We present a methodology for obtaining a valid correlation matrix from an invalid one for financial applications. In contrast to other approaches, the methodology described only requires the use of elementary matrix algebra and a simple randomization procedure.

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Hedge fund replication has become a cottage industry in investing. Among the most popular hedge fund replication frameworks are factor models based on ordinary least squares (OLS) regression, a development that is no doubt due to its simplicity and familiarity among investment practitioners. Despite their widespread use, the OLS regression-based factor models that form the basis for many hedge fund replication programs are often overfitted to a single sample, severely undercutting their predictive effectiveness. As a remedy to the latter shortcoming, in this article the authors apply the regularization method known as “ridge regression” to the replication of hedge fund strategies. Ridge regression works by formally imbuing a regression with additional bias in exchange for a reduction in the variance between training and test samples. Using a simple yet robust methodology, the authors show how to dynamically calibrate the predictively optimal level of bias without significantly reducing the backward-looking explanatory power of a given model. In doing so, the authors demonstrate that ridge regression can help produce generalizable models that are useful in both the ex post risk analysis and ex ante replication of hedge fund strategies.

Unlike mean-variance optimization, a risk parity strategy allocates across asset classes such that each asset class contributes equally to portfolio risk, regardless of its expected returns.n In practice, there are variants of the risk parity strategy due to choices made by the portfolio manager, such as selection of the asset classes, risk measure, targeted volatility, degree of leverage, asset selection using active or passive approach, and tactical risk allocation strategy.n The performance of the risk parity strategy has varied, with critics of the strategy identifying theoretical and practical implementation issues.

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