Testing for structural breaks in return-based style regression models
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Testing for structural breaks in return‑based style regression models Yunmi Kim1 · Douglas Stone2 · Tae‑Hwan Kim3
© Swiss Society for Financial Market Research 2020
Abstract It is important for investors to know not only the style of a fund manager in which they are interested, but also whether this style is constant or changing through time. The style of a fund manager can be estimated by the so-called style regression, and a great deal of research has been carried out to investigate the statistical properties of style regression methods. However, there has been no formal and statistically valid method to test for a change in manager style when the two typically imposed restrictions (sum-to-one and non-negativity) are jointly present in style analysis. In this study, we apply and extend the results of Andrews (Econometrica 61:821–856, 1993; Estimation when a parameter is on a boundary: theory and application, Yale University, 1997a; A simple counterexample to the bootstrap, Yale University, 1997b; Econometrica 67:1341–1383, 1999; Econometrica 68:399–405, 2000) to develop a valid testing procedure for the possibility wherein the location of any possible change does not need to be specified and the case of multiple shifts is accommodated. When our proposed test is applied to the Fidelity Magellan Fund, it is revealed that the fund’s style changed at least twice between 1988 and 2017. Keywords Structural shift · Boundary parameter · Maximum chow test · Style regression JEL Classification C12 · C18
* Tae‑Hwan Kim tae‑[email protected] 1
Department of Economics, University of Seoul, Seoul, Republic of Korea
2
GLP Risk Management, San Diego, USA
3
School of Economics, Yonsei University, 134 Shinchon‑dong, Seodaemun‑gu, Seoul 120‑749, Republic of Korea
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Y. Kim et al.
1 Introduction Analysis of asset manager style based on Sharpe’s (1988, 1992) concept of effective mix has become popular in the investment banking and pension fund management industries. The return-based style analysis (RBSA hereafter) often called “style analysis” is obtained from constrained regression of the returns of a mutual fund on appropriately chosen style indices. The imposed constraints consist of two restrictions: (1) sum of all factor exposures is equal to one (sumto-one restriction), and (2) exposures should be nonnegative (non-negativity restriction). It should be noted that the second non-negativity restriction makes sense only when short positions are not permitted, and in reality, short sales are generously used. Since permitting short sales is likely to render the fund exposed to higher risk and more volatile returns, risk-averse managers tend to impose short sales restrictions. The appeal of style analysis derives from its conceptual elegance and its ease of interpretation. Although RBSA has been popular in analyzing manager style, its one important limitation is the assumption that manager style does not change over time, which unrealistically implies that the manager always adopts the same i
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