{"concept_id":"ALTSS-PERF-024","slug":"direct-alpha","canonical_name":"Direct Alpha","aliases":["direct alpha method"],"kind":"metric","authority":"academic","facets":["PRF"],"domains":["PERFORMANCE"],"display_title":"Direct Alpha","search_aliases":["direct alpha method","direct alpha private equity","gredil griffiths stucke","direct alpha vs ks pme","annualized pme"],"one_sentence_definition":"Direct alpha is the annualised excess return of a private fund over a public index, computed as the IRR of the fund's cash flows after each has been compounded to the valuation date at the index's return.","plain_english":"Direct alpha restates every contribution and distribution in index terms, as KS-PME does, and then asks what annual rate of return those index-adjusted flows earned. If the fund merely matched the index, the answer is zero. A positive figure is the extra return per year the fund earned over the index on its own cash-flow timing.","parent_concepts":["public-market-equivalent"],"child_concepts":[],"related_concepts":["ks-pme","alpha","long-nickels-pme","pme-plus","modified-pme","irr","beta"],"comparison_concepts":[],"not_the_same_as":[{"slug":"ks-pme","distinction":"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."},{"slug":"alpha","distinction":"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."},{"slug":"long-nickels-pme","distinction":"LN-PME compares two IRRs; direct alpha computes a single IRR of index-compounded flows."}],"formula_ids":["F-PERF-024-direct-alpha"],"worked_examples":[{"title":"Illustrative fund and index flows ($ millions)","paragraphs":["LPs fund 100 and then 50 (periods 0 and 1) and receive 20, 60 and 70 over periods 2 to 4; NAV at the end of period 5 is 80. The benchmark, a total-return index, is at 100, 110, 105, 120, 130 and 140 on those dates and so compounds at 7.0% a year. The fund's IRR is 12.9% and its [TVPI](/glossary/tvpi) 1.53x. Compounded to period 5, the net flows are −140.0, −63.6, +26.7, +70.0, +75.4 and +80 (NAV). Their IRR is a direct alpha of **+6.3% a year** (6.1% continuously compounded). The [KS-PME](/glossary/ks-pme) of the same flows is 1.24."],"calc":{"fn":"direct_alpha","inputs":{"contributions":[100,50,0,0,0,0],"distributions":[0,0,20,60,70,0],"nav_final":80,"index":[100,110,105,120,130,140]},"expected":{"direct_alpha":0.063,"direct_alpha_continuous":0.0611},"tol":0.0005}},{"title":"The same fund against a stronger index","paragraphs":["Against an index rising 100, 118, 130, 152, 170, 195, direct alpha is **−1.1% a year** and KS-PME 0.96: the sign of alpha and the side of 1.0 on which KS-PME falls always match."],"calc":{"fn":"direct_alpha","inputs":{"contributions":[100,50,0,0,0,0],"distributions":[0,0,20,60,70,0],"nav_final":80,"index":[100,118,130,152,170,195]},"expected":{"direct_alpha":-0.0108},"tol":0.0005}}],"sections":[{"heading":"Why direct alpha was proposed","paragraphs":["IRR-spread methods ([LN-PME](/glossary/long-nickels-pme), [PME+](/glossary/pme-plus), [mPME](/glossary/modified-pme)) 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."]},{"heading":"Relation to KS-PME","paragraphs":["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."]},{"heading":"Interpreting and reporting it","paragraphs":["Direct alpha has the units of an annual return, so it can be set beside an [alpha](/glossary/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."]},{"heading":"How LPs use it","paragraphs":["LPs use direct alpha when they need a [public market equivalent](/glossary/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](/glossary/pooled-irr) cash flows."]}],"classification_rules":[],"calculation_rules":[],"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."],"external_standard_mappings":[],"source_ids":["SRC-ACAD-GREDIL-GRIFFITHS-STUCKE-2023","SRC-ACAD-KAPLAN-SCHOAR-2005","SRC-ACAD-SORENSEN-JAGANNATHAN-2015"],"citations":[{"source_id":"SRC-ACAD-GREDIL-GRIFFITHS-STUCKE-2023","pinpoint":"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","source":{"source_id":"SRC-ACAD-GREDIL-GRIFFITHS-STUCKE-2023","title":"Benchmarking Private Equity: The Direct Alpha Method","authors":"Oleg R. Gredil; Barry Griffiths; Ruediger Stucke","publisher":"Journal of Corporate Finance","document_type":"paper","url":"https://doi.org/10.1016/j.jcorpfin.2023.102360","doi":"10.1016/j.jcorpfin.2023.102360","year":2023,"publication_date":"Vol. 81, 102360, August 2023; SSRN working paper 2014 (doi:10.2139/ssrn.2403521)","jurisdiction":"intl","status":"Published (paywalled)","last_verified":"2026-10-01"}},{"source_id":"SRC-ACAD-KAPLAN-SCHOAR-2005","pinpoint":"Vol. 60(4), pp. 1791–1823","supports":"Origin of the KS-PME ratio","source":{"source_id":"SRC-ACAD-KAPLAN-SCHOAR-2005","title":"Private Equity Performance: Returns, Persistence, and Capital Flows","authors":"Steven N. Kaplan; Antoinette Schoar","publisher":"The Journal of Finance","document_type":"paper","url":"https://doi.org/10.1111/j.1540-6261.2005.00780.x","doi":"10.1111/j.1540-6261.2005.00780.x","year":2005,"publication_date":"Vol. 60(4), pp. 1791-1823, August 2005","jurisdiction":"intl","status":"Published (journal paywalled; NBER w9807 working paper)","last_verified":"2026-10-01"}},{"source_id":"SRC-ACAD-SORENSEN-JAGANNATHAN-2015","pinpoint":"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","source":{"source_id":"SRC-ACAD-SORENSEN-JAGANNATHAN-2015","title":"The Public Market Equivalent and Private Equity Performance","authors":"Morten Sorensen; Ravi Jagannathan","publisher":"Financial Analysts Journal","document_type":"paper","url":"https://doi.org/10.2469/faj.v71.n4.4","doi":"10.2469/faj.v71.n4.4","year":2015,"publication_date":"Vol. 71(4), pp. 43-50","jurisdiction":"intl","status":"Published (paywalled)","last_verified":"2026-10-01"}}],"faq":[],"seo":{},"first_published":null,"last_reviewed":"2026-10-01","last_modified":"2026-10-01","content_version":"2.0.0","url":"https://altss.com/glossary/direct-alpha","json_url":"https://altss.com/reference/concepts/direct-alpha.json","title":"Direct Alpha","formulas":[{"formula_id":"F-PERF-024-direct-alpha","concept_id":"ALTSS-PERF-024","label":"Direct alpha","plain":"0 = sum over t of (D_t − C_t) × (I_T / I_t) × (1 + a)^(−t) + NAV_T × (1 + a)^(−T); continuous alpha = ln(1 + a)","latex":"0=\\sum_{t=0}^{T}\\left(D_t-C_t\\right)\\frac{I_T}{I_t}\\,(1+a)^{-t}+\\mathrm{NAV}_T\\,(1+a)^{-T},\\qquad \\delta=\\ln(1+a)","variables":[{"symbol":"C_t, D_t","meaning":"contributions and distributions at time t (positive amounts)"},{"symbol":"I_t, I_T","meaning":"total-return index level at time t and at the valuation date T"},{"symbol":"NAV_T","meaning":"fund NAV at the valuation date"},{"symbol":"a","meaning":"direct alpha per period; with quarterly periods annualise as (1 + a)^4 − 1"},{"symbol":"\\delta","meaning":"continuously compounded direct alpha"}],"convention_note":"Gredil, Griffiths and Stucke (working paper 2014; Journal of Corporate Finance 2023). The paper defines direct alpha in continuously compounded form, ln(1 + a) per unit of time, and also reports the discrete rate a in its examples; both forms are in use and should be labelled. Inputs are identical to KS-PME, so the two always agree in sign.","implementation":"direct_alpha"}],"sources":[{"source_id":"SRC-ACAD-GREDIL-GRIFFITHS-STUCKE-2023","title":"Benchmarking Private Equity: The Direct Alpha Method","authors":"Oleg R. Gredil; Barry Griffiths; Ruediger Stucke","publisher":"Journal of Corporate Finance","document_type":"paper","url":"https://doi.org/10.1016/j.jcorpfin.2023.102360","doi":"10.1016/j.jcorpfin.2023.102360","year":2023,"publication_date":"Vol. 81, 102360, August 2023; SSRN working paper 2014 (doi:10.2139/ssrn.2403521)","jurisdiction":"intl","status":"Published (paywalled)","last_verified":"2026-10-01"},{"source_id":"SRC-ACAD-KAPLAN-SCHOAR-2005","title":"Private Equity Performance: Returns, Persistence, and Capital Flows","authors":"Steven N. Kaplan; Antoinette Schoar","publisher":"The Journal of Finance","document_type":"paper","url":"https://doi.org/10.1111/j.1540-6261.2005.00780.x","doi":"10.1111/j.1540-6261.2005.00780.x","year":2005,"publication_date":"Vol. 60(4), pp. 1791-1823, August 2005","jurisdiction":"intl","status":"Published (journal paywalled; NBER w9807 working paper)","last_verified":"2026-10-01"},{"source_id":"SRC-ACAD-SORENSEN-JAGANNATHAN-2015","title":"The Public Market Equivalent and Private Equity Performance","authors":"Morten Sorensen; Ravi Jagannathan","publisher":"Financial Analysts Journal","document_type":"paper","url":"https://doi.org/10.2469/faj.v71.n4.4","doi":"10.2469/faj.v71.n4.4","year":2015,"publication_date":"Vol. 71(4), pp. 43-50","jurisdiction":"intl","status":"Published (paywalled)","last_verified":"2026-10-01"}]}