Two Managers, One Mandate: Which Added Risk-Adjusted Value?
A $400 million pension fund is reviewing two external managers before renewing mandates. Both are benchmarked to the same broad equity index over the same 60-month period, during which the risk-free rate averaged 3.0%, the index returned 10.0% and index volatility was 15.0%.
Manager A: annualised return 12.0%, volatility 8.0%, beta 0.60, and holds 12% cash on average. Manager B: annualised return 18.0%, volatility 20.0%, beta 1.60.
Manager B's marketing deck leads with its superior absolute return. Manager B invests mostly in private credit positions marked monthly by an external appraisal agent; three of its largest holdings have not traded in over a year. The investment committee must renew one mandate and is split. Fund policy states that managers are hired for risk-adjusted value added, not raw return.
1. Compute Sharpe, Treynor, Jensen's alpha and M-squared for both managers. Which manager added more value, and how does the answer change if you put them on a common risk footing?
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Manager A
- Sharpe = (12.0 − 3.0) / 8.0 = 1.125
- Treynor = (12.0 − 3.0) / 0.60 = 15.0%
- Jensen α = 12.0 − [3.0 + 0.60 × (10.0 − 3.0)] = 12.0 − 7.2 = +4.8%
- M² = 3.0 + 1.125 × 15.0 = 19.875%, i.e. +9.875% over the market
Manager B
- Sharpe = (18.0 − 3.0) / 20.0 = 0.75
- Treynor = (18.0 − 3.0) / 1.60 = 9.375%
- Jensen α = 18.0 − [3.0 + 1.60 × 7.0] = 18.0 − 14.2 = +3.8%
- M² = 3.0 + 0.75 × 15.0 = 14.25%, i.e. +4.25% over the market
A wins on all four measures. B's extra 6% of raw return is largely the price of carrying beta 1.6 and 20% volatility, and its alpha is a full percentage point lower.
Common risk footing. A holds 12% cash, which mechanically depresses both beta and volatility. Levering A's whole portfolio 2.667× at the risk-free rate (to bring beta from 0.60 to 1.60) gives expected return ≈ 3.0 + 2.667 × 9.0 = 27.0% at volatility ≈ 2.667 × 8.0 = 21.3% - clearly better than B's 18% at 20% volatility. The raw return comparison in B's deck is therefore an artefact of aggressiveness, not of skill.
2. Manager B argues its Sharpe ratio is directly comparable to Manager A's. Is that defensible given its monthly appraisal-based marks?
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No. Appraisal marks lag traded prices, so reported monthly returns are a smoothed, weighted average of true economic returns. Concretely:
- Autocorrelation in returns mechanically reduces measured volatility. If reported returns are a geometric average of the last few true months, reported σ can be materially below true σ (the classic unsmoothing correction, e.g. the Getmansky–Lo–Makarov MA(k) model, recovers a higher true σ).
- Beta is biased downward for the same reason, because the strategy's contemporaneous co-movement with the index is spread over later reported months. Some of what looks like alpha is simply delayed beta.
- Downside dependence is hidden. Illiquid credit positions often reprice in jumps; the appraisal process postpones the jump, so monthly VaR and drawdown statistics understate tail risk.
Effect on this comparison: B's Sharpe of 0.75 and alpha of 3.8% are upper bounds, not estimates. Before the metrics are used, the committee should request unsmoothed return series (or at minimum the lag coefficients and the fraction of NAV that is appraised rather than traded) and recompute. Manager A's listed equity and cash holdings need no such adjustment.
3. The committee can only renew one mandate. What conditions or evidence would you require before either is renewed?
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Renew A, but not on the strength of the backward-looking ratios alone:
- Normalise A for cash. Judge A against a fully invested version of the mandate; if the 12% cash is a deliberate policy overlay rather than a manager decision, it belongs to the fund, not the manager's track record.
- Verify the alpha is repeatable. Check whether A's +4.8% alpha survives a factor decomposition (size, value, momentum). A concentrated, low-beta portfolio can generate alpha by accident of style exposure.
- Do not close the door on B - reprice it. If B's true volatility after unsmoothing is, say, 28% rather than 20%, its Sharpe falls to roughly 0.54 and the case collapses. Ask for position-level data, transaction prices for at least the traded sleeve, and a liquidity stress test (time-to-liquidate under a redemption scenario).
- Governance test. B's reliance on an appraisal agent for positions that have not traded in a year is an operational and valuation risk the fund cannot diversify. Sizing any B allocation must assume the marks, not the market, set the NAV.
Decision rule: a manager is renewed when value added per unit of trustworthy risk is positive and the residual risks (liquidity, valuation, style drift) are ones the fund is paid to bear.