Description Usage Arguments Details Value Note Author(s) References See Also Examples
View source: R/distributions.r
Density, distribution function, quantile function and random
generation for the Sharpe ratio distribution with df
degrees of freedom
(and optional signalnoiseratio zeta
).
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x, q 
vector of quantiles. 
df 
the number of observations the statistic is based on. This
is one more than the number of degrees of freedom in the
corresponding tstatistic, although the effect will be small
when 
zeta 
the 'signaltonoise' parameter, zeta defined as the population mean divided by the population standard deviation, 'annualized'. 
ope 
the number of observations per 'epoch'. For convenience of
interpretation, The Sharpe ratio is typically quoted in 'annualized'
units for some epoch, that is, 'per square root epoch', though returns
are observed at a frequency of 
... 
arguments passed on to the respective tdistribution functions, namely

p 
vector of probabilities. 
n 
number of observations. 
Suppose xi are n independent draws of a normal random variable with mean mu and variance sigma^2. Let xbar be the sample mean, and s be the sample standard deviation (using Bessel's correction). Let c0 be the 'risk free rate'. Then
z = (xbar  c0)/s
is the (sample) Sharpe ratio.
The units of z is per root time. Typically the Sharpe ratio is annualized by multiplying by sqrt(d), where d is the number of observations per epoch (typically a year).
Letting z = sqrt(d)(xbar  c0)/s, where the sample estimates are based on n observations, then z takes a (noncentral) Sharpe ratio distribution parametrized by n 'degrees of freedom', noncentrality parameter zeta = (mu  c0)/sigma, and annualization parameter d.
The parameters are encoded as follows:
n is denoted by df
.
zeta is denoted by zeta
.
d is denoted by ope
. ('Observations Per Year')
If the returns violate the assumptions of normality, independence, etc (as they always should in the real world), the sample Sharpe Ratio will not follow this distribution. It does provide, however, a reasonable approximation in many cases.
dsr
gives the density, psr
gives the distribution function,
qsr
gives the quantile function, and rsr
generates random deviates.
Invalid arguments will result in return value NaN
with a warning.
This is a thin wrapper on the t distribution.
The functions dt, pt, qt
can accept ncp from
limited range (delta <= 37.62). Some corrections
may have to be made here for large zeta
.
Steven E. Pav [email protected]
Sharpe, William F. "Mutual fund performance." Journal of business (1966): 119138. http://ideas.repec.org/a/ucp/jnlbus/v39y1965p119.html
tdistribution functions, dt, pt, qt, rt
Other sr: as.sr
, confint.sr
,
is.sr
, plambdap
,
power.sr_test
, predint
,
print.sr
, reannualize
,
se
, sr_equality_test
,
sr_test
, sr_unpaired_test
,
sr_vcov
, sr
,
summary.sr
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