Direct Alpha

Formula

Why direct alpha was proposed

IRR-spread methods (LN-PME, PME+, mPME) subtract the IRR of a hypothetical index investment from the fund's IRR. Gredil, Griffiths and Stucke showed that the difference of two IRRs is not, in general, the rate of excess return, because compound rates such as IRR are not additive. Direct alpha computes the excess return in one step: compound every flow at the index return, then solve for the rate that remains. It is the annualised counterpart of KS-PME and is consistent with it.

Relation to KS-PME

Direct alpha and KS-PME use the same index-compounded flows. At a discount rate of zero, the net present value of those flows equals the KS-PME numerator minus its denominator. For the usual pattern of contributions followed by distributions, that net present value falls as the rate rises, so KS-PME > 1 exactly when direct alpha > 0. KS-PME says how much better over the life; direct alpha says how much better per year.

Interpreting and reporting it

Direct alpha has the units of an annual return, so it can be set beside an alpha target or a fee load. It inherits IRR's mechanics: it is money-weighted, it depends on the final NAV for an unrealised fund, and with unusual sign patterns it can have more than one solution. Like KS-PME it applies one unit of the index to each flow with no separately estimated beta, so exposures the index does not capture (size, sector, style) appear in the alpha. Report the index, the compounding convention (discrete or continuous), the period frequency and the valuation date.

How LPs use it

LPs use direct alpha when they need a public market equivalent in rate form: comparing managers with different fund lives, setting excess-return expectations against the fees paid, or aggregating outperformance across a programme on pooled cash flows.

Worked examples

Examples are illustrative; figures are not market data.

Not the same as

• Kaplan–Schoar Public Market Equivalent (KS-PME): KS-PME is the cumulative ratio of index-adjusted value to index-adjusted contributions; direct alpha is the annualised rate implied by the same flows.
• Alpha: Jensen's alpha comes from a regression of periodic returns on market returns; direct alpha comes from a fund's cash flows and an index, with no separately estimated beta.
• Long–Nickels PME: LN-PME compares two IRRs; direct alpha computes a single IRR of index-compounded flows.

Common mistakes

• Calling the difference between the fund's IRR and the index's annual return "alpha".
• Mixing discrete and continuous direct alpha in one comparison.
• Annualising a quarterly alpha by multiplying by four instead of compounding.
• Ignoring that the result depends on how well the index matches the fund's exposures.

Edge cases

• Flows with more than one sign change after index compounding can produce more than one solution.
• Very young funds produce extreme annualised alphas from small differences in NAV.
• If the index and fund currencies differ, all flows must be converted at each date before compounding.

Sources

1. Benchmarking Private Equity: The Direct Alpha Method. Oleg R. Gredil; Barry Griffiths; Ruediger Stucke, Journal of Corporate Finance, Vol. 81, 102360, August 2023; SSRN working paper 2014 (doi:10.2139/ssrn.2403521). Status: Published (paywalled) (checked 2026-10-01). SSRN working paper dated 2014-02-28: section II.A.4 (non-additivity of compound rates), III.A (equations 16-17), III.C (relation to KS-PME) — supports: Direct alpha = ln(1 + a) with a the IRR of index-compounded flows; IRR-spread methods are heuristics because compound rates are not additive; direct alpha is zero when KS-PME equals one
2. Private Equity Performance: Returns, Persistence, and Capital Flows. Steven N. Kaplan; Antoinette Schoar, The Journal of Finance, Vol. 60(4), pp. 1791-1823, August 2005. Status: Published (journal paywalled; NBER w9807 working paper) (checked 2026-10-01). Vol. 60(4), pp. 1791–1823 — supports: Origin of the KS-PME ratio
3. The Public Market Equivalent and Private Equity Performance. Morten Sorensen; Ravi Jagannathan, Financial Analysts Journal, Vol. 71(4), pp. 43-50. Status: Published (paywalled) (checked 2026-10-01). Vol. 71(4), pp. 43–50 — supports: KS-PME equivalent to valuation with Rubinstein's dynamic CAPM; index should approximate investor's wealth portfolio; leverage does not raise PME

• Kaplan–Schoar Public Market Equivalent (KS-PME)
• Alpha
• Internal Rate of Return (IRR)
• Beta
• Public Market Equivalent (PME)

• XIRR (Date-Exact IRR)