Abstract
Mean-Variance Optimization (MVO) is well-known to be extremely sensitive to slight differences in the expected returns and covariances: if these measures change day to day, MVO can specify very different portfolios. Making wholesale changes in portfolio composition can cause the incremental gains to be negated by trading costs. We present a method for regularizing portfolio turnover by using the ℓ1 penalty, with the amount of penalization informed by recent historical data. We find that this method dramatically reduces turnover, while preserving the efficiency of mean-variance optimization in terms of risk-adjusted return. Factoring in reasonable estimates of transaction costs, the turnover-regularized MVO portfolio substantially outperforms a leverage-constrained MVO approach, in terms of risk-adjusted return.
Highlights
For as long as investors have sought capital appreciation by purchasing equities, they have developed strategies to capture returns, thereby compensating them for accepting different sources of risk
For most values of the penalty parameter, the mean Sharpe ratio of the reg-turnover Mean-Variance Optimization (MVO) portfolio exceeds that of the benchmark MVO portfolio, after transaction costs, at confidence levels ranging from 90% to 99.9%
The results show that even before transaction costs, the risk-adjusted returns of the reg-turnover MVO portfolio are higher than those of the benchmark MVO portfolio
Summary
For as long as investors have sought capital appreciation by purchasing equities, they have developed strategies to capture returns, thereby compensating them for accepting different sources of risk. Investors seek an optimal method for determining how to allocate their capital among various investment choices In his seminal paper, Markowitz (1972) describes the process of utilizing information about the expected returns, variances, and covariances of financial assets to construct a portfolio, making optimal trade-offs between risk and return. The resulting portfolio may have quite different realized returns and volatility than expected This issue calls for the application of methods to make the solution robust to small changes in the inputs. We provide a new methodology based on an 1 regularization of portfolio weights towards the weights obtained on a previous day We show that this method substantially reduces turnover and obtains high out-of-sample Sharpe ratios, even in the presence of transaction costs.
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