Function which performs the screening of a universe of returns, and computes the modified Sharpe outperformance ratio.
Matrix (TxN) of T returns for the N
Modified Value-at-Risk level. Default:
A logical value indicating whether
Control parameters (see *Details*).
The modified Sharpe ratio (Favre and Galeano 2002, Gregoriou and Gueyie 2003) is one industry standard for measuring the absolute risk adjusted performance of hedge funds. We propose to complement the modified Sharpe ratio with the fund's outperformance ratio, defined as the percentage number of funds that have a significantly lower modified Sharpe ratio. In a pairwise testing framework, a fund can have a significantly higher modified 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.
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.
'minObsPi' Minimum 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.
msharpe: Vector (of length N) of unconditional modified Sharpe
dmsharpe: Matrix (of size NxN) of modified Sharpe
tstat: Matrix (of size NxN) of t-statistics.
pval: Matrix (of size NxN) of p-values of test for
modified Sharpe ratios differences.
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 (2018).
Some internal functions where adapted from Wolf's R 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. (2018). The Peer Ratios Performance of Hedge Funds. Journal of Banking and Finance 87, pp.351-.368. doi: 10.1016/j.jbankfin.2017.10.014
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
Favre, L., Galeano, J.A. (2002). Mean-modified Value-at-Risk Optimization with Hedge Funds. Journal of Alternative Investments 5(2), pp.21–25. doi: 10.3905/jai.2002.319052
Gregoriou, G. N., Gueyie, J.-P. (2003). Risk-adjusted performance of funds of hedge funds using a modified Sharpe ratio. Journal of Wealth Management 6(3), pp.77–83.
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] ## Modified Sharpe screening msharpeScreening(rets, control = list(nCore = 1)) ## Modified Sharpe screening with bootstrap and HAC standard deviation msharpeScreening(rets, control = list(nCore = 1, type = 2, hac = TRUE))
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