Replication Methods for Financial Indexes

24 Pages Posted: 18 Jul 2017

See all articles by Bruno Remillard

Bruno Remillard

Department of Decision Sciences, HEC Montreal

Bouchra R. Nasri

Department of Mathematics and Statistics, McGill University

Malek Ben-abdellatif

HEC Montreal - Department of Decision Sciences

Date Written: July 11, 2017

Abstract

In this paper, we first present a review of statistical tools that can be used in asset management either to track financial indexes or to create synthetic ones. More precisely, we look at two important replication methods: the strong replication, where a portfolio of very liquid assets is created and the goal is to track an actual index with the portfolio, and weak replication, where a portfolio of very liquid assets is created and used to either replicate the statistical properties of an existing index, or to replicate the statistical properties of a custom asset. In addition, for weak replication, the target is not an index but a payoff, and the replication amounts to hedge the portfolio so it is as close as possible to the payoff at the end of each month. For strong replication, the main tools are predictive tools, so filtering techniques and regression play an important role. For weak replication, which is the main topic of this paper, in order to determine the target payoff, the investor has to find or choose the distribution function of the target index or custom index, as well as its dependence with other assets, and use a hedging technique. Therefore, the main tools for weak replication are modeling (estimation and goodness-of-fit) and optimal hedging. For example, an investor could wish to obtain Gaussian returns that are independent of some ETFs replicating the Nasdaq and S&P 500 indexes. In order to determine the dependence of the target and a given number of indexes, we introduce a new class of easily constructed models of conditional distributions called B-vines. We also propose to use a flexible model to fit the distribution of the assets composing the portfolio and then hedge the portfolio in an optimal way. Examples are given to illustrate all the important steps required for the implementation of this new asset management methodology.

Keywords: ETF, Hedge Funds, Replication, Smart Beta, Copulas, B-Vines, HMM, Hedging

JEL Classification: G11, C14, C15, C52, C58

Suggested Citation

Remillard, Bruno and Nasri, Bouchra R. and Ben-abdellatif, Malek, Replication Methods for Financial Indexes (July 11, 2017). Available at SSRN: https://ssrn.com/abstract=3000340 or http://dx.doi.org/10.2139/ssrn.3000340

Bruno Remillard (Contact Author)

Department of Decision Sciences, HEC Montreal ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada
514-340-6794 (Phone)

Bouchra R. Nasri

Department of Mathematics and Statistics, McGill University ( email )

1001 Sherbrooke St. W
Montreal, Quebec H3A 1G5
Canada

Malek Ben-abdellatif

HEC Montreal - Department of Decision Sciences ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
294
Abstract Views
1,037
rank
130,685
PlumX Metrics