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Decisions in Economics and Finance

Erschienen in:

01.10.2014

Optimal portfolio choice and consistent performance

verfasst von: Xianzhe Chen, Weidong Tian

Erschienen in: Decisions in Economics and Finance | Ausgabe 2/2014

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Abstract

Consistent financial performance is the key element to success in asset management. We use a dynamic wealth constraint to represent the consistent performance requirement, which takes into account the entire historical records as a benchmark so that the wealth always stays at or above the benchmark. The optimal policy under this wealth constraint is characterized, and several implications are presented in this paper. This consistent performance constraint could be an appealing tool to be implemented in a volatile market and have rich practical implications.

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As John C. Bogle addresses it, “there is an important role that past performance can play in helping you to make your fund selections. While you should disregard a single aggregate number showing a fund’s past long-term return, you can learn a great deal by studying the nature of its past return. Above all, look for consistency”. (Excerpted from Common Sense on Mutual Funds by John C. Bogle, p. 96).

The Lipper Fund Award Program is part of the Thomson Reuters Award, the world’s leader in identifying outstanding performance in the investment community. See http://excellence.thomsontruters.com for details.

For instance, Black and Perold (1992), Karoui and Jeanblanc-Picque (1998), and El Karoui et al. (2005) examine the optimal portfolio choice problem under a deterministic wealth benchmark. For the portfolio choice problem with constraints, both the maximum drawdown and the leverage constraints (Grossman and Zhou 1993; Grossman and Vila 1992) lead to portfolio insurance strategies.

Dynamic deterministic benchmark for the portfolio wealth has been studied in Karoui and Jeanblanc-Picque (1998) and El Karoui et al. (2005). It has been shown that, under the dynamic deterministic constraint \(W_t \ge L_t\), the optimal strategy is equivalent to a Merton’s optimal portfolio plus an American-type put option on Merton’s optimal portfolio. See also Grossman and Zhou (1993) when \(L_t\) is a constant.

As demonstrated in the proof of Proposition 1 in “Appendix”, \(b \le r +a\) is necessary to ensure the existence of the optimal policy.

It is far from trivial to derive the upward trend of the endogenous benchmark curve. By its definition in (2), \(M(t_2) \ge M(t_1) \mathrm{e}^{-a(t_2 - t_1)}\). Therefore, the return rate \(\frac{1}{s}\log \left( \frac{M(t+s)}{M(t)}\right) \ge -a, \forall t,s >0\).

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Titel: Optimal portfolio choice and consistent performance
verfasst von: Xianzhe Chen
Weidong Tian
Publikationsdatum: 01.10.2014
Verlag: Springer Milan
Erschienen in: Decisions in Economics and Finance / Ausgabe 2/2014
Print ISSN: 1593-8883
Elektronische ISSN: 1129-6569
DOI: https://doi.org/10.1007/s10203-013-0154-x

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