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Economic Modelling · Single and multifactor models for investment returns

Introduction to Investment Return Models for Actuaries

Updated 11 October 2026 · Fact-checked

Actuaries model investment returns to value liabilities, set capital and test strategies when future returns are uncertain. Models are deterministic (fixed inputs, one outcome) or stochastic (random inputs, a distribution of outcomes), and statistical (fitted to data) or economic (built on theory). A good model is realistic, simple enough to use, and suitably calibrated.

Understand Introduction to Investment Return Models

Insurers and pension funds promise cash flows years ahead. They hold assets whose returns are uncertain. To judge whether assets will cover liabilities, you need a view of how returns may behave. That view is an investment return model.

Actuaries use these models for several jobs: pricing products with investment guarantees, valuing liabilities, setting capital and solvency requirements, choosing an asset allocation, and testing how a fund copes with bad outcomes. A single best-guess return cannot show the risk. A model can.

A deterministic model uses fixed inputs and gives one result. Example: assume 7% a year and project the fund. It is simple, transparent and easy to explain, and it suits scenario or sensitivity tests. But it gives no probabilities. A stochastic model treats returns as random variables. Running it many times (simulation) or solving it analytically gives a distribution of outcomes, so you can state probabilities, percentiles and tail losses. It is harder to build, calibrate and explain.

A second split is by how the model is built. A statistical model (empirical or time-series) is fitted to historical data and describes patterns such as mean, volatility and correlation, without needing a theory for why. An economic model is built from economic or financial theory, such as no-arbitrage or equilibrium, and links returns to underlying variables. Statistical models fit the past well but may break when conditions change. Economic models have a rationale but may fit data less closely. In practice the two are often combined.

A good model should be: realistic enough to capture the features that matter for the purpose; simple enough to understand, explain and run; able to be calibrated with the data available; reasonably consistent with the observed behaviour of markets; and free of obvious arbitrage where it is used for pricing. No model is right for every purpose, so fitness for purpose is the main test.

How to solve Introduction to Investment Return Models questions

Use this method for any written or MCQ question asking you to describe, compare or choose a model.

  1. 1Identify the purpose: pricing, valuation, capital, strategy testing or communication.
  2. 2Identify what the question needs from the model: one answer or a distribution, tail risk, correlations, long or short horizon.
  3. 3Classify the model: deterministic or stochastic, and statistical or economic. Give a one-line definition of each term you use.
  4. 4State the advantages and disadvantages of the chosen type, tied to the purpose in the question.
  5. 5Check against the criteria for a good model: realism, simplicity, calibration, data availability, consistency with markets, arbitrage.
  6. 6Say what you would test or monitor: sensitivity to parameters, back-testing, and the effect of changing conditions.
  7. 7Conclude with a clear recommendation or comparison that answers the exact question asked.

Quickest way: Purpose, type, trade-off

When to use it: For MCQs and short-answer parts worth few marks, where you have about two to three minutes.

  1. Ask: does the question need probabilities or just one projection? Probabilities point to stochastic.
  2. Ask: is it fitted to data or derived from theory? Data means statistical; theory means economic.
  3. Name one advantage and one drawback of your choice.
  4. Link to purpose, such as capital or guarantees needing stochastic and tail information.

Common mistakes in Introduction to Investment Return Models

  • Saying deterministic models are wrong or useless.

    Students assume stochastic is always better.

    Fix: State that deterministic models suit simple projections, sensitivity tests and communication. Choose by purpose.

  • Confusing stochastic with statistical.

    Both words start with 'st' and both involve randomness or data.

    Fix: Stochastic vs deterministic is about randomness in the model. Statistical vs economic is about how the model is built.

  • Listing criteria for a good model as a memorised list with no link to the question.

    Students learn a list and write it out.

    Fix: Pick the criteria that matter for the stated purpose and explain why each does.

  • Claiming a model fitted to past data will predict the future well.

    Good historical fit feels like proof.

    Fix: Note that parameters can change and past regimes may not repeat. Mention back-testing and parameter uncertainty.

  • Saying a more complex model is automatically more realistic and better.

    Realism is mixed up with the number of parameters.

    Fix: Point out that extra parameters can be hard to estimate and explain, and may add error. Balance realism with simplicity.

Worked examples

Example 1

A life insurer sells a savings product with a minimum maturity guarantee. Explain why a stochastic investment model is more suitable than a deterministic one to assess the cost of the guarantee.

Show the solution
  1. Purpose: assess the cost of a guarantee that pays out only if investment returns are low.
  2. A deterministic model with one assumed return gives either a guarantee that is in the money or not. It shows a single outcome.
  3. The cost depends on the chance and size of shortfalls, which needs the distribution of returns.
  4. A stochastic model simulates many return paths, giving the average cost of the guarantee and tail outcomes such as high percentiles of cost.
  5. This supports pricing, reserving and capital decisions.
  6. Drawbacks: harder to calibrate and explain, and results depend on the assumed distribution and parameters, so sensitivity tests are still needed.

Answer: The guarantee pays off only in poor outcomes, so its cost depends on the distribution of returns. A stochastic model provides this, while a deterministic model gives a single scenario and hides the risk.

Example 2

Distinguish between a statistical model and an economic model of investment returns, and give one advantage of each.

Show the solution
  1. Statistical model: fitted to historical data to capture features such as mean, volatility and correlation, without necessarily explaining why they arise.
  2. Advantage: it reflects observed behaviour and is relatively easy to fit.
  3. Economic model: built from economic or financial theory, such as no-arbitrage or market equilibrium, linking returns to underlying variables.
  4. Advantage: it has a rationale for its structure, so it may be more credible when conditions change and can be used for consistent pricing.
  5. Note that a statistical model may fail if conditions change, and an economic model may fit the data less closely.

Answer: A statistical model describes data patterns and fits observed behaviour; an economic model is derived from theory and has a rationale for its structure.

Exam tips

  • Define each term in one line before comparing. Many marks go for clear definitions.
  • Always tie your answer to the stated purpose. Generic lists score less.
  • For comparison questions, give both advantages and disadvantages of each side.
  • In MCQs, check whether the option talks about randomness (stochastic) or construction (statistical or economic).
  • Mention calibration and parameter uncertainty when asked to evaluate a model.

Practice questions from Single and multifactor models for investment returns

Introduction to Investment Return Models in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Introduction to Investment Return Models: frequently asked questions

Why do actuaries model investment returns?

Liabilities are long term and assets are uncertain. Models help value liabilities, price guarantees, set capital and compare investment strategies. They show risk, not just a best estimate.

What is the difference between deterministic and stochastic models?

A deterministic model uses fixed inputs and gives one outcome. A stochastic model uses random inputs and gives a distribution of outcomes, so you can assess probabilities and tail risk.

Is a statistical model the same as a stochastic model?

No. Stochastic describes a model with randomness. Statistical describes a model fitted to data. A statistical model can be stochastic, and often is.

What makes a good investment return model?

It should be realistic for its purpose, simple enough to explain and run, and possible to calibrate with available data. It should also be consistent with observed market behaviour and, for pricing, free of arbitrage.