WORKING PAPER

Explaining International Equity Valuation Ratios: The Role of

Commodity Price Inflation and Relative Asset Volatilities

Andrew Clare, Owain ap Gwilym,

James Seaton &

Stephen Thomas

June 2009

ISSN

Centre for Asset Management Research Cass Business School

City University 106 Bunhill Row London

EC1Y 8TZ UNITED KINGDOM

http://www.cass.city.ac.uk/camr/index

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Explaining International Equity Valuation Ratios: The Role of Commodity Price Inflation and

Relative Asset Volatilities

Andrew Clare,

Owain ap Gwilym,

James Seaton

&

Stephen Thomas1

6th June 2009

Abstract

This paper investigates factors that have influenced stock market valuations across a

number of international markets. Previous studies have found that factors such as long bond

rates and stock and bond volatilities have been able to describe how investors have

historically set equity multiples in the US. We find that these variables do not apply to non-

US markets but that the relative rates of input and consumer inflation are important in

explaining stock valuations internationally. A positive relationship is observed between the

PPI/CPI ratio and stock yields which we conjecture reflects investors’ concerns that rising

commodity prices will manifest in reduced future profitability for companies and lower returns

for equities. We observe that the PPI/CPI ratio is more convincing internationally at

explaining equity valuations compared to the stock and bond volatility approach that has

proved successful in the US. Indeed we also posit that the unprecedented P/E ratios seen

globally around the end of the twentieth century can be attributed in part to the extremely

depressed real price of commodities at that time.

1 Corresponding author Tel: +44 1248 382176 Fax: +44 1248 383228 e-mail: stephen.thomas.1@city.ac.uk

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Introduction

Between 1982 and 2001, the earnings yield of the S&P 500 fell from 12.4% to 4%; this

move explained about 6 percentage points of the 15.5% realized annual return over that

period (Ilmanen, 2003). We believe that explaining valuation multiples is a key and relatively

neglected component of understanding the generation and forecasting of returns. This paper

seeks to explain the evolution of both dividend and earnings yields for a range of

international markets.

Influential papers by Asness (2000; 2003) have provided an extensive discussion of the

history of stock and bond returns and associated valuation metrics in the US over the last

130 years. It is demonstrated that the experience of the last 40 years where earnings yields

and the 10-year Treasury bond yields have been highly correlated was not present during the

first half of the 20th century. Indeed, for a large portion of the earlier period, the dividend yield

was in excess of the bond yield, and was much more volatile than in the second half of the

century. Asness (2000) therefore argues that additional variables are required to explain the

relationship between stocks and bonds, and in a simple but persuasive model the volatilities

of stocks and bonds are introduced as a proxy for their relative risk. This adds significantly to

the explanatory power of a simple valuation model containing nominal interest rates. The

model provides insights as to how stock yields have been set historically and offers a useful

explanation of some of the features of the late 1990’s, such as high valuation multiples. The

use of twenty-year rolling annualised volatility also captures the idea of ‘generational

memory’ in the attitudes of investors to the risk of equities versus bonds (see Campbell and

Shiller, 1998, and Glassman and Hassett, 1999). Further study showed that at the beginning

of the 20th century, stocks were considerably riskier than bonds (using a volatility measure)

and that investors demanded a greater risk premium during this period. As the century

progressed, stock volatility decreased markedly whilst bond volatility increased and thus

investors required a lower risk premium for holding equities.

In addition to stock and bond volatilities, inflation has also been an important factor in how

investors have set aggregate market valuations. The 1970s saw price-earnings ratios in the

US collapse during a period when inflation rose markedly. Modigliani and Cohn (1979)

argued that this inflation caused investors to make two errors. Firstly they capitalized equity

earnings using a nominal interest rate as opposed to a real one, and secondly they failed to

allow for the benefit of seeing nominal corporate liabilities depreciated in real terms. Ritter

and Warr (2002) also find support for this “money illusion” hypothesis whilst Sharpe (2002)

reports that periods of high inflation have been historically consistent with high long-term real

equity returns.

The problem for international investors is that much of the work on explaining market

valuation multiples has been US based. Dimson et al (2006) emphasise how much research

has focussed on US data with respect to the equity risk premium, in large part, due to the

availability of data. They question whether US findings carry over to other countries,

particularly given the superior performance of this economy and thus its status as a relative

outlier. Whilst some of these findings have subsequently been confirmed internationally2,

given the phenomenal performance of the US economy and stock market during the last

century it is likely that not all of the observed relationships are transferable globally. In

particular we extend the role played by inflation in the setting of stock yields by introducing

the relative effects of producer and consumer price inflation. We also re-examine Asness’

(2000) key finding for a range of international developed markets and report a number of

important results which suggest that US findings often do not apply to other markets.

We find:

i) Similar to Asness (2000), correlations between stock valuation metrics, such as

dividend yields and earnings yields, and long-term bond yields are both positive

and high in most countries from 1965 onwards.

ii) The ratio between the Commodity Research Bureau (CRB) Index and consumer

price inflation is positively related to both earnings and dividend yields in the

United States. It is also statistically significant and able to explain a considerable

amount of the variation in these series, particularly with respect to the

extraordinarily high valuations around the late 1990s. The recent commodity

shock is also consistent with the lower valuations accorded to US equities.

iii) The ratio between producer price inflation (PPI) and consumer price inflation

(CPI) is also positively related to both earnings and dividend yields in the United

States and also in the majority of the seven other international markets we

consider.

2 For example, Fama and French (1998) show that value and growth are international effects.

4

iv) Past stock and bond return volatilities are very useful for explaining US 20th

century equity valuations but this does not apply to other international markets.

We find that the PPI/CPI ratio is a more important variable for explaining stock

yields internationally, including the US.

Data and Methodology This study uses a sample of eight countries, namely the US, the UK, France, Germany,

Switzerland, Japan, Canada and the Netherlands. For the US, the S&P 500 index is used as

an aggregate equity market index. A total market index is chosen as an aggregate equity

market measure for the remaining countries, except for Germany. For Germany, the DAX 30

Index is used because the total market index series was incomplete. The data series range

from January 1965 to June 2008 for the US and UK and from January 1973 to June 2008 for

the remaining markets. All of the equity data, along with CPI, PPI, CRB and bond values, are

obtained from Datastream. Both dividend yield and earnings yield values are calculated on a

twelve-month trailing basis. All data is for local markets and calculated using local currency.

The nominal bond yield used is a long-term government bond yield. Throughout the paper,

all regressions containing overlapping observations are adjusted using the Newey and West

(1987) correction.

The Relationship between Bond Yields and Equity Valuations

The notion that stock valuations should be linked to bond yields seems intuitively correct

when one thinks that a stock price should reflect all the future expected discounted cash

flows. Asness (2003) argues, however, that whilst an increase in the discount rate reduces

the present value of future profits this is only true assuming all other factors remain constant.

If inflation also increases contemporaneously then future nominal expected cash flows

should increase accordingly. This effect acts in the opposite direction to the higher interest

rate. If these two effects are offsetting then a higher bond yield should not rationally lead to

lower stock valuations.

We firstly consider the relationship between stocks and bonds by examining the

correlations between yields during the various study periods. Panels A and B of Table 1

show that bond yields were strongly positively correlated with both dividend and earnings

yields for the latter part of the 20th century. The correlations for international markets are

generally similar to those observed for the US although Switzerland is a notable exception

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with respect to the dividend yield correlation, while Germany is much lower for the earnings

yield figure, at 0.27. Germany has the lowest correlation between earnings yield and bond

yields by quite some way, though this is not the case for dividend yields and bond yields. The

tendency for German (and Swiss) firms to payout relatively little of their earnings in the form

of dividends, and for the proportion to be more variable than for other countries lead to this

result (see Panel C of Table 1)3. Otherwise, the evidence on the correlation between both

dividend and earnings yield with the bond yield is surprisingly consistent despite the very

different inflation experiences and corporate structures in these countries. For example,

dividend yields only averaged 1.22% in Japan but 4.30% in the UK. The Granger-Causality

tests suggest that changes in long bond yields typically cause variation in stock yields rather

than vice versa. Table 2 reports the relationship between stocks and bonds in the form of regression

equations. Panel A shows that bond yields in the UK and US are highly statistically

significant and explain over 55% of the variation in earnings yields for 1965-2008. Panel B

confirms these findings for all international markets, with bond yields typically explaining a

considerable portion of the earnings yield variation with the exception of Germany (which is

consistent with the low correlation in Table 1). In all cases the coefficients are positive.

Panels C and D report similar findings when the dependent variable is dividend yield. The

explanatory power of the regressions is typically slightly higher than the comparable earnings

yield equations, though Switzerland is a clear outlier here.

Stock Valuations and Inflation

(a) The impact of inflation on nominal dividend and earnings growth

We now consider the role played by inflation (and indirectly inflation expectations) in the

setting of stock market valuations. If inflation does lead to a requirement for higher nominal

expected returns in order to maintain expected real returns, then stock valuations by

conventional metrics need not decline as long as the expected growth of dividends and

earnings increases by a commensurate amount. For the US between 1926 and 2001,

Asness (2003) finds that on average 94% of decade-long inflation manifested itself in

nominal earnings growth, suggesting that real earnings growth is somewhat insensitive to

inflation rates. Despite this, there are some reasons why inflation could influence market

valuation. Perhaps the most obvious is that investors pay capital gains tax on nominal 3 For further discussion on international payout ratios see ap Gwilym et al (2006).

6

returns as opposed to real returns. Thus, when inflation rates are high, equities may be

priced slightly lower than otherwise expected in order to achieve the same post-tax real

returns as in lower inflation times. In addition, periods of extreme inflation (and deflation)

have been accompanied by considerable uncertainty (e.g. the UK in the late 1970’s) that

may reasonably make investors demand higher expected returns to compensate for

increased perceived risks. Accounting items can also be affected by inflation but these may

have offsetting impacts; for example, in high inflationary times the depreciation charge

reflects historical costs and fails to accurately represent the replacement cost of items whilst,

on the other hand, earnings fail to represent the gain that shareholders accrue from long-

term nominal liabilities being eroded by inflation.

Table 3 reports the impact of inflation on concurrent nominal earnings and dividend growth.

Panel A of Table 3 reports the relationship between 10-year earnings growth and inflation.

The amount of US inflation passing through to earnings growth is not especially high with a

rate of just 28%. This is consistent with Asness’ (2003) observation that the relationship

between earnings growth and inflation is much weaker in recent years. However, the

relationship is far stronger in the UK. Panel B confirms these findings for the US and UK

using 5-year data. France also demonstrates a significant positive coefficient for the

relationship between inflation and earnings. Germany, Switzerland and Canada have

negative coefficients, however, and one may conjecture that low inflation and low and

variable payout ratios lead to different findings: for example, in Germany the payout ratio was

66% in 1973 but only 22% in 2004.

Panel C displays 10-year dividend growth explained by 10-year inflation. Both the US and

UK have about 60% of inflation showing in dividend growth, with reasonable explanatory

power. Panel D shows the 5-year dividend growth for all markets using 5-year inflation as the

explanatory variable. The results for the US and UK confirm the findings in Panel C, and

France again has a significant positive coefficient. Rather surprisingly, Germany, Switzerland

and Netherlands have negative inflation coefficients. Given that these countries have some

of the lowest average inflation rates post-1970 in our sample, one may conjecture that low

inflation leads to reduced concern with maintaining real dividend growth and/or that these

countries have less of a dividend “culture”, as reflected certainly in the case of Germany and

Switzerland having relatively low payout ratios (Panel C of Table 1).

It might be reasonable to expect that inflation has not manifested in dividend growth in

recent years as firms have moved to share repurchases as a method of returning cash to

shareholders. Grullon and Michaely (2002) report how US buyback growth has considerably

7

outpaced dividend growth in the last two decades. Share repurchases, however, are

generally less well established in other international markets: indeed they only became legal

in the UK in the mid-1980s with at least another decade passing before they represented a

significant distribution channel (see Oswald and Young, 2004, for more detail). Lasfer (2001)

studies European repurchases between 1985 and 1998, and finds that the UK has the

majority of the activity. Given that this was low compared to the US, it suggests very low

levels in Continental Europe. Von Eije and Megginson (2008) report that large scale share

repurchases started much later in Europe than the US, although they have grown more

rapidly in recent years. Therefore, share buybacks are unlikely to have affected dividend

growth materially for all but the last few years outside of the US.

(b) Input Prices, Inflation and Stock Yields

It is long established that rising inflation has not been a favourable environment for

investing in equities (see Lintner, 1975, and Bodie, 1976, for examples4). Both Modigliani

and Cohn (1979) and Ritter and Warr (2002) argue that this is due to investors being

seduced by “money illusion” and accordingly misvaluing stocks. History is replete with

examples of the same mistake being made on multiple occasions, for example the continued

existence of Ponzi schemes, and thus there is no guarantee that should high inflation

reappear in the United States that investors, in aggregate, will not react in the same fashion

gain.

in the US by studying how the ratio of the

RB index to CPI affects stock valuation ratios.

a

Gorton and Rouwenhorst (2006) demonstrate that between 1959 and 2004 stocks were

negatively correlated with inflation, unexpected inflation and changes in expected inflation.

They also report that, apart from very short time periods, stocks have been negatively

correlated with commodities. Perhaps the problem for stocks when commodities rise is that

firms struggle to pass on the additional costs in the price of finished goods and services?

Even basic industry firms such as copper producers are affected when the price of oil rises

as energy is a major component in the total cost of extracting the base metal. Given that

most developed markets are less geared to primary goods and far more heavily weighted

towards higher goods and services, it is perhaps not entirely surprising that rising basic input

prices are a negative factor. We investigate this

C

4 More recent examples are, “The ShortView”, Financial Times, 13th August 2008, and “Are Equities a Shelter in Inflationary Times”, Financial Times, 1st September 2008.

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Table 4 shows that CRB/CPI explains a substantial portion of the variation in both the US

earnings and dividend yields. The statistical significance of the results remains largely

unchanged when the long bond is introduced as an additional explanatory variable (while the

adjusted-R2 increases to around 80% in both cases). We also observe no issue of

multicollinearity between the long bond and CRB/CPI with a variance inflation factor (VIF) of

just 1.1. The positive relationship between CRB/CPI and stock yields suggests that, when

commodity prices are rising faster than they can be passed on to consumers, investors

accord equities lower valuations (albeit possibly erroneously) in anticipation of shrinking

margins and profits. Figure 1 provides a visual description of the relationship (for ease of

viewing the ratios are reversed, i.e. CPI/CRB and price-earnings ratio) and shows how the

extended valuations of the turn of the century are almost perfectly described by the relative

rates of commodity and consumer prices. It has often been stated that the high P/E paid by

investors around the turn of the millennium was due to over optimism about the benefits of

technological advances, in particular the internet. Whilst this may be true, perhaps one

equally significant factor was the extremely depressed price of energy as evidenced by oil

prices that were sub-$12/barrel during 1998-99, and in inflation adjusted terms over 80%

below the peak seen in 1980 (see CRB Encyclopedia of Commodity and Financial Prices,

2006, for more details). Indeed Faber (2002) observed that, “never in the history of capitalism

have commodities been as inexpensive compared to the CPI or financial assets as they are

now”. It is also of relevance that the surge in commodity prices in the last few years has

aused the CPI/CRB ratio to decline markedly. This has coincided to a large extent with the c

multiple contraction experienced by the S&P 500.

We further investigate the importance of the relative rates of input and consumer inflation

by considering it in an international context. To accomplish this, we investigate to what extent

the ratio of PPI/CPI can explain stock yields, across eight countries. If the US market

behaviour (for CRB/CPI) were repeated in the other markets we would expect to see PPI/CPI

being positively correlated with stock yields. For earnings yields, Table 5 reports the results

of regressions using the long bond and PPI/CPI as explanatory variables. Panel A shows

that during 1965-2008, PPI/CPI has a significant positive relationship with US earnings

yields, explaining over half the variation. Explanatory power is enhanced further when the

long bond is also included in the equation. A similar pattern emerges in the UK, although with

less explanatory power. Panel B reports the findings over the period 1973-2008 for all eight

countries. Once again PPI/CPI is an important variable for explaining both US and UK

earnings yields. All eight countries demonstrate a statistically significant relationship between

earnings yield and PPI/CPI when the latter is the only explanatory variable (but the sign is

negative for Germany). However, the signs of the PPI/CPI coefficients become negative and

9

insignificant for the UK and France when the long bond is introduced as an additional

variable. In contrast, PPI/CPI dominates the long bond in Germany, Switzerland and

anada.5 From Table 2 it can be observed that the long bond was a statistically significant

gh it generally remains an important factor in the other countries.

hus far, the evidence supports the notion that relative rates of inflation are important in

were

schewed in favour of potential capital gains. It is suggested that this may explain the demise

I in case

e former already captures a significant part of the latter. Following the method of Asness

(2000) we estimate Equations 1-4 fo ternational markets in our sample:

C

factor in these countries.

Table 6 reports the same set of regressions as Table 5 but with dividend yield as the

dependent variable. The results are largely comparable to the earnings yield findings. When

PPI/CPI is used as a single independent variable it is significantly positively related to

dividend yield for all countries. The inclusion of the long bond sees PPI/CPI lose its positive

statistical significance in France and the UK (for the shorter period only, and the coefficient

becomes negative) althou

T

determining stock yields.

(c) Inflation and Stock and Bond Volatilities As discussed earlier, Asness (2000; 2003) observed that whilst stock yields could be

explained largely by nominal bond yields in the latter part of the 20th century this was not the

case in the earlier part, when a negative correlation existed. It is suggested that investors’

attitudes towards stocks and bonds are shaped by their previous experiences. Asness (2003)

models this with considerable success by using the rolling 20-year volatilities of those asset

classes to represent risk and finds that his conclusions remain robust. The notion of

investors’ recent experiences shaping their expectations of the future is also proposed by

Bernstein (2005) who suggests that after the Crash of 1929 investors looked very favourably

on dividends for a relatively safe portion of return. By the late 1990s a high proportion of

investment professionals had only witnessed bullish markets for equities, and dividends

e

of US dividend paying firms highlighted by, amongst others, Fama and French (2001).

Given the success of Asness (2000; 2003) in explaining multiples using stock and bond

volatilities, it seems sensible to incorporate these into any model containing PPI/CP

th

r the eight in

5 We find no major problems with multicollinearity in these equations. All VIFs are 4.3 or below, with the exception of Japan which is 5.9. Whilst there is no absolute value at which a VIF indicates multicollinearity being an issue, we use a ‘rule of thumb’ of anything less than 10 being acceptable.

10

LBST dcbLBaEY σσ +++= Equation 1

)/( LBSTcbLBaEY σσ++= Equation 2

LBST edCPIcPPIbLBaEY σσ ++++= / Equation 3

)/(/ LBSTdCPIcPPIbLBaEY σσ+++= Equation 4

where EY is the earnings yield, LB is the yield on the long bond, PPI/CPI is the ratio of

roducer to consumer price inflation and σST and σLB are the volatilities of stocks and bonds

variable does not affect the signs and

ignificance of the volatility variables. PPI/CPI has negative coefficients, but is only

. Amongst

p

respectively. Given our shorter data periods we use 5- and 10-year volatilities.

Table 7 reports the findings of explaining earnings yields using nominal bond yields,

PPI/CPI and stock and bond volatilities. Panel A exhibits the findings using 10-year

volatilities over the period 1975-2008. We observe that the US results confirm the findings of

Asness (2000) with the earnings yield being positively related to stock volatility, negatively

related to bond volatility and positively related to the ratio of stock to bond volatility. This also

seems intuitively correct since when stocks are more volatile (risky) investors require a

greater return and when a competing asset class like bonds is more volatile, stocks become

relatively more appealing and thus a lower return is demanded. Combining the two, an

increase in the stock/bond volatility ratio should lead to higher earnings yields. The UK

results also offer support to this intuitive explanation. Both stock and bond volatility in

Equation 1 have the expected coefficient signs, but the latter is not significant. The

stock/bond volatility ratio has the expected significant positive coefficient. When PPI/CPI is

introduced in Equations 3 and 4 it is a very influential variable in the US case. All other

explanatory variables, including long bond, lose their statistical significance. For the UK case,

the introduction of PPI/CPI as an explanatory

s

statistically significant in Equation 3.

Panel B displays the results for all eight countries during the period 1978-2008 using five-

year volatilities. In Equations 1 and 2 it is noticeable that only the US, France and Canada

have the expected combination of positive σST and negative σLB coefficients, and these are

insignificant. France and Canada are the only countries where σST/σLB is positive and

statistically significant. When PPI/CPI is introduced as an additional explanatory variable in

the US, it again dominates not only the volatility variables, but also the long bond

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the other countries, the PPI/CPI coefficient is positive and significant for all except the UK

explanatory

ariables retain their significance. For the UK, all volatility coefficients are insignificant in

of multicollinearity being present in Equation 3 for Japan with VIFs of

0.9 for the LB variable and 15.6 for PPI/CPI. In all other countries, however, there is no VIF

domestic bond/equity volatility relationship whilst other

ountries that have possibly been more open to international diversification fail to

and France. In many cases, it dominates the long bond and volatility coefficients.

Table 8 reports the findings of estimating similar regressions but with dividend yield as the

dependent variable. Panel A again reports results for the 1975-2008 period using 10-year

volatilities. For the US, in Equations 1 and 2 the volatility coefficients are strongly significant

and of the expected sign, consistent with Asness (2000). The inclusion of PPI/CPI sees its

coefficient once again both positive and significant, but unlike Table 7 the other

v

Panel A. The PPI/CPI coefficient is again negative but now strongly significant.

Panel B reports results for 1978-2008 using 5-year volatilities. The US and UK results are

consistent with Panel A. Apart from the US, Canada is the only other case where the pattern

of stock and bond volatilities observed by Asness (2000) is supported. PPI/CPI is positive

and significant in six cases, with the UK and France again being the exceptions. We do

observe some evidence

1

value greater than 6.7.

As a possible explanation for the lack of confirmation of previous US findings, perhaps the

assumption that when domestic bonds are more volatile, domestic equities become more

attractive and thus command higher valuations fails to hold true in globalized markets. If

investors dislike the volatility profile of local bonds it is now far easier than in the past to

invest in other international bonds that may have more agreeable volatilities (or alternative

asset classes such as hedge funds or private equity), rather than simply allocate more capital

to domestic equities thus bidding prices higher. This explanation has the appeal that North

America, which has traditionally been regarded as somewhat sceptical of overseas asset

allocation conforms to the expected

c

demonstrate the same relationship.

An alternative potential explanation for the lack of consistency in the volatility variables,

although one that fails to adequately describe the differences between the US experience

and the rest of the world, is that volatility in itself is not the only issue. From a behavioural

perspective, perhaps investors are willing to accept volatility as long as they are invested in

an asset class that is generally rising with the prospect of more gains to come, particularly

when returns from alternative asset classes are declining. It would seem somewhat illogical

12

to switch out of say higher volatility equities and into lower volatility bonds if investors

o low in a period of high inflation as described by Modigliani and Cohn

979), the reverse was true at the turn of the century due to the extremely depressed real

odities.

n. Whilst this is valid it does appear that dividend and earnings

rowth internationally has failed to keep pace with inflation in the same way that Asness

believed the former had a positive expected return and the latter a negative expected return.

Overall, we conclude that input inflation in excess of consumer inflation has historically

been negative for stock valuations across a number of developed international markets. We

find this to remain true even when stock and bond volatilities are accounted for, which

Asness (2000) has shown to be able to explain US stock yields. This has implications for the

effectiveness of equities as a hedge against inflation. Stock valuations appear to be able to

cope with inflation as long as companies are able to pass their rising costs on to consumers.

If companies have to absorb cost pressure themselves then investors view this as a negative

and stock yields rise accordingly. On a slightly different tack, it perhaps should be of some

concern that investors have priced stocks so expensively when input costs were at historic

lows compared to consumer prices. If one believes in mean reversion, there should be a

contraction of multiples at such extremes to take account of the PPI/CPI ratio moving back to

historic levels. Grantham (2008) observes that the correlation in the US between P/Es and

profit margins is +0.32 and suggests that this does not even have the correct sign. Arguably

if stocks were priced to

(1

price of comm

Conclusion The focus of this paper has been very much on the determination of valuation metrics.

Prior research on the US market has highlighted how, despite sound economic reasons not

to, investors have in the past forty years set stock market valuations largely based on

nominal long-term interest rates. In this paper we have investigated whether this is a US

specific investor response by examining a number of additional international markets. We

observe that correlations between stock and bond yields internationally have been

consistently high from 1965 onwards with the latter explaining a significant amount of the

former. In the past investors have been criticised for setting market valuations too low when

there has been high inflatio

g

(2003) observes in the US.

We find that a considerable portion of the variation in US stock yields can be explained by

the ratio of the CRB Index to CPI. The positive relationship indicates that investors reduce

the multiple they are willing to pay for equities when the prices of inputs are rising faster than

13

they can be passed on to consumers, possibly in anticipation of lower future profits. We do

not argue that investors were correct in following this pattern, indeed they may have been

suffering from money illusion as first described by Modigliani and Cohn (1979), but instead

observe that this is what actually occurred. The statistical significance of the CRB/CPI ratio in

xplaining both earnings and dividend yields is not diminished when the long bond is

d in over half of the countries studied. A similar pattern emerges when dividend

ields are explained, although the evidence is again somewhat weaker for the UK and

rates of input and consumer inflation is an important factor in explaining how

stocks have historically been priced internationally, and is more important than asset

volatilities.

e

included as an additional explanatory variable.

We extend the analysis to an international context by considering how the relative rates of

PPI and CPI affect stock valuations across eight countries. The PPI/CPI ratio is found to be

positively related and statistically significant in explaining earnings yields in all countries

when used as the only explanatory variable. When the long bond was also included in the

regression equations the significant positive relationship was maintained in all markets

except the UK and France. Indeed we find the PPI/CPI ratio to be more important than the

long bon

y

France.

Asness (2000) demonstrates that within the US a considerable improvement on just using

nominal yields to explain equity market valuations can be made by including the rolling

volatility of stocks and bonds. International evidence fails to provide clear support for this

finding. Despite our use of shorter volatility periods we still report similar results for the US

market but find very little confirmation for non-US markets. Including volatilities in the

valuation models generally improves the explanatory power compared to nominal yields

alone but the relationships fail to conform to the expected pattern. We also include the

PPI/CPI ratio in these regressions, observing that in the US much of the significance of stock

and bond volatilities disappears when explaining earnings yields. Volatilities appear to be

more important in the US when measured over longer periods, consistent with Bernstein

(2005) who argues that investors’ expectations are shaped over long time frames. We find

that after the inclusion of stock volatilities PPI/CPI still has a positive relation with earnings

yield across seven of the eight countries considered and that in the majority of cases this is

significant. A similar pattern is observed when dividend yield is explained although the

positive PPI/CPI relationship is not found in France and the UK. Overall, we conclude that

the relative

14

15

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17

18

Table 1 Summary Statistics for Earnings, Dividend and Long Bond Yields

Earnings Yield & Bond Yield Dividend Yield & Bond Yield Correlation F-Stat

(1) F-Stat

(2) Correlation F-Stat

(1) F-Stat

(2) A. 1965-2008 United States +0.75 3.85** 13.46** +0.80 3.05* 16.70** United Kingdom +0.74 0.38 10.85** +0.74 0.83 12.31** B. 1973-2008 United States +0.76 3.25** 10.87** +0.84 3.17** 13.81** United Kingdom +0.77 1.51 5.57** +0.86 0.38 9.17** France +0.73 2.07* 9.84** +0.78 1.23 12.23** Germany +0.27 2.96* 2.44* +0.68 3.12** 1.50 Switzerland +0.58 1.63 2.00 +0.43 2.83* 3.90** Japan +0.66 0.36 1.75 +0.68 1.26 1.47 Canada +0.58 2.07 10.27** +0.75 1.17 15.43** Netherlands +0.71 2.90* 2.59* +0.80 1.17 3.00* Average Earnings Yield Average Dividend

Yield Average Payout

Ratio C. 1973-2008 United States 6.84% 3.19% 47.2% United Kingdom 8.69% 4.30% 52.4% France 8.37% 3.72% 44.7% Germany 7.28% 2.71% 37.1% Switzerland 7.78% 2.12% 27.6% Japan 3.21% 1.22% 37.9% Canada 7.36% 3.05% 42.7% Netherlands 9.47% 4.26% 46.5% N.B. F-Statistics are for Granger causality tests using 5 lags. (1) tests for stock yields Granger-causing long bond yields and (2) tests for long bond yields Granger-causing stock yields. * significant at the 95% level ** significant at the 99% level

Table 2 Regression Equations using Long Bond Yields to Explain Stock Yields

Constant Bond Yield Adjusted R2 A. Earnings Yield 1965-2008 US 0.006

(1.36) 0.838

(12.54) 56.0%

UK 0.006 (0.66)

0.851 (7.16)

55.4%

B. Earnings Yield 1973-2008 US 0.002

(0.38) 0.883

(12.66) 57.3%

UK 0.007 (0.71)

0.867 (7.35)

59.3%

France 0.035 (8.36)

0.594 (11.90)

53.8%

Germany 0.058 (8.32)

0.230 (2.33)

7.1%

Switzerland 0.028 (3.46)

1.151 (5.98)

33.8%

Japan 0.016 (7.06)

0.339 (8.22)

45.6%

Canada 0.025 (5.05)

0.575 (8.76)

33.3%

Netherlands -0.002 (-0.21)

1.398 (8.22)

51.0%

C. Dividend Yield 1965-2008 US 0.003

(1.34) 0.403

(14.59) 63.1%

UK 0.018 (6.64)

0.276 (9.28)

54.1%

D. Dividend Yield 1973-2008 US -0.002

(-0.75) 0.444

(15.82) 69.8%

UK 0.015 (6.30)

0.308 (11.24)

73.8%

France 0.011 (4.30)

0.325 (10.65)

60.1%

Germany 0.007 (2.56)

0.314 (7.98)

43.1%

Switzerland 0.011 (5.27)

0.230 (4.51)

18.5%

Japan 0.005 (7.00)

0.142 (7.92)

43.5%

Canada 0.007 (3.29)

0.282 (12.49)

55.7%

Netherlands 0.002 (0.65)

0.582 (12.64)

63.4%

19

Table 3 The Effect of Inflation on Nominal Dividend and Earnings Growth

Constant Average Inflation Adjusted R2 A. 10–year Earnings Growth 1965-2008 (Monthly) US 0.052

(7.75) 0.279 (2.25)

5.7%

UK 0.032 (11.33)

0.873 (23.41)

82.5%

B. 5–year Earnings Growth 1973-2008 (Monthly) US 0.063

(3.16) 0.171 (0.59)

0.0%

UK 0.045 (4.59)

0.672 (5.65)

29.7%

France 0.076 (6.30)

0.605 (2.69)

10.0%

Germany 0.134 (9.27)

-2.410 (-5.26)

26.7%

Switzerland 0.104 (6.29)

-1.643 (-3.31)

12.9%

Japan 0.040 (2.92)

0.052 (0.20)

-0.2%

Canada 0.091 (4.45)

-0.277 (-0.65)

0.5%

Netherlands 0.064 (6.07)

0.313 (1.03)

1.2%

C. 10–year Dividend Growth 1965-2008 (Monthly) US 0.028

(8.08) 0.589 (9.94)

44.0%

UK 0.041 (6.17)

0.659 (8.40)

37.0%

D. 5-year Dividend Growth 1973-2008 (Monthly) US 0.029

(3.90) 0.746 (6.71)

27.8%

UK 0.030 (3.51)

0.961 (7.94)

51.9%

France 0.073 (9.89)

0.482 (3.83)

15.2%

Germany 0.112 (8.27)

-2.427 (-7.03)

34.1%

Switzerland 0.106 (6.68)

-1.502 (-3.21)

14.0%

Japan 0.028 (2.83)

0.087 (0.47)

-0.0%

Canada 0.065 (5.24)

0.073 (0.33)

-0.1%

Netherlands 0.077 (12.47)

-0.330 (-2.65)

3.5%

20

Table 4 Explaining US Stock Yields using Long Interest Rates and the Ratio of the CRB Index to CPI

Constant Long Bond CRB/CPI Adjusted-R2 A. 1965-2008 US Earnings Yield 0.015

(3.12) - 0.013

(8.80) 48.7%

US Earnings Yield -0.017 (-3.92)

0.646 (11.06)

0.009 (8.63)

78.2%

US Dividend Yield 0.009 (3.60)

-

0.006 (8.89)

47.3%

US Dividend Yield -0.007 (-3.61)

0.321 (14.13)

0.004 (8.76)

82.8%

21

Table 5 Explaining International Earnings Yields using Long Interest Rates and the Ratio of the PPI to CPI

Constant Long Bond PPI/CPI Adjusted-R2 A. Earnings Yield (1965-2008) US -0.107

(-6.43) - 0.149

(9.55) 52.0%

US -0.088 (-6.88)

0.585 (9.35)

0.097 (7.89)

73.0%

UK -0.155 (-3.66)

- 0.218 (5.36)

22.5%

UK 0.054 (1.46)

0.942 (5.86)

-0.052 (-1.22)

55.9%

B. Earnings Yield (1973-2008) US -0.163

(-11.79) - 0.203

(15.69) 79.0%

US -0.140 (-8.73)

0.264 (2.82)

0.165 (8.77)

81.3%

UK -0.233 (-4.79)

- 0.297 (6.36)

38.2%

UK 0.107 (1.91)

1.098 (4.95)

-0.113 (-1.68)

60.5%

France 0.015 (0.71)

- 0.057 (2.92)

19.2%

France 0.051 (3.20)

0.681 (8.10)

-0.020 (-1.06)

54.8%

Germany -0.009 (-0.40)

- -0.074 (3.77)

17.3%

Germany -0.030 (-1.40)

-0.172 (-1.37)

0.103 (4.57)

18.5%

Switzerland -0.063 (-6.52)

- 0.116 (13.74)

78.6%

Switzerland -0.063 (-6.66)

0.065 (0.64)

0.114 (14.15)

78.6%

Japan -0.031 (-6.24)

- 0.052 (13.83)

64.8%

Japan -0.047 (-6.20)

-0.171 (-2.47)

0.072 (8.27)

66.7%

Canada -0.194 (-7.04)

- 0.262 (9.42)

55.2%

Canada -0.173 (-4.77)

0.124 (1.21)

0.231 (5.41)

55.9%

Netherlands -0.151 (-5.99)

- 0.220 (9.09)

60.8%

Netherlands -0.121 (-4.49)

0.501 (2.13)

0.163 (4.73)

63.2%

22

Table 6 Explaining International Dividend Yields using Long Interest Rates and the Ratio of the PPI to CPI

Constant Long Bond PPI/CPI Adjusted-R2 A. Dividend Yield (1965-2008) US -0.056

(-8.86) - 0.075

(12.91) 64.7%

US -0.047 (-11.00)

0.268 (13.18)

0.051 (12.81)

86.3%

UK -0.064 (-5.85)

- 0.098 (9.52)

42.2%

UK -0.017 (-1.04)

0.208 (3.87)

0.038 (2.01)

57.2%

B. Dividend Yield (1973-2008) US -0.096

(-21.33) - 0.114

(27.72) 93.0%

US -0.087 (-18.40)

0.061 (2.05)

0.102 (18.87)

93.3%

UK -0.056 (-5.89)

- 0.091 (10.03)

50.7%

UK 0.049 (5.07)

0.376 (12.29)

-0.038 (-3.45)

82.2%

France -0.032 (-3.32)

- 0.060 (6.53)

41.0%

France 0.034 (1.93)

0.416 (5.00)

-0.027 (-1.29)

65.1%

Germany -0.044 (-4.72)

- 0.064 (7.23)

48.7%

Germany -0.042 (-3.92)

0.016 (0.26)

0.061 (4.94)

48.6%

Switzerland -0.017 (-5.49)

- 0.032 (11.59)

66.1%

Switzerland -0.018 (-5.86)

-0.080 (-2.87)

0.035 (13.78)

67.7%

Japan -0.009 (-3.91)

- 0.017 (8.03)

41.7%

Japan -0.029 (-6.63)

-0.152 (-5.06)

0.040 (8.00)

52.6%

Canada -0.060 (-5.25)

- 0.088 (7.84)

47.7%

Canada -0.014 (-1.42)

0.236 (7.32)

0.022 (1.90)

71.0%

Netherlands -0.058 (-5.58)

- 0.090 (9.24)

63.8%

Netherlands -0.037 (-3.38)

0.273 (5.04)

0.054 (4.39)

69.8%

23

Table 7 Explaining International Earnings Yields using Long Interest Rates, the Ratio of the PPI to CPI and Stock

and Bond Volatilities Constant LB PPI/CPI σST σLB σST / σLB Adj-R2 A. Earnings Yield (1975-2008) – 10yr Volatilities US -0.048

(-2.51) 0.673 (8.52)

- 0.722 (4.15)

-0.317 (-2.35)

- 66.8%

-0.052 (-3.49)

0.703 (9.76)

- - - 0.059 (4.01)

68.1%

-0.190 (-10.71)

0.169 (1.81)

0.187 (9.09)

0.125 (0.99)

0.115 (1.31)

- 84.6%

-0.153 (-9.34)

0.184 (1.92)

0.187 (8.62)

- - -0.004 (-0.31)

83.9%

UK 0.030 (0.57)

0.395 (2.33)

- 0.301 (3.52)

-0.318 (-0.77)

- 68.3%

-0.007 (-0.96)

0.426 (4.19)

- - - 0.034 (4.80)

68.0%

0.095 (1.86)

0.556 (3.41)

-0.087 (-2.00)

0.316 (3.44)

-0.231 (-0.53)

- 69.2%

0.054 (1.54)

0.570 (4.16)

-0.069 (-1.70)

- - 0.034 (4.40)

68.6%

B. Earnings Yield (1978-2008) – 5yr Volatilities US -0.003

(-0.29) 0.869

(13.24) - 0.050

(0.77) -0.032 (-0.33)

- 66.0%

-0.014 (-1.35)

0.855 (12.83)

- - - 0.013 (1.57)

68.2%

-0.229 (-10.94)

-0.077 (-0.77)

0.260 (11.71)

-0.034 (-1.36)

0.117 (2.43)

- 87.2%

-0.211 (-11.65)

-0.097 (-0.90)

0.263 (10.91)

- - -0.008 (-1.92)

86.6%

UK -0.030 (-1.29)

0.581 (8.40)

- 0.038 (0.83)

0.413 (1.99)

- 67.0%

0.015 (1.74)

0.667 (8.54)

- - - 0.005 (0.76)

64.1%

0.027 (0.49)

0.724 (5.31)

-0.062 (-1.21)

0.036 (0.79)

0.387 (1.83)

- 67.6%

0.079 (1.74)

0.833 (5.85)

-0.073 (-1.45)

- - 0.005 (0.65)

65.1%

France 0.022 (1.70)

0.523 (8.95)

- 0.131 (1.91)

-0.064 (-0.46)

- 67.7%

0.017 (1.68)

0.538 (10.14)

- - - 0.013 (2.16)

68.4%

-0.008 (-0.33)

0.422 (4.35)

0.030 (1.11)

0.105 (1.44)

0.014 (0.11)

- 68.1%

0.012 (0.58)

0.511 (5.55)

0.008 (0.31)

- - 0.012 (1.70)

68.3%

Germany 0.013 (0.80)

0.348 (3.42)

- 0.019 (0.52)

0.282 (2.62)

- 14.4%

0.061 (5.85)

0.241 (2.19)

- - - -0.002 (-0.58)

7.8%

-0.148 (-4.33)

-0.165 (-1.46)

0.154 (5.38)

0.042 (1.32)

0.456 (4.05)

- 33.7%

-0.024 (-0.92)

-0.149 (-1.21)

0.102 (3.80)

- - -0.003 (-0.77)

17.4%

Switzerland 0.120 (6.34)

0.368 (1.79)

- -0.207 (-4.48)

-0.217 (-3.38)

- 41.3%

0.038 (5.62)

0.816 (4.00)

- - - 0.000 (0.05)

20.1%

-0.108 0.022 0.136 0.055 0.084 - 80.5%

24

Table 7 Explaining International Earnings Yields using Long Interest Rates, the Ratio of the PPI to CPI and Stock

and Bond Volatilities Constant LB PPI/CPI σST σLB σST / σLB Adj-R2

(-5.15) (0.21) (12.22) (1.65) (1.90) -0.067

(-8.06) -0.054 (-0.56)

0.121 (15.48)

- - 0.001 (0.53)

79.5%

Japan 0.041 (10.36)

0.193 (5.29)

- -0.126 (-8.47)

0.000 (9.76)

- 65.9%

0.022 (9.66)

0.360 (8.97)

- - - -0.012 (-3.30)

42.1%

-0.007 (-0.30)

-0.010 (-0.10)

0.042 (1.99)

-0.078 (-2.79)

0.000 (9.31)

- 68.0%

-0.056 (-4.21)

-0.148 (-1.61)

0.085 (6.06)

- - -0.012 (-4.44)

61.1%

Canada 0.068 (5.28)

0.588 (9.65)

- 0.155 (2.28)

-0.574 (-7.45)

- 67.4%

-0.020 (-2.19)

0.441 (6.61)

- - - 0.039 (6.51)

66.2%

-0.080 (-3.82)

0.283 (4.15)

0.182 (9.19)

0.070 (1.59)

-0.540 (11.34)

- 81.4%

-0.131 (-8.26)

0.193 (2.70)

0.141 (7.24)

- - 0.032 (7.05)

74.2%

Netherlands -0.119 (-6.56)

1.388 (10.24)

- -0.105 (-1.14)

1.171 (6.72)

- 69.4%

0.067 (3.10)

1.179 (7.84)

- - - -0.039 (-3.01)

56.1%

-0.179 (-9.06)

0.596 (3.29)

0.152 (6.31)

-0.136 (-1.59)

0.759 (3.89)

- 75.5%

-0.112 (-4.55)

0.217 (1.56)

0.210 (10.27)

- - -0.029 (2.69)

72.8%

25

26

Table 8 Explaining International Dividend Yields using Long Interest Rates, the Ratio of the PPI to CPI and Stock

and Bond Volatilities Constant LB PPI/CPI σST σLB σST / σLB Adj-R2 A. Dividend Yield (1975-2008) – 10yr Volatilities US -0.033

(-4.06) 0.328

(10.38) - 0.419

(5.39) -0.163 (-3.67)

- 82.4%

-0.029 (-5.48)

0.357 (13.20)

- - - 0.029 (5.86)

81.1%

-0.084 (-12.64)

0.150 (4.54)

0.066 (9.09)

0.208 (4.62)

-0.010 (-0.44)

- 92.9%

-0.065 (-9.92)

0.169 (5.01)

0.069 (8.63)

- - 0.006 (2.22)

91.0%

UK 0.011 (0.94)

0.256 (5.79)

- 0.027 (1.08)

0.024 (0.26)

- 78.1%

0.015 (6.63)

0.272 (8.81)

- - - 0.002 (0.80)

77.8%

0.039 (3.19)

0.327 (7.99)

-0.038 (-3.68)

0.034 (1.39)

0.062 (0.65)

- 79.8%

0.043 (4.94)

0.340 (9.70)

-0.032 (-3.15)

- - 0.002 (0.83)

79.1%

B. Dividend Yield (1978-2008) – 5yr Volatilities US -0.003

(-0.75) 0.428

(17.86) - 0.066

(2.87) -0.058 (-2.09)

- 80.1%

-0.012 (-4.18)

0.425 (18.27)

- - - 0.010 (4.65)

83.2%

-0.088 (-12.90)

0.072 (2.49)

0.098 (15.81)

0.035 (3.81)

-0.002 (-0.17)

- 93.8%

-0.082 (-14.61)

0.089 (3.02)

0.093 (13.73)

- - 0.003 (3.19)

93.7%

UK 0.013 (1.92)

0.266 (11.49)

- 0.025 (1.65)

0.008 (0.11)

- 81.4%

0.012 (5.00)

0.271 (13.81)

- - - 0.004 (2.14)

81.5%

0.046 (3.93)

0.351 (10.57)

-0.036 (-3.57)

0.024 (1.88)

-0.008 (-0.12)

- 83.2%

0.044 (4.91)

0.353 (12.38)

-0.036 (-3.66)

- - 0.004 (2.33)

83.4%

France -0.000 (-0.01)

0.292 (7.97)

- 0.041 (1.14)

0.035 (0.46)

- 64.0%

0.006 (1.32)

0.302 (7.82)

- - - 0.003 (1.01)

63.7%

0.040 (2.37)

0.429 (5.87)

-0.040 (-2.18)

0.076 (1.93)

-0.070 (-0.87)

- 66.8%

0.040 (2.95)

0.473 (6.90)

-0.053 (-3.02)

- - 0.010 (2.41)

68.3%

Germany 0.007 (0.80)

0.211 (4.79)

- -0.035 (-2.15)

0.097 (1.80)

- 37.4%

0.020 (4.11)

0.204 (5.03)

- - - -0.005 (-2.38)

36.6%

-0.072 (-6.33)

-0.041 (-0.80)

0.075 (6.63)

-0.025 (-1.88)

0.182 (4.53)

- 59.1%

-0.033 (-2.96)

-0.036 (-0.70)

0.063 (5.22)

- - -0.005 (-3.19)

53.7%

Switzerland 0.027 (4.32)

0.140 (1.96)

- -0.075 (-5.04)

-0.006 (-0.29)

- 29.3%

0.015 (7.82)

0.224 (3.62)

- - - -0.004 (-2.17)

17.0%

-0.052 0.021 0.047 0.015 0.097 - 82.7%

Table 8 Explaining International Dividend Yields using Long Interest Rates, the Ratio of the PPI to CPI and Stock

and Bond Volatilities Constant LB PPI/CPI σST σLB σST / σLB Adj-R2

(-9.83) (0.84) (18.26) (1.67) (8.13) -0.015

(-5.82) -0.027 (-0.87)

0.035 (14.92)

- - -0.003 (-4.14)

73.9%

Japan 0.017 (10.91)

0.051 (3.63)

- -0.049 (-7.63)

0.000 (5.54)

- 50.8%

0.008 (9.34)

0.104 (6.02)

- - - -0.002 (-1.59)

26.7%

-0.019 (-1.75)

-0.099 (-2.13)

0.031 (3.22)

-0.013 (-1.14)

0.000 (5.09)

- 59.4%

-0.028 (-5.16)

-0.128 (-3.34)

0.039 (6.78)

- - -0.002 (-2.14)

55.5%

Canada 0.017 (4.48)

0.294 (11.76)

- 0.020 (1.14)

-0.132 (-5.05)

- 77.6%

-0.004 (-1.27)

0.254 (9.73)

- - - 0.008 (4.02)

75.9%

0.001 (0.24)

0.262 (9.23)

0.019 (2.87)

0.011 (0.66)

-0.128 (-5.37)

- 78.6%

-0.011 (-1.83)

0.238 (7.79)

0.009 (1.38)

- - 0.008 (4.08)

76.0%

Netherlands -0.028 (-3.57)

0.584 (12.82)

- 0.052 (1.63)

0.186 (3.29)

- 67.3%

0.007 (1.06)

0.524 (10.99)

- - - -0.002 (-0.43)

61.4%

-0.045 (-4.04)

0.364 (5.05)

0.042 (2.77)

0.043 (1.44)

0.072 (1.08)

- 70.8%

-0.039 (-3.19)

0.274 (5.11)

0.055 (4.37)

- - 0.001 (0.46)

69.7%

27

S&P Price-Earnings Ratio and the Ratio of Consumer Price Inflation to the CRB Index

0

5

10

15

20

25

30

35

40

45

50

Jan-65 Jan-70 Jan-75 Jan-80 Jan-85 Jan-90 Jan-95 Jan-00 Jan-05

P/E

Rat

io

0

0.1

0.2

0.3

0.4

0.5

0.6

CPI

/CR

B

P/E Ratio CPI/CRB

28

Figure 1