How to calculate the Treynor ratio TR risk-adjusted return

Calculate Treynor ratio TR = (Rp-Rf)/β ratio excess return on systematic risk beta CAPM. Portfolio performance fund managers risk-adjusted. Jack Treynor 1965 Harvard Business Review paper. USA Wharton MIT Stanford Booth NYU.

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How to calculate the Treynor ratio: risk-adjusted performance index measuring excess return per unit systematic risk (CAPM beta). Formula: TR = (R_p - R_f) / β. Sharpe analog using beta instead of sigma standard deviation. Suitable well-diversified portfolios where idiosyncratic risk eliminated.

Jack L. Treynor (USA 1930-2016) Haverford College + Harvard Business School + Arthur D. Little Boston + MIT Sloan 1962 paper unpublished MIT 'Toward a Theory of Market Value of Risky Assets' anteced CAPM William Sharpe 1964. Treynor 1965 paper Harvard Business Review 43:63 'How to Rate Management of Investment Funds' formal Treynor ratio fund manager performance.

CAPM: William Sharpe (USA 1934-) Stanford GSB Nobel Economics 1990; John Lintner (USA 1916-1983) Harvard Business School 1965; Jan Mossin (Norway 1936-1987) NHH 1966 independent CAPM. Modern Portfolio Theory MPT: Harry Markowitz (USA 1927-2023) UC San Diego CUNY Nobel 1990 1952 paper Journal of Finance 7:77 'Portfolio Selection' efficient frontier.

Essential tool for: fund managers performance; asset management mutual funds; pension funds; hedge funds; private banking; investment banking research.

USA finance research: Wharton UPenn Philadelphia 1881 first business school world; Harvard Business School Boston MA 1908; Stanford GSB Palo Alto CA 1925; Chicago Booth IL 1898 Fama Booth; Columbia Business NYC 1916; NYU Stern New York 1900; MIT Sloan Cambridge MA 1914 Treynor visiting; Yale SOM New Haven CT 1976; Northwestern Kellogg Evanston IL 1908; Duke Fuqua 1969; Berkeley Haas 1898.

USA Nobel finance laureates: Harry Markowitz Nobel 1990 MPT 1952; William Sharpe Stanford Nobel 1990 CAPM 1964; Merton Miller Chicago Nobel 1990 capital structure; Robert Merton Harvard MIT Nobel 1997 Black-Scholes-Merton; Myron Scholes Stanford Chicago Nobel 1997; Eugene Fama Chicago Nobel 2013 EMH efficient markets; Lars Peter Hansen Chicago Nobel 2013 GMM; Robert Shiller Yale Nobel 2013 housing market index.

USA banks asset management: JPMorgan Chase NYC 2000 300000 + asset management; Bank of America Charlotte NC 1998 200000 + Merrill Lynch wealth management; Goldman Sachs NYC 1869 47000 investment banking; Morgan Stanley NYC 1935 80000; Wells Fargo San Francisco CA 1852 240000; Citigroup NYC 1998 240000.

USA mutual funds asset management: Vanguard Group Malvern PA 1975 $7T AUM founded John Bogle index funds pioneer; BlackRock NYC 1988 $10T AUM largest world; Fidelity Investments Boston MA 1946 $4.5T AUM family-owned; State Street Boston MA 1792 $4T custodian + SPDR ETFs; T. Rowe Price Baltimore MD 1937 $1.5T AUM; Charles Schwab San Francisco CA 1971 $7T retail brokerage; Capital Group LA CA 1931 $2T American Funds; Pimco Newport Beach CA 1971 $1.8T Pacific Investment Management bonds; Invesco Atlanta GA 1935.

USA pension funds: CalPERS Sacramento CA 1932 $500B largest US public pension; NYS Common Retirement Fund Albany NY 1921; Federal Reserve Washington DC 1913.

USA hedge funds: Bridgewater Associates Westport CT 1975 Ray Dalio $150B AUM; Renaissance Technologies East Setauket NY 1982 Jim Simons; Citadel Chicago IL 1990 Ken Griffin; D.E. Shaw NYC 1988; Two Sigma NYC 2001; Millennium Management NYC 1989 Israel Englander.

Treynor formula

TR = (R_p - R_f) / β. R_p portfolio return; R_f risk-free (T-Bill 12m); β beta CAPM. USA: Wharton 1881; Harvard Business School 1908; Stanford GSB 1925; Chicago Booth 1898; MIT Sloan 1914.

History and context

Jack Treynor 1962 unpublished MIT + 1965 HBR paper. CAPM Sharpe 1964 + Lintner 1965 + Mossin 1966. Markowitz 1952 MPT. USA finance pioneers Nobel: Markowitz 1990 MPT; Sharpe 1990 CAPM Stanford GSB; Miller 1990 Modigliani-Miller capital structure; Merton 1997 Harvard MIT Black-Scholes-Merton; Scholes 1997 Stanford Chicago; Fama 2013 Chicago efficient market hypothesis EMH; Hansen 2013 Chicago GMM; Shiller 2013 Yale housing index. USA universities finance: Wharton UPenn Philadelphia 1881 founded Joseph Wharton steel magnate first business school world; Harvard Business School Boston MA 1908 founded MBA case method; Stanford GSB Palo Alto CA 1925; MIT Sloan Cambridge MA 1914 Alfred Sloan; Chicago Booth IL 1898 University Chicago; Columbia Business NYC 1916; NYU Stern New York 1900; Yale SOM New Haven CT 1976; Northwestern Kellogg Evanston IL 1908; Duke Fuqua Durham NC 1969; UCLA Anderson Los Angeles CA 1935; UC Berkeley Haas 1898 oldest public business school; Cornell Johnson NY 1865; Carnegie Mellon Tepper Pittsburgh PA 1949. USA mutual funds asset management: Vanguard Group Malvern PA 1975 founded John C. Bogle 18000 employees $7T AUM index funds pioneer; BlackRock NYC 1988 founded Larry Fink 19000 employees $10T AUM largest world iShares ETFs; Fidelity Investments Boston MA 1946 founded Edward Johnson 70000 family-owned Abigail Johnson chairman $4.5T AUM mutual funds 401k; State Street Boston MA 1792 founded oldest US bank custodian $4T + SPDR ETFs SPY; T.

Rowe Price Baltimore MD 1937 1500 employees $1.5T AUM; Charles Schwab San Francisco CA 1971 founded $7T retail brokerage 35000 employees; Capital Group LA CA 1931 9000 American Funds $2T; Pimco Newport Beach CA 1971 founded Bill Gross 3000 $1.8T bonds; Invesco Atlanta GA 1935 8000; Franklin Templeton San Mateo CA 1947 9000; J.P. Morgan Asset Management NYC subsidiary $3T. USA pension funds: CalPERS California Public Employees Retirement System Sacramento CA 1932 $500B largest US public pension 2000 employees; NYS Common Retirement Fund Albany NY 1921 + NYC Pension Fund $250B; Texas Teacher Retirement System Austin TX 1937 $200B; Federal Reserve System Washington DC 1913 12 regional banks data; Social Security Trust Fund Federal $2.8T US largest. USA hedge funds: Bridgewater Associates Westport CT 1975 founded Ray Dalio 1500 $150B AUM Pure Alpha All Weather; Renaissance Technologies East Setauket NY 1982 founded Jim Simons mathematics medallion fund quantitative; Citadel Chicago IL 1990 founded Ken Griffin Citadel Securities market making; D.E. Shaw NYC 1988 founded David Shaw quantitative; Two Sigma NYC 2001 quantitative; Millennium Management NYC 1989 Israel Englander multi-strategy. USA banks: JPMorgan Chase NYC 2000 fusion JP Morgan + Chase Manhattan 300000 + asset management $3T; Bank of America Charlotte NC 1998 fusion 200000 + Merrill Lynch wealth management $4T; Goldman Sachs NYC 1869 founded Marcus Goldman 47000 investment banking;

Morgan Stanley NYC 1935 80000 wealth management $4T; Wells Fargo San Francisco CA 1852 240000; Citigroup NYC 1998 240000.

Treynor values table

  • TR = (Rp - Rf)/β: definition
  • TR negative: underperforms risk-free
  • TR 0-2: low
  • TR 2-5: acceptable
  • TR 5-10: good
  • TR 10-20: excellent
  • TR > 20: exceptional
  • S&P 500 historical TR: 6-7
  • USA hedge funds top decile: 8-15
  • β = 1: market index
  • β 0.6-0.9: defensive
  • β 1.2-1.5: aggressive growth
  • β > 2: speculative
  • β < 0: counter-cyclical gold
  • R_f USA T-Bill 12m: 4.5-5% 2024
  • R_f USA 10y T-Note: 4.2-4.5% 2024
  • Treynor 1965 HBR paper: 43:63
  • Treynor 1962 unpublished: anteced CAPM
  • Sharpe 1964: Journal Finance 19:425
  • Markowitz 1952: Journal Finance 7:77 MPT
  • Sharpe Markowitz Miller: Nobel 1990
  • Merton Scholes: Nobel 1997
  • Fama Hansen Shiller: Nobel 2013
  • USA Wharton 1881: first business school
  • USA Harvard Business 1908: MBA case
  • USA Stanford GSB 1925
  • USA Chicago Booth 1898: Fama EMH
  • USA MIT Sloan 1914: Treynor visiting
  • USA Vanguard 1975: $7T AUM Bogle
  • USA BlackRock 1988: $10T largest
  • USA Fidelity 1946: $4.5T family
  • USA State Street 1792: $4T SPDR
  • USA Bridgewater 1975: $150B Dalio
  • USA Renaissance 1982: Simons quant
  • USA CalPERS 1932: $500B largest pension
  • USA Federal Reserve 1913: 12 regional

Numerical examples

Example 1 - S&P 500 market. R_p=10%, R_f=3%, β=1.0. TR=7 good. USA: Vanguard Malvern PA 1975 $7T; BlackRock 1988 $10T iShares.

Example 2 - Aggressive tech growth. R_p=15%, β=1.5. TR=8 good. USA: Apple Cupertino 1976; Microsoft Redmond WA 1975; Google Mountain View 1998; Tesla Austin TX 2003.

Example 3 - Defensive utility. R_p=7%, β=0.6. TR=6.67. USA: Duke Energy Charlotte NC 1900; Southern Company Atlanta GA 1945; Dominion Energy Richmond VA 1983.

Example 4 - Underperforming. R_p=2%, β=0.8. TR=-1.25 negative.

Example 5 - Hedge fund top. R_p=25%, β=1.8. TR=12.2 excellent. USA: Bridgewater Associates Westport CT 1975 $150B; Renaissance East Setauket NY 1982; Citadel Chicago IL 1990.

Limitations

  1. Well-diversified only: Treynor for diversified portfolios. Concentrated need Sharpe.
  2. Beta backward-looking: historical regression, not predictive.
  3. Single-factor CAPM: Fama-French multi-factor more accurate.
  4. Risk-free constant assumption: realistic non-stochastic.
  5. Market efficient hypothesis: anomalies violate.
  6. Time period sensitivity: 3y vs 5y vs 10y rolling differ.
  7. Currency effects: international portfolios.
  8. Benchmark choice: S&P 500 vs FTSE MIB vs MSCI.
  9. Higher moments ignored: skewness kurtosis.
  10. Liquidity risk: illiquid assets.

Common errors

Treynor vs Sharpe: Treynor β systematic; Sharpe σ total. Different applications.

Beta = 0: undefined. Cash equivalents use Sharpe.

R_f choice: Treasury 12m matching horizon.

Annualization: standard. Mixing daily/monthly/annual error.

Market index: S&P 500 USA, MSCI World global. Confusing benchmark.

Practical applications

  1. Fund manager evaluation: USA Vanguard $7T + BlackRock $10T + Fidelity $4.5T + T. Rowe Price $1.5T + Pimco $1.8T.
  2. Asset management mutual funds: Capital Group $2T + Franklin Templeton + Invesco; State Street $4T SPDR ETFs.
  3. Pension funds: USA CalPERS $500B + NYS Common $250B + Texas Teacher $200B + Social Security Trust Fund $2.8T.
  4. Hedge funds: Bridgewater Westport CT 1975 $150B Dalio + Renaissance East Setauket NY 1982 Simons + Citadel Chicago 1990 Griffin + D.E. Shaw NYC 1988 + Two Sigma NYC 2001.
  5. Private banking wealth: Morgan Stanley $4T + Bank of America Merrill Lynch $4T + Goldman Sachs Private Wealth + JPMorgan Private Bank $3T.
  6. Investment banking research: Goldman Sachs NYC 1869 47000 + Morgan Stanley NYC 1935 80000.
  7. ETF benchmarking: BlackRock iShares + State Street SPDR + Vanguard ETFs + Invesco PowerShares + Charles Schwab ETFs.
  8. Robo-advisors: Betterment NYC 2008; Wealthfront Palo Alto CA 2008; Acorns Irvine CA 2014.
  9. Insurance investment: USA Berkshire Hathaway Omaha NE 1839 Buffett $700B + AIG NYC 1919 + Liberty Mutual Boston MA 1912.
  10. University finance research: Wharton UPenn 1881 + Harvard Business School Boston MA 1908 + Stanford GSB Palo Alto CA 1925 + Chicago Booth IL 1898 Fama EMH.

Updated July 2026

Frequently Asked Questions

What is Treynor ratio?

Risk-adjusted performance index ratio excess return per unit systematic risk: TR = (R_p - R_f) / β. R_p portfolio return; R_f risk-free; β CAPM beta. Sharpe analog using beta instead sigma. Suitable well-diversified portfolios. Jack Treynor 1965 Harvard Business Review 43:63 'How to Rate Management of Investment Funds'. CAPM William Sharpe 1964 Stanford Nobel Economics 1990. USA: Wharton UPenn 1881; Harvard Business School 1908; Stanford GSB 1925; Chicago Booth 1898 Fama EMH Nobel 2013.

How to calculate Treynor ratio?

Procedure: (1) TR = (R_p - R_f) / β; (2) R_p portfolio return % annualized; (3) R_f risk-free rate (T-Bill 12m USA 4.5-5% 2024); (4) β CAPM beta regression; (5) calculate. Example: R_p=10% S&P 500 R_f=3% β=1: TR=(10-3)/1=7 good. Typical market 6-7. USA: Vanguard Malvern PA 1975 $7T AUM Bogle index funds; BlackRock NYC 1988 $10T iShares; Fidelity Boston MA 1946 $4.5T.

Who defined Treynor ratio?

Jack L. Treynor (USA 1930-2016) Haverford + Harvard Business School + Arthur D. Little Boston + MIT Sloan 1962 unpublished MIT 'Toward Theory Market Value of Risky Assets' anteced CAPM (Treynor circulated 1962, Sharpe published 1964). Treynor 1965 HBR 43:63 'How to Rate Management of Investment Funds' formal Treynor ratio. CAPM co-developers: Sharpe Stanford GSB Nobel 1990; Lintner HBS 1965; Mossin Norway NHH 1966; Markowitz UC San Diego CUNY Nobel 1990 1952 MPT.

Difference Treynor vs Sharpe?

Treynor TR = (Rp-Rf)/β uses beta systematic risk only. Sharpe = (Rp-Rf)/σ uses sigma total risk standard deviation. Treynor for well-diversified portfolios (residual eliminated); Sharpe more general for concentrated. Index funds passive similar; specialized active Sharpe more informative. USA: Wharton UPenn 1881 first business school; Harvard Business 1908 case method; Stanford GSB 1925 Sharpe Nobel 1990 CAPM.

What is CAPM beta?

β CAPM Capital Asset Pricing Model portfolio market sensitivity. β = Cov(R_p, R_m) / Var(R_m) regression excess returns. β=1 market passive index; β>1 volatile growth tech; β<1 defensive utilities; β=0 no correlation; β<0 counter-cyclical gold mining. CAPM Sharpe 1964 Nobel 1990 + Lintner 1965 + Mossin 1966 + Markowitz 1952 MPT. USA: Apple Cupertino β~1.2; Tesla β~2.0+; Duke Energy β~0.5; Berkshire Hathaway β~0.85.

Which risk-free rate to use?

R_f Treasury 12 months matching portfolio horizon. USA: T-Bill 12m 4.5-5% 2024 (Federal Reserve System Washington DC 1913 12 regional banks); 10y T-Note 4.2-4.5%; 30y T-Bond 4.5-4.8%. Annualized standard. Error using overnight rate for annual returns. USA: US Treasury Washington DC 1789 Alexander Hamilton; SEC NYC 1934 + FINRA 2007.

What are Treynor applications?

Applications: fund managers USA Vanguard Malvern PA 1975 $7T + BlackRock NYC 1988 $10T + Fidelity Boston 1946 $4.5T + State Street Boston MA 1792 $4T SPDR; pension funds CalPERS Sacramento $500B + NYS Common $250B + Texas Teacher $200B; hedge funds Bridgewater Westport CT 1975 $150B Dalio + Renaissance East Setauket NY 1982 Simons + Citadel Chicago 1990 Griffin; investment banking Goldman Sachs NYC 1869 + Morgan Stanley 1935; private banking JPMorgan Private Bank $3T + Morgan Stanley Wealth $4T.

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