Fused Lasso approach in portfolio selection

Split Bregman iteration for multi-period mean variance portfolio optimization

“…In this section we extend the fused lasso model presented in [4] with the aim of guaranteeing the investor in the case of early exit. The model refers to either a medium or long-term investment, in which the investor could exit before the term; thus, at this purpose, the expected minimum wealth is fixed at each rebalancing date.…”

“…The fusion term, that is the l 1 norm applied to the time variation Δ w , has a smoothing effect on solution, preserving patterns of non-zero values across time. Its financial interpretation is a penalty on the portfolio turnover; it has then the effect of reducing transaction cost [4] . This term is weighted by τ 2 > 0.…”

“…In order to evaluate them we define the matrix with: for and . Note that, as in [4] , in order to discard variations not significant from the financial point of view, we neglet the differences below . The number of estimated transactions of the optimal strategy is therefore: We then relate T opt to the maximum value that it can assume, that is, to the number of transactions of the portfolio with full turnover, which is the size N of the portfolio: M4 the excess return (ER) calculated in comparison to the benchmark: M5 the Sharpe Ratio (SR) [31] is the ratio between the average of the expected return of the portfolio and its standard deviation.…”

“…The l 1 penalty in (1) promotes sparse solutions, and the term ‖ L w ‖ 1 is included to produce smooth solutions. Problems described by fused lasso models arise, e.g., in image processing [2] , classification [3] , finance [4] . The nonsmoothness of the l 1 -type regularization terms precludes the use of standard descent methods for smooth objective functions.…”

“…In [4] a model based on the fused lasso approach is presented in a multi-period setting. This seems to be very promising, since the fusion term is a penalty on portfolio turnover, which produces strategies with low transaction cost by preserving the pattern of active position over time.…”