ایجاد توازن نمونه کارها با افق سرمایه گذاری و هزینه های معاملات

In this paper we consider the problem of rebalancing an existing financial portfolio, where transaction costs have to be paid if we change the amount held of any asset. These transaction costs can be fixed (so paid irrespective of the amount traded provided a trade occurs) and/or variable (related to the amount traded). We indicate the importance of the investment horizon when rebalancing such a portfolio and illustrate the nature of the efficient frontier that results when we have transaction costs. We model the problem as a mixed-integer quadratic programme with an explicit constraint on the amount that can be paid in transaction cost. Our model incorporates the interplay between optimal portfolio allocation, transaction costs and investment horizon. We indicate how to extend our model to include cardinality constraints and present a number of enhancements to the model to improve computational performance. Results are presented for the solution of publicly available test problems involving up to 1317 assets.

In forming a portfolio of financial assets (such as stocks, equities) the basic approach adopted derives from the well-known work of Markowitz [41] who considered the problem as one of trading off reward (as measured by mean portfolio return) against the risk involved (as measured by variance in portfolio return). The approach he proposed is now well-known and often seen in graphical form (an efficient frontier, with return being plotted against risk). In this paper we will assume that the reader is familiar with the basic approach adopted in Markowitz mean–variance portfolio optimisation. In this paper we consider the problem of rebalancing an existing financial portfolio, where transaction costs have to be paid if we change the amount held of any asset. These transaction costs can be fixed (so paid irrespective of the amount traded provided a trade occurs) and/or variable (related to the amount traded). Introducing transaction costs into a Markowitz framework, effectively incurring a financial penalty for trading, means that the investment horizon over which we will hold the rebalanced portfolio unchanged is important. This contrasts with the basic Markowitz model where the investment horizon is effectively irrelevant, since in that model there are no transaction costs and so no penalty associated with trading.

In this paper we have considered the problem of rebalancing an existing financial portfolio, where transaction costs (fixed and/or variable in nature) have to be paid if we change the amount held of any asset. We discussed the importance of the investment horizon when rebalancing such a portfolio. We modelled the portfolio rebalancing problem as a mixed-integer quadratic programme with an explicit constraint on the amount that can be paid in transaction cost. Our model incorporated the interplay between optimal portfolio allocation, transaction costs and investment horizon. We extended our model to include cardinality constraints and presented a number of enhancements to the model to improve computational performance. Computational results were presented for the solution of publicly available test problems involving up to 1317 assets. We illustrated the discontinuous nature of the portfolio and efficient frontiers that result and their variation with the length of the investment horizon.