Alphas in disguise: A new approach to uncovering them

• Date: 01 July 2017
• Author: Natasa Todorovic,Venkata Chinthalapati,Cesario Mateus
• DOI: http://doi.org/10.1002/ijfe.1581
• Published date: 01 July 2017

RESEARCH ARTICLE

Alphas in disguise: A new approach to uncovering them

Venkata Chinthalapati

1

| Cesario Mateus

1

| Natasa Todorovic

2

1

University of Greenwich, London, UK

2

The Centre for Asset Management

Research, Cass Business School, City,

University of London, UK

Correspondence

Natasa Todorovic, The Centre for Asset

Management Research, Cass Business

School, City, University of London, UK.

Email: n.todorovic@city.ac.uk

JEL Classification: G10; G11; C6

Abstract

Four‐factor Carhart alphas of passive indices should be zero, but recent empirical

evidence shows otherwise. We propose an optimization algorithm that makes small

(fixed) adjustments to the time series of the market, size, value, and momentum fac-

tors, which ensures a zero alpha for any (single) self‐designated benchmark index of

a mutual fund. Our “adjusted factors”can then be used to estimate a mutual fund's

“adjusted alpha.”We test this methodology on a sample of 1,281 active and 102

tracker U.S. equity mutual funds (reporting S&P 500 index as their prospectus

benchmark). Our time series adjustment of the Carhart 4 factors leads to an increase

(decrease) in a fund's “adjusted alpha”in periods of fund‐benchmark

underperformance (outperformance). On the whole, our “adjusted alphas”of both

active and tracker funds are statistically significantly negative. This is particularly

pronounced for tracker funds.

KEYWORDS

Carhart alpha adjustment, n on‐zero benchmark alphas, optimization algorithm, performanceevaluation

1|INTRODUCTION

Carhart (1997) four‐factor and Fama and French (1993)

three‐factor model alphas have been accepted as standard

measures of portfolio performance among academics. How-

ever, a number of recent papers report non‐zero three‐and

four‐factor alphas for the general passive indices. Neverthe-

less, if the performance estimation model is correct, a passive

benchmark index should not generate abnormal return. This

is recognized by Chen and Knez (1996) who state that one

of the conditions, an admissible performance measure should

conform to, is to generate no out/underperformance for all

passive portfolio benchmarks that can be constructed. In this

paper, we revisit the question of non‐zero alphas in passive

indices, and we provide “adjusted”Carhart (four factor)

alphas for active and tracker equity mutual funds that account

for benchmark's alpha and compare these with funds' stan-

dard Carhart alphas.

Fama and French (1993) in their seminal paper give an

account of positive alphas of large value portfolio (0.21%

per month, t‐value 3.17) and negative alphas of small‐cap

growth portfolio (−0.34% per month, t‐value −3.14). More

recently Chan, Dimmock, and Lakonishok (2009) report a

significant Fama–French alpha of −4.74% for Russell 2000

Growth index over a 13‐year sample period. Moreover, they

illustrate that using alternatives in performance evaluation

models leads to unacceptable performance differentials. For

instance, Russell 2000 Value index abnormal return goes

from 3.5% when estimated in a model with market and

value‐weighted composite size and value factors to −3.18%

using Wilshire size and style indices in Sharpe (1992) style

model. Cremers, Petajisto, and Zitzewitz (2012), CPZ hereaf-

ter, document non‐zero alphas in well‐diversified passive U.

S. indices, such as S&P 500 and Russell 2000 among others.

They find that growth and general large cap indices exhibit

significant outperformance, whereas value and general

small‐cap indices significantly underperform based on

Carhart (1997) four‐factor model.

The reasons why passive indices exhibit non‐zero alphas

can be attributed to wrong choice of the factors or the choice

of factors is correct, but there are errors in their construction.

In the original three‐factor model paper, Fama and French

(1993) state that “… the choice of any particular version of

the factors is somewhat arbitrary”.

Received: 26 April 2016 Revised: 21 June 2017 Accepted: 21 June 2017

DOI: 10.1002/ijfe.1581

234 Copyright © 2017 John Wiley & Sons, Ltd. Int J Fin Econ. 2017;22:234–243.wileyonlinelibrary.com/journal/ijfe