BFF5270 Chap.4 Portfolio Performance Evaluation
Portfolio Performance Evaluation
Performance evaluation tests value added, mandate compliance and consistency with expected risk. This chapter matches measures to portfolio roles, tests benchmark quality, introduces downside evidence and diagnoses sampling, market and risk-control errors. Raw return is never the end of the analysis: the student must identify the relevant risk basis and explain what decision produced the difference.
A dedicated M2 section translates a total-risk ranking into return units after matching the manager to market volatility. Conclusions should remain conditional on benchmark quality, fees and the mandate.
What this chapter covers
- 01
Sharpe reasoning
- 02
M2 comparison
- 03
Jensen alpha
- 04
Treynor measure
- 05
Information ratio
- 06
Downside risk
- 07
Benchmark quality
- 08
Sampling bias
Worked example · free
Interpret active return against a style mismatch
- 1Calculate active return: 9.4% minus 7.8% = 1.6 percentage points.
- 1Identify the persistent small-company style difference.
- 1Test whether the broad benchmark is appropriate for the permitted mandate.
- 1Review fees and active risk before attributing the difference to skill.
- 1Conclude that the positive difference is evidence to investigate, not proof by itself.
Key terms
- Active Return
- Active return is the portfolio return minus the benchmark return over the same period.
- Total Risk
- Total risk is overall return variability, commonly represented by standard deviation.
- Systematic Risk
- Systematic risk is market-related exposure that remains relevant inside a diversified portfolio.
- Active Risk
- Active risk is variability in portfolio return relative to its benchmark.
- Value at Risk
- Value at risk is a model-based adverse-return threshold for a stated tail probability and horizon.
Portfolio Performance Evaluation FAQ
Why can the best raw return be the weakest result?
A high return may come from greater market exposure, volatility, concentration or active risk rather than repeatable skill. Risk adjustment and benchmark comparison ask what was required to earn the result. A ranking that ignores those inputs answers a different question from the one the investor usually cares about.
What makes a benchmark credible?
The lecture emphasises an investable passive alternative with unambiguous composition, appropriate risk and style, prior specification and objective construction. These tests prevent hindsight selection and unfair comparison. A benchmark should represent what the client could reasonably have held instead of the active mandate.
Why are downside measures only supplements?
Downside measures focus on adverse outcomes and can help when return distributions are asymmetric or the mandate emphasises loss control. They do not remove the need to understand total, systematic or active risk. The analyst should explain which portfolio feature makes the downside lens useful.
Exam move
Create a four-branch measure tree: whole portfolio, diversified component, active sleeve and downside-sensitive mandate. Place each ratio under the correct branch and justify the risk basis. Practise benchmark evaluation on mismatched style cases. For back-tests, write the theory, sample, market control and risk control before accepting the ranking. Use percentage points for return differences.
Start every calculation by labelling the portfolio role. If it is the investor's complete risky holding, total volatility belongs in the analysis. If it is one component of a diversified portfolio, beta-based contribution is more relevant. If it is an active sleeve paired with an index, active risk matters. If the mandate focuses on harmful asymmetry, add a downside measure and state why.
Build a benchmark checklist from the lecture's five tests: investable, unambiguous, appropriate, specified in advance and objectively constructed. Apply each adjective to a new case instead of reciting the list. A small-company manager compared with a broad market index should trigger an appropriateness check; a private rule revealed after the period should trigger a prior-specification check.
Recompute the lecture-style value-at-risk expression using a new mean and volatility, but describe the result only within the selected model and tail probability. Never call it the maximum possible loss. For back-tests, mark where look-ahead or survivorship bias could enter, then ask whether the test spans more than one market regime and controls for risk.
Use a reconciliation paragraph after every ratio: observed performance, relevant risk, comparator quality, fees and the decision to retain, reduce, investigate or change monitoring. This sequence makes the final recommendation evidence-led rather than a ranking based on one attractive statistic.
Add the M2 transformation to your review: risk-match the manager to the market with the risk-free asset and compare returns at equal volatility. Predict the sign from the Sharpe ranking before calculating. If the two signs disagree, audit the risky weight, complement and unit basis.
Close by identifying whether a weak result reflects the manager, the selected benchmark, a changed portfolio composition or a method that does not fit the mandate.
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