CFA Level III · Level III Core

Investment Manager Selection: formula sheet

Full chapter guide

Key formulas

Selection process sequence: Mandate and objectives → universe → quantitative screen → qualitative due diligence → fees and contract → appointment → monitoring and review; Know the order and what each step is meant to answer. Wording of steps varies, but the logic does not.
Quantitative vs qualitative role: Quantitative = what happened and how; Qualitative = why, and will it last; Numbers narrow the list. Qualitative work decides between finalists.
Qualitative review areas (five Ps): People, Parent, Process, Portfolio, Performance; Use this checklist to structure due diligence answers.
Fit test: Manager style and benchmark must match the mandate and the client's constraints; A good manager with the wrong style or benchmark is the wrong hire.
Ex-post alpha (single factor): α = Rp − [Rf + β × (Rm − Rf)]; Realized return minus the return expected for the beta taken. Positive is a historical estimate of value added, not proof of skill.
Active return: Active return = Rp − Rb; Portfolio return minus benchmark return for the same period.
Tracking risk: Tracking risk = standard deviation of (Rp − Rb); Also called active risk or tracking error.
Information ratio: IR = (Rp − Rb) ÷ tracking risk; Active return per unit of active risk. Higher means more consistent active performance.
Sharpe ratio: Sharpe = (Rp − Rf) ÷ σp; Use for the whole portfolio. Total risk is the denominator.
t-statistic for alpha: t = α ÷ standard error of α; Larger absolute values mean alpha is less likely to be luck. Roughly 2 or more is a common threshold at about 95% confidence for a long sample.
Returns-based style regression: Rp = b1×F1 + b2×F2 + … + bn×Fn + e, with weights ≥ 0 and summing to 1; The weights show the effective style mix. The error term e is the part not explained by styles, often read as selection.
The five Ps: Philosophy, Process, People, Parent organization, Performance; Learn the order and what each one tests. Questions usually name a weakness and ask which P it belongs to.
Consistency test: Philosophy → Process → Portfolio → Performance; Each link should follow from the previous one. A break in the chain is a red flag.
Performance as evidence: Performance is judged against the stated philosophy and process, not alone; Good returns that the process cannot explain are a concern, not a comfort.
Returns-based style regression: R(manager) = a + b1·R(index 1) + b2·R(index 2) + … + bn·R(index n) + e; Coefficients are style weights. In Sharpe-style analysis they are constrained to be ≥ 0 and to sum to 1. The residual e is the return not explained by style. It reflects selection and any factors the chosen indexes miss.
Style R-squared (explained share): Style R² = share of manager return variance explained by style indexes; 1 − R² = share of variance not explained by style; A high R² means style explains most of the return pattern. A low R² suggests a poor index set, a manager who changes style, or large selection effects. The unexplained share is not by itself a measure of selection skill.
Active return: Active return = Manager return − Benchmark return; Only meaningful if the benchmark fits the manager's style.
Benchmark quality checks: Specified in advance, appropriate, measurable, unambiguous, reflective of current investment opinions, accountable, investable; Use as a checklist when testing any proposed benchmark. These are the same seven properties listed in the concept section.
Universe bias checklist: Survivorship bias, classification (composition) bias, backfill bias, small or ill-defined universe; Survivorship bias overstates universe returns, so a manager can look worse against it than against the full set of managers.
Ad valorem fee: Fee = fee rate × AUM; Use average or end-of-period AUM exactly as the contract states. Tiered schedules apply each rate only to its own band.
Performance fee with hard hurdle: Incentive fee = incentive rate × max(0, return − hurdle) × AUM; Only the excess over the hurdle is shared.
Performance fee with soft hurdle: Incentive fee = incentive rate × total gain, if return > hurdle; otherwise 0; The whole gain is shared once the hurdle is cleared.
Performance fee with high water mark: Incentive fee = incentive rate × max(0, ending NAV − max(HWM, hurdle-adjusted starting NAV)); Read the contract for how the hurdle and HWM combine. Fee is zero if NAV is at or below the HWM.
Net return: Net return = gross return − (fees ÷ beginning AUM); Equivalent form: Net return = (ending value net of fees − beginning value) ÷ beginning value. Compare net return with the benchmark, not gross return.
Active return: Active return = Portfolio return − Benchmark return; Used to judge results versus the mandate benchmark over a full market cycle, not one quarter.
Tracking error (active risk): Tracking error = standard deviation of active returns; A sharp rise suggests style drift or a change in process. Compare with the level agreed at hiring.
Information ratio: IR = Average active return ÷ Tracking error; Measures active return per unit of active risk. A falling IR is a monitoring signal.
Total cost of replacing a manager: Total cost = Transition costs + Search and legal costs + Fee difference + Opportunity cost; Terminate only if the expected benefit of the new manager exceeds this cost.
Termination test (rule): Terminate if reasons for hiring no longer hold AND expected gain > total cost of switching; Poor short-term returns alone are not a sufficient reason.

Quick revision

Selection is a process: define the need, screen, diligence, agree terms, hire, monitor.
Start from the client's objectives and constraints, not from past returns.
Past performance alone does not prove skill; check how the returns were earned.
Quantitative work tests style consistency, risk-adjusted results and benchmark fit.
The five Ps: people, philosophy, process, portfolio, performance.
A good benchmark is appropriate for the style and investable, and is agreed in advance.
Style drift is a warning sign, especially when it adds unrewarded risk.
Fees affect net returns; check structure, any performance fee terms and alignment of interests.
The investment management agreement should set out mandate, guidelines, reporting and termination terms.
Monitoring compares actual behavior with what you expected at hiring, not only recent returns.
Termination should follow stated criteria, such as broken process or key staff loss, not short-term underperformance alone.
In essays, match the command word and justify in few words using vignette facts.

Common mistakes

Starting the search with manager returns instead of the client's objectives. Fix: Always state the mandate, benchmark and constraints first. Screens only make sense against them.
Treating strong past performance as proof of skill. Fix: Ask why the manager earns excess return and whether the process and team will persist. Check results against the style benchmark.
Treating a high historical alpha as a forecast of future alpha. Fix: Say ex-post alpha is an estimate with error. Ex-ante alpha needs a forward view of skill, adjusted for fees, capacity and persistence.
Ranking managers by raw return. Fix: Adjust for risk first. Use alpha, information ratio or Sharpe, and compare with the right benchmark.
Starting and ending with past performance. Fix: Treat performance as evidence to test the other four Ps. Ask whether the process explains the returns.
Confusing philosophy with process. Fix: Philosophy is the belief about why returns exist. Process is the step-by-step method that applies it.
Treating the manager's stated style as the true style. Fix: Always verify with holdings or returns-based evidence. If evidence conflicts with the label, the evidence wins.
Saying returns-based analysis needs holdings data. Fix: Returns-based uses only return series and style index returns. Holdings-based uses portfolio securities and their characteristics.
Treating a soft hurdle like a hard hurdle. Fix: Hard: fee on the excess only. Soft: fee on the whole gain once the hurdle is beaten.
Paying a performance fee on a recovery of earlier losses. Fix: Compare ending NAV with the HWM. No fee until NAV exceeds it.

Exam tips

Expect vignettes where a sponsor's process has a flaw. Spot the missing or misordered stage.
In essays, answer the command word exactly. Identify means list, Justify means give the reason, so keep each answer short and linked to the client.
Do not rely on recent performance as the reason for a hire. Look for evidence of a repeatable process.
Remember that monitoring and termination are part of the process, so include them in any full-process answer.
Use the five Ps as a quick structure when asked what to examine in due diligence.
Match the command word. If asked to calculate, show the formula and the number. If asked to justify, give the evidence and the conclusion in one or two sentences.
Always state both sides of skill versus luck: the statistic that supports skill and the limit, such as a short record or bias.
Distinguish ex-post alpha (realized, historical) from ex-ante alpha (expected, forward-looking) in a single clear line when the question uses either term.