Function which performs the screening of a universe of returns, and computes the Sharpe outperformance ratio.
Matrix (TxN) of T returns for the N
Control parameters (see *Details*).
The Sharpe ratio (Sharpe 1992) is one industry standard for measuring the absolute risk adjusted performance of hedge funds. We propose to complement the Sharpe ratio with the fund's outperformance ratio, defined as the percentage number of funds that have a significantly lower Sharpe ratio. In a pairwise testing framework, a fund can have a significantly higher Sharpe ratio because of luck. We correct for this by applying the false discovery rate approach by Storey (2002).
For the testing, only the intersection of non-
NA observations for the
two funds are used.
The methodology proceeds as follows:
(1) compute all
pairwise tests of Sharpe differences using the bootstrap approach of Ledoit
and Wolf (2002). This means that for a universe of N funds, we perform
N*(N-1)/2 tests. The algorithm has been parallelized and the
computational burden can be splitted across several cores. The number of cores
can be defined in
control, see below.
(2) for each fund, the false discovery rate approach by Storey (2002) is used to determine the proportions over, equal, and underperfoming funds, in terms of Sharpe ratio, in the database.
control is a list that can supply any of the following
'type' Asymptotic approach (
type = 1) or
studentized circular bootstrap approach (
type = 2). Default:
type = 1.
'ttype' Test based on ratio (
type = 1)
or product (
type = 2). Default:
type = 2.
'hac' Heteroscedastic-autocorrelation consistent standard
hac = FALSE.
'nBoot' Number of boostrap replications for computing the p-value. Default:
'bBoot' Block length in the circular bootstrap. Default:
bBoot = 1, i.e. iid bootstrap.
bBoot = 0 uses optimal
'pBoot' Symmetric p-value (
pBoot = 1) or
asymmetric p-value (
pBoot = 2). Default:
pBoot = 1.
'nCore' Number of cores to be used. Default:
nCore = 1.
'minObs' Minimum number of concordant observations to compute
the ratios. Default:
minObs = 10.
number of observations to compute pi0. Default:
minObsPi = 1.
'lambda' Threshold value to compute pi0. Default:
= NULL, i.e. data driven choice.
A list with the following components:
n: Vector (of length N) of number of non-
npeer: Vector (of length N) of number of available peers.
sharpe: Vector (of length N) of unconditional Sharpe ratios.
dsharpe: Matrix (of size NxN) of Sharpe ratios
tstat: Matrix (of size NxN) of t-statistics.
pval: Matrix (of size NxN) of pvalues of test for Sharpe
lambda: vector (of length N) of lambda values.
pizero: vector (of length N) of probability of equal
pipos: vector (of length N) of probability of outperformance
pineg: Vector (of length N) of probability of underperformance
Further details on the methdology with an application to the hedge fund industry is given in in Ardia and Boudt (2016).
Some internal functions where adapted from Michael Wolf MATLAB code.
Application of the false discovery rate approach applied to the mutual fund industry has been presented in Barraz, Scaillet and Wermers (2010).
David Ardia and Kris Boudt.
Ardia, D., Boudt, K. (2015). Testing equality of modified Sharpe ratios. Finance Research Letters 13, pp.97-104. doi: 10.1016/j.frl.2015.02.008
Ardia, D., Boudt, K. (2016). The peer performance ratios of hedge funds. Working paper. doi: 10.2139/ssrn.2000901
Barras, L., Scaillet, O., Wermers, R. (2010). False discoveries in mutual fund performance: Measuring luck in estimated alphas. Journal of Finance 65(1), pp.179-216. doi: 10.1111/j.1540-6261.2009.01527.x
Sharpe, W.F. (1994). The Sharpe ratio. Journal of Portfolio Management 21(1), pp.49-58. doi: 10.3905/jpm.1994.409501
Ledoit, O., Wolf, M. (2008). Robust performance hypothesis testing with the Sharpe ratio. Journal of Empirical Finance 15(5), pp.850-859. doi: 10.1016/j.jempfin.2008.03.002
Storey, J. (2002). A direct approach to false discovery rates. Journal of the Royal Statistical Society B 64(3), pp.479-498. doi: 10.1111/1467-9868.00346
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## Load the data (randomized data of monthly hedge fund returns) data("hfdata") rets = hfdata[,1:10] ## Sharpe screening sharpeScreening(rets, control = list(nCore = 1)) ## Sharpe screening with bootstrap and HAC standard deviation sharpeScreening(rets, control = list(nCore = 1, type = 2, hac = TRUE))
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