Asset allocation under predictability and parameter uncertainty using LASSO
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Asset allocation under predictability and parameter uncertainty using LASSO Andrea Rigamonti1
· Alex Weissensteiner1
Received: 18 October 2019 / Accepted: 10 April 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We consider a short-term investor who exploits return predictability in stocks and bonds to maximize mean-variance utility. Since the true parameters are unknown, we resort to portfolio optimization in form of linear regression with LASSO in order to mitigate problems related to estimation errors. As standard cross-validation relies on the assumption of i.i.d. returns, we propose a new type of cross-validation that selects λ from simulated returns sampled from a multivariate normal distribution. We find an inverse U-shaped relationship between the selected λ and the expected utility, and we show that the optimal value of λ declines as the number of observations used to estimate the parameters increases. We finally show how our strategy outperforms some commonly employed benchmarks. Keywords LASSO · Cross-validation · Return predictability · Parameter uncertainty · Portfolio selection
1 Introduction Predictability of stock and bond returns has spurred an increasing interest in the empirical finance and asset allocation literature. Convincing evidence of predictability in bond excess returns is provided, among others, by Cochrane and Piazzesi (2005). Campbell et al. (2003) and Campbell and Viceira (2005) successfully exploit predictability in stock and bond returns for the optimization problem of a mean-variance investor that updates the portfolio weights every month, using a VAR(1) model with interest rates, dividend-price ratios and yield spreads as predictors.
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Andrea Rigamonti [email protected] Alex Weissensteiner [email protected]
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Free University of Bozen-Bolzano, Universitätsplatz 1, 39100 Bolzano, Italy
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A. Rigamonti, A. Weissensteiner
Even when the model used by the investor to produce a forecast of the inputs for the optimization problem is in principle correct, he is still faced with parameter uncertainty. This problem is well known from the standard setting in which sample estimates of the mean μ and covariance Σ are used instead of the true values (plug-in approach), which typically leads to unstable portfolios whose weights can be very distant from the true optimal portfolio, and perform very poorly out-of-sample (see, e.g., Broadie 1993; Chopra and Ziemba 1993). In fact, a naïve 1/N rule that puts equal weights on all assets generally outperforms the mean-variance optimization applied via the plug-in approach. The issue is not solved when forecasting the value of μ and Σ with a VAR instead of using a sample estimate. On the contrary, this can lead to even more extreme portfolio positions. Barberis (2000) sets up a VAR(1) model for the asset allocation problem of a long-term investor taking into account the impact of parameter uncertainty, and his setting is later borrowed by Dangl and Weissensteiner (2020). Both find that
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