Function which performs the screening of a universe of returns, and computes the alpha outperformance ratio.
alphaScreening(
X,
factors = NULL,
control = list(),
screen_beta = NULL,
Y = NULL
)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.
alpha: Vector (of length \(N\)) of unconditional alpha.
dalpha: Matrix (of size \(N \times N\)) of alpha
differences.
tstat: Matrix (of size \(N \times N\)) of t-statistics.
pval: Matrix (of size \(N \times N\)) of p-values of test for alpha
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.
Matrix \((T \times N)\) of \(T\) returns for the \(N\)
funds. NA values are allowed.
Matrix \((T \times K)\) of \(T\) returns for the
\(K\) factors. NA values are allowed.
Control parameters (see *Details*).
Boolean to screen all factors' coefficients (beta).
Default: screen_beta = NULL, in which case the value is taken from
control$screen_beta (itself defaulting to FALSE, i.e. only the
alpha is screened). When supplied directly, the argument takes precedence
over the control list. If TRUE, each element of the returned list will
have a new first dimension representing each coefficient (the first one being
alpha).
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 (or a
one-column matrix). Columns of Y identical to the focal fund (e.g.
when X is a subset of Y) are automatically excluded. Default:
Y = NULL, i.e. within-group screening.
David Ardia and Kris Boudt.
The alpha measure (Treynor and Black 1973, Carhart 1997, Fung and Hsieh 2004) is one industry standard for measuring the absolute risk adjusted performance of hedge funds. We propose to complement the alpha measure with the fund's alpha outperformance ratio, defined as the percentage number of funds that have a significantly lower alpha. In a pairwise testing framework, a fund can have a significantly higher alpha because of luck. We correct for this by applying the false discovery rate approach by Storey (2002).
The methodology proceeds as follows:
(1) compute all pairwise tests of alpha differences. 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 of over, equal, and underperforming funds, in terms of alpha, in the database.
The argument control is a list that can supply any of the following
components:
'hac' Heteroscedastic-autocorrelation consistent
standard errors. Default: hac = FALSE.
'minObs' Minimum number of concordant observations to compute the ratios. Default:
minObs = 10.
'minObsPi' Minimum number of observations
for computing the p-values). Default: minObsPi = 1.
'nCore' Number of cores used to perform the screening. Default:
nCore = 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; e.g., qnorm(0.4) is about -0.25), and
the expected fraction 1 - gammaPos of false positives among the
equal-performing peers is then subtracted. Smaller values count more peers
before the correction. 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.
'screen_beta' Screen the factor exposures (betas) in addition to
the alpha; see the screen_beta argument. Default:
screen_beta = FALSE.
Ardia, D., Boudt, K. (2015). Testing equality of modified Sharpe ratios. Finance Research Letters 13, pp.97--104. tools:::Rd_expr_doi("10.1016/j.frl.2015.02.008")
Ardia, D., Boudt, K. (2018). The peer performance ratios of hedge funds. Journal of Banking and Finance 87, pp.351--368. tools:::Rd_expr_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.
Carhart, M. (1997). On persistence in mutual fund performance. Journal of Finance 52(1), pp.57--82.
Fama, E., French, K. (2010). Luck versus skill in the cross-section of mutual fund returns. Journal of Finance 65(5), pp.1915--1947.
Fung, W., Hsieh, D. (2004). Hedge fund benchmarks: A risk based approach. Financial Analysts Journal 60(5), pp.65--80.
Storey, J. (2002). A direct approach to false discovery rates. Journal of the Royal Statistical Society B 64(3), pp.479--498.
Treynor, J. L., Black, F. (1973). How to use security analysis to improve portfolio selection. Journal of Business 46(1), pp.66--86.
sharpeScreening and msharpeScreening.
## Load the data (randomized data of monthly hedge fund returns)
data("hfdata")
rets = hfdata[,1:4]
## Run alpha screening
ctr = list(nCore = 1)
alphaScreening(rets, control = ctr)
## Run alpha screening with HAC standard deviation
ctr = list(nCore = 1, hac = TRUE)
alphaScreening(rets, control = ctr)
## Cross-group screening: a single focal fund against a peer group
alphaScreening(hfdata[, 1], Y = hfdata[, 11:20], control = list(nCore = 1))
## Cross-group screening: peer group X against peer group Y
alphaScreening(hfdata[, 1:5], Y = hfdata[, 11:20], control = list(nCore = 1))
Run the code above in your browser using DataLab