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| In [[finance]], the '''Sharpe ratio''' (also known as the '''Sharpe index''', the '''Sharpe measure''', and the '''reward-to-variability ratio''') is a way to examine the performance of an investment by adjusting for its [[financial risk|risk]]. The ratio measures the [[excess return]] (or [[risk premium]]) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk (and is a [[deviation risk measure]]), named after [[William Forsyth Sharpe]].<ref name="sharpe1966" />
| | BSOD or the Blue Screen of Death, (equally known as blue screen bodily memory dump), is an error that occurs on a Windows program - when the computer just shuts down or automatically reboots. This error may occur merely as the computer is booting up or several Windows application is running. Whenever the Windows OS discovers an unrecoverable error it hangs the system or leads to memory dumps.<br><br>You might find which there are registry cleaners which are free plus those that you'll have to pay a nominal sum for. Some registry products provide a bare bones system for free with the way of upgrading to a more advanced, efficient variation of the same system.<br><br>Although this issue affects millions of computer consumers throughout the globe, there is an convenient way to fix it. You see, there's 1 reason for a slow loading computer, plus that's because the PC cannot read the files it needs to run. In a nutshell, this simply means that when you do anything on Windows, it must read up on how to do it. It's traditionally a truly 'dumb' system, that has to have files to tell it to do everything.<br><br>It is usual which the imm32.dll error is caused due to a mis-deletion activity. If you cannot find the imm32.dll anywhere on a computer, there is not any question which it need to be mis-deleted whenever uninstalling programs or different unneeded files. Hence, you can directly cope it from other programs or download it from a secure web and then place it on the computer.<br><br>The final step is to create certain that you clean the registry of the computer. The "registry" is a large database that stores significant files, settings & options, plus info. Windows reads the files it requires inside order for it to run programs through this database. If the registry gets damaged, afflicted, or clogged up, then Windows are not capable to correctly access the files it needs for it to load up programs. As this occurs, difficulties plus errors like the d3d9.dll error happen. To fix this and avoid future setbacks, you must download and run a registry cleaning tool. The highly recommended software is the "Frontline [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities 2014]".<br><br>Reinstall Windows 7 - If nothing appears to work, reinstall Windows 7 with the installation disc that came with the pack. Kindly backup or restore all a data to a flash drive or another hard drive/CD etc. before operating the reinstallation.<br><br>The disk demands space inside order to run smoothly. By freeing up certain area from your disk, you are able to speed up a PC a bit. Delete all file in the temporary internet files folder, recycle bin, obvious shortcuts and icons from the desktop that we never use and remove programs you do not use.<br><br>Fortunately, there's a simple method to fix almost all a computer mistakes. You just have to be able to fix corrupt registry files on a computer. And to do which, we could really utilize a tool termed as a registry cleaner. These easy pieces of software really scan through a PC and fix each corrupt file which could result a problem to Windows. This enables a computer to use all files it wants, which not only speeds it up - and stops all of the errors on the system also. |
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| ==Definition==
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| Since its revision by the original author, William Sharpe, in 1994,<ref>{{cite doi|10.3905/jpm.1994.409501}}</ref> the ''ex-ante'' Sharpe ratio is defined as:
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| : <math>S = \frac{E[R_a-R_b]}{\sigma} = \frac{E[R_a-R_b]}{\sqrt{\mathrm{var}[R_a-R_b]}},</math>
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| where <math>R_a</math> is the asset return, <math>R_b</math> is the return on a benchmark asset, such as the [[risk free rate]] of return or an index such as the S&P 500. <math>E[R_a-R_b]</math> is the [[expected value]] of the excess of the asset return over the benchmark return, and <math>{\sigma}</math> is the [[standard deviation]] of this excess return. This is often confused with the [[information ratio]], in part because the newer definition of the Sharpe ratio matches the definition of information ratio ''within the field of finance''. Outside of this field, information ratio is simply mean over the standard deviation of a series of measurements.
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| The ''ex-post'' 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.
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| ==Use in finance==
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| The Sharpe ratio characterizes how well the return of an asset compensates the investor for the risk taken. When comparing two assets versus a common benchmark, the one with a higher Sharpe ratio provides better return for the same risk (or, equivalently, the same return for lower risk). However, like any other mathematical model, it relies on the data being correct. [[Pyramid schemes]] with a long duration of operation would typically provide a high Sharpe ratio when derived from reported returns, but the inputs are false. When examining the investment performance of assets with smoothing of returns (such as [[with-profits]] funds) the Sharpe ratio should be derived from the performance of the underlying assets rather than the fund returns.
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| Another reason for a misleadingly high Sharpe ratio might be benchmark mis-specification.
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| Sharpe ratios, along with [[Treynor ratio]]s and [[Jensen's alpha]]s, are often used to rank the performance of portfolio or [[mutual fund]] managers.
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| ==Tests==
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| Several statistical tests of the Sharpe ratio have been proposed. These include those proposed by Jobson & Korkie<ref name=Jobson1981>{{cite journal |author1=Jobson JD |author2=Korkie B |date=September 1981 |title=Performance hypothesis testing with the Sharpe and Treynor measures |journal=The Journal of Finance |volume=36 |issue=4 |pages=888–908 |jstor=2327554}}</ref> and Gibbons, Ross & Shanken.<ref name=Gibbons1989>{{cite journal |author1=Gibbons M |author2=Ross S |author3=Shanken J |date=September 1989 |title=A test of the efficiency of a given portfolio |journal=Econometrica |volume=57 |issue=5 |pages=1121–1152 |jstor=1913625}}</ref>
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| ==History==
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| 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) and σ is standard deviation of returns.<ref>{{cite journal|last=Roy|first=Arthur D.|date=July 1952|title=Safety First and the Holding of Assets|journal=Econometrica |volume=20 |issue=3 |pages=431–450 |jstor=1907413}}</ref> This ratio is just the Sharpe ratio, only using minimum acceptable return instead of the risk-free rate in the numerator, and using standard deviation of returns instead of standard deviation of excess returns in the denominator.
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| In 1966, [[William Forsyth Sharpe]] developed what is now known as the Sharpe ratio.<ref name="sharpe1966">{{cite journal|last=Sharpe|first=W. F.|year=1966|title=Mutual Fund Performance|journal=Journal of Business|volume=39|issue=S1|pages=119–138|doi=10.1086/294846}}</ref> 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:
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| :<math>S = \frac{E[R-R_f]}{\sqrt{\mathrm{var}[R]}}.</math>
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| 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:
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| :<math>S = \frac{E[R-R_b]}{\sqrt{\mathrm{var}[R-R_b]}}.</math>
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| Note, if ''R''<sub>f</sub> is a constant risk-free return throughout the period,
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| :<math>\sqrt{\mathrm{var}[R-R_f]}=\sqrt{\mathrm{var}[R]}.</math>
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| Recently, the (original) Sharpe ratio has often been challenged with regard to its appropriateness as a fund performance measure during evaluation periods of declining markets.<ref>{{cite journal|last=Scholz|first=Hendrik|year=2007|title=Refinements to the Sharpe ratio: Comparing alternatives for bear markets|journal=Journal of Asset Management|volume=7|issue=5|pages=347–357|doi=10.1057/palgrave.jam.2250040}}</ref>
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| ==Examples==
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| 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; suppose we assess the risk of the asset, defined as standard deviation of the asset's excess return, as 10%. The risk-free return is constant. Then the Sharpe ratio (using the old definition) will be 1.5
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| (<math>R - R_f = 0.15 </math> and <math>\sigma = 0.10 </math>).
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| For an example of calculating the more commonly used ''ex-post'' Sharpe ratio - which uses ''realized'' rather than ''expected returns'' - based on the contemporary definition, consider the following table of weekly returns.
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| {| class="wikitable"
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| ! Date !! Asset Return!! S&P 500 total return || Excess Return
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| | 7/6/2012 || -0.0050000 || -0.0048419 || -0.0001581
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| | 7/13/2012 || 0.0010000 || 0.0017234 || -0.0007234
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| | 7/20/2012 || 0.0050000 || 0.0046110 || 0.0003890
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| |}
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| We assume that the asset is something like a large-cap U.S. equity fund which would logically be benchmarked against the S&P 500.
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| The mean of the excess returns is -0.0001642 and the (population) standard deviation is 0.0005562248, so the Sharpe ratio is -0.0001642/0.0005562248, or -0.2951444.
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| ==Strengths and weaknesses==
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| The Sharpe ratio has as its principal advantage that it is directly computable from any observed series of returns without need for additional information surrounding the source of profitability. Other ratios such as the [[Bias ratio (finance)|bias ratio]] have recently been introduced into the literature to handle cases where the observed volatility may be an especially poor proxy for the risk inherent in a time-series of observed returns.
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| While the [[Treynor ratio]] works only with systemic risk of a portfolio, the Sharpe ratio observes both systemic and idiosyncratic risks.
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| <blockquote>The returns measured can be of any frequency (i.e. daily, weekly, monthly or annually), as long as they are [[Normal distribution|normally distributed]], as the returns can always be annualized. Herein lies the underlying weakness of the ratio - not all asset returns are normally distributed. Abnormalities like [[Kurtosis risk|kurtosis]], [[Fat tail|fatter tails]] and higher peaks, or [[Skewness risk|skewness]] on the [[Probability distribution|distribution]] can be problematic for the ratio, as standard deviation doesn't have the same effectiveness when these problems exist. Sometimes it can be downright dangerous to use this formula when returns are not normally distributed. <ref>{{cite web|url=http://www.investopedia.com/articles/07/sharpe_ratio.asp|accessdate=March 14, 2011|title=Understanding The Sharpe Ratio}}</ref></blockquote> | |
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| Bailey and López de Prado (2012)<ref>Bayley, D. and M. López de Prado (2012): "The Sharpe Ratio Efficient Frontier", Journal of Risk, 15(2), pp.3-44. Available at http://ssrn.com/abstract=1821643</ref> 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 selection of portfolio managers on the basis of their Sharpe ratios, these authors have proposed a ''Sharpe ratio indifference curve''<ref> 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 http://ssrn.com/abstract=2003638</ref> 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.
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| Because it is a dimensionless ratio, laypeople find it difficult to interpret Sharpe ratios of different investments. For example, how much better is an investment with a Sharpe ratio of 0.5 than one with a Sharpe ratio of -0.2? This weakness was well addressed by the development of the [[Modigliani risk-adjusted performance]] measure, which is in units of percent return – universally understandable by virtually all investors.
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| ==See also==
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| * [[Bias ratio (finance)]]
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| * [[Calmar ratio]]
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| * [[Capital asset pricing model]]
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| * [[Coefficient of variation]]
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| * [[Hansen–Jagannathan bound]]
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| * [[Information ratio]]
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| * [[Jensen's alpha]]
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| * [[List of financial performance measures]]
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| * [[Modern portfolio theory]]
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| * [[Risk adjusted return on capital]]
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| * [[Roy's safety-first criterion]]
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| * [[Sortino ratio]]
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| * [[Treynor ratio]]
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| * [[Upside potential ratio]]
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| * [[V2 ratio]]
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| * [[Z score]]
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| * [[Signal-to-noise_ratio#Alternative_definition | Signal-to-noise ratio]]
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| ==References==
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| {{Reflist}}
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| ==Further reading==
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| * Bacon ''Practical Portfolio Performance Measurement and Attribution 2nd Ed'': Wiley, 2008. ISBN 978-0-470-05928-9
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| * Bruce J. Feibel. ''Investment Performance Measurement''. New York: Wiley, 2003. ISBN 0-471-26849-6
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| ==External links==
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| * [http://www.stanford.edu/~wfsharpe/art/sr/sr.htm The Sharpe ratio]
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| * [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1028715 Generalized Sharpe Ratio]
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| * [http://www.ilukacg.com/articles/All%20Hail%20the%20Sharpe%20Ratio.pdf All Hail the Sharpe Ratio] - Uses and abuses of the Sharpe Ratio
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| {{Financial risk}}
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| {{Financial ratios}}
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| [[Category:Financial ratios]]
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| [[Category:Statistical ratios]]
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BSOD or the Blue Screen of Death, (equally known as blue screen bodily memory dump), is an error that occurs on a Windows program - when the computer just shuts down or automatically reboots. This error may occur merely as the computer is booting up or several Windows application is running. Whenever the Windows OS discovers an unrecoverable error it hangs the system or leads to memory dumps.
You might find which there are registry cleaners which are free plus those that you'll have to pay a nominal sum for. Some registry products provide a bare bones system for free with the way of upgrading to a more advanced, efficient variation of the same system.
Although this issue affects millions of computer consumers throughout the globe, there is an convenient way to fix it. You see, there's 1 reason for a slow loading computer, plus that's because the PC cannot read the files it needs to run. In a nutshell, this simply means that when you do anything on Windows, it must read up on how to do it. It's traditionally a truly 'dumb' system, that has to have files to tell it to do everything.
It is usual which the imm32.dll error is caused due to a mis-deletion activity. If you cannot find the imm32.dll anywhere on a computer, there is not any question which it need to be mis-deleted whenever uninstalling programs or different unneeded files. Hence, you can directly cope it from other programs or download it from a secure web and then place it on the computer.
The final step is to create certain that you clean the registry of the computer. The "registry" is a large database that stores significant files, settings & options, plus info. Windows reads the files it requires inside order for it to run programs through this database. If the registry gets damaged, afflicted, or clogged up, then Windows are not capable to correctly access the files it needs for it to load up programs. As this occurs, difficulties plus errors like the d3d9.dll error happen. To fix this and avoid future setbacks, you must download and run a registry cleaning tool. The highly recommended software is the "Frontline tuneup utilities 2014".
Reinstall Windows 7 - If nothing appears to work, reinstall Windows 7 with the installation disc that came with the pack. Kindly backup or restore all a data to a flash drive or another hard drive/CD etc. before operating the reinstallation.
The disk demands space inside order to run smoothly. By freeing up certain area from your disk, you are able to speed up a PC a bit. Delete all file in the temporary internet files folder, recycle bin, obvious shortcuts and icons from the desktop that we never use and remove programs you do not use.
Fortunately, there's a simple method to fix almost all a computer mistakes. You just have to be able to fix corrupt registry files on a computer. And to do which, we could really utilize a tool termed as a registry cleaner. These easy pieces of software really scan through a PC and fix each corrupt file which could result a problem to Windows. This enables a computer to use all files it wants, which not only speeds it up - and stops all of the errors on the system also.