Ex-ante return
Also written Ex-ante expected return
The forward-looking expected rate of return: the sum of the possible returns multiplied by their probabilities. The opposite of ex-post return, which is computed from historical data.
In plain language
"Ex ante" means before the event. An ex-ante return is a forecast: what the investment should return, averaged across the outcomes you think are possible.
The workbook defines the expected rate of return of an individual investment as the sum of the expected returns multiplied by their corresponding probabilities, and says such a return is also known as ex-ante return. Returns calculated from historical data are ex-post returns.
The important thing to grasp is that the ex-ante return is a probability-weighted average, not a prediction of any single outcome. A stock can have an ex-ante return of 11% even if none of its possible scenarios delivers exactly 11%.
How it works
For one security (section 3.3). List the states of the world, attach a probability and a return to each, multiply and add.
The workbook's Table 3.1:
| State | Probability | Stock A | Stock B |
|---|---|---|---|
| Boom | 0.3 | 15% | 25% |
| Normal | 0.5 | 10% | 10% |
| Recession | 0.2 | 2% | 1% |
E(R_A) = 0.3(15%) + 0.5(10%) + 0.2(2%) = 4.5 + 5.0 + 0.4 = 9.9%
For a portfolio (section 3.5). The ex-ante return is the weighted average of the expected returns of the assets. The workbook's Table 3.3 gives four assets:
0.2(9%) + 0.1(12%) + 0.3(15%) + 0.4(18%)
= 1.8 + 1.2 + 4.5 + 7.2 = 14.7%
Its partner, ex-ante risk (section 3.4). The same probabilities produce the variance, and its square root is the ex-ante risk. In the workbook's second illustration — 8%, 10%, 12%, 14% at 0.25 each — the expected return is 11% and the ex-ante standard deviation 2.24%.
The formula
E(R) = Σ Pᵢ × Rᵢ (one security)
E(R_portfolio) = Σ Wᵢ × E(Rᵢ) (portfolio)
where Pᵢ is the probability of return Rᵢ, and Wᵢ is the weight of asset i in the portfolio.
A worked example
Scenarios, probabilities and amounts are illustrative.
A Category III AIF manager in Mumbai forecasts a long-biased equity scheme for the coming year:
| Scenario | Probability | Return |
|---|---|---|
| Bull market | 0.25 | 30% |
| Base case | 0.50 | 12% |
| Bear market | 0.25 | −10% |
Ex-ante return = 0.25(30) + 0.50(12) + 0.25(−10)
= 7.5 + 6.0 − 2.5 = 11%
On an investor's Rs 1 crore, the expected gain is Rs 11 lakh. But notice that no scenario pays Rs 11 lakh: the investor ends up with a gain of Rs 30 lakh, Rs 12 lakh, or a loss of Rs 10 lakh.
A year later the scheme has actually returned 4%. That 4% is the ex-post return. It does not prove the 11% forecast was wrong; it tells you which part of the distribution turned up.
Why NISM asks about it
Chapter 3, sections 3.3 (Expected rate of return for individual security) and 3.5 (Expected rate of return for a portfolio), define ex-ante return and compute it; section 3.4 builds ex-ante risk on the same probabilities. Chapter 7 then measures funds on historical returns, which is the ex-post side. Expect a probability-table computation, a portfolio weighted-average computation, and a "which term describes forecast returns" definition question.
Common exam traps
- Ex-ante = forecast, from probabilities. Ex-post = history, from actual returns. Swapping them is the classic error.
- The probabilities must add up to 1 before you multiply. If a question gives 0.3, 0.5 and 0.2, check it.
- The ex-ante return need not match any single scenario.
- Portfolio ex-ante return is a simple weighted average; portfolio risk is not, because covariance enters.
- Workbook arithmetic slip in Table 3.1: the table gives Stock B a 10% return in the normal state, but the worked answer uses 20% and reports 17.7%. With the table's 10%, B's expected return is 0.3(25) + 0.5(10) + 0.2(1) = 12.7%. Recompute from the numbers in front of you rather than recalling 17.7%.
Where this is taught
Free preparation for NISM Series XXI-BRelated terms
- RiskThe possibility that actual returns turn out different from what was expected — measured as the dispersion of returns around their own average, and not the same thing as uncertainty.
- Standard deviationA measure of how far returns typically stray from their own average — the standard statistic for total risk, counting company-specific and market-wide causes alike.
- VarianceA measure of how widely a scheme's periodic returns fluctuate around its own average return — the square of standard deviation, and a risk measure relevant to both debt and equity schemes.
- Modern Portfolio TheoryMarkowitz's framework for building portfolios on expected return and risk together, in which the co-movement between holdings — not their individual riskiness — decides the risk of the whole.
- Required Rate of ReturnThe minimum return an investor expects before committing money: the nominal risk-free rate plus a risk premium. It is not a guaranteed, forecast or realised return.
- Ex-post returnA return calculated from historical data — what an investment actually earned — as distinct from the forward-looking, probability-weighted ex-ante return.