| Summary: | This paper proposes a self-calibrated sparse learning approach for estimating a sparse target vector, which is a product of a precision matrix and a vector, and investigates its application to finance to provide an innovative construction of a relative-volatility-managed portfolio. The proposed iterative algorithm, called DECODE, jointly estimates a performance measure of the market and the effective parameter vector in the optimal portfolio solution, where the relative-volatility timing is introduced into the risk exposure of an efficient portfolio via the control of its sparsity. The portfolio’s risk exposure level, which is linked to its sparsity in the proposed framework, is automatically tuned with the latest market condition without using cross validation. The algorithm is efficient as it costs only a few computations of quadratic programming. We prove that the iterative algorithm converges and show the oracle inequalities of the DECODE, which provide sufficient conditions for a consistent estimate of an optimal portfolio. The algorithm can also handle the curse of dimensionality in that the number of training samples is less than the number of assets. Our empirical studies of over-12-year backtest illustrate the relative-volatility timing feature of the DECODE and the superior out-of-sample performance of the DECODE portfolio, which beats the equally weighted portfolio and improves over the shrinkage portfolio.
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