Random matrix theory filters in portfolio optimisation: a stability and risk assessment
Daly, Justin and Crane, Martin and Ruskin, Heather J. (2008) Random matrix theory filters in portfolio optimisation: a stability and risk assessment. Physica A: Statistical Mechanics and its Applications, 387 (16-17). pp. 4248-4260. ISSN 0378-4371
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Random matrix theory (RMT) filters, applied to covariance matrices of financial
returns, have recently been shown to offer improvements to the optimisation of stock
portfolios. This paper studies the effect of three RMT filters on realised portfolio
risk, and on the stability of the filtered covariance matrix, using bootstrap analysis
and out-of-sample testing.
We propose an extension to an existing RMT filter, (based on Krzanowski stabil-
ity), which is observed to reduce risk and increase stability, compared to other RMT
filters tested. We also study a scheme for filtering the covariance matrix directly, as
opposed to the standard method of filtering correlation, where the latter is found
to lower realised risk on average, by up to 6.7%.
We consider both equally and exponentially weighted covariance matrices in our
analysis, and observe that the overall best method out-of-sample was that of ex-
ponentially weighted covariance, with our Krzanowski stability-based filter applied
to the correlation matrix. We also find that the optimal out-of-sample decay fac-
tors, for both filtered and unfiltered forecasts, were higher than those suggested by
Riskmetrics , with those for the latter approaching a value of alpha = 1.
In conclusion, RMT filtering reduced realised risk on average, and in the majority
of cases, when tested out-of-sample, but increased realised risk on a marked number
of individual days, in some cases more than doubling it.
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