Separate performance from the sources of performance

Learning goals

• Calculate returns, attribution and risk-adjusted results consistently.
• Distinguish measurement, attribution and appraisal.

Draft · approximately 60 minutes, excluding further revision.

Decision case · fictional facts

A fictional two-sector portfolio holds 60% A and 40% B; the benchmark holds 50% each. Sector returns are 10%/2% in the portfolio and 8%/4% in the benchmark. All are same-period total returns before fees and without external flows. A second strategy earns 8% with 12% volatility, risk-free return 2%, benchmark 6%, and tracking error 4%.

Measurement must respect cash flows and risk

Time-weighted returns link subperiod returns separated by external flows and largely remove their timing effect; money-weighted returns reflect size and timing of capital and can be appropriate when the manager controls those decisions. Specify valuation frequency, fees, taxes and currency. Arithmetic averaging is not compounding; stale or smoothed valuations can understate risk.

Measurement tells what happened, attribution explains decisions contributing to it, and appraisal asks whether results support skill after risk and uncertainty. A valid benchmark should be specified in advance, investable, measurable, unambiguous, appropriate, accountable and reflective of current investment opinions. A manager-selected favorable benchmark after the fact undermines appraisal.

Attribute decisions before interpreting ratios

For Brinson–Fachler attribution, allocation by sector is (wp−wb)(Rb,sector−Rb,total), selection is wb(Rp,sector−Rb,sector), and interaction is (wp−wb)(Rp,sector−Rb,sector). Sum across sectors and reconcile to active return under the same arithmetic convention. Holdings-based analyses can miss intraperiod trades; transaction-based analyses require reliable timing and data. Fixed-income attribution should identify curve, spread, currency and security effects under an explicit model.

Sharpe uses excess return over total volatility; information ratio uses active return over tracking error. Treynor uses systematic beta, while appraisal ratio isolates residual risk after a specified factor model. Downside measures depend on the target and distribution. Estimate uncertainty, nonnormality, leverage, regime exposure and selection bias before interpreting a high historical ratio as persistent skill.

Return attribution and risk attribution answer different questions

Return attribution explains realized portfolio return or excess return. Risk attribution explains sources of total or active uncertainty and their contributions before or after the period. Macro attribution can examine an asset owner’s policy, allocation and manager choices; micro attribution examines decisions within a manager’s mandate. A security can add realized return while also adding unacceptable concentration risk.

For a pension, first separate board-controlled asset-class shifts from a manager’s security selection. Do not give the manager credit for a policy overweight the board imposed, or infer low risk merely because that overweight paid off this year.

Data richness determines the attribution method

Returns-based attribution uses return series and estimated exposures; it is feasible without holdings but can misidentify style when exposures change. Holdings-based attribution uses dated positions and security returns, which can miss intraperiod trades. Transactions-based attribution incorporates trade timing and cash flows but requires accurate reconciled transaction data and valuation conventions.

A manager sells a falling stock on day 2 and buys a rising one on day 3. Month-end holdings alone can falsely imply the winning stock was held all month. A detailed trade ledger can resolve the mismatch; unreconciled data can create false precision instead.

Reconcile an allocation-selection bridge

A two-sector benchmark has weights 50/50 and sector returns 10%/2%, so return 6%. The portfolio weights 60/40 with sector returns 12%/1%, so return 7.6%. In this specified two-effect bridge, allocation=Σ(wp−wb)Rb=.8%; selection including interaction=Σwp(Rp−Rb)=.8%. Together they explain 1.6% excess.

A three-effect attribution can separate interaction rather than include it in selection. Define the model before comparing tables; an unexplained residual may reflect timing, currency, fees or data rather than skill.

Fixed-income attribution separates curve and spread decisions

Suppose rate duration 5, spread duration 4, a benchmark-yield fall 20 bpand spread rise 10 bp. First-order rate contribution≈+1%; spread contribution≈−.4%; combined price effect≈+.6%, before carry, convexity, currency and trading. An attribution table should distinguish curve level, key-rate positioning, spread/sector and issue selection according to the chosen model.

A positive bond return after yields fall does not establish credit-selection skill. Verify the benchmark shock and security cash-flow conventions; callable bonds can have changing effective duration.

Choose risk attribution consistent with the decision

A total-risk decomposition asks which holdings or factors drive portfolio volatility; an active-risk decomposition uses differences from the benchmark. Marginal risk multiplied by position weight can produce a component contribution under a homogeneous risk measure. Correlations matter: a hedge can have a negative contribution, and equal weights are not equal risks.

Select security, sector, factor or scenario attribution based on the mandate and available data. Check covariance stability and whether nonlinear options need a scenario model. A historical risk decomposition is not a guarantee of future diversification.

Evaluate the asset owner and manager at their control boundaries

The owner selects policy, manager lineup, mandates and sometimes tactical overlays; each manager controls decisions delegated by its contract. Macro evaluation can compare actual manager allocation with policy weights, then examine manager performance against appropriate mandates. A manager cannot fairly be judged for currency hedging the owner prohibited.

A complete report identifies decision-maker, benchmark, fee and risk for each layer. Unallocated residuals should be investigated rather than automatically assigned to the last manager in the process.

Liability benchmarks measure funding relevance

A pension liability benchmark can reflect the present value and sensitivity of promised payments under a specified valuation basis. If assets return 4% while liability value rises 7%, a positive asset return can coincide with worsening funded status. Liability duration, inflation, currency and discount assumptions must be documented; the benchmark is not a freely chosen high-return target.

Evaluate surplus changes and funded ratio alongside asset-manager results. The asset manager may still meet its delegated mandate even when the overall liability-relative policy needs revision.

Asset-based benchmarks encode different opportunities

Broad-market indexes, style indexes, custom security baskets, manager-universe comparisons and absolute-return targets capture different investment opportunities and limitations. A custom benchmark should be defined prospectively with transparent inclusion, weighting and reconstitution rules. A peer median is not necessarily investable and may contain survivorship or reporting bias.

A small-cap mandate needs a suitable small-cap opportunity set rather than a convenient large-cap index. Changing the benchmark after observing performance compromises appraisal.

Test benchmark quality before judging skill

A useful benchmark is clearly specified, measurable, appropriate to the mandate and known in advance; investability and accountability also matter. Check whether returns, currency, risk and constituent rules match the opportunity set. Compare portfolio exposures and residual patterns to identify style mismatch. A benchmark should not be selected because it makes alpha look largest.

A consistent data reconciliation can still use an unsuitable benchmark. Separate calculation accuracy from economic appropriateness and disclose any material mandate or benchmark change.

Benchmark misspecification creates false attribution

A value manager measured against a growth index may appear skilled or unskilled mainly because the styles cycle differently. The same mismatch contaminates allocation/selection attribution, information ratios and performance fees if used without adjustment. Test the intended investment universe and factor exposures before interpreting residual return as security-selection alpha.

Use a mandate-consistent benchmark prospectively; show a secondary broad-market comparison if useful without substituting it for the formal standard. Don’t erase a bad result by retroactively picking a favorable index.

Alternative benchmarks must respect timing and valuation

Private funds may report IRR and estimated NAV while public indexes report time-weighted returns. Illiquid marks can lag market movements; fund vintage, leverage, cash-call timing and fees differ. A defensible comparison may use a documented public-market equivalent or vintage/strategy cohort, with data and limitations disclosed rather than equating unlike return metrics.

Hedge-fund peer indexes can suffer survivorship, backfill and selection bias. A smoother reported series does not prove superior downside control.

Appraisal ratios and drawdowns need stated conventions

With return 12%, target 3% and downside deviation 6%, the defined Sortino=(12−3)/6=1.5. Alpha 2% divided by residual risk 4% gives appraisal ratio.5. In matched up periods, portfolio 12% versus benchmark 10% gives 120% up capture; in matched down periods,−8% versus−10% gives 80% down capture. Always specify period aggregation and denominator conventions.

For wealth path 100,120,90,110,125 at equal dates, the peak-to-trough maximum drawdown is 25%. Recovery occurs three periods after the 120 peak. Drawdown duration measures time underwater; it does not equal standard deviation or guarantee a repeatable recovery horizon.

Appraisal metrics are conditional summaries

Sharpe, Sortino, appraisal and capture ratios depend on sample length, benchmark, return frequency and estimated risk. Non-normal payoffs, stale marks and serial correlation can make annualized ratios misleading. Short samples and multiple strategy searches can produce impressive results by chance. Use drawdowns, scenario losses, confidence ranges and process evidence alongside ratios.

A strategy selling crash insurance can show a high Sharpe for years before a large loss. The historical ratio alone cannot reveal that unobserved tail; inspect positions and stress the payoff structure.

Skill assessment needs more than positive alpha

Evaluate economic rationale, appropriate benchmark, factor exposure, fees, capacity, process stability and evidence of repeatability. Statistical significance can be weak with limited independent observations; multiple testing and survivorship matter. An apparently persistent result may be a systematic risk premium rather than manager skill.

A hiring decision combines quantitative appraisal with operational and investment diligence. Predefine review triggers and allow for expected style cycles instead of firing solely after one weak quarter or retaining solely after one lucky gain.

Formula and assumptions

Rp=ΣwpRp,i; allocation=Σ(wp−wb)(Rb,i−Rb); selection=Σwb(Rp,i−Rb,i); interaction=Σ(wp−wb)(Rp,i−Rb,i)

Errors to catch

• Mixing arithmetic attribution with compounded returns without reconciliation.
• Treating one favorable ratio as proof of skill.

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Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.cfainstitute.org