1292:
magnitude of the Sharpe ratio is sensitive to the time period over which the underlying returns are measured. This is because the nominator of the ratio (returns) scales in proportion to time; while the denominator of the ratio (standard deviation) scales in proportion to the square root of time. Most diversified indexes of equities, bonds, mortgages or commodities have annualized Sharpe ratios below 1, which suggests that a Sharpe ratio consistently above 2.0 or 3.0 is unrealistic.
1291:
In recent years, many financial websites have promoted the idea that a Sharpe Ratio "greater than 1 is considered acceptable; a ratio higher than 2.0 is considered very good; and a ratio above 3.0 is excellent." While it is unclear where this rubric originated online, it makes little sense since the
1287:
call and selling one out-of-the-money put. This portfolio generates an immediate positive payoff, has a large probability of generating modestly high returns, and has a small probability of generating huge losses. Shah (2014) observed that such a portfolio is not suitable for many investors, but fund
1271:
Bailey and López de Prado (2012) show that Sharpe ratios tend to be overstated in the case of hedge funds with short track records. These authors propose a probabilistic version of the Sharpe ratio that takes into account the asymmetry and fat-tails of the returns' distribution. With regards to the
467:
Even in less extreme cases, a reliable empirical estimate of Sharpe ratio still requires the collection of return data over sufficient period for all aspects of the strategy returns to be observed. For example, data must be taken over decades if the algorithm sells an insurance that involves a high
995:
The Sharpe ratio is convenient because it can be calculated purely from any observed series of returns without need for additional information surrounding the source of profitability. However, this makes it vulnerable to manipulation if opportunities exist for smoothing or discretionary pricing of
519:
In 1952, Arthur D. Roy suggested maximizing the ratio "(m-d)/σ", where m is expected gross return, d is some "disaster level" (a.k.a., minimum acceptable return, or MAR) and σ is standard deviation of returns. This ratio is just the Sharpe ratio, only using minimum acceptable return instead of the
447:
The Sharpe ratio seeks to characterize how well the return of an asset compensates the investor for the risk taken. When comparing two assets, the one with a higher Sharpe ratio appears to provide better return for the same risk, which is usually attractive to investors.
988:. However, a negative Sharpe ratio can be made higher by either increasing returns (a good thing) or increasing volatility (a bad thing). Thus, for negative values the Sharpe ratio does not correspond well to typical investor
268:
463:
will have a high empirical Sharpe ratio until one of those puts is exercised, creating a large loss. In both cases, the empirical standard deviation before failure gives no real indication of the size of the risk being run.
845:
Suppose the asset has an expected return of 15% in excess of the risk free rate. We typically do not know if the asset will have this return. We estimate the risk of the asset, defined as standard deviation of the asset's
531:
developed what is now known as the Sharpe ratio. Sharpe originally called it the "reward-to-variability" ratio before it began being called the Sharpe ratio by later academics and financial operators. The definition was:
1259:
can be used to convert the Sharpe ratio into a rate of return. The Kelly criterion gives the ideal size of the investment, which when adjusted by the period and expected rate of return per unit, gives a rate of return.
923:
983:
A negative Sharpe ratio means the portfolio has underperformed its benchmark. All other things being equal, an investor typically prefers a higher positive Sharpe ratio as it has either higher returns or lower
827:
1276:
This curve illustrates the fact that it is efficient to hire portfolio managers with low and even negative Sharpe ratios, as long as their correlation to the other portfolio managers is sufficiently low.
502:
had a Sharpe ratio of 0.76 for the period 1976 to 2011, higher than any other stock or mutual fund with a history of more than 30 years. The stock market had a Sharpe ratio of 0.39 for the same period.
1283:
determined that the best strategy to maximize a portfolio's Sharpe ratio, when both securities and options contracts on these securities are available for investment, is a portfolio of selling one
710:
612:
483:
funds), the Sharpe ratio should be derived from the performance of the underlying assets rather than the fund returns (Such a model would invalidate the aforementioned Ponzi scheme, as desired).
974:
472:
algorithm may only require a week of data if each trade occurs every 50 milliseconds, with care taken toward risk from unexpected but rare results that such testing did not capture (see
1263:
The accuracy of Sharpe ratio estimators hinges on the statistical properties of returns, and these properties can vary considerably among strategies, portfolios, and over time.
520:
risk-free rate in the numerator, and using standard deviation of returns instead of standard deviation of excess returns in the denominator. Roy's ratio is also related to the
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1107:
415:
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1796:
Bailey, D. and M. Lopez de Prado (2013): "The
Strategy Approval Decision: A Sharpe Ratio Indifference Curve approach", Algorithmic Finance 2(1), pp. 99-109 Available at
1147:
432:
Sharpe ratio uses the same equation as the one above but with realized returns of the asset and benchmark rather than expected returns; see the second example below.
617:
Sharpe's 1994 revision acknowledged that the basis of comparison should be an applicable benchmark, which changes with time. After this revision, the definition is:
740:
325:
298:
1127:
1207:
382:
1026:, as the returns can always be annualized. Herein lies the underlying weakness of the ratio - asset returns are not normally distributed. Abnormalities like
832:
The (original) Sharpe ratio has often been challenged with regard to its appropriateness as a fund performance measure during periods of declining markets.
2678:
2653:
109:
511:
Several statistical tests of the Sharpe ratio have been proposed. These include those proposed by Jobson & Korkie and
Gibbons, Ross & Shanken.
1978:
1924:
853:
1336:
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An investor has a portfolio with an expected return of 12% and a standard deviation of 10%. The rate of interest is 5%, and is risk-free.
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1288:
sponsors who select fund managers primarily based on the Sharpe ratio will give incentives for fund managers to adopt such a strategy.
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is a generalization of the Sharpe ratio that uses as benchmark some other, typically risky index rather than using risk-free returns.
1858:
78:
of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk.
2829:
2293:
1897:
1810:
1356:
1351:
1944:
1784:
Bailey, D. and M. López de Prado (2012): "The Sharpe Ratio
Efficient Frontier", Journal of Risk, 15(2), pp.3-44. Available at
524:, which also uses MAR in the numerator, but uses a different standard deviation (semi/downside deviation) in the denominator.
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1971:
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can be problematic for the ratio, as standard deviation doesn't have the same effectiveness when these problems exist.
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1311:
2811:
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938:
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1991:
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459:, for example, will have a high empirical Sharpe ratio until they fail. Similarly, a fund that sells low-strike
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1316:
1039:
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Jobson JD; Korkie B (September 1981). "Performance hypothesis testing with the Sharpe and
Treynor measures".
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1964:
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The returns measured can be of any frequency (i.e. daily, weekly, monthly or annually), as long as they are
63:
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469:
332:
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will equal the Sharpe Ratio times the square root of T (the number of returns used for the calculation).
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2014:
1301:
997:
985:
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Additionally, when examining the investment performance of assets with smoothing of returns (such as
1677:
Scholz, Hendrik (2007). "Refinements to the Sharpe ratio: Comparing alternatives for bear markets".
1611:
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2610:
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selection of portfolio managers on the basis of their Sharpe ratios, these authors have proposed a
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59:
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1016:
499:
418:
75:
55:
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Gibbons M; Ross S; Shanken J (September 1989). "A test of the efficiency of a given portfolio".
1956:
1829:
Lo, Andrew W. "The statistics of Sharpe ratios." Financial analysts journal 58.4 (2002): 36-52
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850:, as 10%. The risk-free return is constant. Then the Sharpe ratio using the old definition is
528:
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1256:
1210:
1112:
1012:
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1735:
1489:
Gatfaoui, Hayette. "Sharpe Ratios and Their
Fundamental Components: An Empirical Study".
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17:
2547:
2532:
2170:
2131:
1950:
1306:
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263:{\displaystyle S_{a}={\frac {E}{\sigma _{a}}}={\frac {E}{\sqrt {\mathrm {var} }}},}
1914:
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2557:
2303:
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2201:
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2006:
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70:. It is defined as the difference between the returns of the investment and the
1550:
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2074:
2070:
1879:
Goetzmann, William; Ingersoll, Jonathan; Spiegel, Matthew; Welch, Ivo (2002),
51:
1529:
2776:
2752:
2718:
2527:
1459:
452:
918:{\displaystyle {\frac {R_{a}-R_{f}}{\sigma _{a}}}={\frac {0.15}{0.10}}=1.5}
1830:
2730:
2385:
1521:
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1031:
1004:
are sometimes used to indicate the potential presence of these problems.
1880:
97:
Since its revision by the original author, William Sharpe, in 1994, the
2440:
1663:
1628:
1583:
1537:
1505:
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989:
99:
31:
1642:
Roy, Arthur D. (July 1952). "Safety First and the
Holding of Assets".
2724:
2507:
1766:
Lo, Andrew W. (July–August 2002). "The
Statistics of Sharpe Ratios".
1919:
1797:
1785:
1655:
1620:
455:, so that standard deviation does not capture all aspects of risk.
2631:
1427:
1019:. Which one is more relevant will depend on the portfolio context.
2690:
1837:
Practical
Portfolio Performance Measurement and Attribution 2nd Ed
1252:
is the numerical fraction of wealth suggested for the investment.
822:{\displaystyle {\sqrt {\mathrm {var} }}={\sqrt {\mathrm {var} }}.}
388:
of the excess of the asset return over the benchmark return, and
2522:
86:
67:
2635:
1960:
1015:
of a portfolio, the Sharpe ratio considers both systematic and
1932:"A Comparison of Different Measures of Risk-adjusted Return"
494:, are often used to rank the performance of portfolio or
742:
is a constant risk-free return throughout the period,
705:{\displaystyle S={\frac {E}{\sqrt {\mathrm {var} }}}.}
607:{\displaystyle S={\frac {E}{\sqrt {\mathrm {var} }}}.}
1506:"Risks and Portfolio Decisions Involving Hedge Funds"
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112:
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1951:Calculating and Interpreting Sharpe Ratios online
1414:Sharpe, W. F. (1966). "Mutual Fund Performance".
1281:Goetzmann, Ingersoll, Spiegel, and Welch (2002)
468:liability payout once every 5–10 years, and a
2647:
1972:
1865:The Sharpe Ratio: Statistics and Applications
8:
1941:- Some example calculations of Sharpe ratios
1737:Paul Wilmott introduces Quantitative Finance
1551:http://docs.lhpedersen.com/BuffettsAlpha.pdf
1409:
1407:
969:{\displaystyle {\frac {0.12-0.05}{0.1}}=0.7}
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2002:
1979:
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1957:
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1504:Agarwal, Vikas; Naik, Narayan Y. (2004).
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996:illiquid assets. Statistics such as the
1831:https://doi.org/10.2469/faj.v58.n4.2453
1403:
1899:The Principal-Agent Problem in Finance
1888:, National Bureau of Economic Research
1812:The Principal-Agent Problem in Finance
1337:List of financial performance measures
2759:Present value of growth opportunities
2679:Cyclically adjusted price-to-earnings
1927:- Uses and abuses of the Sharpe Ratio
7:
2725:Enterprise value/gross cash invested
451:However, financial assets are often
27:Formula for measuring financial risk
1947:- Risk adjusted return calculations
1741:(Second ed.). Wiley. pp.
1447:The Journal of Portfolio Management
1267:Drawback as fund selection criteria
1851:Investment Performance Measurement
1576:10.1111/j.1540-6261.1981.tb04891.x
801:
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221:
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25:
1798:https://ssrn.com/abstract=2003638
1786:https://ssrn.com/abstract=1821643
50:) measures the performance of an
2254:Conditional Value-at-Risk (CVaR)
1713:"Understanding The Sharpe Ratio"
1245:{\displaystyle \mu /\sigma ^{2}}
1045:For Brownian walk, Sharpe ratio
421:of the asset excess return. The
2830:Risk-adjusted return on capital
1510:The Review of Financial Studies
1352:Risk adjusted return on capital
1274:Sharpe ratio indifference curve
2573:Strategic financial management
2376:Asset and liability management
1217:, and, indeed, Kelly fraction
811:
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1:
1280:
1174:{\displaystyle 1/{\sqrt {T}}}
1102:{\displaystyle 1/{\sqrt {T}}}
410:{\displaystyle {\sigma _{a}}}
2691:Cash return on cash invested
1939:What is a good Sharpe Ratio?
1691:10.1057/palgrave.jam.2250040
1357:Roy's safety-first criterion
1109:, because the excess return
1066:{\displaystyle \mu /\sigma }
103:Sharpe ratio is defined as:
2151:Operational risk management
1815:, CFA Institute, p. 14
1679:Journal of Asset Management
1441:Sharpe, William F. (1994).
1312:Capital asset pricing model
1002:first order autocorrelation
48:reward-to-variability ratio
2916:
2812:Return on capital employed
2323:Proportional hazards model
2274:Interest rate immunization
1768:Financial Analysts Journal
1491:IESEG School of Management
486:Sharpe ratios, along with
66:, after adjusting for its
2824:Return on tangible equity
2669:
2606:
1992:financial risk management
1925:All Hail the Sharpe Ratio
1853:. New York: Wiley, 2003.
2777:Price-earnings to growth
2269:First-hitting-time model
2234:Arbitrage pricing theory
1945:Sharpe ratio in MS excel
1920:Generalized Sharpe Ratio
1882:Sharpening Sharpe Ratios
1322:Hansen–Jagannathan bound
1317:Coefficient of variation
979:Strengths and weaknesses
453:not normally distributed
2719:Enterprise value/EBITDA
2578:Stress test (financial)
2284:Modern portfolio theory
1896:Shah, Sunit N. (2014),
1809:Shah, Sunit N. (2014),
1460:10.3905/jpm.1994.409501
1342:Modern portfolio theory
1142:{\displaystyle \sigma }
2731:Enterprise value/sales
1733:Wilmott, Paul (2007).
1564:The Journal of Finance
1382:Upside potential ratio
1255:In some settings, the
1246:
1215:dimensionless quantity
1203:
1175:
1143:
1123:
1103:
1067:
970:
919:
823:
736:
706:
608:
470:high-frequency trading
411:
378:
333:U.S. Treasury security
321:
294:
264:
85:, who developed it in
2616:Investment management
2518:Investment management
2244:Replicating portfolio
2020:Sovereign credit risk
1362:Signal-to-noise ratio
1247:
1204:
1176:
1144:
1124:
1104:
1068:
1034:and higher peaks, or
971:
935:The Sharpe ratio is:
920:
824:
737:
735:{\displaystyle R_{f}}
707:
609:
412:
379:
322:
320:{\displaystyle R_{b}}
300:is the asset return,
295:
293:{\displaystyle R_{a}}
265:
2800:Return on net assets
2621:Mathematical finance
2553:Risk-return spectrum
2543:Mathematical finance
2498:Fundamental analysis
2431:Exchange traded fund
2015:Consumer credit risk
1221:
1185:
1153:
1149:are proportional to
1133:
1122:{\displaystyle \mu }
1113:
1081:
1075:dimensional quantity
1049:
1024:normally distributed
939:
854:
749:
719:
624:
539:
392:
339:
304:
277:
110:
18:Market price of risk
2685:Capitalization rate
2611:Financial economics
2568:Statistical finance
2334:Value-at-Risk (VaR)
2239:Black–Scholes model
2079:Holding period risk
1867:. CRC Press, 2022.
1416:Journal of Business
1202:{\displaystyle 1/T}
1129:and the volatility
1017:idiosyncratic risks
1011:considers only the
81:It was named after
38:(also known as the
2895:Portfolio theories
2890:Statistical ratios
2858:Sustainable growth
2588:Structured product
2583:Structured finance
2563:Speculative attack
2249:Cash flow matching
2212:Non-financial risk
2109:Interest rate risk
2035:Concentration risk
1953:- Cloud calculator
1522:10.1093/rfs/hhg044
1443:"The Sharpe Ratio"
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500:Berkshire Hathaway
419:standard deviation
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76:standard deviation
2872:
2871:
2806:Return on capital
2674:Buffett indicator
2629:
2628:
2401:Corporate finance
2396:Capital structure
2350:Cash flow at risk
2346:Liquidity at risk
2319:Survival analysis
2220:
2219:
2166:Reputational risk
2040:Credit derivative
1934:. September 2013.
1873:978-1-032-01930-7
1849:Bruce J. Feibel.
1845:978-0-470-05928-9
1752:978-0-470-31958-1
1327:Information ratio
1209:correspondingly.
1169:
1097:
990:utility functions
958:
907:
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814:
787:
697:
696:
599:
598:
529:William F. Sharpe
437:information ratio
377:{\displaystyle E}
255:
254:
172:
83:William F. Sharpe
74:, divided by the
16:(Redirected from
2907:
2885:Financial ratios
2818:Return on equity
2794:Return on assets
2748:Operating margin
2663:Financial ratios
2656:
2649:
2642:
2633:
2503:Growth investing
2421:Enterprise value
2371:Asset allocation
2354:Earnings at risk
2336:and extensions (
2279:Market portfolio
2143:Operational risk
2128:Refinancing risk
2003:
1981:
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1915:The Sharpe ratio
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1605:(5): 1121–1152.
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329:risk-free return
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72:risk-free return
21:
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2904:
2900:Yield (finance)
2875:
2874:
2873:
2868:
2765:Price/cash flow
2708:Dividend payout
2665:
2660:
2630:
2625:
2602:
2538:Systematic risk
2436:Expected return
2416:Economic bubble
2411:Diversification
2406:Cost of capital
2359:
2216:
2185:
2137:
2119:Volatility risk
2083:Price area risk
2049:
2025:Settlement risk
1994:
1985:
1930:
1911:
1902:, CFA Institute
1895:
1894:
1885:
1878:
1877:
1863:Steven E. Pav.
1839:: Wiley, 2008.
1826:
1824:Further reading
1821:
1820:
1808:
1807:
1803:
1795:
1791:
1783:
1779:
1765:
1764:
1760:
1753:
1732:
1731:
1727:
1717:
1715:
1711:
1710:
1706:
1676:
1675:
1671:
1656:10.2307/1907413
1641:
1640:
1636:
1621:10.2307/1913625
1612:10.1.1.557.1995
1596:
1595:
1591:
1561:
1560:
1556:
1549:
1545:
1503:
1502:
1498:
1488:
1487:
1483:
1473:
1471:
1440:
1439:
1435:
1422:(S1): 119–138.
1413:
1412:
1405:
1400:
1298:
1269:
1257:Kelly criterion
1232:
1219:
1218:
1211:Kelly criterion
1183:
1182:
1151:
1150:
1131:
1130:
1111:
1110:
1079:
1078:
1047:
1046:
1013:systematic risk
981:
944:
937:
936:
884:
873:
860:
859:
852:
851:
838:
774:
747:
746:
722:
717:
716:
683:
648:
635:
622:
621:
563:
550:
537:
536:
517:
509:
492:Jensen's alphas
445:
396:
390:
389:
361:
348:
337:
336:
307:
302:
301:
280:
275:
274:
241:
228:
199:
186:
179:
162:
148:
135:
128:
113:
108:
107:
95:
64:risk-free asset
28:
23:
22:
15:
12:
11:
5:
2913:
2911:
2903:
2902:
2897:
2892:
2887:
2877:
2876:
2870:
2869:
2867:
2866:
2861:
2855:
2850:
2847:Short interest
2844:
2839:
2833:
2827:
2821:
2815:
2809:
2803:
2797:
2791:
2786:
2780:
2774:
2771:Price-earnings
2768:
2762:
2756:
2750:
2745:
2740:
2734:
2728:
2722:
2716:
2713:Earnings yield
2710:
2705:
2703:Dividend cover
2700:
2697:Debt-to-equity
2694:
2688:
2682:
2676:
2670:
2667:
2666:
2661:
2659:
2658:
2651:
2644:
2636:
2627:
2626:
2624:
2623:
2618:
2613:
2607:
2604:
2603:
2601:
2600:
2595:
2590:
2585:
2580:
2575:
2570:
2565:
2560:
2555:
2550:
2545:
2540:
2535:
2530:
2525:
2520:
2515:
2510:
2505:
2500:
2495:
2494:
2493:
2488:
2483:
2478:
2473:
2468:
2463:
2458:
2453:
2448:
2438:
2433:
2428:
2423:
2418:
2413:
2408:
2403:
2398:
2393:
2388:
2383:
2378:
2373:
2367:
2365:
2364:Basic concepts
2361:
2360:
2358:
2357:
2342:Margin at risk
2338:Profit at risk
2331:
2329:Tracking error
2326:
2316:
2311:
2306:
2301:
2299:Risk-free rate
2296:
2291:
2286:
2281:
2276:
2271:
2266:
2261:
2256:
2251:
2246:
2241:
2236:
2230:
2228:
2222:
2221:
2218:
2217:
2215:
2214:
2209:
2204:
2199:
2197:Execution risk
2193:
2191:
2187:
2186:
2184:
2183:
2178:
2176:Political risk
2173:
2168:
2163:
2158:
2153:
2147:
2145:
2139:
2138:
2136:
2135:
2124:Liquidity risk
2121:
2116:
2114:Inflation risk
2111:
2106:
2104:Margining risk
2101:
2096:
2094:Valuation risk
2091:
2086:
2063:Commodity risk
2059:
2057:
2051:
2050:
2048:
2047:
2045:Securitization
2042:
2037:
2032:
2027:
2022:
2017:
2011:
2009:
2000:
1996:
1995:
1988:Financial risk
1986:
1984:
1983:
1976:
1969:
1961:
1955:
1954:
1948:
1942:
1936:
1928:
1922:
1917:
1910:
1909:External links
1907:
1906:
1905:
1892:
1875:
1861:
1847:
1833:
1825:
1822:
1819:
1818:
1801:
1789:
1777:
1758:
1751:
1725:
1704:
1685:(5): 347–357.
1669:
1650:(3): 431–450.
1634:
1589:
1570:(4): 888–908.
1554:
1543:
1496:
1481:
1433:
1428:10.1086/294846
1402:
1401:
1399:
1396:
1395:
1394:
1389:
1384:
1379:
1374:
1372:Sterling ratio
1369:
1364:
1359:
1354:
1349:
1344:
1339:
1334:
1332:Jensen's alpha
1329:
1324:
1319:
1314:
1309:
1304:
1297:
1294:
1268:
1265:
1239:
1235:
1230:
1226:
1198:
1194:
1190:
1168:
1162:
1158:
1138:
1118:
1096:
1090:
1086:
1077:and has units
1062:
1058:
1054:
980:
977:
965:
962:
957:
953:
950:
947:
914:
911:
906:
903:
898:
891:
887:
880:
876:
872:
867:
863:
837:
834:
830:
829:
818:
813:
810:
807:
803:
800:
797:
791:
786:
781:
777:
773:
770:
767:
763:
760:
757:
729:
725:
713:
712:
701:
695:
690:
686:
682:
679:
676:
672:
669:
666:
660:
655:
651:
647:
644:
641:
638:
632:
629:
615:
614:
603:
597:
594:
591:
587:
584:
581:
575:
570:
566:
562:
559:
556:
553:
547:
544:
516:
513:
508:
505:
488:Treynor ratios
444:
443:Use in finance
441:
403:
399:
386:expected value
373:
368:
364:
360:
355:
351:
347:
344:
314:
310:
287:
283:
271:
270:
259:
253:
248:
244:
240:
235:
231:
227:
223:
220:
217:
211:
206:
202:
198:
193:
189:
185:
182:
176:
169:
165:
160:
155:
151:
147:
142:
138:
134:
131:
125:
120:
116:
94:
91:
62:compared to a
44:Sharpe measure
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2912:
2901:
2898:
2896:
2893:
2891:
2888:
2886:
2883:
2882:
2880:
2865:
2862:
2859:
2856:
2854:
2851:
2848:
2845:
2843:
2840:
2837:
2834:
2831:
2828:
2825:
2822:
2819:
2816:
2813:
2810:
2807:
2804:
2801:
2798:
2795:
2792:
2790:
2789:Profit margin
2787:
2784:
2781:
2778:
2775:
2772:
2769:
2766:
2763:
2760:
2757:
2754:
2753:Price-to-book
2751:
2749:
2746:
2744:
2741:
2738:
2737:Loan-to-value
2735:
2732:
2729:
2726:
2723:
2720:
2717:
2714:
2711:
2709:
2706:
2704:
2701:
2698:
2695:
2692:
2689:
2686:
2683:
2680:
2677:
2675:
2672:
2671:
2668:
2664:
2657:
2652:
2650:
2645:
2643:
2638:
2637:
2634:
2622:
2619:
2617:
2614:
2612:
2609:
2608:
2605:
2599:
2596:
2594:
2593:Systemic risk
2591:
2589:
2586:
2584:
2581:
2579:
2576:
2574:
2571:
2569:
2566:
2564:
2561:
2559:
2556:
2554:
2551:
2549:
2546:
2544:
2541:
2539:
2536:
2534:
2531:
2529:
2526:
2524:
2521:
2519:
2516:
2514:
2511:
2509:
2506:
2504:
2501:
2499:
2496:
2492:
2489:
2487:
2484:
2482:
2479:
2477:
2474:
2472:
2469:
2467:
2464:
2462:
2459:
2457:
2454:
2452:
2449:
2447:
2444:
2443:
2442:
2439:
2437:
2434:
2432:
2429:
2427:
2424:
2422:
2419:
2417:
2414:
2412:
2409:
2407:
2404:
2402:
2399:
2397:
2394:
2392:
2391:Capital asset
2389:
2387:
2384:
2382:
2381:Asset pricing
2379:
2377:
2374:
2372:
2369:
2368:
2366:
2362:
2355:
2351:
2347:
2343:
2339:
2335:
2332:
2330:
2327:
2324:
2320:
2317:
2315:
2314:Sortino ratio
2312:
2310:
2307:
2305:
2302:
2300:
2297:
2295:
2292:
2290:
2287:
2285:
2282:
2280:
2277:
2275:
2272:
2270:
2267:
2265:
2262:
2260:
2257:
2255:
2252:
2250:
2247:
2245:
2242:
2240:
2237:
2235:
2232:
2231:
2229:
2227:
2223:
2213:
2210:
2208:
2207:Systemic risk
2205:
2203:
2200:
2198:
2195:
2194:
2192:
2188:
2182:
2179:
2177:
2174:
2172:
2169:
2167:
2164:
2162:
2159:
2157:
2156:Business risk
2154:
2152:
2149:
2148:
2146:
2144:
2140:
2133:
2129:
2125:
2122:
2120:
2117:
2115:
2112:
2110:
2107:
2105:
2102:
2100:
2097:
2095:
2092:
2090:
2087:
2084:
2080:
2076:
2072:
2068:
2064:
2061:
2060:
2058:
2056:
2052:
2046:
2043:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2021:
2018:
2016:
2013:
2012:
2010:
2008:
2004:
2001:
1997:
1993:
1989:
1982:
1977:
1975:
1970:
1968:
1963:
1962:
1959:
1952:
1949:
1946:
1943:
1940:
1937:
1933:
1929:
1926:
1923:
1921:
1918:
1916:
1913:
1912:
1908:
1901:
1900:
1893:
1884:
1883:
1876:
1874:
1870:
1866:
1862:
1860:
1859:0-471-26849-6
1856:
1852:
1848:
1846:
1842:
1838:
1834:
1832:
1828:
1827:
1823:
1814:
1813:
1805:
1802:
1799:
1793:
1790:
1787:
1781:
1778:
1773:
1769:
1762:
1759:
1754:
1748:
1744:
1739:
1738:
1729:
1726:
1714:
1708:
1705:
1700:
1696:
1692:
1688:
1684:
1680:
1673:
1670:
1665:
1661:
1657:
1653:
1649:
1645:
1638:
1635:
1630:
1626:
1622:
1618:
1613:
1608:
1604:
1600:
1593:
1590:
1585:
1581:
1577:
1573:
1569:
1565:
1558:
1555:
1552:
1547:
1544:
1539:
1535:
1531:
1527:
1523:
1519:
1515:
1511:
1507:
1500:
1497:
1492:
1485:
1482:
1470:
1466:
1461:
1456:
1452:
1448:
1444:
1437:
1434:
1429:
1425:
1421:
1417:
1410:
1408:
1404:
1397:
1393:
1390:
1388:
1385:
1383:
1380:
1378:
1377:Treynor ratio
1375:
1373:
1370:
1368:
1367:Sortino ratio
1365:
1363:
1360:
1358:
1355:
1353:
1350:
1348:
1345:
1343:
1340:
1338:
1335:
1333:
1330:
1328:
1325:
1323:
1320:
1318:
1315:
1313:
1310:
1308:
1305:
1303:
1300:
1299:
1295:
1293:
1289:
1286:
1282:
1278:
1275:
1266:
1264:
1261:
1258:
1253:
1237:
1233:
1228:
1224:
1216:
1212:
1196:
1192:
1188:
1166:
1160:
1156:
1136:
1116:
1094:
1088:
1084:
1076:
1060:
1056:
1052:
1043:
1041:
1037:
1033:
1029:
1025:
1020:
1018:
1014:
1010:
1009:Treynor ratio
1005:
1003:
999:
993:
991:
987:
978:
976:
963:
960:
955:
951:
948:
945:
933:
930:
929:
925:
912:
909:
904:
901:
896:
889:
885:
878:
874:
870:
865:
861:
849:
848:excess return
843:
842:
835:
833:
816:
808:
789:
779:
775:
771:
768:
745:
744:
743:
727:
723:
699:
688:
684:
680:
677:
653:
649:
645:
642:
636:
630:
627:
620:
619:
618:
601:
592:
568:
564:
560:
557:
551:
545:
542:
535:
534:
533:
530:
525:
523:
522:Sortino ratio
514:
512:
506:
504:
501:
497:
493:
489:
484:
482:
477:
475:
471:
465:
462:
458:
457:Ponzi schemes
454:
449:
442:
440:
438:
433:
431:
426:
424:
420:
401:
397:
387:
366:
362:
358:
353:
349:
342:
334:
330:
312:
308:
285:
281:
257:
246:
242:
238:
233:
229:
204:
200:
196:
191:
187:
180:
174:
167:
163:
153:
149:
145:
140:
136:
129:
123:
118:
114:
106:
105:
104:
102:
101:
92:
90:
88:
84:
79:
77:
73:
69:
65:
61:
57:
53:
49:
45:
41:
37:
33:
19:
2841:
2548:Moral hazard
2533:Risk of ruin
2309:Sharpe ratio
2308:
2171:Country risk
2132:Deposit risk
2030:Default risk
1898:
1881:
1864:
1850:
1836:
1811:
1804:
1792:
1780:
1771:
1767:
1761:
1736:
1728:
1716:. Retrieved
1707:
1682:
1678:
1672:
1647:
1644:Econometrica
1643:
1637:
1602:
1599:Econometrica
1598:
1592:
1567:
1563:
1557:
1546:
1516:(1): 63–98.
1513:
1509:
1499:
1490:
1484:
1472:. Retrieved
1453:(1): 49–58.
1450:
1446:
1436:
1419:
1415:
1307:Calmar ratio
1290:
1279:
1273:
1270:
1262:
1254:
1214:
1074:
1044:
1040:distribution
1032:fatter tails
1021:
1006:
994:
982:
934:
931:
927:
926:
844:
840:
839:
831:
714:
616:
526:
518:
510:
485:
481:with-profits
478:
466:
450:
446:
434:
429:
427:
272:
98:
96:
80:
47:
43:
40:Sharpe index
39:
36:Sharpe ratio
35:
29:
2836:Risk return
2783:Price-sales
2721:(EV/EBITDA)
2598:Toxic asset
2558:Speculation
2491:social work
2476:engineering
2304:Risk parity
2289:Omega ratio
2202:Profit risk
2089:Equity risk
2067:Volume risk
2055:Market risk
2007:Credit risk
1347:Omega ratio
498:managers.
496:mutual fund
474:flash crash
461:put options
423:t-statistic
331:(such as a
2879:Categories
2733:(EV/Sales)
2687:(Cap Rate)
2181:Legal risk
2161:Model risk
2075:Shape risk
2071:Basis risk
1999:Categories
1398:References
1302:Bias ratio
1007:While the
998:bias ratio
986:volatility
93:Definition
54:such as a
52:investment
46:, and the
2528:Risk pool
2441:Financial
1718:March 14,
1699:154908707
1607:CiteSeerX
1530:0893-9454
1234:σ
1225:μ
1137:σ
1117:μ
1061:σ
1053:μ
949:−
928:Example 2
886:σ
871:−
841:Example 1
772:−
715:Note, if
681:−
646:−
561:−
527:In 1966,
398:σ
359:−
239:−
197:−
164:σ
146:−
60:portfolio
2727:(EV/GCI)
2451:analysis
2386:Bad debt
2264:Drawdown
2226:Modeling
1474:June 12,
1469:55394403
1387:V2 ratio
1296:See also
1036:skewness
1028:kurtosis
836:Examples
56:security
2864:Treynor
2853:Sortino
2832:(RAROC)
2693:(CROCI)
2466:betting
2456:analyst
2446:adviser
2099:FX risk
1664:1907413
1629:1913625
1584:2327554
1538:1262669
1392:Z score
1038:on the
515:History
430:ex-post
417:is the
384:is the
327:is the
100:ex-ante
32:finance
2842:Sharpe
2826:(ROTE)
2814:(ROCE)
2802:(RONA)
2767:(P/CF)
2761:(PVGO)
2681:(CAPE)
2508:Hazard
2259:Copula
2126:(e.g.
2065:(e.g.
1871:
1857:
1843:
1835:Bacon
1749:
1745:–432.
1697:
1662:
1627:
1609:
1582:
1536:
1528:
1467:
273:where
42:, the
34:, the
2860:(SGR)
2849:(SIR)
2838:(RRR)
2820:(ROE)
2808:(ROC)
2796:(ROA)
2785:(P/S)
2779:(PEG)
2773:(P/E)
2755:(P/B)
2743:Omega
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