Sharpe ratio - YouTube

in finance the Sharpe ratio is a way to

examine the performance of an investment

by adjusting for its risk the ratio

measures the excess return per unit of

deviation in an investment asset or a

trading strategy typically referred to

as risk named after William Forsythe

sharp definition since its revision by

the original author William Sharpe in

1994 the ex-ante Sharpe ratio is defined

as where is the asset return is the

return on a benchmark asset such as the

risk-free rate of return or an index

such as the S&P 500 is the expected

value of the excess of the asset return

over the benchmark return and is the

standard deviation of this excess return

this is often confused with the

information ratio in part because the

new 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

the ex-post Sharpe ratio uses the same

equation as the one above but with

realised returns of the asset and

benchmark rather than expected returns

see the second example below use in

finance 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 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 but

smoothing of returns the Sharpe ratio

should be derived from the performance

of the underlying assets rather than the

fund returns Sharpe ratios along with

Trena ratios and Jensen's alphas are

often used to rank the performance of

portfolio or mutual fund managers tests

several statistical tests of the Sharpe

ratio have been proposed these include

those

posed by Jobson and Corki and Gibbons

Ross and shangkun history in 1952

Alfred e Roy suggested maximizing the

ratio M D /f Lauren where M is expected

gross return D's some disaster level and

I Florin is standard deviation of

returns this ratio is just the Sharpe

ratio only using minimum acceptable

return instead of a risk-free rate in

the numerator and using standard

deviation of returns instead of standard

deviation of excess returns in the

denominator

in 1966 William Forsythe Sharpe

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 sharps 1994

revision acknowledged that the basis of

comparison should be an applicable

benchmark

which changes with time after this

revision the definition is note if our F

is a constant risk free return

throughout the period recently the

Sharpe ratio has often been challenged

with regard to its appropriateness as a

fun performance measure during

evaluation periods of declining markets

examples 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 a standard deviation of the

asset success return as 10% the

risk-free return is constant then the

Sharpe ratio will be 1.5 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 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 the mean of the excess returns is

minus 0.0001 642 and the standard

deviation is zero point zero zero

five five six two two four eight so the

Sharpe ratio is minus 0.0001 six four

two over zero point zero zero zero five

five six two two four eight or minus

zero point two nine five one four four

four strengths and weaknesses 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 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 while the

Treena ratio works only with systematic

risk of a portfolio the Sharpe ratio

observes both systematic and

idiosyncratic risks their returns

measured can be of any frequency as long

as they are normally distributed as the

returns can always be analyzed herein

lies the underlying weakness of the

ratio not all asset returns are normally

distributed abnormalities like kurtosis

fatter tails and high peaks or skewness

on the 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 bailey and la cubed PES de

prado show that sharp 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 and

difference curve 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 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 and 1 with a Sharpe ratio of minus

0.2 this weakness was well addressed by

the development of the medallion a

risk-adjusted performance measure which

is in units of percent returned a euro

universally understandable by virtually

all investors in some settings the Kelly

criterion can be used to convert the

Sharpe ratio into a rate of return the

accuracy of Sharpe ratio estimators

hinges on the statistical properties of

returns and these properties can vary

considerably among strategies portfolios

and overtime see also bias ratio karma

ratio capital asset pricing model

coefficient of variation unseen a euro

jaganathan bound information ratio

Jensen's alpha list of financial

performance measures modern portfolio

theory risk adjusted return on capital

ROI safety first criterion Sortino ratio

Treynor ratio upside potential ratio V

to ratio z-score signal-to-noise ratio

references further reading bacon

practical portfolio performance

measurement and attribution 2nd ed Wiley

2008 ISBN 978-0-444-53286-2