Luck-Corrected Peer Performance Analysis with PeerPerformance
In PeerPerformance: Luck-Corrected Peer Performance Analysis in R

knitr::opts_chunk$set(collapse = TRUE, comment = "#>", fig.width = 7,
                      fig.height = 3.4)

Overview

PeerPerformance evaluates the performance of investment funds relative to their peers, with a correction for luck that is robust to false discoveries. For each fund $i$ it estimates three peer performance ratios that sum to one:

$\hat\pi^+_i$ -- the proportion of peers fund $i$ significantly outperforms,
$\hat\pi^0_i$ -- the proportion of peers with equal performance,
$\hat\pi^-_i$ -- the proportion of peers that outperform fund $i$.

The estimators implement the methodology of Ardia and Boudt (2018, Journal of Banking & Finance); the modified Sharpe ratio test follows Ardia and Boudt (2015, Finance Research Letters). A naive percentile rank ignores that many funds may be statistically indistinguishable; the false-discovery-rate (FDR) correction of Storey (2002) corrects for this.

library(PeerPerformance)
data("hfdata")          # 60 monthly returns for 100 anonymized hedge funds
dim(hfdata)

Alpha peer performance screening

alphaScreening() runs all pairwise tests and returns the three ratios for each fund. With factors = NULL it compares raw returns; supply a factors matrix to compare risk-adjusted alphas.

set.seed(1234)
rets <- hfdata[, 1:15]
sc <- alphaScreening(rets, control = list(nCore = 1))
round(rbind(pipos = sc$pipos, pizero = sc$pizero, pineg = sc$pineg), 3)[, 1:6]

The three ratios sum to one for every fund. A summary() method ranks the funds and reports the win/loss counts:

summary(sc, top = 3)

The ratios are point estimates; confint() attaches confidence intervals by a nonparametric peer (pairwise) bootstrap that resamples each fund's peers:

set.seed(1234)
round(confint(sc, parm = "pipos")[1:6, ], 3)

The plot() method reproduces the Ardia and Boudt (2018) screening plot (funds sorted by performance; stacked out-/equal-/under-performance bars with the naive percentile-rank diagonal):

plot(alphaScreening(hfdata[, 1:30], control = list(nCore = 1)))

Sharpe and modified Sharpe ratios

round(sharpe(rets[, 1:6]), 3)
round(msharpe(rets[, 1:6], level = 0.95), 3)

Equality of two funds' (modified) Sharpe ratios is tested with sharpeTesting() / msharpeTesting(). The asymptotic test is the default; a studentized bootstrap (recommended for short or autocorrelated series) is requested with control = list(type = 2).

res <- msharpeTesting(hfdata[, 1], hfdata[, 2], level = 0.95)
c(dmsharpe = res$dmsharpe, tstat = res$tstat, pval = res$pval)

sharpeScreening() and msharpeScreening() build the peer performance ratios from Sharpe (resp. modified Sharpe) comparisons instead of alphas.

Comparing a fund (or group) against a separate peer group

The Y argument (or the convenience wrapper targetPeerPerformance()) screens a chosen fund, or subset of funds, against a separate universe.

focal <- hfdata[, 1]
peers <- hfdata[, 11:40]
res_xy <- alphaScreening(focal, Y = peers, control = list(nCore = 1))
round(c(pizero = res_xy$pizero, pipos = res_xy$pipos, pineg = res_xy$pineg), 3)

Control parameters

All screening/testing functions share a control list. Common fields include nCore (parallel cores), lambda (the $\lambda$ threshold for $\hat\pi^0$, NULL = data-driven), gammaPos/gammaNeg (the one-sided thresholds, default 0.4/0.6), hac (HAC standard errors), and for the Sharpe/mSR routines type (asymptotic/bootstrap), nBoot, and bBoot. See ?alphaScreening.

Note that with the data-driven lambda (the default) the bias correction of $\hat\pi^0$ dominates the run time on large universes. Setting control = list(fastAdjust = TRUE) inverts it in vectorised form and is several times faster, at the price of differing from the published code path by a few $10^{-5}$; and setting a fixed lambda skips the selection entirely.

References

Ardia, D., Boudt, K. (2018). The peer performance ratios of hedge funds. Journal of Banking & Finance 87, 351--368.
Ardia, D., Boudt, K. (2015). Testing equality of modified Sharpe ratios. Finance Research Letters 13, 97--104.
Storey, J. (2002). A direct approach to false discovery rates. Journal of the Royal Statistical Society B 64(3), 479--498.