sharpeScreening: Screening using the Sharpe outperformance ratio
In PeerPerformance: Luck-Corrected Peer Performance Analysis in R

sharpeScreening

R Documentation

Screening using the Sharpe outperformance ratio

Description

Function which performs the screening of a universe of returns, and computes the Sharpe outperformance ratio.

Usage

sharpeScreening(X, control = list(), Y = NULL)

Arguments

`X`	Matrix `(T \times N)` of `T` returns for the `N` funds. `NA` values are allowed.
`control`	Control parameters (see Details).
`Y`	Optional matrix `(T \times M)` of returns for a second (peer) group of `M` funds. When supplied, the ratios are computed for each fund in `X` against the funds in `Y` (cross-group screening) instead of against the other funds in `X`; a single focal fund versus a peer group corresponds to `X` being a vector. Columns of `Y` identical to the focal fund are automatically excluded. Default: `Y = NULL`, i.e. within-group screening.

Details

The Sharpe ratio (Sharpe 1994) 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 split 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 underperforming funds, in terms of Sharpe ratio, in the database.

The argument control is a list that can supply any of the following components:

'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 errors. Default: hac = FALSE.
'nBoot' Number of bootstrap replications for computing the p-value. Default: nBoot = 499.
'bBoot' Block length in the circular bootstrap. Default: bBoot = 1, i.e. iid bootstrap. (The data-driven choice bBoot = 0 is only available in sharpeTesting, not in screening.)
'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: lambda = NULL, i.e. data driven choice.
'gammaPos' One-sided quantile level (of the standard Normal distribution) used as the critical value for counting outperformed peers: a peer counts as outperformed when the pairwise t-statistic exceeds qnorm(gammaPos) (a negative threshold for gammaPos < 0.5), and the expected fraction 1 - gammaPos of false positives among the equal-performing peers is then subtracted. Default: gammaPos = 0.4 (the value recommended in Ardia and Boudt, 2018).
'gammaNeg' Mirror image of gammaPos for the peers that outperform the focal fund: the count uses tstat <= qnorm(gammaNeg) and subtracts the expected fraction gammaNeg of false positives. Default: gammaNeg = 0.6.
'fastAdjust' Use a fast vectorised inversion in the truncated-normal bias correction of \pi^0 instead of one uniroot call per value. This is the dominant cost when lambda is data driven and gives a large speed-up on big universes. The bisection locates the root to about 1e-12; since uniroot stops at its own tolerance (about 1.2e-4), the two paths typically differ by a few 1e-5, the fast path being the more accurate. Default: fastAdjust = FALSE, i.e. the original code path, kept as default so that published results reproduce exactly.

Value

A list with the following components:

n: Vector (of length N) of number of non-NA observations.

npeer: Vector (of length N) of number of available peers.

sharpe: Vector (of length N) of unconditional Sharpe ratios.

dsharpe: Matrix (of size N \times N) of Sharpe ratios differences.

tstat: Matrix (of size N \times N) of t-statistics.

pval: Matrix (of size N \times N) of pvalues of test for Sharpe ratios differences.

lambda: vector (of length N) of lambda values.

pizero: vector (of length N) of probability of equal performance.

pipos: vector (of length N) of probability of outperformance performance.

pineg: Vector (of length N) of probability of underperformance performance.

Note

Further details on the methodology with an application to the hedge fund industry is given in Ardia and Boudt (2018).

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 Barras, Scaillet and Wermers (2010).

Author(s)

David Ardia and Kris Boudt.

References

Ardia, D., Boudt, K. (2015). Testing equality of modified Sharpe ratios. Finance Research Letters 13, 97–104.

Ardia, D., Boudt, K. (2018). The peer performance ratios of hedge funds. Journal of Banking and Finance 87, 351–368.

Barras, L., Scaillet, O., Wermers, R. (2010). False discoveries in mutual fund performance: Measuring luck in estimated alphas. Journal of Finance 65(1), 179–216.

Sharpe, W.F. (1994). The Sharpe ratio. Journal of Portfolio Management 21(1), 49–58.

Ledoit, O., Wolf, M. (2008). Robust performance hypothesis testing with the Sharpe ratio. Journal of Empirical Finance 15(5), 850–859.

Storey, J. (2002). A direct approach to false discovery rates. Journal of the Royal Statistical Society B 64(3), 479–498.

Examples

## Load the data (randomized data of monthly hedge fund returns)
data("hfdata")
rets = hfdata[,1:4]

## Sharpe screening
sharpeScreening(rets, control = list(nCore = 1))

## Sharpe screening with HAC standard errors (asymptotic test)
sharpeScreening(rets, control = list(nCore = 1, hac = TRUE))

## Sharpe screening with the studentized circular bootstrap
## (the 'hac' flag is ignored when type = 2)
sharpeScreening(rets, control = list(nCore = 1, type = 2))

PeerPerformance documentation built on Aug. 3, 2026, 1:08 a.m.