Abstract:

When measuring the risk of the portfolio, the investment manager will consider not only the risk exposed by the portfolio itself, but also the risked exposed compared to a benchmark, i.e. active risk. In addition, the manager will set some constraints according to the rules of the market. Taking account of the risk and the transaction constraints in real market, we consider the absolute risk (CVaR) and the relative risk (Tracking Error) as the risk constraints while we consider the transaction costs, short-sale constraint and the multiple weight constraints as the transaction constraints. Then, we construct a new model of portfolio based on the constraints above and use the nonlinear algorithm and dynamic programming to solve it. Finally, an empirical study is presented based on the benchmark of SSE 50 in empirical study. The result proves the priority of the multi-stage portfolio compared to the single-stage one in terms of the return of the portfolio. Although adding the multiple weight constraints reduces the return of the portfolio in in-sample, we prove that the portfolio can be more efficient by using the multiple weight constraints incorporated by the correct forecast of the investment manager. The portfolio proposed not only conforms to the rules in reality but also shows advantages on the return and risk.

Key words: tracking error, CVaR, multi-stage, dynamic programming, nonlinear algorithm