration analysis.
The groups should be comparable. A raw ratio can mislead when exposure sizes, observation time, eligibility, or risk characteristics differ.
| Measure | Calculation or focus | Key distinction |
|---|---|---|
| Risk ratio | Probability in Group A divided by probability in Group B | Direct comparison of cumulative event probabilities |
| Risk difference | Probability in Group A minus probability in Group B | Absolute percentage-point change |
| Odds ratio | Odds in Group A divided by odds in Group B | Can differ materially from risk ratio when events are common |
| Rate ratio | Events per unit of exposure time in one group divided by another | Uses person-time, account-time, transaction volume, or another exposure base |
| Hazard ratio | Relative instantaneous event rate in a time-to-event model | Model-based and not a simple probability ratio |
| Loss ratio | Claims or losses divided by premium or another financial base | Measures financial loss burden, not relative event probability |
Do not label an odds ratio, rate ratio, or loss ratio as a risk ratio. The measures can answer different questions even when they use the same source data.
Use consistent inclusion rules, dates, account status, product definitions, and follow-up periods. Avoid comparing a seasoned portfolio with newly originated accounts without adjustment.
Specify what counts as default, fraud, claim, chargeback, or incident. Changes in reporting or classification can create an apparent risk change without a change in economic behavior.
A zero reference probability makes the ratio undefined. A near-zero denominator can produce a very large and unstable ratio. Small event counts require particular caution.
Point estimates should be accompanied by confidence intervals or another appropriate uncertainty analysis when based on sample data. A ratio above 1 is not automatically a statistically or economically meaningful difference.
Confounding, selection bias, missing data, censoring, and changing economic conditions can distort the comparison. Multivariable or matched analysis may be needed when groups differ materially.
These public statistical sources use health examples, but the probability-ratio definition is the same. Finance applications require finance-specific event definitions, exposure data, and economic-impact analysis.
This article provides general financial and statistical education. It is not personalized investment, credit, insurance, actuarial, legal, regulatory, or risk-management advice.