Investment Analysts Journal – No. 63 2006 31
Book-to-market ratio and returns on the JSE
1. INTRODUCTION
Many firm-specific attributes or characteristics are
understood to be proxies for what Fama and French
(1992: p428) refer to as “the unnamed sources of risk”.
Perhaps the most notorious of these is the size of the
firm or its market value, first documented by Banz
(1981). The relationship between size and average
returns has become known as the “size effect”.
Ball (1978) argues that the ratio of earnings-to-price, or
E/P ratio, is a blanket proxy for unnamed risk factors in
expected returns. Other firm attributes such as
financial leverage (see Bhandari, 1988), dividend yield
(see Litzenberger and Ramaswamy, 1979), and book-
to-market ratio (see Rosenberg et al., 1985) have also
been found to exhibit significant correlations with
average returns. Each of these, according to Ho,
Strange and Piesse (2000), may be proxies for certain
risk factors that are related to asset returns.
The last of these factors, the book-to-market (BTM)
ratio, is the ratio of book value of equity (total assets
minus total liabilities) as per the balance sheets to
market value of equity (stock price times the number of
shares outstanding). Fama and French (1992) find a
strong positive BTM effect, suggesting that firms with
higher BTM ratios have higher expected average
returns. Furthermore, in their analysis performed on
US data from 1962 to 1989, Fama and French (1992:
p428) find that “although the size effect has attracted
more attention, book-to-market equity has a
consistently stronger role in average returns.”
Internationally, literature documenting the explanatory
power of the BTM ratio over stock returns is not
scarce. Stattman (1980), for example, finds a positive
relationship between average return and BTM for U.S.
stocks, as do Rosenberg, Reid, and Lanstein (1985).
Chan, Hamao, and Lakonishok (1992) find that BTM is
useful in explaining Japanese stock returns.
1.1 BTM and risk
The book value of a firm is the difference between total
assets (resources expected to result in inflows of
economic benefits) and total liabilities (obligations
expected to result in outflows of economic benefits), or
a measure of net expected inflows of economic
*Respectively Senior lecturer of Business Finance and associate
lecturer of Economics, School of Economics and Business
Sciences, University of the Witwatersrand, Private Bag 3, Wits
2050, South Africa
Email: auretc@sebs.wits.ac.za
sinclairer@sebs.wits.ac.za
benefits, or earnings. However, there is inherent
uncertainty surrounding those earnings.
Investments in two firms, each with similar book value
to the other, are likely to be valued differently if there is
more uncertainty surrounding the returns of one versus
the other. The investment with the lesser uncertainty
(lower risk) is likely to be preferred to the investment
with the greater uncertainty (higher risk), since the
marginal utility of risk is assumed to be always
negative, as per Markowitz (1959). As a result, the
market value of the less risky investment is likely to be
higher than the market value of the more risky
investment. Since the BTM ratio is the ratio of book
value to market value, the less risky investment is
therefore likely to have a lower BTM ratio than a more
risky investment. Given that higher returns are
necessary to induce investors to purchase a riskier
investment, a positive relationship between BTM and
returns results.
This idea that BTM may be a proxy for risk is
documented by Fama and French (1992), Davis, Fama
and French (2000), Keim (1988), and Hawawini and
Keim in Jarrow, Maksimovic and Ziemba (1995),
Daniel and Titman (1997), Strong and Xu (1997), Ho,
Strange and Piesse (2000), Drew (2003) and Griffin
and Lemmon (2002), to name but a few. Some of the
markets tested include those in the U.S., U.K., Hong
Kong, Korea, Malaysia, Italy and the Philipines.
Chen and Zhang (1998) suggest BTM may capture
three different types of risk: distress of a firm, financial
risk, and riskiness of cash flow. Akgun and Gibson
(2001), on the other hand, suggest that BTM (as well
as size) may subsume useful information regarding
both the probability of bankruptcy and recovery rates,
as well as distress risk. Vassalou and Xing (2004)
posit that the BTM effect is largely a default effect, but
exists only in segments of the market with high default
risk.
For the purposes of this study, it will suffice to simply
recognise that BTM is a proxy for certain elements of
risk of the firm, without postulating exactly what those
elements are, in the fashion of Fama and French
(1992). Attempting to dissect the BTM effect into the
various types of risk for which it may proxy remains an
intriguing avenue for further research.
Earlier studies on returns on the Johannesburg Stock
Exchange (JSE) have largely been performed within
the context of the CAPM, with various firm-specific
attributes being tested jointly with the CAPM’s risk
measure, beta, in order to provide evidence for or
against the CAPM.
CJ Auret* and RA Sinclaire
Book-to-market ratio and returns on the JSE
32 Investment Analysts Journal – No. 63 2006
For instance, Page and Palmer (1991) find evidence
for an earnings effect1, but no size effect. De Villiers,
Lowings, Pettit and Affleck-Graves (1986) find no
evidence of a size effect, whilst Affleck-Graves,
Bradfield and Barr (1988) find that the normal one-
parameter CAPM is well-specified, with the exception
of gold shares. Specifically, they found that there was
no dividend yield, size or liquidity effect. Affleck-
Graves, Gilbertson and Money (1982) find a portfolio
of low-priced stocks performed better than a portfolio
of high-priced stocks.
Due to the scant research on the JSE outside of the
context of the CAPM, van Rensburg and Robertson
(2003) undertook to identify those attributes which
have the ability to explain average monthly returns
over a 10-year sample on the JSE, from July 1990 to
June 2000, independent of the CAPM’s risk measure,
beta.2 This was done by initially regressing returns on
each of 24 different attributes3 separately. These
variables included most of the more common attributes
typically put forward to explain stock returns, with the
exception of the BTM ratio.4 Afterwards, regressions
were performed on all combinations of pairs of
attributes to determine how well they jointly explained
stock returns. The analysis was extended to groups of
three attributes, and the process continued as long as
1The effect of the price-to-earnings ratio (PE) on returns.
2They do perform similar tests within the context of the CAPM
too, but find no empirical support for the CAPM at all.
3These included: Price-to-earnings, dividend yield, price-to-
profit, price-to-NAV, cash flow-to-price, sustainable growth,
retention rate, size, return-on-equity, return-on-assets, debt-to-
cash flow, debt-to-assets, long term loans-to-assets, debt-to-
equity, leverage, financial distress, current ratio, quick ratio,
owner’s interest, previous one month’s return, previous six
month’s return, previous one year’s return, trading volume and
shares in issue.
4The paper does, however, include a price-to-net asset value
per share (P-NAV) ratio. Upon reflection, this turns out to be
similar to the inverse of the BTM ratio, though there are a few
accounting differences (for example, the treatment of
redeemable and irredeemable preference shares). There are
however, three more important reasons why the P-NAV will not
substitute for BTM. Firstly, the BTM ratio is well documented in
the literature, whereas there is less research conducted on the
P-NAV ratio. Secondly, regressing returns on BTM and on P-
NAV will yield very different results. If a linear regression on one
of the variables is correctly specified, then a linear regression on
its inverse must be misspecified since the latter will involve a
non-linear function. Thirdly, since book value (the numerator in
BTM) can be negative, and market value (denominator) is
nonnegative, the relationship between book value and BTM
(holding market value constant) is continuous. In contrast, the
relationship between book value and P-NAV is characterized by
a large discontinuity as book value approaches zero from above
and below. This means that a minor change in book value from
just below zero to just above zero will cause a jump in P-NAV,
moving it from the very bottom of the distribution to the very top.
Clearly then, using P-NAV is not a good substitute for BTM ratio.
no variables became insignificant at the 5% level in the
regression. The resulting optimal model to explain
average stock returns was found to be a two-factor
model with size and price-to-earnings as explanatory
variables.
Fama and French (1992) find that size and BTM
combine to capture cross-sectional variation in stock
returns, absorbing the influence of leverage and the
earnings-to-price ratio. In light of this, it is important to
check the robustness of the van Rensburg and
Robertson (2003) size-P/E model by including the
BTM ratio as a candidate explanatory variable.
[The element of risk related to BTM can be
incorporated into a returns model either indirectly
through a HML (high-minus-low)-type risk factor, or
directly in the form of a “return to styles” approach. The
former extracts the signal from the difference of returns
on two artificial portfolios, one with high BTM values,
and one with low BTM values. The latter simply uses a
stock’s BTM ratio as an explanatory variable in
explaining stock returns. Although the debate as to
which is more appropriate continues5, this study will
concentrate on the multi-attribute approach in
explaining stock returns, as per Fama and French
(1992) and van Rensburg and Robertson (2003) for
the sake of comparability.]
The remainder of the paper is divided into the following
sections: section two deals with issues relating to data
and methodology. Section three presents and
discusses results, and the final section concludes.
2. DATA AND METHODOLOGY
The data was generously supplied by Paul van
Rensburg and Michael Robertson, and covers the
same sample period as their study.
Financial ratios were obtained from the
McGregor/Bureau of Financial Analysis (McG/BFA)
database of standardised financial accounts, from July
1990 to June 2000. The sample contains stocks in all
sectors of the JSE. Returns data were obtained from
the BARRA organisation’s data set of monthly stock
returns, adjusted for all capital events and dividends. A
thin trading filter was applied conservatively to ensure
that all firms in the sample were traded at least once
during each month. Cash shell companies are
excluded. The data set shows missing values for de-
listed shares only after the de-listings, which helps
eliminate the problem of survivorship bias. It also
augments the data set. Variables have been cross-
5Daniel and Titman (1997) argue that the latter is a better
approach in explaining stock returns than the former, in an
analysis using both size and BTM attributes. See also Cohen
and Polk (1995). Davis, Fama and French (2000), on the other
hand, find that the factor approach performs better than the
characteristic approach for the book-to-market ratio.
Book-to-market ratio and returns on the JSE
Investment Analysts Journal – No. 63 2006 37
Finally, this study opens doors for further research in
this area. Contributions yet to be made include the use
of a larger data set, using weights to remove the
influence of stocks too small for institutional investors,
and an investigation in more depth of the nature of the
risk for which the BTM ratio is a proxy.
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