BAFI6010 · Advanced Investment Management
Testing Portfolios
Topic 6 is the stress-test-before-you-implement stage of the investment management process. Risk decomposition (marginal contribution to risk) only gives an average risk contribution, so before a Strategic Asset Allocation goes live it is put through three testing methodologies — sensitivity analysis, back-testing (with the in-sample vs out-of-sample discipline) and scenario / Monte-Carlo analysis — then checked across the business cycle (expansion / contraction) and the market cycle (upturn / downturn). In BAFI 6010 this topic is not examined in the final exam, but it is directly assessed in the Excel group assignment, so the payoff is choosing the right test, running it cleanly, and interpreting the downside.
What this chapter covers
- 011. Why test — MCR gives only an average risk contribution; testing reveals event- and regime-specific behaviour
- 022. Sensitivity analysis — flex ONE input (a capital-market assumption or correlation), hold the rest fixed
- 033. Back-testing — run the strategy on historical data vs a benchmark; read tracking error, downside risk and attribution
- 044. In-sample vs out-of-sample — build/optimise on one window, validate on withheld data to catch over-fitting
- 055. Scenario analysis — probability-weighted economic states give the portfolio's expected return and scenario risk
- 066. Monte-Carlo simulation — generate many return paths stochastically from each asset's mean and variance
- 077. Business cycle vs market cycle — survive expansion AND contraction, not one benign stretch
- 088. Data-period discipline — long multi-cycle window for SAA, upturn/downturn window for TAA, consistent dates across assets
Scenario analysis on a proposed 70/30 allocation
- +1Check the state set is valid: the probabilities must sum to one. 0.45 + 0.35 + 0.20 = 1.00 ✓.
- +2Expected return is the probability-weighted mean: E(R) = 0.45(14) + 0.35(7) + 0.20(−6) = 6.30 + 2.45 − 1.20 = 7.55%.
- +1Form each squared deviation from the mean, weighted by its probability: 0.45(14 − 7.55)² = 0.45(41.6025) = 18.72; 0.35(7 − 7.55)² = 0.35(0.3025) = 0.11; 0.20(−6 − 7.55)² = 0.20(183.6025) = 36.72.
- +2Sum for the scenario variance and square-root for the standard deviation: Var = 18.72 + 0.11 + 36.72 = 55.55 (%²), so SD = √55.55 = 7.45%. Remember the variance is in percent-squared — square-root it back to a percentage.
Key terms
- Why test (the MCR blind spot)
- Marginal contribution to risk answers 'on average, how much portfolio risk comes from each position?' — a single average number. It cannot show how the allocation behaves in a specific event or regime. Testing fills that gap by revealing the sources of risk and the portfolio's event-specific behaviour.
- Sensitivity analysis
- Vary ONE input (a capital-market assumption, an expected return, or a correlation) while holding the others fixed, and watch portfolio risk/return respond. Strength: exposes the single assumption the allocation is fragile to. Weakness: ignores joint moves — inputs rarely change one at a time.
- Back-testing
- 'Walk in the fund manager's shoes': run the strategy on historical data against a benchmark (asset classes proxied by appropriate indices), producing tracking error, downside-risk measures and return attribution. Strength: uses real observed relationships. Weakness: history may not repeat and it is prone to over-fitting / look-back bias.
- In-sample vs out-of-sample
- In-sample = tested on the same data used to build and optimise the model; out-of-sample = tested on data withheld from estimation. Every strategy looks good in-sample, so out-of-sample performance is the honest test of whether it generalises or was curve-fit to noise.
- Scenario analysis
- Define a small set of economic states (good / normal / bad) whose probabilities sum to one, assign each a portfolio return, and compute the probability-weighted mean and variance. The acceptance test is that the portfolio behaves reasonably even in the negative state — not that it has the highest expected return.
- Monte-Carlo simulation
- Scenario analysis industrialised: instead of a handful of hand-picked states, generate thousands of return paths stochastically from each asset's mean and variance (and correlations), then read the full distribution of portfolio outcomes.
- Business cycle vs market cycle
- The business cycle is the expansion / contraction of real economic activity (peak → trough → peak); the market cycle is the parallel upturn / downturn in asset prices. They overlap but differ — markets often turn ahead of the economy — and the portfolio should be tested across both.
- Data-period discipline
- Match the test window to the decision: a long, multi-cycle period for a Strategic Asset Allocation (it must survive several regimes) and an upturn/downturn window for Tactical tilts, keeping start/end dates and frequency consistent across all assets.
Testing Portfolios FAQ
Is Testing Portfolios examined in the final exam?
No. In BAFI 6010 Topic 6 is explicitly excluded from the final exam. It is, however, directly assessed in the Excel group assignment, where you build a Strategic Asset Allocation and then test it. So do not treat it as free final-exam marks — there are none — but do master it, because the marks live in the assignment (choosing the right test, running it cleanly, interpreting the downside).
What is the difference between sensitivity, scenario and Monte-Carlo analysis?
Sensitivity analysis flexes ONE input at a time and holds the rest fixed. Scenario analysis describes whole-economy STATES (good / normal / bad) with probabilities attached and reads the portfolio's return in each. Monte-Carlo simulation generates many return paths stochastically from each asset's mean and variance. Blurring sensitivity and scenario is the most common slip: sensitivity flexes an assumption, a scenario describes a state of the world.
Why is an impressive back-test not enough?
Because it is almost certainly an in-sample result. An optimiser handed a fixed history will fit the noise as happily as the signal, so a glowing in-sample back-test is expected even from a pure curve-fit. The honest check is out-of-sample performance on data withheld from estimation, and it is usually weaker than the paper version — treat in-sample results as a sanity check only.
How do I compute expected return and risk in scenario analysis?
First confirm the state probabilities sum to one. Then the expected return is the probability-weighted mean, E(R) = Σ p·R. For risk, compute each squared deviation from the mean weighted by its probability, Σ p·(R − E)², to get the variance, then take the square root for the standard deviation. Watch the units: variance is in percent-squared, so square-root it back to a percentage.
What is the difference between the business cycle and the market cycle?
The business cycle is the expansion / contraction of the real economy (activity rising to a peak, then falling to a trough). The market cycle is the parallel upturn / downturn in asset prices, which overlaps the business cycle but is not identical — prices often turn before the real economy. Cycle testing checks that size and style tilts (small vs large caps, value vs growth) are a deliberate, survivable bet across both, rather than an accident of one sample window.
Exam move
Learn the three methodologies as a set you can contrast on demand — for each, a one-line strength and a one-line weakness, because the assignment (and any short-answer) is graded like a checklist. Drill the one calculation that turns up: scenario analysis. Build a state table (state, probability, return), check the probabilities sum to one, then get the expected return as the probability-weighted mean and the risk as the square-root of the probability-weighted squared deviations — and always report the standard deviation, not the raw percent-squared variance. Anchor the two disciplines that separate a robust strategy from a curve-fit: out-of-sample validation (never trust an in-sample back-test) and testing across the whole business cycle, not one benign stretch. Finally, remember the framing — this topic is not on the final exam but is assessed in the group assignment, so the effort you put in here pays off directly in that case study.
