DO FUNDAMENTALS DRIVE RELATIVE VALUATION? EVIDENCE FROM GLOBAL STOCK MARKET INDICES

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DO FUNDAMENTALS DRIVE RELATIVE VALUATION?

EVIDENCE FROM GLOBAL STOCK MARKET INDICES

KOMLA AGUDZE^*and OYAKHILOME IBHAGUI Baum Tenpers Research, 23401 Lagos, Nigeria

*agudze.k@baumtenpers.com

Received 1 July 2019 Accepted 29 April 2020 Published 16 December 2020

In this paper, we use aggregate-level data from global, developed and emerging markets to empirically examine how fundamentals of publicly listed ¯rms drive their relative valuation multiples. First, we ¯nd that, in each market, there is a dynamic link between fundamentals and relative valuation: relative valuation multiples are negatively linked to their past, suggesting that overvalued markets, based on high relative valuation multiples, often experience correc- tions that subsequently lower their relative valuation multiples, making them less overvalued, fairly valued or even undervalued, compared with previous periods. Secondly, we document that fundamentals do indeed have signi¯cant e®ects on relative valuation multiples. This reveals that fundamentals are an important driver of relative valuation multiples at the aggregate level in the stock market. Hence, practitioners should not ignore outlook for relative valuation multiples of aggregate stock market that is deduced from fundamentals.

Keywords: Fundamentals; valuation; S&P 500; developed; emerging; global market; macroeconomic factors.

1. Introduction

To determine whether to buy or sell a security or an index of securities in the equities market, shrewd practitioners often examine the current worth of a security, collec- tion of securities or an index of securities using either absolute valuation methods or relative valuation techniques or a combination of both. Absolute valuation estimates the actual or intrinsic value of a security or an index of securities based on the actual business performance or fundamentals of the companies associated with the securities. It uses the ability of companies to optimally continue as a going concern, to determine the actual worth or intrinsic value of their equities. Under absolute valuation, the intrinsic value of a company, which is used to compute the intrinsic or fair

*Corresponding author.

This is an Open Access article published by World Scienti¯c Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Journal of Financial Management, Markets and Institutions Vol. 8, No. 2 (2020) 2050002 (42 pages)

#.c The Author(s)

DOI:10.1142/S2282717X20500024

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value of its stock, is taken as the present value of future cash °ows (free cash °ows or dividends), discounted at an appropriate cost of capital. If the estimate of value arrived at via absolute valuation is greater than the price at which the security trades in the market, then it is said that the security is undervalued and trades at a discount in the market. If, however, the security trades in the market at a price greater than the estimated intrinsic value, then the security is said to be overvalued and trades at a premium in the market. Absolute valuation attempts to determine intrinsic worth without reference to another company or industry average.

Relative valuation is a di®erent concept. A relative valuation model compares a company's worth at a given point to that of its competitors or industry peers. It uses relative valuation multiples to measure where a security or index of securities might be expected to trade in the near term based on what market participants are willing to pay for it, which may or may not be re°ective of the security's actual worth. Thus, relative valuation measures the target price, that is, the level at which a security is expected to trade in the near term, which is not necessarily its intrinsic value. The relative valuation comprises several ratios, otherwise called multiples, that are compared among securities within the same industry. These ratios include, among others, the price-to-earnings ratio (P/E ratio), the enterprise value-to-earnings before interest, taxes, depreciation and amortization ratio (EV/EBITDA ratio) and the price-to-cash °ows ratio (P/CF ratio). The security with the least relative valuation multiple is often taken to be trading at a discount relative to peers. For this reason, market participants would normally expect its worth to rise in the market, more so than those of its peers with signi¯cantly higher multiples. In this instance, the subsequent relative valuation multiple of the security would also rise to become higher than its previous levels or higher than those of peers, which could then mean that the security has begun trading at a premium to peers, dampening expectations for further rise in performance.

One major issue in ¯nancial economics, empirical corporate ¯nance or even asset pricing literature is the relationship between fundamentals and stock valuations.

This is because analysis of fundamentals is important for examining the state of a

¯rm, pro¯tability, dividend and risk and for making investment decisions (Baresa et al. 2013;Muhammad et al. 2018). Fundamentals are also useful for evaluating ¯rm performance. All else equal, ¯rms with stronger fundamentals such as superior pro¯tability and cash °ow positions, better future potential and lower risk of debt overhang relative to size are said to be in good health and exhibit better ¯rm performance than those with weaker fundamentals. For example,Ibhagui & Olokoyo (2018) have shown that ¯rm performance is most negatively a®ected by a rise in debt when the size of the ¯rm taking on higher debt is small.

In the theoretical literature, the subject of valuation has attracted interests from scholars, following contradictory submissions on the subject. The earlier works of LeRoy & Porter(1981),Shiller(1981) andSummers (1986) argue that there is no relationship between fundamentals and stock valuations. In contrast, in°uential papers of Fama (1990) and Schwert (1989) posit that there are signi¯cant J. Fin. Mngt. Mar. Inst. 2020.08. Downloaded from www.worldscientific.com by 134.122.89.123 on 01/18/22. Re-use and distribution is strictly not permitted, except for Open Access articles.

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relationships between fundamentals and stock valuations. In the empirical literature, several studies have investigated the relationship. However, these studies have continued to yield contradictory evidence. For instance, while Black et al. (2003), Laopodis (2006) and Becchetti et al. (2007) report that stock valuations tend to deviate from fundamentals, other studies have noted that the deviations are a short- run phenomenon which tends to revert to fundamentals in the long run (Coakley &

Fuertes 2006,Boucher 2007, Manzan et al. 2007). Still, studies have reported that the relationship between fundamentals and valuations is strong (Pan 2007,Balke &

Wohar 2009,Chen & Fraser 2010,Yuhn et al. 2015,Velinov & Chen 2015).

However, most of these studies are based on individual stocks at the micro level, and the impact of fundamentals on relative valuation multiples in the equities market at the aggregate level has been largely ignored. One (potential) reason for this is that obtaining aggregate-level data for equities index and the associated fundamentals of companies which make up the index might pose some di±culty. We remedy this situation by drawing on the Morgan Stanley Capital International (MSCI) aggregate-level data for equities market and company fundamentals.

As such, in this paper, we examine whether company fundamentals are important drivers of relative valuation multiples at the aggregate level in the equities market.

Speci¯cally, we ask two main questions: (1) do fundamentals drive relative valuation multiples at the aggregate level and (2) are the relative valuation e®ects of company fundamentals similar across developed and emerging markets. We also perform a comparison of the relationship for separate economic groups. We believe this is worthwhile considering the di®erences in the regulatory business environment, ac- counting systems, taxation laws and other industry and economic policies plausibly unique to each economic group.

We use time series econometric techniques to assess if and how fundamentals drive relative valuations. The fundamentals considered are gross margin, operating margin, return on asset and return on equity. Relative valuation metrics used are price-to-earnings ratio, price-to-book ratio, enterprise value-to-sales ratio, enterprise value-to-EBIT ratio, enterprise value-to-EBITDA ratio and dividend yield. The choice of the four measures of fundamentals stems from the fact that they are the common measures identi¯ed in the literature. Other measures that could have been included are performance coverage ratios associated with credit risk, e.g. interest coverage ratios and others. However, our four measures adopted adequately proxy company fundamentals.

We capture aggregate-level data in the equities markets using MSCI World Index for developed markets, MSCI Emerging Markets index for emerging markets and MSCI ACWI, which is a combination of MSCI for developed markets and MSCI for emerging markets, to capture the world market. We also examine the impact of fundamentals on relative valuation in the US equities market using the S&P 500 Index. Our paper adopts fundamentals and relative valuation indices separately for both developed and emerging markets, including the US, because behavior of these indices might not be the same across di®erent markets. As believed among J. Fin. Mngt. Mar. Inst. 2020.08. Downloaded from www.worldscientific.com by 134.122.89.123 on 01/18/22. Re-use and distribution is strictly not permitted, except for Open Access articles.

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policymakers, it is quite possible that ¯rm performance and hence fundamentals are better in some developed markets, for instance, in S&P 500, than other developed and emerging markets, leading to di®erences in outcomes for relative valuation metrics.

Ultimately, we contribute to the existing literature by documenting evidence on the relative valuation e®ects of ¯rm fundamentals in the overall global, developed, emerging, as well as in the US markets. To our knowledge, previous studies have not formally documented the empirical relations between ¯rm fundamentals and relative valuation metrics at the aggregate level. This paper ¯lls this void in the literature.

After presenting some stylized facts in Sec.1.1, we structure the rest of the paper as follows: Sec.2presents description of the data and methodology employed. Empirical results and interpretation are presented in Sec.3. Lastly, Sec.4concludes the study.

1.1. Stylized facts

In this section, we present a brief stylized fact on the behavior of the variables considered in the study. As shown in Figs.3and4, ¯rm fundamentals, measured by ROA, seem better for emerging markets than S&P 500 and developed markets at

Fig. 1. Price earnings ratio across markets.

Fig. 2. Enterprises value-sales ratio across.

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most periods under analysis. In contrast, gross margin is relatively higher for S&P 500 than other markets. Regarding the relative valuation metrics, Figs.1and2show that price-earnings ratio and enterprise value-sales ratio are relatively higher for S&P 500 and developed economies than emerging economies. The fundamentals and relative valuation metrics seem correlated in the four markets. They show signs of high correlation for the global and developed market indices as they move together across all valuation metrics. Results of the correlation matrix presented in Sec.3also con¯rm this.

2. Methodology

2.1. Empirical analysis

To examine the relations between fundamentals and relative valuation multiples, we regress relative valuation multiples ðVAL_tÞ on fundamentals ðFUNDM_tÞ via an empirical model which is speci¯ed as follows:

VAL_t¼ ₀þ ₁FUNDM_tþ _t; ð2:1Þ

Fig. 3. Gross margin across markets.

Fig. 4. ROA across markets.

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whereVAL_t represents the relative valuation ratios such as price to earnings ratio, price to book ratio, enterprise value to sales ratio, enterprise value to EBIT ratio and dividend yield. FUNDM_t represents fundamental indicators such as gross margin, operating margin, return on asset and return on equity. To obtain a relation in levels in the regression in (2.1) when variables are not stationary, cointegration will need to be established.

Cointegration among variables refers to the existence of stationarity in their linear combination or residuals when all variables are not individually stationary.

Put di®erently, the variables might be cointegrated if either they are individually integrated of order 1I(1) or the integration is mixed, that is, I(1) and I(0). Coin- tegration between fundamentals and relative valuation indices is important to avoid spurious regressions and obtain coherent estimates.

Having tested for unit roots which reported a mixed order ofI(0) and I(1) for the variables (Table 3), we adopt the autoregressive distributed lag (ARDL) following Pesaran et al. (2001). This method allows for mixed order of integration for inves- tigating relationships among variables. It also enables the simultaneous investigation of short- and long-run relations, i.e. relationships in changes and levels. The empirical model on the relationship between fundamentals and relative valuation within un- restricted error correction mechanism (UECM) is speci¯ed as follows:

VAL_t¼ ₀þX^j

i¼1

_1iVAL_tiþX^k

_1iFUND_ti

þ ₁FUND_t1þ ₂VAL_t1þ _1t ð2:2Þ where is the di®erence operator, and are coe±cient estimates of the related variables, is the white noise term and j and k are the optimal lag lengths selected based on the AIC. The existence of cointegration in Eq. (2.2) is examined based on the joint F-statistics. Thus, the null hypothesis of no cointegration, H₀:₁¼ ₂¼ 0, is tested against the alternative hypothesis H₀:₁ ¼ ₂6¼ 0.

Because of the non-standard nature of the test statistics under the null hypothesis, Pesaran et al. (2001) produce critical value bounds for the F-test. If calculated F-statistics fall below the lower critical bound, I(0), the null hypothesis cannot be rejected; on the contrary, if calculatedF-statistics exceed the upper critical bound, I(1), the null will be rejected and the series are more likely to be cointegrated.

2.2. Data

Following the empirical literature, we proxy fundamentals with gross margin, operating margin, return on asset and return on equity. We use ¯ve relative valuation measures: price-to-earnings ratio, price-to-book ratio, enterprise value-to-sales ratio, enterprise value-to-EBIT ratio, enterprise value-to-EBITDA ratio and dividend yield. We capture developed markets using MSCI World Index for developed markets; for emerging markets, we use MSCI Emerging Markets Index. Finally, we J. Fin. Mngt. Mar. Inst. 2020.08. Downloaded from www.worldscientific.com by 134.122.89.123 on 01/18/22. Re-use and distribution is strictly not permitted, except for Open Access articles.

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capture the global stock market using MSCI ACWI, a combination of MSCI for developed markets and MSCI for emerging markets. Due to the scale of the US stock market, it cannot be ignored; thus, we also analyze the US stock market separately using S&P 500 data.

These indices give information on major companies listed in these markets. For instance, the MSCI World Index captures large and mid-cap representation across 23 developed markets countries. With 1633 constituents, the index covers approximately 85% of the free °oat-adjusted market capitalization in each country.

The MSCI Emerging Markets Index represents large and mid-capitalized ¯rms across 24 emerging markets. With 1136 constituents, the index covers approximately 85% of the free °oat-adjusted market capitalization in each country. To- gether, the MSCI ACWI captures large and mid-capitalized ¯rms across 23 developed markets and 24 emerging markets countries. With 2771 constituents, the index covers approximately 85% of the global investable equity opportunity set.

These indices are described in Table1. We also control for macroeconomic factors that a®ect relative valuations apart from company fundamentals. We adopt three variables: short term interest rate, the growth rate of industrial production and in°ation rate. Data for short-term interest rate and in°ation rate for developed economies and the U.S. were sourced from the OECD database, whereas those for emerging market were sourced from the IMF's international ¯nancial statistics database. Data for the growth rate of industrial production for both economies and the U.S. were sourced from the IMF's IFS database. The study period covers 1995Q1 to 2019Q3.

Table 1. Data, sources and descriptions.

Variables Description Source

Gross margin This is the gross margin MSCI/Bloomberg

Operating margin This is captured with operating margin MSCI/Bloomberg Return on assets This is the ratio of pro¯t to total assets MSCI/Bloomberg Return on equity This is the ratio of pro¯t to total equity MSCI/Bloomberg Price-earnings ratio This is the ratio of price-earnings ratio MSCI/Bloomberg Price-book value ratio This is the ratio of price-book value ratio MSCI/Bloomberg EV-sales ratio This is the ratio of enterprises value to

SALES ratio

MSCI/Bloomberg EV-EBITDA ratio This is the ratio of enterprises value to

EBITDA

MSCI/Bloomberg Dividend yield This measures the dividend of ¯rms MSCI/Bloomberg

Short-term interest rate This is the same as the money market rate OECD Database and IMF's IFS Database

In°ation rate This is the average growth rate of the consumer price index for each country group

OECD Database and the IMF's IFS Database

Growth rate of industrial production

This is the average growth rate of sea- sonality adjusted index of industrial production for each country group

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3. Empirical Results and Discussions

We begin by presenting simple descriptive statistics before formally discussing results of the relationship between fundamentals and relative valuation. The results of the descriptive statistics for the global market (developed and emerging equities market) are presented in Table2. The mean return on asset is 1.62 with a standard deviation of 0.51, showing that pro¯tability in terms of return on assets exhibits a very low dispersion. This is further con¯rmed by return on equity with mean and standard deviation of 10.90 and 3.57, respectively. Other fundamentals such as operating and gross margins also maintain similar consistency. Overall, gross margin has the highest value followed by return on equity, operating margin and return on assets. For the relative valuation ratios, price–earnings ratio has the highest average with a mean value of 19.94 and standard deviation of 5.16. EV/EBITDA ratio has mean and standard deviation of 10.06 and 1.34, respectively. Besides, the standard deviation of these variables indicates that they display low dispersion over the period of analysis. For the macroeconomic variables adopted in the study, the short-term interest rate has the highest mean and standard deviation. This reveals the di®erences in the interest rate set by monetary authorities across developed economies and emerging markets. In°ation rate, on the other hand, has both a low average and standard deviation. This re°ects the low rate of in°ation witnessed in both developed and some emerging markets.

3.1. Unit root tests

Before examining the relationship in Eq. (2.1), we examine the unit root properties of the variables to determine the most appropriate technique for our analysis. The results of the unit root test based on the Augment Dickey fuller test for unit root with a linear trend are presented in Table3. The results show that ROA, ROE, OPM, INF and IND are stationary at levels whereas GROSSM, P/E, P/B, EV/S, EV/EB, DIVY and INT are stationary at ¯rst di®erence. Since the model contains a mixture

Table 2. Descriptive statistics for the global market.

DIVY EVEB EVS GROSSM IND INF INT OPM PB PE ROA ROE

Mean 2.27 10.06 1.78 29.53 0.63 1.54 6.18 10.45 2.24 19.94 1.62 10.90 Maximum 4.21 13.44 2.43 31.89 20.35 3.11 49.79 13.16 3.51 36.50 2.28 16.79 Minimum 1.25 6.79 1.12 26.29 8.09 0.30 2.45 7.18 1.43 11.74 0.15 0.31 Std. Dev. 0.51 1.34 0.29 1.35 2.53 0.58 5.80 1.51 0.40 5.16 0.51 3.57

Obs. 97 99 99 97 98 98 99 97 99 97 97 99

Notes: ROA¼ return on assets; ROE ¼ return on equity; OPM ¼ operating margin; GROSSM ¼ gross margin; PE¼ price/earnings ratio; PB ¼ price/book-value ratio; EVS ¼ enterprises value-sales ratio; EVEB¼ enterprises value-EBITDA ratio; DIVY ¼ dividend yield; IND ¼ growth rate of industrial production (%); INF¼ inflation rate (%) and INT ¼ interest rate (%). Fundamentals are in % while relative valuations are expressed as times (xÞ except dividend yield DIVY which is in %.

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of I(0) and I(1) variables, the autoregressive distributed lag (ARDL) technique is employed for estimating the desired relationship.

3.2. Correlation matrix

Table4presents simple preliminary correlation matrix for the global market with the level of signi¯cance also indicated. The results reveal that fundamental variables are highly correlated. As such, including them all at once in the same empirical speci-

¯cation may yield spurious results due to the problem of multicollinearity. To prevent this, we will proceed by including the highly correlated ones separately in our model speci¯cations and at the same time controlling for macroeconomic factors. The results also show that relative valuation metrics are highly correlated, pointing to the presence of a global factor in the fundamental drivers of relative valuation metrics.

3.3. Granger causality test

We perform Granger causality tests to identify the direction of causality between fundamental and relative valuation variables and at the same time to detect issues of

Table 4. Descriptive statistics for emerging market.

Mean 2.43 6.97 1.54 25.30 0.59 1.30 9.13 12.90 1.55 14.77 2.88 12.96 Max 4.24 10.81 2.48 32.58 5.24 3.22 49.79 15.87 2.80 39.88 4.65 17.77 Min 1.20 2.89 0.63 17.87 11.22 0.44 3.89 7.45 0.58 4.74 0.02 6.08 Std. Dev. 0.54 1.75 0.30 3.10 1.98 0.58 7.21 1.60 0.42 5.68 1.05 2.80

Obs. 97 97 97 93 98 98 99 97 97 97 97 78

Notes: ROA¼ return on assets; ROE ¼ return on equity; OPM ¼ operating margin; GROSSM ¼ gross margin; PE¼ price/earnings ratio; PB ¼ price/book-value ratio; EVS ¼ enterprises value-sales ratio; EVEB¼ enterprises value-EBITDA ratio; DIVY ¼ dividend yield; IND ¼ growth rate of industrial production (%); INF¼ inflation rate (%) and INT ¼ interest rate (%). Fundamentals are in % while relative valuations are expressed as times (xÞ except dividend yield DIVY which is in %.

Table 3. Descriptive statistics for developed economies.

Obs. 96 98 98 96 97 98 98 96 98 96 96 98

Notes: ROA¼ return on assets; ROE ¼ return on equity; OPM ¼ operating margin; GROSSM ¼ gross margin; PE¼ price/earnings ratio; PB ¼ price/book-value ratio; EVS ¼ enterprises value-sales ratio;

EVEB¼ enterprises value-EBITDA ratio; DIVY ¼ dividend yield; IND ¼ growth rate of industrial production (%); INF¼ inflation rate (%) and INT ¼ interest rate (%). Fundamentals are in % while relative valuations are expressed as times (xÞ except dividend yield DIVY which is in %.

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reverse causality between them. The optimal lag length was selected based on the Akaike information criterion. Table6 presents results of the Granger causality test between the fundamental variables adopted in the model and price–earnings ratio, a measure of relative valuation.

The Granger causality test reveals the presence of a bidirectional causal relationship between operating margin and the price–earnings ratio as the null hypothesis of the absence of Granger causality between the variables was rejected at the 5% level of signi¯cance. This indicates the presence of reverse causality between

Table 5. Descriptive statistics for S&P 500.

Obs. 97 97 97 97 99 97 99 97 97 97 97 97

Notes: ROA¼ return on assets; ROE ¼ return on equity; OPM ¼ operating margin; GROSSM ¼ gross margin; PE¼ price/earnings ratio; PB ¼ price/book-value ratio; EVS ¼ enterprises value- sales ratio; EVEB¼ enterprises value-EBITDA ratio; DIVY ¼ dividend yield; IND ¼ growth rate of industrial production (%); INF¼ inflation rate (%) and INT ¼ interest rate (%). Fundamentals are in % while relative valuations are expressed as times (xÞ except dividend yield DIVY which is in %.

Table 6. Unit root test of the variables.

Variables Level First di®erence

DIVY 2.922 8.469***

EVEB 2.856 10.346***

EVS 2.370 10.388***

GROSSM 2.424 10.403***

IND 13.732***

INF 4.612***

INT 2.828 5.384***

OPM 3.744**

PB 2.864 11.844***

PE 3.282* 8.921***

ROA 4.687***

ROE 4.552***

Notes: ***, ** and * indicate 1%, 5% and 10%

signi¯cant levels, respectively. ROA¼ return on assets; ROE¼ return on equity; OPM ¼ operating margin; GROSSM=gross margin;

PE¼ price–earnings ratio; PB ¼ price to book- value ratio; EVS¼ enterprises value-sales ratio; EVEB¼ enterprises value-EBITDA ratio;

DIVY¼ dividend yield; IND ¼ growth rate of industrial production; INF¼ inflation rate and INT¼ interest rate.

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Table7.Correlationmatrix. DIVYEVEBEVSGROSSMINDINFINTOPMPBPEROAROE DIVY1 EVEB0.584***1 EVS0.609***0.895***1 GROSSM0.0190.433***0.540***1 IND0.311***0.1370.0800.1481 INF0.269***0.282***0.0850.344***0.217**1 INT0.501***0.1040.0830.623***0.304***0.597***1 OPM0.0930.1430.376***0.587***0.0690.1000.497***1 PB0.878***0.722***0.796***0.0420.1330.189*0.412***0.0121 PE0.607***0.532***0.374***0.1460.1330.0040.406***0.652***0.612***1 ROA0.1230.1170.270***0.185*0.1380.0250.216**0.770***0.214**0.507***1 ROE0.0960.0750.308***0.259**0.1660.0330.233**0.805***0.214**0.539***0.967***1 Notes:***,**and*indicate1%,5%and10%signi¯cantlevels,respectively.ROA¼returnonassets;ROE¼returnonequity;OPM¼operating margin;GROSSM¼grossmargin;PE¼price–earningsratio;PB¼pricetobook-valueratio;EVS¼enterprisesvalue-salesratio;EVEB¼ enterprisesvalue-EBITDAratio;DIVY¼dividendyield;IND¼growthrateofindustrialproduction;INF¼inflationrateandINT¼interestrate.

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the variables. The results also reveal the lack of a causal relationship running from other fundamental variables to the price–earnings ratio.

This may suggest that these fundamentals do not a®ect price–earnings ratio independently, but alongside other controlled variables.

Granger causality test was also conducted on the relationship between the price– book value ratio (PB) and fundamental variables. The results, presented in Table6, detect a unidirectional causal relationship running from ROE to price-to-book value, among the four fundamental variables adopted. This also suggests that these fundamentals may not a®ect price-to-book value ratio independently but only when other variables are controlled, as we conjectured in the price–earnings ratio model.

Reverse causality was also detected as the hypothesis that the price to book value ratio does not Granger the operating margin (OPM) was rejected at the 5% level of signi¯cance.

The Granger causality test for the relationship between enterprises value-sales ratio (EVS) and fundamentals reveals the lack of a unidirectional causal relationship running from fundamentals to the EVS. Reverse causality was however detected as the null hypothesis that the EVS does not Granger cause OPM and GROSSM was rejected at the 5% level of signi¯cance, indicating the presence of unidirectional relationship °owing from the EVS to OPM and GROSSM rather than the other way round.

For the relationship between the enterprises value-EBITDA (EVEB) ratio and fundamentals, however, the Granger causality test presented in Table8detects several reserve causalities between GROSSM and EVEB as the null hypothesis of the absence of Granger causality between them was rejected at the 5% level of signi¯cance.

Finally, results of the Granger causality test for the relationship between fundamentals and dividend yield (DIVY) presented in Table 9 also detect reverse causality as DIVY Granger causes returns on asset (ROA) and operating margin (OPM), rather than the other way around. There was also no causal unidirectional relationship running from all fundamental variables to DIVY, an outcome similar to

Table 8. Granger causality test between price–earnings ratio (PE) and fundamentals.

Ho: Fundamentals do not Granger Granger cause price–earnings ratio

Ho: Price earnings ratio does not cause fundamentals

Lag Chi-sq Prob. Lag Chi-sq Prob.

2 ROE to PE 0.224952 0.8936 2 PE to ROE 1.857287 0.3951

2 ROA to PE 0.770691 0.6802 2 PE to ROA 1.888575 0.389

2 OPM to PE 9.071502 0.0107 2 PE to OPM 7.316438 0.0258

2 GROSSM to PE 0.531281 0.7667 2 PE to GROSSM 5.507337 0.0637 Notes: ROA¼ return on assets; ROE ¼ return on equity; OPM ¼ operating margin; GROSSM ¼ gross margin; PE¼ price–earnings ratio; PB ¼ price to book-value ratio; EVS ¼ enterprises value-sales ratio; EVEB¼ enterprises value-EBITDA ratio; DIVY ¼ dividend yield; IND ¼ growth rate of industrial production; INF¼ inflation rate and INT ¼ interest rate.

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the modal outcomes documented above for the majority of the relative valuation multiples.

It might appear that some of the variables for which there is no evidence of Granger causality should in fact not be cointegrated. While this is plausible, intro- ducing the macroeconomic factors into the system ensures that we can obtain cointegration, wherever it exists, even when Granger causality tests suggest that the other variables, excluding the macroeconomic factors, show no evidence of Granger causality. It therefore follows that the macroeconomic variables included in each system of non-Granger causing variables either Granger-cause or are Granger-caused by at least one of those variables in the system. This is an additional bene¯t of controlling for the macroeconomic factors.

In what follows, we include the fundamental variables separately in the ARDL model and add macroeconomic variables as controls. It is also worthy to note that by adopting the lagged values of valuation and fundamental variables, the ARDL model on its own helps to minimize issues from any reverse casuality.

3.4. The e®ect of fundamentals on relative valuation

Our estimation strategy involves including each fundamental variable separately into each relative valuation model, each time controlling for the macroeconomic

Table 10. Granger causality test between enterprises value-sales ratio (EVS) and fundamentals.

Ho: Fundamentals do not Granger cause enterprises value-sales ratio

Ho: Enterprises value-sales ratio does not Granger cause fundamentals

2 ROA to EVS 1.373059 0.5033 2 EVS to ROA 1.679235 0.4319

2 ROE to EVS 0.381788 0.8262 2 EVS to ROE 1.151497 0.5623

2 OPM to EVS 1.577797 0.4543 2 EVS to OPM 8.909914 0.0116

2 GROSSM to EVS 3.314514 0.1907 2 EVS to GROSSM 9.961313 0.0069 Table 9. Granger causality test between price–book value ratio (PB) and fundamentals.

Ho: Fundamentals do not Granger cause price–book value ratio

Ho:Price–book value ratio does not Granger cause fundamentals

2 ROA to PB 0.58187 0.7476 2 PB to ROA 4.878344 0.0872

2 ROE to PB 0.066834 0.9671 2 PB to ROE 3.879189 0.1438

2 OPM to PB 1.253192 0.5344 2 PB to OPM 7.46963 0.0239

2 GROSSM to PB 0.20531 0.9024 2 PB to GROSSM 0.620375 0.7333 Notes: ROA¼ return on assets; ROE ¼ return on equity; OPM ¼ operating margin; GROSSM ¼ gross margin; PE¼ price–earnings ratio; PB ¼ price to book-value ratio; EVS ¼ enterprises value- sales ratio; EVEB¼ enterprises value-EBITDA ratio; DIVY ¼ dividend yield; IND ¼ growth rate of industrial production; INF¼ inflation rate and INT ¼ interest rate.

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variables. This helps prevent issues of high multicollinearity among fundamentals and ensures we pass cointegration test, wherever cointegration exists.

The results are presented in Tables 10–20. Table10shows the empirical results for the global market (combination of developed and emerging markets). As shown in the results, the lagged values of the price–earnings ratio (PE) are statistically signi¯cant at the ¯rst and fourth lag for all models (model 1 which includes ROE, model 2 which includes ROA and model 3 which includes OPM and GROSSM). This reveals the importance of allowing for su±cient lags to capture the dynamic nature of relative valuation metrics that can be self-propagating. Our results reveal that the price–earnings ratio has a negative short-run relationship with its value in previous quarters. Speci¯cally, price-earnings in the immediate past quarter and up to fourth quarter negatively a®ect its present and future values. This is intuitive and consis- tent with the relative valuation cycle observed in the equities markets: previously overvalued markets, based on high relative valuation metrics, often experience a sell o®, correction or pro¯t taking, which causes prices to subsequently decline and lowers relative valuation ratios.

Looking at the e®ects of fundamentals, all variables, REO, ROA, OPM and GROSSM exert a signi¯cant impact on the price–earnings ratio, but at di®erent lag lengths. All macroeconomic factors adopted as controls, except for in°ation, also have a signi¯cant short-run relationship with the price–earnings ratio. More im- portantly, the view that fundamentals-valuation nexus is a short-run concept is refuted by our empirical results. Indeed, in all the three models of price–earnings ratio for the global market, we reject the hypothesis of the absence of long-run

Table 12. Granger causality test between dividend yield (DIVY) and fundamentals.

Ho: Fundamentals do not Granger cause dividend yield

Ho: Dividend yield does not Granger cause fundamentals

2 ROA to DIVY 0.857701 0.6513 2 DIVY to ROA 6.099255 0.0474

2 ROE to DIVY 0.403689 0.8172 2 DIVY to ROE 6.539273 0.4927

2 OPM to DIVY 2.568395 0.2769 2 DIVY to OPM 12.04187 0.0024

2 GROSSM to DIVY 0.396006 0.8204 2 DIVY to GROSSM 3.388226 0.1838 Table 11. Granger causality test between enterprises value-EBITDA (EVEB) ratio and fundamentals.

Ho: Fundamentals do not Granger cause enterprises value-sales ratio

Ho: Enterprises value-sales ratio does not Granger cause fundamentals

2 ROAto EVEB 4.267893 0.1184 2 EVEB to ROA 2.073867 0.3545

2 ROE to EVEB 2.204618 0.3321 2 EVEB to ROE 1.415744 0.4927

2 OPM to EVEB 5.432921 0.0661 2 EVEB to OPM 9.698258 0.0078

2 GROSSM to EVEB 6.776488 0.0338 2 EVEB to GROSSM 10.11038 0.0064

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Table13.Resultsfortheglobalmarket(PEmodel). (1)(2)(3) C10.2792***(2.491)9.724354***(2.594252)14.93383*(8.850763) lag(1)0.390303***(0.08516)0.370728***(0.083393)0.473601***(0.099644) lag(2)0.109619(0.099801)0.084204(0.100061) lag(3)0.04676(0.079276)0.031356*(0.081514) lag(4)0.23695***(0.078862)0.246168***(0.0033) ROE(1)1.12603***(0.240061) ROE(2)0.455128*(0.262013) ROE(3)0.466003**(0.208563) ROE(4)0.498313***(0.164536) ROA(1)7.155947***(1.608371) ROA(2)2.538182(1.78635) ROA(3)2.651708*(1.404639) ROA(4)3.563488***(1.133604) OPM1.133465***(0.39324) GROSSM(1)1.062213**(0.45011) GROSSM(2)0.763678*(0.446967) GROSSM(3)0.533331(0.434465) GROSSM(4)0.224988(0.430846) GROSSM(5)0.992966**(0.415398) GROSSM(6)0.44788(0.433022) GROSSM(7)0.682679(0.435576) GROSSM(8)0.820399*(0.422062) INT(1)1.365281***(0.345479)1.200122***(0.347166)1.175347***(0.377296) INT(2)0.480609(0.413957)0.312503(0.413525)0.203078(0.470358) INT(3)0.322475(0.424445)0.171229(0.416946)0.372009(0.460038) INT(4)0.952343**(0.385771)1.101182***(0.383528)0.401837(0.468419) INT(5)1.269211***(0.473933) INT(6)1.026563***(0.351865) INT(7)0.639671*(0.330812) IND(1)0.599321***(0.176437)0.587007***(0.177786)0.738414***(0.201057) IND(2)0.179358(0.255944)0.123276(0.242766)0.903043***(0.272525) IND(3)0.820165***(0.231165)0.783472***(0.219013)1.738896***(0.234364)

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Table13.(Continued) (1)(2)(3) IND(4)0.271421**(0.121924)0.264712**(0.124654)1.422988***(0.233359) IND(5)0.378357*(0.201864) INF0.899355*(0.514664) INF(1)0.118263(0.602662)0.001558(0.611885) ECM0.390303***(0.069098)0.370728***(0.066646)0.473601***(0.074128) Long-runresults ROE0.612664**(0.241114) ROA3.556019*(1.810945) OPM2.393292***(0.849143) GROSSM0.371386(0.601062) INT1.01299***(0.191155)1.051319***(0.191628)0.616824**(0.255842) IND2.430251***(0.879662)2.153929**(0.895746)4.161842**(1.628689) INF4.627291***(1.361411)5.208795***(1.361411)1.898974**(0.768241) C26.33647***(3.188368)26.33647***(3.188368)31.53252(18.92818) R20.7056360.695160.732475 DWStat2.156622.2405082.06695 Boundtest(F-Statcalc.)4.9631194.8132985.31673 Boundtest(F-Stat:Upperandlowerat5%)2.56and3.492.56and3.492.39and3.38 VIFtestYesYesYes Notes:1¼ROEincluded;2¼ROAincluded;3¼OPMandGROSSMincluded.***,**and*indicate1%,5%and10%signi¯cantlevels, respectively.

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Table14.Resultsfortheglobalmarket(PBmodel). (1)(2)(3) C0.271621**0.1178090.259987(0.161121)0.427126(0.716651) lag(1)0.178573***(0.050609)0.317517***(0.072962)0.404729***(0.125848) lag(2)0.256714***(0.078125)0.351394***(0.097091)0.267937***(0.087609) lag(3)0.1518*(0.081299)0.438098***(0.101582)0.277761***(0.092665) lag(4)0.29371***(0.098794)0.291315***(0.096894) lag(5)0.242358**(0.100857)0.026606(0.107731) lag(6)0.421299***(0.094789)0.313693***(0.100741) lag(7)0.056873(0.097997) lag(8)0.239078**(0.090439) ROE0.018185***(0.005977) ROA(1)0.331867***(0.120857) ROA(2)0.22425*(0.11778) OPM0.089248***(0.031326) GROSSM(1)0.102655**(0.039174) GROSSM(2)0.013681(0.038313) GROSSM(3)0.035782(0.036913) GROSSM(4)0.102047***(0.037106) GROSSM(5)0.064505*(0.033944) GROSSM(6)0.028048(0.039216) GROSSM(7)0.001623(0.037853) GROSSM(8)0.098274***(0.034835) INT(1)0.097339***(0.02227)0.10782***(0.027323)0.108816***(0.031118) INT(2)0.008596(0.036795)0.016962(0.044092) INT(3)0.017149(0.035173)0.050397(0.04224) INT(4)0.026779(0.036)0.109373**(0.042279) INT(5)0.142129***(0.035397)0.089169**(0.041481) INT(6)0.012369(0.035387)0.062757(0.03767) INT(7)0.089655***(0.031003) IND(1)0.009493(0.00995)0.036797**(0.014255)0.024504(0.015253) IND(2)0.025676***(0.006941)0.082877***(0.028209)0.05061(0.037118) IND(3)0.129255***(0.025872)0.087246**(0.033127) IND(4)0.1102188**(0.023252)0.069787**(0.029506)