Double Sampling Kalman Filter with Applications in Investment Fund Reconstruction Problems

Abstract

The investment fund replication techniques and related financial product have been developed in recent years. It is understood that investing in the replicated fund can help investors gain similar returns without suffering drawbacks of the target fund. However, it is difficult to produce reliable replications using traditional quantitative techniques based on factor models with selective market assets that are correlated with the fund portfolio. The methodologies require specially tuned input parameters and/or time windows in order to output strategies with practical transactions, less long-term tracking errors and lower rebalancing costs. In this work, we propose to reconstruct the target fund with its actual assets and weights. It is done using an innovative non-parametric technique called Double Sampling Kalman Filter, derived from the ordinary Kalman Filter. The algorithm is designed to estimate optimal filter parameters from the data, as well as to identify the sudden changes (jumps) in the portfolio weight. The algorithm is discussed and compared with other types of Kalman Filters. It is later tested using generated portfolios with different scenarios. Finally, we demonstrate the reconstruction results of a real market portfolio.

Keywords: Kalman Filter, Filtering, Portfolio Replication, Portfolio Reconstruction, Jump Detection

JEL Classification: C13, C14