De facto time‐varying indices‐based benchmarks for mutual fund returns

• Published date: 01 June 2023
• Author: Tingting Cheng,Cheng Yan,Yayi Yan
• Date: 01 June 2023
• DOI: http://doi.org/10.1111/jfir.12318

Received: 18 August 2021

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Accepted: 24 January 2023

DOI: 10.1111/jfir.12318

ORIGINAL ARTICLE

De facto time‐varying indices‐based benchmarks

for mutual fund returns

Tingting Cheng

1

|Cheng Yan

2

|Yayi Yan

3

1

School of Finance, Nankai University, Tianjin,

China

2

Essex Business School, Essex University,

Colchester, UK

3

School of Statistics and Management,

Shanghai University of Finance and

Economics, Shanghai, China

Correspondence

Cheng Yan, Essex Business School, Essex

University, Colchester, CO4 3SQ, UK.

Email: yancheng54@gmail.com

Abstract

We question time‐invariant indices as fund benchmarks

and propose a regime‐switching methodology to

identify time‐varying de facto benchmarks from a pool

of market‐based indices, with or without a risk‐free

asset. To ameliorate the benchmark mismatch issue, we

highlight the importance of using time‐varying indices‐

based benchmarks for fund performance evaluation.

Our de facto benchmark captures fund styles better

than other benchmark choices, substantially improves

the identification of significant fund alphas, and

provides better out‐of‐sample forecasts. We uncover

several new findings in terms of fund performance

evaluation using our de facto benchmarks.

JEL CLASSIFICATION

C15, G11, G12, G23

Any analysis of long‐term stock price performance invariably grapples with the choice of an appropriate

benchmark. The issue is central in studies of stock market efficiency, such as tests of the profitability of trading

strategies. Research on the impact of various managerial decisions, such as equity offerings, dividend initiations or

omissions, and share repurchase programs, also faces the problem of measuring stock returns in excess of some

normal level.

Chan et al. (2009)

J Financ Res. 2023;46:469–496. wileyonlinelibrary.com/journal/JFIR

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© 2023 The Southern Finance Association and the Southwestern Finance Association.

1|INTRODUCTION

The techniques for fund performance evaluation can be classified into two approaches: (1) returns‐based

performance evaluation and (2) portfolio holding‐based performance evaluation.

1

Each approach has its own

(dis)advantages. Returns‐based approaches rely on less information but can be sensitive to the choice of the

benchmark portfolio (Chan et al., 2009; Lehmann & Modest, 1987;Roll,1978).

2

Holding‐based approaches

allow a more precise construction of a benchmark to address Roll's (1978)criticism,

3

but holding data

(if available) are available on a much less frequent basis and hence have limited usefulness. In this article,

we not only question the appropriateness of commonly used fund benchmarks in the literature but also

develop and propose a new benchmark identification method that does not require holding data and yields a

much more accurate fund benchmark than returns‐based benchmarks. Our solution to the benchmark choice

question is a flexible regime‐switching methodology based on a pool of popular passive Standard & Poor's

(S&P) and Russell indices,

4

and we use our proposed time‐varying benchmark to investigate the potential

influences of the benchmark choice on fund performance evaluation.

We differ from the performance evaluation literature

5

as we are first, to our knowledge, to focus on de facto

time‐varying indices‐based benchmarks for fund returns. The literature (Sensoy, 2009) focuses on either de jure

(i.e., self‐designated) and/or time‐invariant indices‐based benchmarks.

We begin by proposing a regime‐switching approach to identify a time‐varying indices‐based benchmark for US

equity mutual funds via minimizing the variance of fund alphas from a pool of 17 popular passive S&P and Russell

indices (which are defined on size and value/growth dimensions), with or without a risk‐free asset. We find a much

higher portion of fund benchmark mismatch in our time‐varying setting than in the time‐invariant setting in Sensoy

(2009). To ameliorate the benchmark mismatch issue, we highlight the importance of fund cash holdings (Panageas

& Westerfield, 2009; Sensoy, 2009; Simutin, 2014). We evaluate our choice of indices‐based benchmark via: (1) the

statistical significance of Fama–French (1993) three‐factor loadings in explaining funds' monthly benchmark‐

adjusted returns

6

and (2) the explanatory power of benchmarks on fund excess returns (i.e., average R2). Intuitively,

we find that S&P 500–related indices (i.e., the sum of S&P 500, S&P 500 Value, S&P 500 Growth) are the most

popular indices‐based benchmarks for mutual funds. Our empirical results also show that the de facto time‐varying

indices‐based benchmark we identify captures the fund styles better than the official/self‐declared benchmarks

as well as the alternative benchmarks Sensoy (2009) identifies, and they partially overlap with the official/

self‐declared benchmarks.

1

See Ferson (2010) and Wermers (2011) for references and reviews of the earlier literature. See Wermers (in press) for a recent

excellent survey paper.

2

We follow Cremers et al. (2013, p. 6) and define a benchmark as “a passively managed portfolio with factor exposures similar to the

portfolio whose performance we are evaluating.”We acknowledge, however, that there are other definitions of fund benchmarks in

the literature.

3

For instance, Grinblatt and Titman (1993) circumvent Roll's (1978) criticism by proposing a holding‐based performance evaluation

approach. Daniel et al. (1997) propose benchmarks based on the characteristics of stocks held by the portfolios that are evaluated.

4

We believe that a fund benchmark is better constructed by passive investable indices (i.e., indices‐based benchmark) than a

combination of arbitrage pricing theory factors (i.e., factors‐based benchmark) as we find statistically significant alphas (i.e.,

unobserved risk compensation) and correlated residuals when we regress popular indices on factors. Berk and van Binsbergen

(2015) and Pástor et al. (2015) provide two additional reasons: (1) Fama–French factors do not take into account transaction cost

and (2) some of the factors are discovered later than the mutual fund databases. Hence, identifying tradable time‐varying indices‐

based benchmarks is much simpler and meaningful than trying to identify the potentially numerous time‐varying factors.

5

For instance, a large literature focuses on cross‐sectionally controlling for the multiple‐hypothesis‐testing problem (i.e., skill vs. luck;

Blake et al., 2013; Blake et al., 2014; Cai et al., 2018; Cheng & Yan, 2017; Fama & French, 2010; Kosowski et al., 2006; Kosowski

et al., 2007; Zhang and Yan 2018), false discovery (Andrikogiannopoulou & Papakonstantinou, 2019; Bajgrowicz & Scaillet, 2012;

Bajgrowicz et al., 2015; Barras et al., 2010; Ferson & Chen, 2020; Yan & Cheng, 2019), and time‐varying fund alphas and betas

(Avramov & Chordia, 2006; Bollen & Whaley, 2009; Cai et al., 2018; Cheng et al., 2021; Christopherson et al., 1998; Ferson &

Schadt, 1996; Jones & Mo, 2021; Kacperczyk et al., 2014; Mamaysky et al., 2007,2008; Pástor et al., 2015).

6

This is similar to the criterion used in Sensoy (2009), and Ferson (2010, p. 211) justifies it as “benchmark portfolio that has the same

regression betas on the risk factors as the fund is an appropriate benchmark.”

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