NDLI: Optimal mean-variance portfolio construction in cointegrated vector autoregressive systems

Content Provider	IEEE Xplore Digital Library
Author	Rudoy, M.B. Rohrs, C.E.
Copyright Year	2008
Description	Author affiliation: Digital Signal Process. Group, Massachusetts Inst. of Technol., Cambridge, MA (Rudoy, M.B.; Rohrs, C.E.)
Abstract	We study the problem of optimal portfolio construction when the log-prices follow a discrete-time cointegrated vector autoregressive model. We follow the classical Markowitz mean-variance optimization approach, and derive expressions for the optimal portfolio weight vector over a single decision interval, both for a finite-time horizon and in the limit of an infinite horizon. It is often stated in the literature that given assets whose price dynamics exhibit cointegration, the portfolio weights should be chosen from the space of cointegrating relations, resulting in what is commonly referred to as the beta portfolio. However, we show here that the optimal action in the mean-variance sense for a finite trading interval is to buy the portfolio with a component both in the beta direction and a component in the direction of expected change. Furthermore, we prove that the beta portfolio is optimal only in the limit of an infinite trading horizon. Additionally, we derive the conditions under which the optimal portfolio is proportional to the disequilibrium readjustment forces of the cointegration model. Our results rely on a careful eigenanalysis of the underlying state space model, in which we derive a closed form solution for the optimal Markowitz portfolio, which is well-behaved despite the nonstationarity of the underlying price dynamics. We demonstrate our results with evaluations using both simulated and historical data.
Starting Page	2510
Ending Page	2515
File Size	230433
Page Count	6
File Format	PDF
ISBN	9781424420780
ISSN	07431619
DOI	10.1109/ACC.2008.4586868
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-06-11
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Portfolios Closed-form solution Infinite horizon Asset management Reactive power Signal processing Vectors Optimal control Digital signal processing State-space methods
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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