submitted to the Journal of Portfolio Management in July 2004

The importance of being value

François Bourguignon and Marielle de Jong[*]

Abstract

In the investment management community value stocks are considered an equity class with a distinct price performance. They are believed to outperform the stock market in the long run and to have a distinct price volatility. There is an unresolved debate among researchers on how to explain this market phenomenon. We throw new light on the debate by reconsidering the definition that is used to recognise value stocks. We decompose the definition along a time axe into a structural component and a transitory component, and find that both components help to explain price volatilities across stocks, yet that, interestingly, only one of them –the transitory component- gives rise to systematic outperformance.

JEL code : G1

Value stocks are generally recognised to be a class of stocks within the equity market with a distinct price performance. They are believed to have a price trend which is superior to that of the market in the long run, and in addition the volatility of their price movements is considered to be different. Fama and French [1992, 1996, 1998] explore this market phenomenon in a series of articles and conclude that the premium they observe on value stocks is related to a sense of distress in the underlying firms. Distress depresses stock prices -low prices being generally attributed to value stocks- and pushes stocks into a risk profile which is distinctly different from that of other stocks and which is apparently being rewarded in the long run.

Their position has since been highly debated. Daniel and Titman [1997, 2001] suggest that value is rather a proxy for certain fundamental firm characteristics, and that there is a premium associated with these characteristics. Others like DeBondt and Thaler [1987] explain the value premium by investors’ behaviour who seem to systematically overreact to certain market events. There are also non-believers, like Philips [2002] who argues that the premium must be offset by free cash flows such as dividends and share buy-backs, that are not included in the test experiments, or Black [1993] who considers the evidence a chance result.

We enter this debate from another angle. We focus on the definition that is generally used to identify the value stocks, and decompose it along a time axis into a structural component and a transitory component. While doing this we discover very different price behaviours between the two components. In a previous article [2003] we give evidence that only the transitory component gives rise to systematic outperformance, not the structural component. In this article we confirm this result in another set of experiments by which we show that, interestingly, both value components help to explain price volatilities across stocks.

We conclude that value, in the way it is generally defined, represents two separate factors of risk, of which only one is remunerated. This theorem is, as far as we are aware, not considered before and, we argue, throws new light on the ongoing value debate.

DECOMPOSING VALUE

Based on the principle that value stocks are relatively low-priced compared to their firm fundamentals, value stocks are usually recognised by comparing the share price with the firm value (per share), which can be measured in terms of book value. A high book-to-price (BP) ratio indicates a value stock. The value stocks are thus, according to the standard definition, the highest ones in a stock ranking based on BP ratios that are measured at an instant in time.

In our previous article [2003] we had already cast doubt on the validity of this definition. In the stock ranking, stocks are being compared of which some are in price equilibrium in respect to their firm fundamentals and others are not, for some (temporary) market-related events. The method is therefore, since it is ignoring the time dimension of the BP ratios, set to confuse structural elements with more timely price effects. In order to avoid such a confusion, we had refined the definition, distinguishing explicitly between stocks that are low-priced structurally and ones that are low-priced temporarily, by decomposing the BP ratios into the historic average book-to-price, denoted as , and the divergence from the average, as follows :

for stock i=1,..,N at time t=1,..,T(1)

The stocks with a high average BP ratio are called the structural value stocks and the ones with a BP higher than its average the transitory value stocks.

The experiments we had carried out with this decomposed value definition, reveal a difference in price performance between the two value groups that result. It appears that the transitory value stocks tend to outperform the market in the long run, whereas the structural value stocks do not. In this article we continue this study and explore whether the two value groups differ in their risk behaviour as well.

In order to analyse risk we study an equity risk model that contains a value factor. We adopt the Fama and French [1998] two-factor model which they use to demonstrate that value indeed represents a source of risk. We decompose the value factor into two components according to equation (1), obtaining as such two risk models, as follows :

2F :Rit = i + iMt + BPitVt + it(2)

3F : Rit = i + iMt +Vtstruc + (BPit -) Vttrans + it

where

Rit is the excess return of stock i at time t over the risk-free rate,

Mt is the excess market return at time t,

i is the stock alpha, i the market beta,

it are the residuals which are assumed to be i.i.d. and independent of the factors, and

the book-to-price ratios are as defined in equation (1) .

The three-factor model (3F) is spanned by the market factor (M), the structural value factor (Vstruc) and the transitory value factor (Vtrans). This model would naturally default back to the two-factor model (2F) if the two value components were identical :

t=1,..,T(3)

In other words, the two-factor model is the constrained version of the three-factor model with T constraints as given in equation (3). Hence to test which of the two model is the most valid, can be carried out by applying standard likelihood ratio (LR) tests[1] for testing the validity of the constraints. If the constraints are valid, it means that there are two distinct sources of risk attributable to value, otherwise there is one[2].

Fama and French (FF) specify the two-factor model slightly differently. They define :

FF :Rit = i + iMt + iVt + it(4)

where i is the constant exposure of stock i to the value factor Vt. The value factor is constructed, according to the standard definition, on the basis of BP stock rankings that are carried out at an instant in time once a year. The factor returns are the returns of a zero-invested portfolio that is long high BP stocks and short low BP stocks. Note the difference in role of the BP ratios. In the 2F model the BP ratios are individual stock exposures to an unobservable common factor, that is estimated. In the FF model the BP ratios are used as proxies to commonly capture the value factor, after which the individual stock exposures are estimated.

The two models differ most importantly in the way the stock exposures are specified. In the FF model they are considered constant in time over the entire estimation period, whereas in the 2F model they vary. We find the FF model not intuitive at this point; assuming that stocks have a fixed sensitivity to a value factor, which is directly associated with firms’ distress, should be interpreted as stocks having the same price reaction to general distress that occurs at times. Instead it is more intuitive to think that distress occurs in individual firms at times independent of each other, by letting the individual exposures of stocks to ‘distress’ vary, and that there is a recognisable price pattern among such stocks.

Thus, for reasons of comprehension as well as for facilitating the testing of the value decomposition, we have chosen the model specification as given in (2). When we decompose the value factor of the 2F model to obtain the 3F model, we purposely obtain a structural component that has relatively constant exposures over time compared to those of the transitory component. This is an important element in the experiment set-up, that we elaborate on later in the article.

TWO VALUE FACTORS


We estimate the two models (2) on 13 major equity markets over a 15-year period from 1989 to 2003, and we carry out likelihood ratio tests in order to determine which of the two models is the most valid. The results are given in Exhibit 1.

The 3F model is accepted in all markets. That is a significant result. It proves the existence of two separate value effects in all markets. It means that on the one hand, prices of structurally low BP stocks tend to move together, in opposite direction as those of structurally high BP stocks, and on the other hand, opposite price movements are confirmed to exist between stocks with a BP above its average and a BP below its average.

Let us firm up this result, in a second more stringent experiment. If there are truly two persistent value effects in the market and not one, it should be beneficial to make use of this knowledge in a portfolio optimisation exercise. Let us compare the ex post performance of two risk-optimal portfolios, one that is based on the 2F model which identifies one value effect, and the other based on the 3F model that identifies two value effects.

To be precise, we seek the portfolios to be minimally affected by the market and value movements. This can be achieved by minimising the residual risk, or tracking error, which is the volatility of the portfolio return in excess of the factor returns. In order to minimise excess market risk, the optimised portfolios will typically hold high- as well as low market beta stocks, so that the total portfolio beta resembles the market beta, which is one by definition. With such balanced beta the portfolio is set to imitate (or track) the market movements. In the same way the portfolio that is optimised using the 2F model, will in addition be balanced for high and low BP stocks, so that it is weathered for potential diversions in performance between these stocks. Likewise the portfolio that is optimised with the 3F model, is weathered for transitory value effects and structural value effects. In the Appendix the details of the experiment are described, in Exhibit 2 are the results.


The ex post risk of the 3F-optimised portfolios is in nearly all markets lower than that of the 2F-optimised portfolios. In other words, the portfolios that anticipate two value effects are structurally less risky than the ones anticipating one value effect. Though the gain in risk is limited (13 basis points on average), it is a significant result considering that we measure out-of-sample risk without foresight in the model estimation. The results confirm the existence of two distinct and persistent effects that are attributable to value.

Before giving our interpretation of these findings, in next section, we first discuss the factor estimates that result from the first experiment. The factor returns that are estimated in the models (2), can be interpreted as the return of a portfolio that imitates the factor. The portfolio which represents the value factor of the 2F model is a zero-invested portfolio that is long high BP stocks and short low BP stocks. Note that such portfolio is in principle very similar to the one constructed by Fama and French in their model (4). Under the assumption (which lies behind the standard value definition) that high BP equals value, it is the optimal portfolio an investor would hold who wants to pursue a value investment strategy, of course when disregarding practical considerations such as transactions costs or short-selling constraints. The performance of the value portfolio is displayed in Exhibit 3 in terms of cumulated returns starting at a base of 100, for the United States.


The value factor exhibits a consistent positive price performance over the period, with an annual rate of 11.8 %. Naturally this rate doesn’t include the market trend, which is captured separately by the market factor and which is not displayed. This significant outperformance confirms the existence of a value premium in the US.

In the same way as is described above for the value factor, the cumulated return of the structural value factor and of the transitory value factor of the 3F model are calculated and displayed as well. The factor returns are rescaled, by a method that is explained in the Appendix, in order to make direct comparison possible. Interestingly, the transitory value factor yields higher than the value factor (with an annual rate of 12.7 %), whereas the structural value factor yields lower (8.7 %).

The same picture is observed in all markets, as can be seen in Exhibit 4. In the Exhibit annual average returns are given per market. The annual return rate of the value factor is 12 % per year on average in the six largest markets, the transitory value factor yields at 15 % and the structural factor at 9 % on average (all excluding the market trend). It confirms our connotation that we had made in our previous article, that the value premium stems from the transitory component of value. In that article we had constructed the factor portfolios directly in the way Fama and French do, obtaining very similar results.


INTERPRETING VALUE

Resuming, we find two value effects in the market, a structural value effect and a transitory value effect, the latter giving rise to systematic outperformance. Let us now give our interpretation of these results. In the structural value effect we recognise the value/growth-style division, that is often made by researchers and practitioners, see for a general reference Coggin and Fabozzi [2003]. A high BP level is characteristic for a value firm which has business operations that generate moderate revenue over time. The BP level is high as opposed to that of a growth firm which typically has an ambitious development program aimed at gaining market share in the short run at the expense of current revenue. A growth firm has a low book value relative to the stock price, as the price reflects a certain optimism in future growth not yet accounted in the book value.

It is plausible that, as the experiments in this article indeed show, these two types of firms have different price patterns, since they react differently to market news or events. For example, a heavily indebted firm, which typically figures a low BP ratio, may have a negative price reaction to an interest rate rise, unlike a self-financed enterprise who may gain a relative advantage. However, it is not plausible to think that there is a systematic difference in their market performance over time. We disagree therefore with Daniel and Titman [2001] who associate the value premium with fundamental firm characteristics.

The transitory value effect is a pure price effect : undervalued stocks tend to outperform overvalued stocks. This is the case when there is a mean-reversion effect of stock prices in the market. The mimicking portfolio of the transitory value factor buys stocks whose BP is positively diverted from its mean and sells the ones negatively diverted from their mean. Consequently stocks are systematically bought at a low price and sold at a high price, and are as such producing the value premium.

It is an interesting phenomenon that stock prices move in a more or less predictable way, however, we don’t consider it a market anomaly in the sense that it is in disagreement with Ross’ [1976] arbitrage pricing theory. One should realise that the undervalued stocks is an undefined group that is not easy to identify. Moreover, it is a group of stocks that changes of constituents erratically with the spurs of the market. Seizing the seeming arbitrage opportunity the value premium insinuates, would require an effective screening criterion that identifies the undervalued stocks yet that doesn’t alter too erratically in order to keep the transactions costs down that are involved in maintaining a portfolio of undervalued stocks.

In our experiment the screening criterion is simple, yet, as the exposures to the transitory value factor are highly variable, the factor-mimicking portfolio generates significant trading, to the extent that the transactions costs largely outweigh the value premium. Therefore, we argue, our experiment is no proof for an arbitrage opportunity.

The value decomposition we study was chosen purposely in a way so that the transitory component captures the time variability and the structural component remains constant in time. The structural value portfolio is consequently a more or less buy-and-hold portfolio, and consistent with our argumentation such portfolio indeed shouldn’t outperform. We have not reduced the variability of the structural component to exactly zero, which would be possible by taking average BP ratios over the entire estimation period, because this would introduce foresight into the experiment. Instead we have taken averages over a trailing time-window, leaving as such a small variability, which is our explanation of the minor excess return this factor exhibits.

We repeat that the transitory value stocks (the undervalued stocks) stand in no relation to the value stocks that were opposed to the growth stocks in the description above. They are two interpretations of value with each a distinct price behaviour. DeBondt and Thaler [1987] evidently relate to the first type of value stocks when they explain the value premium by a systematic overreaction of investors. Daniel and Titman [2001] evidently relate to the other addressing firm characteristics. One would say that Fama and French also mean the undervalued stocks, when explaining the value premium by a distress factor, considering that distress is not a lasting state of affairs. But that is not coherent with their main conclusion that ‘value stocks have higher returns than growth stocks’, giving the allusion of a relatively permanent stock division.