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 [1], 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.