بهینه سازی سبد سرمایه گذاری مستقیم داده محور با احتمال کمبود تضمین

This paper proposes a novel methodology for optimal allocation of a portfolio of risky financial assets. Most existing methods that aim at compromising between portfolio performance (e.g., expected return) and its risk (e.g., volatility or shortfall probability) need some statistical model of the asset returns. This means that: (i) one needs to make rather strong assumptions on the market for eliciting a return distribution, and (ii) the parameters of this distribution need be somehow estimated, which is quite a critical aspect, since optimal portfolios will then depend on the way parameters are estimated. Here we propose instead a direct, data-driven, route to portfolio optimization that avoids both of the mentioned issues: the optimal portfolios are computed directly from historical data, by solving a sequence of convex optimization problems (typically, linear programs). Much more importantly, the resulting portfolios are theoretically backed by a guarantee that their expected shortfall is no larger than an a-priori assigned level. This result is here obtained assuming efficiency of the market, under no hypotheses on the shape of the joint distribution of the asset returns, which can remain unknown and need not be estimated.

In this paper, we presented a novel data-driven approach for computing optimal portfolio compositions directly from historical data. The proposed approach is based on i.i.d. and stationarity hypotheses on the returns process, but avoids assumptions on the cross-sectional distribution model of the returns, and does not need estimation of distribution parameters. The key feature of the method is that the optimal portfolios come with a rigorously established probability tag, guaranteeing that their out-of-sample expected short-fall probability is no larger than an a-priori assigned level. Computationally, the method is effective, in that it typically requires the solution of a sequence of linear programming problems. Numerical tests with both synthetic and real financial data seem to support the practical effectiveness of the proposed methodology.