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Use a complete, non-overlapping scenario set
The fictional rate model has rise, unchanged and fall scenarios. Their weights sum to one. A bond fund’s positive-return probability is specified separately within each scenario. The numbers are learning assumptions, not estimates of actual future interest rates or fund performance.
Calculate each scenario’s contribution
Multiply each conditional probability by the probability of its scenario. The contributions are joint probabilities of the scenario and positive return.
| Scenario | Scenario weight | Positive return given scenario | Joint positive-return contribution |
|---|---|---|---|
| Rise | 40% | 20% | 8% |
| Unchanged | 35% | 55% | 19.25% |
| Fall | 25% | 85% | 21.25% |
| Total | 100% | 48.5% |
Explain the unweighted-average error
A simple average of 20%, 55% and 85% gives approximately 53.33%. That calculation gives equal weight to the three scenarios, contrary to the supplied 40%, 35% and 25% weights. It answers a different model.
Do not reuse a branch probability in the other direction
Under these assumptions, the probability of a rise given positive return is 8%/48.5%, approximately 16.49%. It is not the 20% probability of positive return given a rise. The conditioning event changed, so the denominator changed.