1281:
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.
1280:
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
1276:
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
1260:
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
456:
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
984:
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
508:
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
436:
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.
977:. 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
257:
452:
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.
834:
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
520:
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:
1248:
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.
912:
972:
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
816:
1265:
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.
491:
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.
1272:
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
699:
601:
472:
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).
963:
461:
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
1252:
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.
509:
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
1239:
1168:
1096:
404:
1060:
1785:
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
1136:
421:
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.
606:
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:
729:
314:
287:
1116:
1196:
371:
1015:, as the returns can always be annualized. Herein lies the underlying weakness of the ratio - asset returns are not normally distributed. Abnormalities like
821:
The (original) Sharpe ratio has often been challenged with regard to its appropriateness as a fund performance measure during periods of declining markets.
2667:
2642:
98:
500:
Several statistical tests of the Sharpe ratio have been proposed. These include those proposed by Jobson & Korkie and
Gibbons, Ross & Shanken.
1967:
1913:
842:
1325:
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2414:
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1739:
921:
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.
737:
1277:
sponsors who select fund managers primarily based on the Sharpe ratio will give incentives for fund managers to adopt such a strategy.
428:
is a generalization of the Sharpe ratio that uses as benchmark some other, typically risky index rather than using risk-free returns.
1847:
67:
of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk.
2818:
2282:
1886:
1799:
1345:
1340:
1933:
1773:
Bailey, D. and M. López de Prado (2012): "The Sharpe Ratio
Efficient Frontier", Journal of Risk, 15(2), pp.3-44. Available at
513:, which also uses MAR in the numerator, but uses a different standard deviation (semi/downside deviation) in the denominator.
2635:
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612:
527:
1310:
1960:
1031:
can be problematic for the ratio, as standard deviation doesn't have the same effectiveness when these problems exist.
2883:
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2139:
1300:
2800:
2311:
927:
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2812:
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2399:
1980:
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448:, for example, will have a high empirical Sharpe ratio until they fail. Similarly, a fund that sells low-strike
2888:
2257:
2222:
1305:
1028:
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1920:
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Jobson JD; Korkie B (September 1981). "Performance hypothesis testing with the Sharpe and
Treynor measures".
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2272:
2214:
1953:
1330:
1011:
The returns measured can be of any frequency (i.e. daily, weekly, monthly or annually), as long as they are
52:
2262:
1595:
1370:
458:
321:
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414:
will equal the Sharpe Ratio times the square root of T (the number of returns used for the calculation).
2753:
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2008:
1350:
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1209:
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2419:
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2003:
1290:
986:
974:
468:
Additionally, when examining the investment performance of assets with smoothing of returns (such as
1666:
Scholz, Hendrik (2007). "Refinements to the Sharpe ratio: Comparing alternatives for bear markets".
1600:
2725:
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2599:
2556:
2067:
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selection of portfolio managers on the basis of their Sharpe ratios, these authors have proposed a
1141:
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380:
48:
1037:
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2551:
2439:
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1648:
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1522:
1453:
1005:
488:
407:
64:
44:
1586:
Gibbons M; Ross S; Shanken J (September 1989). "A test of the efficiency of a given portfolio".
1945:
1818:
Lo, Andrew W. "The statistics of Sharpe ratios." Financial analysts journal 58.4 (2002): 36-52
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2018:
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1735:
1514:
1320:
1315:
839:, as 10%. The risk-free return is constant. Then the Sharpe ratio using the old definition is
517:
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71:
1121:
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2736:
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1412:
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317:
60:
1701:
707:
292:
265:
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2526:
2501:
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2449:
2424:
2404:
2394:
2107:
2071:
2013:
1245:
1199:
1101:
1001:
990:
1724:
1478:
Gatfaoui, Hayette. "Sharpe Ratios and Their
Fundamental Components: An Empirical Study".
1173:
2701:
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2326:
2317:
2185:
2164:
2112:
2102:
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2033:
1976:
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1360:
374:
327:
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2144:
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1365:
1355:
1024:
1016:
997:
836:
510:
476:
445:
1457:
2536:
2521:
2159:
2120:
1939:
1295:
469:
252:{\displaystyle S_{a}={\frac {E}{\sigma _{a}}}={\frac {E}{\sqrt {\mathrm {var} }}},}
1903:
1431:
1679:
2731:
2586:
2546:
2292:
2277:
2190:
2077:
2055:
2043:
1995:
1335:
484:
462:
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59:. It is defined as the difference between the returns of the investment and the
1539:
2169:
2149:
2063:
2059:
1868:
Goetzmann, William; Ingersoll, Jonathan; Spiegel, Matthew; Welch, Ivo (2002),
40:
1518:
2765:
2741:
2707:
2516:
1448:
441:
907:{\displaystyle {\frac {R_{a}-R_{f}}{\sigma _{a}}}={\frac {0.15}{0.10}}=1.5}
1819:
2719:
2374:
1510:
1375:
1020:
993:
are sometimes used to indicate the potential presence of these problems.
1869:
86:
Since its revision by the original author, William Sharpe, in 1994, the
2429:
1652:
1617:
1572:
1526:
1494:
1380:
978:
88:
20:
1631:
Roy, Arthur D. (July 1952). "Safety First and the
Holding of Assets".
2713:
2496:
1755:
Lo, Andrew W. (July–August 2002). "The
Statistics of Sharpe Ratios".
1908:
1786:
1774:
1644:
1609:
444:, so that standard deviation does not capture all aspects of risk.
2620:
1416:
1008:. Which one is more relevant will depend on the portfolio context.
2679:
1826:
Practical
Portfolio Performance Measurement and Attribution 2nd Ed
1241:
is the numerical fraction of wealth suggested for the investment.
811:{\displaystyle {\sqrt {\mathrm {var} }}={\sqrt {\mathrm {var} }}.}
377:
of the excess of the asset return over the benchmark return, and
2511:
75:
56:
2624:
1949:
1004:
of a portfolio, the Sharpe ratio considers both systematic and
1921:"A Comparison of Different Measures of Risk-adjusted Return"
483:, are often used to rank the performance of portfolio or
731:
is a constant risk-free return throughout the period,
694:{\displaystyle S={\frac {E}{\sqrt {\mathrm {var} }}}.}
596:{\displaystyle S={\frac {E}{\sqrt {\mathrm {var} }}}.}
1495:"Risks and Portfolio Decisions Involving Hedge Funds"
1212:
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383:
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101:
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365:
308:
281:
251:
1940:Calculating and Interpreting Sharpe Ratios online
1403:Sharpe, W. F. (1966). "Mutual Fund Performance".
1270:Goetzmann, Ingersoll, Spiegel, and Welch (2002)
457:liability payout once every 5–10 years, and a
2636:
1961:
1854:The Sharpe Ratio: Statistics and Applications
8:
1930:- Some example calculations of Sharpe ratios
1726:Paul Wilmott introduces Quantitative Finance
1540:http://docs.lhpedersen.com/BuffettsAlpha.pdf
1398:
1396:
958:{\displaystyle {\frac {0.12-0.05}{0.1}}=0.7}
2643:
2629:
2621:
1991:
1968:
1954:
1946:
1599:
1493:Agarwal, Vikas; Naik, Narayan Y. (2004).
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100:
985:illiquid assets. Statistics such as the
1820:https://doi.org/10.2469/faj.v58.n4.2453
1392:
1888:The Principal-Agent Problem in Finance
1877:, National Bureau of Economic Research
1801:The Principal-Agent Problem in Finance
1326:List of financial performance measures
2748:Present value of growth opportunities
2668:Cyclically adjusted price-to-earnings
1916:- Uses and abuses of the Sharpe Ratio
7:
2714:Enterprise value/gross cash invested
440:However, financial assets are often
16:Formula for measuring financial risk
1936:- Risk adjusted return calculations
1730:(Second ed.). Wiley. pp.
1436:The Journal of Portfolio Management
1256:Drawback as fund selection criteria
1840:Investment Performance Measurement
1565:10.1111/j.1540-6261.1981.tb04891.x
790:
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210:
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14:
1787:https://ssrn.com/abstract=2003638
1775:https://ssrn.com/abstract=1821643
39:) measures the performance of an
2243:Conditional Value-at-Risk (CVaR)
1702:"Understanding The Sharpe Ratio"
1234:{\displaystyle \mu /\sigma ^{2}}
1034:For Brownian walk, Sharpe ratio
410:of the asset excess return. The
2819:Risk-adjusted return on capital
1499:The Review of Financial Studies
1341:Risk adjusted return on capital
1263:Sharpe ratio indifference curve
2562:Strategic financial management
2365:Asset and liability management
1206:, and, indeed, Kelly fraction
800:
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628:
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578:
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360:
334:
240:
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147:
121:
1:
1269:
1163:{\displaystyle 1/{\sqrt {T}}}
1091:{\displaystyle 1/{\sqrt {T}}}
399:{\displaystyle {\sigma _{a}}}
2680:Cash return on cash invested
1928:What is a good Sharpe Ratio?
1680:10.1057/palgrave.jam.2250040
1346:Roy's safety-first criterion
1098:, because the excess return
1055:{\displaystyle \mu /\sigma }
92:Sharpe ratio is defined as:
2140:Operational risk management
1804:, CFA Institute, p. 14
1668:Journal of Asset Management
1430:Sharpe, William F. (1994).
1301:Capital asset pricing model
991:first order autocorrelation
37:reward-to-variability ratio
2907:
2801:Return on capital employed
2312:Proportional hazards model
2263:Interest rate immunization
1757:Financial Analysts Journal
1480:IESEG School of Management
475:Sharpe ratios, along with
55:, after adjusting for its
2813:Return on tangible equity
2658:
2595:
1981:financial risk management
1914:All Hail the Sharpe Ratio
1842:. New York: Wiley, 2003.
2766:Price-earnings to growth
2258:First-hitting-time model
2223:Arbitrage pricing theory
1934:Sharpe ratio in MS excel
1909:Generalized Sharpe Ratio
1871:Sharpening Sharpe Ratios
1311:Hansen–Jagannathan bound
1306:Coefficient of variation
968:Strengths and weaknesses
442:not normally distributed
2708:Enterprise value/EBITDA
2567:Stress test (financial)
2273:Modern portfolio theory
1885:Shah, Sunit N. (2014),
1798:Shah, Sunit N. (2014),
1449:10.3905/jpm.1994.409501
1331:Modern portfolio theory
1131:{\displaystyle \sigma }
2720:Enterprise value/sales
1722:Wilmott, Paul (2007).
1553:The Journal of Finance
1371:Upside potential ratio
1244:In some settings, the
1235:
1204:dimensionless quantity
1192:
1164:
1132:
1112:
1092:
1056:
959:
908:
812:
725:
695:
597:
459:high-frequency trading
400:
367:
322:U.S. Treasury security
310:
283:
253:
74:, who developed it in
2605:Investment management
2507:Investment management
2233:Replicating portfolio
2009:Sovereign credit risk
1351:Signal-to-noise ratio
1236:
1193:
1165:
1133:
1113:
1093:
1057:
1023:and higher peaks, or
960:
924:The Sharpe ratio is:
909:
813:
726:
724:{\displaystyle R_{f}}
696:
598:
401:
368:
311:
309:{\displaystyle R_{b}}
289:is the asset return,
284:
282:{\displaystyle R_{a}}
254:
2789:Return on net assets
2610:Mathematical finance
2542:Risk-return spectrum
2532:Mathematical finance
2487:Fundamental analysis
2420:Exchange traded fund
2004:Consumer credit risk
1210:
1174:
1142:
1138:are proportional to
1122:
1111:{\displaystyle \mu }
1102:
1070:
1064:dimensional quantity
1038:
1013:normally distributed
928:
843:
738:
708:
613:
528:
381:
328:
293:
266:
99:
2674:Capitalization rate
2600:Financial economics
2557:Statistical finance
2323:Value-at-Risk (VaR)
2228:Black–Scholes model
2068:Holding period risk
1856:. CRC Press, 2022.
1405:Journal of Business
1191:{\displaystyle 1/T}
1118:and the volatility
1006:idiosyncratic risks
1000:considers only the
70:It was named after
27:(also known as the
2884:Portfolio theories
2879:Statistical ratios
2847:Sustainable growth
2577:Structured product
2572:Structured finance
2552:Speculative attack
2238:Cash flow matching
2201:Non-financial risk
2098:Interest rate risk
2024:Concentration risk
1942:- Cloud calculator
1511:10.1093/rfs/hhg044
1432:"The Sharpe Ratio"
1231:
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904:
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489:Berkshire Hathaway
408:standard deviation
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279:
249:
65:standard deviation
2861:
2860:
2795:Return on capital
2663:Buffett indicator
2618:
2617:
2390:Corporate finance
2385:Capital structure
2339:Cash flow at risk
2335:Liquidity at risk
2308:Survival analysis
2209:
2208:
2155:Reputational risk
2029:Credit derivative
1923:. September 2013.
1862:978-1-032-01930-7
1838:Bruce J. Feibel.
1834:978-0-470-05928-9
1741:978-0-470-31958-1
1316:Information ratio
1198:correspondingly.
1158:
1086:
979:utility functions
947:
896:
883:
803:
776:
686:
685:
588:
587:
518:William F. Sharpe
426:information ratio
366:{\displaystyle E}
244:
243:
161:
72:William F. Sharpe
63:, divided by the
2896:
2874:Financial ratios
2807:Return on equity
2783:Return on assets
2737:Operating margin
2652:Financial ratios
2645:
2638:
2631:
2622:
2492:Growth investing
2410:Enterprise value
2360:Asset allocation
2343:Earnings at risk
2325:and extensions (
2268:Market portfolio
2132:Operational risk
2117:Refinancing risk
1992:
1970:
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1904:The Sharpe ratio
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1594:(5): 1121–1152.
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1274:out-of-the-money
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318:risk-free return
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61:risk-free return
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2889:Yield (finance)
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2863:
2862:
2857:
2754:Price/cash flow
2697:Dividend payout
2654:
2649:
2619:
2614:
2591:
2527:Systematic risk
2425:Expected return
2405:Economic bubble
2400:Diversification
2395:Cost of capital
2348:
2205:
2174:
2126:
2108:Volatility risk
2072:Price area risk
2038:
2014:Settlement risk
1983:
1974:
1919:
1900:
1891:, CFA Institute
1884:
1883:
1874:
1867:
1866:
1852:Steven E. Pav.
1828:: Wiley, 2008.
1815:
1813:Further reading
1810:
1809:
1797:
1796:
1792:
1784:
1780:
1772:
1768:
1754:
1753:
1749:
1742:
1721:
1720:
1716:
1706:
1704:
1700:
1699:
1695:
1665:
1664:
1660:
1645:10.2307/1907413
1630:
1629:
1625:
1610:10.2307/1913625
1601:10.1.1.557.1995
1585:
1584:
1580:
1550:
1549:
1545:
1538:
1534:
1492:
1491:
1487:
1477:
1476:
1472:
1462:
1460:
1429:
1428:
1424:
1411:(S1): 119–138.
1402:
1401:
1394:
1389:
1287:
1258:
1246:Kelly criterion
1221:
1208:
1207:
1200:Kelly criterion
1172:
1171:
1140:
1139:
1120:
1119:
1100:
1099:
1068:
1067:
1036:
1035:
1002:systematic risk
970:
933:
926:
925:
873:
862:
849:
848:
841:
840:
827:
763:
736:
735:
711:
706:
705:
672:
637:
624:
611:
610:
552:
539:
526:
525:
506:
498:
481:Jensen's alphas
434:
385:
379:
378:
350:
337:
326:
325:
296:
291:
290:
269:
264:
263:
230:
217:
188:
175:
168:
151:
137:
124:
117:
102:
97:
96:
84:
53:risk-free asset
17:
12:
11:
5:
2904:
2903:
2900:
2892:
2891:
2886:
2881:
2876:
2866:
2865:
2859:
2858:
2856:
2855:
2850:
2844:
2839:
2836:Short interest
2833:
2828:
2822:
2816:
2810:
2804:
2798:
2792:
2786:
2780:
2775:
2769:
2763:
2760:Price-earnings
2757:
2751:
2745:
2739:
2734:
2729:
2723:
2717:
2711:
2705:
2702:Earnings yield
2699:
2694:
2692:Dividend cover
2689:
2686:Debt-to-equity
2683:
2677:
2671:
2665:
2659:
2656:
2655:
2650:
2648:
2647:
2640:
2633:
2625:
2616:
2615:
2613:
2612:
2607:
2602:
2596:
2593:
2592:
2590:
2589:
2584:
2579:
2574:
2569:
2564:
2559:
2554:
2549:
2544:
2539:
2534:
2529:
2524:
2519:
2514:
2509:
2504:
2499:
2494:
2489:
2484:
2483:
2482:
2477:
2472:
2467:
2462:
2457:
2452:
2447:
2442:
2437:
2427:
2422:
2417:
2412:
2407:
2402:
2397:
2392:
2387:
2382:
2377:
2372:
2367:
2362:
2356:
2354:
2353:Basic concepts
2350:
2349:
2347:
2346:
2331:Margin at risk
2327:Profit at risk
2320:
2318:Tracking error
2315:
2305:
2300:
2295:
2290:
2288:Risk-free rate
2285:
2280:
2275:
2270:
2265:
2260:
2255:
2250:
2245:
2240:
2235:
2230:
2225:
2219:
2217:
2211:
2210:
2207:
2206:
2204:
2203:
2198:
2193:
2188:
2186:Execution risk
2182:
2180:
2176:
2175:
2173:
2172:
2167:
2165:Political risk
2162:
2157:
2152:
2147:
2142:
2136:
2134:
2128:
2127:
2125:
2124:
2113:Liquidity risk
2110:
2105:
2103:Inflation risk
2100:
2095:
2093:Margining risk
2090:
2085:
2083:Valuation risk
2080:
2075:
2052:Commodity risk
2048:
2046:
2040:
2039:
2037:
2036:
2034:Securitization
2031:
2026:
2021:
2016:
2011:
2006:
2000:
1998:
1989:
1985:
1984:
1977:Financial risk
1975:
1973:
1972:
1965:
1958:
1950:
1944:
1943:
1937:
1931:
1925:
1917:
1911:
1906:
1899:
1898:External links
1896:
1895:
1894:
1881:
1864:
1850:
1836:
1822:
1814:
1811:
1808:
1807:
1790:
1778:
1766:
1747:
1740:
1714:
1693:
1674:(5): 347–357.
1658:
1639:(3): 431–450.
1623:
1578:
1559:(4): 888–908.
1543:
1532:
1485:
1470:
1422:
1417:10.1086/294846
1391:
1390:
1388:
1385:
1384:
1383:
1378:
1373:
1368:
1363:
1361:Sterling ratio
1358:
1353:
1348:
1343:
1338:
1333:
1328:
1323:
1321:Jensen's alpha
1318:
1313:
1308:
1303:
1298:
1293:
1286:
1283:
1257:
1254:
1228:
1224:
1219:
1215:
1187:
1183:
1179:
1157:
1151:
1147:
1127:
1107:
1085:
1079:
1075:
1066:and has units
1051:
1047:
1043:
969:
966:
954:
951:
946:
942:
939:
936:
903:
900:
895:
892:
887:
880:
876:
869:
865:
861:
856:
852:
826:
823:
819:
818:
807:
802:
799:
796:
792:
789:
786:
780:
775:
770:
766:
762:
759:
756:
752:
749:
746:
718:
714:
702:
701:
690:
684:
679:
675:
671:
668:
665:
661:
658:
655:
649:
644:
640:
636:
633:
630:
627:
621:
618:
604:
603:
592:
586:
583:
580:
576:
573:
570:
564:
559:
555:
551:
548:
545:
542:
536:
533:
505:
502:
497:
494:
477:Treynor ratios
433:
432:Use in finance
430:
392:
388:
375:expected value
362:
357:
353:
349:
344:
340:
336:
333:
303:
299:
276:
272:
260:
259:
248:
242:
237:
233:
229:
224:
220:
216:
212:
209:
206:
200:
195:
191:
187:
182:
178:
174:
171:
165:
158:
154:
149:
144:
140:
136:
131:
127:
123:
120:
114:
109:
105:
83:
80:
51:compared to a
33:Sharpe measure
15:
13:
10:
9:
6:
4:
3:
2:
2902:
2901:
2890:
2887:
2885:
2882:
2880:
2877:
2875:
2872:
2871:
2869:
2854:
2851:
2848:
2845:
2843:
2840:
2837:
2834:
2832:
2829:
2826:
2823:
2820:
2817:
2814:
2811:
2808:
2805:
2802:
2799:
2796:
2793:
2790:
2787:
2784:
2781:
2779:
2778:Profit margin
2776:
2773:
2770:
2767:
2764:
2761:
2758:
2755:
2752:
2749:
2746:
2743:
2742:Price-to-book
2740:
2738:
2735:
2733:
2730:
2727:
2726:Loan-to-value
2724:
2721:
2718:
2715:
2712:
2709:
2706:
2703:
2700:
2698:
2695:
2693:
2690:
2687:
2684:
2681:
2678:
2675:
2672:
2669:
2666:
2664:
2661:
2660:
2657:
2653:
2646:
2641:
2639:
2634:
2632:
2627:
2626:
2623:
2611:
2608:
2606:
2603:
2601:
2598:
2597:
2594:
2588:
2585:
2583:
2582:Systemic risk
2580:
2578:
2575:
2573:
2570:
2568:
2565:
2563:
2560:
2558:
2555:
2553:
2550:
2548:
2545:
2543:
2540:
2538:
2535:
2533:
2530:
2528:
2525:
2523:
2520:
2518:
2515:
2513:
2510:
2508:
2505:
2503:
2500:
2498:
2495:
2493:
2490:
2488:
2485:
2481:
2478:
2476:
2473:
2471:
2468:
2466:
2463:
2461:
2458:
2456:
2453:
2451:
2448:
2446:
2443:
2441:
2438:
2436:
2433:
2432:
2431:
2428:
2426:
2423:
2421:
2418:
2416:
2413:
2411:
2408:
2406:
2403:
2401:
2398:
2396:
2393:
2391:
2388:
2386:
2383:
2381:
2380:Capital asset
2378:
2376:
2373:
2371:
2370:Asset pricing
2368:
2366:
2363:
2361:
2358:
2357:
2355:
2351:
2344:
2340:
2336:
2332:
2328:
2324:
2321:
2319:
2316:
2313:
2309:
2306:
2304:
2303:Sortino ratio
2301:
2299:
2296:
2294:
2291:
2289:
2286:
2284:
2281:
2279:
2276:
2274:
2271:
2269:
2266:
2264:
2261:
2259:
2256:
2254:
2251:
2249:
2246:
2244:
2241:
2239:
2236:
2234:
2231:
2229:
2226:
2224:
2221:
2220:
2218:
2216:
2212:
2202:
2199:
2197:
2196:Systemic risk
2194:
2192:
2189:
2187:
2184:
2183:
2181:
2177:
2171:
2168:
2166:
2163:
2161:
2158:
2156:
2153:
2151:
2148:
2146:
2145:Business risk
2143:
2141:
2138:
2137:
2135:
2133:
2129:
2122:
2118:
2114:
2111:
2109:
2106:
2104:
2101:
2099:
2096:
2094:
2091:
2089:
2086:
2084:
2081:
2079:
2076:
2073:
2069:
2065:
2061:
2057:
2053:
2050:
2049:
2047:
2045:
2041:
2035:
2032:
2030:
2027:
2025:
2022:
2020:
2017:
2015:
2012:
2010:
2007:
2005:
2002:
2001:
1999:
1997:
1993:
1990:
1986:
1982:
1978:
1971:
1966:
1964:
1959:
1957:
1952:
1951:
1948:
1941:
1938:
1935:
1932:
1929:
1926:
1922:
1918:
1915:
1912:
1910:
1907:
1905:
1902:
1901:
1897:
1890:
1889:
1882:
1873:
1872:
1865:
1863:
1859:
1855:
1851:
1849:
1848:0-471-26849-6
1845:
1841:
1837:
1835:
1831:
1827:
1823:
1821:
1817:
1816:
1812:
1803:
1802:
1794:
1791:
1788:
1782:
1779:
1776:
1770:
1767:
1762:
1758:
1751:
1748:
1743:
1737:
1733:
1728:
1727:
1718:
1715:
1703:
1697:
1694:
1689:
1685:
1681:
1677:
1673:
1669:
1662:
1659:
1654:
1650:
1646:
1642:
1638:
1634:
1627:
1624:
1619:
1615:
1611:
1607:
1602:
1597:
1593:
1589:
1582:
1579:
1574:
1570:
1566:
1562:
1558:
1554:
1547:
1544:
1541:
1536:
1533:
1528:
1524:
1520:
1516:
1512:
1508:
1504:
1500:
1496:
1489:
1486:
1481:
1474:
1471:
1459:
1455:
1450:
1445:
1441:
1437:
1433:
1426:
1423:
1418:
1414:
1410:
1406:
1399:
1397:
1393:
1386:
1382:
1379:
1377:
1374:
1372:
1369:
1367:
1366:Treynor ratio
1364:
1362:
1359:
1357:
1356:Sortino ratio
1354:
1352:
1349:
1347:
1344:
1342:
1339:
1337:
1334:
1332:
1329:
1327:
1324:
1322:
1319:
1317:
1314:
1312:
1309:
1307:
1304:
1302:
1299:
1297:
1294:
1292:
1289:
1288:
1284:
1282:
1278:
1275:
1271:
1267:
1264:
1255:
1253:
1250:
1247:
1242:
1226:
1222:
1217:
1213:
1205:
1201:
1185:
1181:
1177:
1155:
1149:
1145:
1125:
1105:
1083:
1077:
1073:
1065:
1049:
1045:
1041:
1032:
1030:
1026:
1022:
1018:
1014:
1009:
1007:
1003:
999:
998:Treynor ratio
994:
992:
988:
982:
980:
976:
967:
965:
952:
949:
944:
940:
937:
934:
922:
919:
918:
914:
901:
898:
893:
890:
885:
878:
874:
867:
863:
859:
854:
850:
838:
837:excess return
832:
831:
824:
822:
805:
797:
778:
768:
764:
760:
757:
734:
733:
732:
716:
712:
688:
677:
673:
669:
666:
642:
638:
634:
631:
625:
619:
616:
609:
608:
607:
590:
581:
557:
553:
549:
546:
540:
534:
531:
524:
523:
522:
519:
514:
512:
511:Sortino ratio
503:
501:
495:
493:
490:
486:
482:
478:
473:
471:
466:
464:
460:
454:
451:
447:
446:Ponzi schemes
443:
438:
431:
429:
427:
422:
420:
415:
413:
409:
390:
386:
376:
355:
351:
347:
342:
338:
331:
323:
319:
301:
297:
274:
270:
246:
235:
231:
227:
222:
218:
193:
189:
185:
180:
176:
169:
163:
156:
152:
142:
138:
134:
129:
125:
118:
112:
107:
103:
95:
94:
93:
91:
90:
81:
79:
77:
73:
68:
66:
62:
58:
54:
50:
46:
42:
38:
34:
30:
26:
22:
2830:
2537:Moral hazard
2522:Risk of ruin
2298:Sharpe ratio
2297:
2160:Country risk
2121:Deposit risk
2019:Default risk
1887:
1870:
1853:
1839:
1825:
1800:
1793:
1781:
1769:
1760:
1756:
1750:
1725:
1717:
1705:. Retrieved
1696:
1671:
1667:
1661:
1636:
1633:Econometrica
1632:
1626:
1591:
1588:Econometrica
1587:
1581:
1556:
1552:
1546:
1535:
1505:(1): 63–98.
1502:
1498:
1488:
1479:
1473:
1461:. Retrieved
1442:(1): 49–58.
1439:
1435:
1425:
1408:
1404:
1296:Calmar ratio
1279:
1268:
1262:
1259:
1251:
1243:
1203:
1063:
1033:
1029:distribution
1021:fatter tails
1010:
995:
983:
971:
923:
920:
916:
915:
833:
829:
828:
820:
703:
605:
515:
507:
499:
474:
470:with-profits
467:
455:
439:
435:
423:
418:
416:
261:
87:
85:
69:
36:
32:
29:Sharpe index
28:
25:Sharpe ratio
24:
18:
2825:Risk return
2772:Price-sales
2710:(EV/EBITDA)
2587:Toxic asset
2547:Speculation
2480:social work
2465:engineering
2293:Risk parity
2278:Omega ratio
2191:Profit risk
2078:Equity risk
2056:Volume risk
2044:Market risk
1996:Credit risk
1336:Omega ratio
487:managers.
485:mutual fund
463:flash crash
450:put options
412:t-statistic
320:(such as a
2868:Categories
2722:(EV/Sales)
2676:(Cap Rate)
2170:Legal risk
2150:Model risk
2064:Shape risk
2060:Basis risk
1988:Categories
1387:References
1291:Bias ratio
996:While the
987:bias ratio
975:volatility
82:Definition
43:such as a
41:investment
35:, and the
2517:Risk pool
2430:Financial
1707:March 14,
1688:154908707
1596:CiteSeerX
1519:0893-9454
1223:σ
1214:μ
1126:σ
1106:μ
1050:σ
1042:μ
938:−
917:Example 2
875:σ
860:−
830:Example 1
761:−
704:Note, if
670:−
635:−
550:−
516:In 1966,
387:σ
348:−
228:−
186:−
153:σ
135:−
49:portfolio
2716:(EV/GCI)
2440:analysis
2375:Bad debt
2253:Drawdown
2215:Modeling
1463:June 12,
1458:55394403
1376:V2 ratio
1285:See also
1025:skewness
1017:kurtosis
825:Examples
45:security
2853:Treynor
2842:Sortino
2821:(RAROC)
2682:(CROCI)
2455:betting
2445:analyst
2435:adviser
2088:FX risk
1653:1907413
1618:1913625
1573:2327554
1527:1262669
1381:Z score
1027:on the
504:History
419:ex-post
406:is the
373:is the
316:is the
89:ex-ante
21:finance
2831:Sharpe
2815:(ROTE)
2803:(ROCE)
2791:(RONA)
2756:(P/CF)
2750:(PVGO)
2670:(CAPE)
2497:Hazard
2248:Copula
2115:(e.g.
2054:(e.g.
1860:
1846:
1832:
1824:Bacon
1738:
1734:–432.
1686:
1651:
1616:
1598:
1571:
1525:
1517:
1456:
262:where
31:, the
23:, the
2849:(SGR)
2838:(SIR)
2827:(RRR)
2809:(ROE)
2797:(ROC)
2785:(ROA)
2774:(P/S)
2768:(PEG)
2762:(P/E)
2744:(P/B)
2732:Omega
2728:(LTV)
2704:(E/P)
2688:(D/E)
2502:Hedge
2460:crime
2450:asset
2283:RAROC
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