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Are equities good ination hedges? A frequency domain perspective

Cetin Ciner

Department of Economics and Finance, Cameron School of Business, University of North Carolina Wilmington, Wilmington, NC 28403, United States

a b s t r a c ta r t i c l e i n f o

Article history:

Received 28 April 2014

Received in revised form 5 December 2014

Accepted 10 December 2014

Available online 17 December 2014

JEL classication:

GO

G1

Keywords:

Ination

Stock returns

Frequency domain

By using industry level data, we examinethe relation between equity returns and ination in a frequencydepen-

dent framework. Our analysis shows that a positive relation in fact exists between equity returns and high fre-

quency ination shocks for commodity and technology related industries. Since higher frequency shocks are

independent fromtrendand aretransitory in nature, ourndingsimplya positive relation betweenstock returns

and the unexpected component of ination. Furthermore, we show that the results are robust to rm-level data

by usinga sample from the oil industry. Hence, our study provides a new look at theimpact of ination on equi-

ties by showing the sensitivity of conclusions in prior work to frequency dependence in data.

2014 Elsevier Inc. All rights reserved.

1. Introduction

The relation between ination and equity prices, motivated by the

Fisher hypothesis, is one of the most frequently investigated topics innance and economics. The underlying intuition of this hypothesis is

that stocks represent claims on real assets and therefore, their valua-

tions should increase with ination. Thus, a positive relation is predicted

between ination and stock price movements, in which case it can be

argued that equities provide a good hedge against the ination risk.

Unfortunately, empirical studies, beginning with the early work

ofBodie (1976)andFama and Schwert (1977),consistently report a

negative correlation between stock returns and ination.Ang et al.

(2011)and Hagmann and Lenz (2004)are examples of more recent

papers that reach similar conclusions. One of the explanations offered

for this counter-intuitive nding is the proxy hypothesis ofFama

(1981)and Kaul (1987). The argument of these authors is that the

documented negative correlation with ination is spurious. It arises

because the stock market anticipates the negative impact of higherination on growth, which lowers the market valuations.1

In this paper our objective is to provide a further examination of

the relation between stock returns and ination by using a recently

developed frequency domain decomposition method byAshley and

Verbrugge (2009). The principal advantage of this method is to allowus to examine whether there is persistency dependence in the stock

return-ination linkage, which could occur if higher and lower frequen-

cyinationary shocks have different effects on stock price movements.2

We argue that differential effects of expected and unexpected ination-

ary shocks on stock valuations can be investigated by utilizing this

method of analysis.

Specically, lower frequency shocks are those that tend to be persis-

tent and are likely to represent a continuation of the trend in ination.

Thus, at least to some extent, these shocks can be anticipated by market

participants. Higher frequencyshocks, on theother hand, arethose with

less persistence and are, therefore, transitoryin nature. These shocksare

difcult to forecast by denition and hence, represent the unexpected

component of ination. Hence, our empirical method provides a novel

approach to dene unexpected ination as those corresponding tohigher frequencies on the spectra. Our primary hypothesis is that if

equities are good ination hedges then we should expect a positive

relation between stock returns and unexpectedination.

Many studies in prior work have also examined the stock return

ination linkage by obtaining proxies for expected and unexpected

Review of Financial Economics 24 (2015) 1217

I am grateful to Richard Ashley for providing the code to conduct the frequency

domain decomposition used in this paper. Comments provided by an anonymous referee

signicantly improved the paper. All remaining errors are mine.

Tel.: +1 910 962 7497.

E-mail address:cinerc@uncw.edu.1 Geske andRoll (1983) and Pearceand Roley (1988) providediscussions of alternative

hypotheses on the negative correlation between ination and stock returns.

2 While there are other frequency decomposition methods suggested in the literature,

the AshleyVerbrugge approach is unique because it is robust to feedback between the

variables as discussed further below. In other words, it continues to be valid even when

there is causality from equities to ination, which is plausible under the present value

models of asset prices.

http://dx.doi.org/10.1016/j.rfe.2014.12.001

1058-3300/ 2014 Elsevier Inc. All rights reserved.

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inationary shocks. For example, Fama and Schwert (1977) use changes

in the short term interest rate to infer the expected ination.Bodie

(1976)relies on ARIMA models to construct proxies for expected ina-

tion.Hagmann and Lenz (2004)andHess and Lee (1999)use vector

autoregression (VAR) models to decompose ination into expected

and unexpected components. In related work, McQueen and Roley

(1993) and Pearce and Roley (1988) rely on forecasts by Money Market

Services International to identify the surprise element in ination an-

nouncements. More recently,Wei (2009)uses a time series regressionmodel that also includes lagged values of monthly unemployment rate

to estimate the unexpected component of ination. These studies in

general support the conclusion of earlier papers that the relation

between stock returns and unexpected ination is also negative.

Furthermore, in papers closely related to the present article, Lee and

Ni (1996)use the Chebyshev lter to obtain estimates of unexpected

ination as the transitory component of inationary shocks. These

authors argue that there are differences in the relation between stock

returns and ination based on the frequency components of ination.

Kim and In (2006) rely on a multi-scale wavelet decomposition

approach to examine the same relation. Interestingly, they detect a

positive relation between ination and stock returns at the shortest

scale, which corresponds to the highest frequency shocks. We provide

a further discussion in the following section on why we have preferred

the AshleyVerbrugge decomposition in the present paper rather than

the abovementioned method of analyses.3

We also examine the stock returnination relation by relying on

industry portfolios. This permits us to determine whether some sectors

of the stock market may be considered better hedges against ination.

For example,Boudoukh et al. (1994)argue that non-cyclical stocks tend

to be more positively correlated with ination than cyclical stocks. Stocks

of natural resource companies are usually considered as better ination

hedges because of the sensitivity of commodity prices to ination. In the

empirical analysis, therefore, we rst calculate the conventional ination

betas using 48 industry portfolios by estimating conventional stock

returnination regressions. Our data cover the period between 1990

and 2013 and hence, a further contribution of our analysis is to update

evidence in the literature for a more recent period. Consistent with

prior work, we nd that, in general, ination betas are negative.Subsequently, we estimate the same model by replacing ination

with its frequency components obtained by theAshley and Verbrugge

(2009)decomposition. The results of this analysis lend support to

the central claim of the paper, which is that the stock return ination

relation shows dependency on the persistence of inationary shocks.

Specically, we nd that while long term, trend shocks, replicate the

negative ination betas obtained above as expected, ination betas

forunexpected (high frequency) shocks arein factpositivefor 18 indus-

try portfolios. These positive unexpected ination betas exist in

commodity-sensitive (such as coal, mines, oil, gold and agricultural)

and technology-related industries (such as telecoms, software and

chips) among others.

Therst part of theempirical analysis utilizes value-weighted indus-

try portfolios and hence, could simply be an artifact of data, since largercompanies dominate value-weighted indices. To investigate the robust-

ness of the ndings to rm size, we conduct the analysis by using

equally-weighted industry portfolios. We nd largely similar results.

Again, unexpected ination betas for commodity-sensitive industries

(gold, mines and oil) as well as technology-related industries (telecom,

hardware and chips) have positive, and statistically signicant, unex-

pected ination betas.

In the next section, we outline the statistical method of analysis used

in the paper. In Section 3, we present the data set, and discuss the

empirical ndings inSection 4. We provide the concluding comments

of the paper in the nal section of the study.

2. Statistical method of analysis

Conventional time domain regressions are linear and force a xed

coefcient to describe the relation between the variables that is sup-

posed to be constant at all frequencies. For instance, in the context of

our paper, the conventional regression analysis suggests that the sensi-

tivity of industry portfolio returns to transitory (high frequency) shocks

in ination is exactly the same as it is to permanent (low frequency)

shocks. However, there is no a priori reason to expect this to always ob-tain and researchers have long recognized that estimating a frequency

dependent regression model, in which the coefcient is permitted to

vary over time, is likely to yield richer dynamics. Early research by

Hannan (1963) and Engle (1974), further developed by Tan and

Ashley (1999), suggests to transform the time series regressions into

frequency domain by means of spectral regression models. Forexample,

consider the following generalized linear regression model:

Y X ; N 0;2

j

1

in whichYis T 1 and Xis T K. The objective of the approach is to

transform the equation in such a manner that the components of the

variables correspond to frequencies rather than time periods. This is ac-

complished by pre-multiplying the regression by a T T matrix A,whose (s,t)th element is given by

As;t

1

T

1=2; for s 1;

2

T

1=2

cos s t1

T

; for s 2; 4; 6; ; T2 or T1

2

T

12

sin s1 t1

T

; f or s 3; 5; 7; ; T1 or T;

1

T

12

1 t1

; for s TwhenTiseven

8>>>>>>>>>>>>>>>>>>>>>>>:

AY AXA

A is an orthogonal matrix and the pre-multiplication gives:

Y

X

;

n 0;

2I

: 2

In Eq.(2), the components of the variables now represent frequen-

cies instead of time periods. Next, the T frequency components are

partitioned intoMfrequency bands and dummy variables are created

to deneMvectors of lengthT, which can be written asD1, ..DM.

These dummy variables are used in a manner that for elements, which

fall into thesth frequency band,DsequalsXjand the elements are

zero otherwise. Consequently, the regression equation can be rewritten

as follows:

Y

X

jf g jf g Mm1j;mD

m

3

in whichX{j} istheX* with itsjth column deleted and{j} is thevector

with itsjth component deleted. Hence, frequency-dependent coef-

cientsj,1 .. j,Mcan be estimated and hypotheses tests can be

conducted on the signicance of these parameters.

However,Ashley and Verbrugge (2009)argue that an important

weakness exists in the above approach. In particular, since pre-

multiplying with matrixA mixes past andfutures valuesof thevariables,

theMfrequency components will be correlated with the error terms, if

there is feedback between the dependent and any of the independent

variables, which is likely in nance and economics data. This would

yield inconsistent estimates if the partitioned frequency components

are used in an OLS regression.

The main contribution ofAshley and Verbrugge (2009)is that they

present a solution to this problem by applying a one-sided, rather3

We thank an anonymous referee for recommending this discussion.

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than a two-sided bandpass lter. In essence, they suggest decomposing

Xj into frequency components by applying the same transformation

above in a movingM-month window and keeping only the most recent

value. They show that this transformation effectively resolves estimation

problems due to possible feedback. In this manner, with an M-month

window, parameters on all frequencies can be estimated without any a

priori selection of frequency bands. In this approach, the selection of the

M-month window also signies the longest persistency that will be con-

sidered. That is because shocks with greater thanM-month persistencyare considered long term trend shocks and are lumped together at zero

frequency.

In the present paper, we consider a 36-month window, which im-

plies that all temporary inationary movements should dissipate in

36-months. The AshleyVerbrugge decomposition approach has been

used in several recent papers in the literature. Both Ashley and Tsang

(2013)andYanfeng (2013)examine the frequency dependence in oil

priceeconomic output relation.Ashley et al. (2011)use this method

of analysis to examine the Taylor rule in monetary policy. Ciner

(2014)relies on this approach to examine the relation between con-

sumer sentiment and stock return, while Ciner (2013) focuses on sensi-

tivity of the oil pricestock return relation to frequency of shocks.

Also, as mentionedin the Introduction, our paper is closely related to

Lee and Ni (1996),who use the Chebyshev lter, and toKim and In

(2006), who use the wavelet theory, to similarly decompose ination

into its high and low frequency components. Thus, it is important to

highlight why the AshleyVerbrugge approach is preferred in the present

study. In regards to the wavelet theory used by Kim and In (2006), while

their approach is helpfulin understandingtimevariation in a regression it

is largely because a new wavelet is needed in every time period. On the

other hand, there is a major disadvantage associated with this methodol-

ogy because there is not one set of wavelets, rather a number of wavelet

families that a researcher has to choose from. As a consequence, it is dif-

cult to interpret regression coefcients when the wavelet decomposi-

tion is used. This is perhaps the most important advantage of the

AshleyVerbrugge approach over the wavelet analysis. The estimated

coefcients can be easily interpreted in the AshleyVerbrugge method

as reecting the persistency of shocks in dependent variables.4

In regards to the Chebyshev lter used byLee and Ni (1996), itshould be mentioned that their analysis is a novel econometric

approach and is consistent withthe key points of the AshleyVerbrugge

decomposition method. First, the Chebyshev lter also uses only past

values of input series; hence, when the decomposed parts are used in

a regression, coefcients will not suffer from simultaneity bias if there

is feedback between the variables. Secondly, the estimated coefcients

have economically meaningful interpretations again similar to the

AshleyVerbrugge approach. On the other hand, Chebyshev lters do

have an important disadvantage over spectrallters in that leakage in

thelter is unavoidable since they are time domain based, which causes

phase and amplitude distortions, and consequently, results will not be

as precise as those from a spectral lter.

Finally, one could also use a time series model, such as a VAR or an

ARMA model, to conduct the ltering exercise. However, these modelscannot be constructed with specic cutoff points determined by the re-

searcher and hence,the frequencyof the resultinglteredseries will not

be known. Again, this would make the economic interpretation of the

regression results using the ltered series rather difcult. A secondary

problem with this approach is that the true forecasting model is never

known making researchers likely to use different time series models

for expected ination, giving rise to different conclusions. Note the

separate models inHagmann and Lenz (2004)andWei (2009)as an

example of this point. The AshleyVerbrugge approach denes expect-

ed versus unexpected inationary shocks as a measure of persistency

and hence, avoids determining the correct forecasting model.

3. Data

The data used in our study include the CPI, measured as a monthly

series of annual percentage change in headline ination, and the

monthly returns on 48 stock industry portfolios. The series span the

period between January of 1990 and December of 2012.5 The ination

series are obtained from the Fred database at the St. Louis Federal

Reserve and the industry stock returns are found on Kenneth French's

website. Table 1provides the summary statistics of monthly stockreturns. It can be observed that the returns are positive and statistically

signicantly indifferent from zero, consistent with the view that stock

prices are a submartingale process. We also detect negative skewness

and excess kurtosis in returns similar to prior work.

As mentioned in the Introduction, the essential part of the empirical

analysis of this study involves decomposing the ination rate into its

frequency components using the AshleyVerbrugge approach. The

36-month window used in the application decomposes the ination

rate into 19 frequency components including the zero frequency. We

could estimate the stock returnination regressions by substituting

the ination variable by its 19 frequency components. However, this

would involve a substantial loss in degrees of freedom and, also, differ-

entndings across individual frequencies could make interpreting the

results difcult. Therefore, we generate four new groups from the

frequency components that have intuitive motivations.

Specically, we create fournew variables by regrouping the frequency

components as follows:

Long Medium1 Medium2 Short

N36-months 12-months 36-months 3-months b 12-months b3-months

In this specication, Long represents the trend in ination as the

component with the greatest persistency. Medium1 represents ina-

tionary shockswith persistency between 12-and 36-months, while Me-

dium2 consists of shocks with persistency between 3- and 12-months.

Andnally, Short stands for the highest frequency component of ina-

tion. These are shocks with persistency of less than 3-months and

hence, by denition represent the most transitory components ofination changes.

Recall that, by construction, the sum of these variables equals the

original ination variable and can therefore be used in regressions to

replace the ination rate to test for frequency dependence in the stock

returnination dynamic. The determination of the frequency bands

to regroup the variables discussed above can be considered somewhat

arbitrary. However, our approach relies on the intuition that the highest

frequency shocks constitute the most transitory and unexpected com-

ponent of ination. For that reason, Short is constructed to include

only shocks with persistency between 2- and 3-months, which is the

primary variable of interest in the paper.

InFigs. 15we provide graphs of these new variables. An examina-

tion of the ination components suggests that the AshleyVerbrugge

approach achieves a decompositionof the aggregateination consistentwith our expectations. The trend in ination, captured by Long, closely

replicates the ination rate, which is expected because a majority of

changes in monthly ination rate are simply a continuation of the long

term trend in data, especially for highly persistent macroeconomic

data like the ination rate. At the other end of the spectrum, high

frequency shocks in ination, captured by Short, have much greater

volatility and do not resemble the overall ination series. This is also

expected because by construction these should be short term and

hence, unpredictable shocks, which should not have a smooth pattern.

4

We thank Richard Ashley for providing this information in private conversation.

5 As discussed above, theAshleyVerbrugge methodto obtainthe movingwindows for

the36-monthtrendfrequency resultsin a lossof therst34 observations,hencethe effec-

tive data cover the period between October of 1992 and December of 2012 for a total of

243 observations.

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4. Empirical ndings

The primary model to estimate the relation between stock returns

and ination is the following equation:

Rit convt t 4

In whichconvstands for conventional estimates of ination betas,Ritis

monthly return of an industry portfolio and tstands for monthly

ination rate. This is the standard model used in several papers in

prior work includingAng et al. (2011)andBekaert and Wang (2010)

as recent examples. The conventional ination beta, in this framework,

measures the ination hedging ability of a stock and it is expected to be

positive if equities are good ination hedges. As discussed above the

central contribution of the present study is to decompose the rate of

ination into its frequency components and construct an enhanced

model as follows:

Rit LongLong Medium1Medium1 Medium2Medium2ShortShort t: 5

Our primary argument is that that a frequency dependence on the

inationequity return relation is likely to exist and, therefore, ination

betas will show variation across components of ination. In particular, a

good ination hedge can be specied as a positive and statistically

signicantShortcoefcient in this framework as this would indicate a

positive reaction to unexpected ination shocks. We estimate both the

conventional and frequency-dependent regression models using

monthly industry return data and report the results inTable 2.

We rst observe that all of the estimated conventional ination

betas are negative and furthermore, are statistically signicant for 28

out of 48 industries in our sample. As discussed in the Introduction,this is consistent with the evidence reported in the literature starting

with early work in the 1970s, suggestinga negative covariance between

the stock market movements and ination. Even the commodity sensi-

tive stocks, which areusually considered effectiveination hedges, have

negative conventional ination betas including coal, oil, gold and mines.

In other words, the conclusion of this analysis is that equities do not

provide protection against ination risk at the industry level.

We proceed to estimate the frequency dependent regression model

depicted in Eq.(5)and report the ination betas on the decomposed

ination series, also in Table 2. Consistent with our a priori expectation,

the analysis now reveals the impact of different inationary shocks on

industry stock returns. Long term betas are largely consistent with

conventional betas in that they are always negative and are statically

signicant for a majority of the industries in our sample. This is not

Table 1

Summary statistics.

Industry Mean Std. dev. Skewness Kurtosis

Agric 1.14 (.00) 6.43 .52 1.84

Food .74 (.00) 3.97 .13 1.68

Soda 1.36 (.00) 7.67 .24 3.59

Beer .84 (.00) 4.93 .41 2.03

Smoke 1.22 (.00) 7.23 .14 2.38

Toys .47 (.24) 6.42 .23 1.19

Fun 1.05 (.04) 8.03 .23 3.57Books .63 (.08) 5.59 .26 4.70

Hshld .86 (.00) 4.25 .39 2.34

Clths .87 (.03) 6.83 .17 1.86

Hlth .78 (.06) 6.61 .33 1.04

MedEq .85 (.00) 4.82 .92 2.23

Drugs .92 (.00) 4.57 .15 .09

Chems .94 (.01) 5.82 .08 2.14

Rubbr .92 (.01) 6.05 .06 4.02

Txtls .56 (.30) 8.53 1.14 11.42

BldMt .89 (.03) 6.53 .10 6.16

Cnstr 1.08 (.01) 7.12 .38 1.07

Steel .78 (.17) 8.86 .29 1.79

FabPr .48 (.36) 8.32 .07 3.08

Mach 1.11 (.01) 6.99 .49 2.11

ElcEq 1.25 (.00) 6.56 .31 1.15

Aero 1.22 (.00) 6.33 .93 2.56

Ships 1.42 (.00) 7.58 .11 1.96Guns 1.09 (.00) 6.48 .72 2.49

Gold .82 (.25) 11.24 1.25 8.47

Mines 1.16 (.02) 8.10 .50 2.48

Coal 1.81 (.02) 12.47 .11 .89

Oil 1.07 (.00) 5.53 .04 .87

Util .77 (.00) 4.13 .60 .91

Telcm .68 (.05) 5.42 .23 1.24

Persv .61 (.12) 6.20 .19 .92

Bussv .72 (.03) 5.25 .69 2.27

Hardw 1.32 (.02) 8.80 .33 1.23

Softw 1.18 (.01) 7.75 .01 .86

Chips 1.09 (.05) 8.78 .46 1.26

LabEq .95 (.04) 7.23 .28 1.19

Paper .77 (.02) 5.31 .12 2.72

Boxes .79 (.05) 6.36 .39 1.15

Trans .86 (.01) 5.30 .38 .99

Whlsl .74 (.01) 4.78 .65 2.33

Rtail .88 (.00) 5.01 .19 .53Meals .96 (.00) 4.87 .42 .51

Banks .83 (.04) 6.33 .81 2.86

Insur .84 (.01) 5.40 .69 3.90

Real .68 (.17) 7.79 .94 15.01

Fin 1.14 (.01) 7.39 .49 .89

Note This table provides the summary statistics of the data.

Fig. 1.Aggregate CPI.

Fig. 2.Long.

Fig. 3.Medium1.

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surprising because, as mentioned above, monthly ination changes

largely reect a continuation of the long term trend.

Perhaps, the most interesting result for our paper is the behavior of

stock returns with respect to unexpected inationary shocks, which

are captured by short term betas in Eq.(5). Specically, we detect that

several industry indexes react differently to transitory ination shocks.

Wend that unexpected ination betas arepositive andstatistically sig-

nicant for18 industry portfolios. Moreover,while there are exceptions,

there seems to be two groups of industries with positive unexpected

ination betas.

Therst group consists of commodity sensitive industries, such as

mines, coal, gold and oil. As mentioned in the Introduction, commodity

prices tend to be closely associated with ination, which is consistent

with this nding. The second group consists of technology related

industries such as telecoms, chips and software. It can be argued that

these industries are natural candidates as ination hedges. There is a

greater level of innovation in technology and companies in this group

tend to have more pricing power. Consequently, they are more likely

to pass the inationary shocks to their prots and ultimately, to their

stock prices.6

The above analysis uses value-weighted portfolios, whichcan poten-

tially be dominated by larger companies in an industry. In an attempt to

determine whether thendings reported above can be generalized for a

broader range of companies, we re-conduct the analysis using equally-weighted industry portfolio returns. These are, of course, more sensitive

to thebehavior of smaller companieswithin a given industry. We report

the results of this analysis inTable 3, which show that the conclusions

are largely robust to the company size effect. Conventional ination

betas continue to be negative without an exception. When the frequen-

cy dependent regressions are estimated, unexpected ination betas are

found to be positive and statistically signicant for the samegrouping of

industries as above. In other words, commodity sensitive industries

(gold and oil) and technology related industries (telecoms and chips)

continue to have positive sensitivities to unexpected ination.

Finally, we conduct the analysis using rm-level data. Even the

equally-weighted industry indices could mask the behavior of individu-

al stocks. Moreover, some investors will rely on stand-alone stocks

in their investments rather than portfolios; hence, the analysis couldbe useful in that aspect. We select our rm-level data from the oil

and gas sector primarily because the above analysis shows that this in-

dustry is a candidate for providing a hedge against ination risk. We

consider six large integrated oil and gas companies: Chevron (CVX),

ConocoPhillips (COP), Exxon Mobil (XOM), Hess (HES), Marathon Oil

(MRO) and Murphy Oil (MUR). We report the ndings for this part of

the analysis inTable 4and, save for MUR, there is a positive and statis-

tically signicant relation between the unexpected component of ina-

tion and these individual stock returns at the 10% level, suggesting that

6 To examine therobustness of ourndings, we also usedtime series modelsto decom-

pose ination. Specically, we estimated expected ination using both VAR(1) and

AR(2) models for three selected industries; reit,n and gold. We chose those industries

because they have positive andstatistically signicant unexpected ination betas. Theun-

expected ination betas are.31 (.79) forreit,.96 (.40) forn and 1.93 (.27) forgoldwhen a

VAR(1)modelis used. When, anAR(2)modelis used, they are1.01(.17)for reit, 1.33 (.29)

forn and 2.86 (.13) for gold. These results are consistent with the view that time series

models areunlikely to capture thedynamics uncovered by theAshleyVerbrugge decom-

position used in the paper and also, that it is difcult to determine the correct forecasting

model to determine expected ination. We thank an anonymous referee for suggesting

this analysis.

Table 2

Ination betas: value-weighted industry portfolios.

Ind ustr y Co nvent iona l Lon g Medium1 Medium2 Shor t

Agric .10 (.81) .09 (.86) 3.24 (.22) 2.54 (.22) 24.06 (.00)

Food .19 (.45) .22 (.47) .26 (.68 ) .17 (.85 ) 4 .2 0 (.46 )

Soda 1.03 (.03) 1.19 (.02) 1.69 (.25) .66 (.78) .68 (.94)

Beer .29 (.36) .45 (.18) .25 (.73) .82 (.43) 1.20 (.83)

Smoke .02 (.95) .02 (.96) 1.09 (.31) .94 (.59) 6.15 (.48)

Toys .70 (.11) .54 (.26) .75 (.60) 1.74 (.41) 7.15 (.33)

Fun 1.59 (.01) 1.89 (.00) .73 (.69) .06 (.97) 8.65 (.42)

Books 1.19 (.01) 1.62 (.00) 1.36 (.34) 2.11 (.22) 10.31 (.11)

Hshld .34 (.26) .58 ( .07 ) .61 (.46 ) .67 (.54 ) 1.26 (.79)

Clths .79 (.07) .94 (.06) .31 (.81) .18 (.92) 3.47 (.67)

Hlth .12 (.79) .23 (.59) 1.91 (.10) 2.10 (.22) 4.72 (.59)

MedEq .52 (.05) .66 (.05) .83 (.32) .89 (.55) 13.06 (.07)

Drugs .29 (.26) .27 (.38) .56 (.46) .13 (.90) 5.33 (.32)

Chems .92 (.04) 1.05 (.04) 1.22 (.28) .42 (.80) 14.41 (.07)

Rubbr .88 (.09) 1.04 (.05) 1.03 (.52) .42 (.78) 4.44 (.51)

Txtls 1.20 (.22) 1.47 (.13) .93 (.73 ) .62 (.82 ) 1 .6 3 (.89 )BldMt 1.01 (.08) .98 (.11) 1.37 (.43) .82 (.63) 9.51 (.20)

Cnstr .93 (.04) .69 (.21) 2.03 (.16) 1.67 (.37) 9.80 (.23)

Steel 1.04 (.08) .85 (.26) 2.20 (.27) 1.17 (.65) 29.50 (.00)

FabPr .56 (.30) .78 (.28) 1.60 (.38) 1.88 (.41) 11.50 (.25)

Mach 1.01 (.03) 1.09 (.06) 1.79 (.18) .38 (.81) 19.53 (.01)

ElcEq 1.02 (.02) 1.05 (.04) .84 (.54) .76 (.61) 17.90 (.01)

Aero .75 (.06) .70 (.13) .46 (.68) 1.25 (.39) 8.16 (.30)

Ships .81 (.14) .75 (.22) .74 (.76) 1.21 (.54) 11.43 (.24)

Guns .26 (.52) .38 (.44) .03 (.97) .44 (.79) 3.46 (.70)

Gold .99 (.14) .31 (.72) 2.41 (.15) 4.42 (.16) 29.06 (.06)

Mines 1.61 (.00) 1.33 (.06) 2.97 (.07) 2.34 (.30) 20.95 (.04)

Coal .94 (.27) 1.75 (.10) 2.23 (.17) 6.23 (.05) 31.30 (.05)

Oil .39 (.28) .30 (.49) 1.71 (.07) .12 (.93) 18.56 (.00)

Util .10 (.69) .17 (.60) .30 (.68 ) .59 (.56 ) 3 .4 9 (.46 )

Telcm .80 (.01) .81 (.04) .99 (.33) .40 (.75) 14.47 (.02)

Persv .21 (.59) .08 (.86) .62 (.61) .82 (.58) 3.15 (.63)

Bussv

.64 (.04)

.65 (.10)

1.41 (.13) .21 (.87) 12.88 (.02)Hardw 1.16 (.01) 1.45 (.01) .32 (.79 ) .36 (.83 ) 8 .4 5 (.36 )

Softw .87 (.01) .95 (.06) 1.06 (.30) .06 (.96) 19.17 (.03)

Chips .78 (.08) .78 (.20) 1.50 (.23) .02 (.99) 21.52 (.02)

LabEq .64 (.08) .72 (.16) 1.69 (.12) 1.00 (.56) 22.10 (.00)

Paper .82 (.04) 1.07 (.01) .85 (.48) 1.10 (.47) 6.55 (.31)

Boxes .95 (.01) 1.00 (.01) .96 (.40) .58 (.74) .51 (.94)

Trans .26 (.49) .43 ( .29 ) .39 (.73 ) .54 (.71 ) 6 .9 7 (.31 )

Whlsl .55 (.07) .57 (.14) 1.05 (.22) .10 (.93) 10.59 (.07)

Rtail .61 (.03) .65 (.06) .84 (.33) .14 (.90) 2.43 (.69)

Meals .51 (.08) .40 (.24) .25 (.78) 1.92 (.20) 5.82 (.36)

Banks .41 (.84) .64 ( .21 ) .04 (.97 ) .94 (.65 ) 4 .0 0 (.64 )

Insur .69 (.10) .73 (.12) .45 (.73) .51 (.77) 5.09 (.46)

Real 1.39 (.06) 1.26 (.08) 2.46 (.27) 1.20 (.63) 22.98 (.03)

Fin .94 (.03) .87 (.12) 2.34 (.07) .13 (.94) 15.94 (.08)

Note This table provides the ination beta for value-weighted industry portfolios

calculated by the conventional and frequencydecomposition approaches. Bold entries

signify statistical signicance.

Fig. 4.Medium2. Fig. 5.Short.

16 C. Ciner / Review of Financial Economics 24 (2015) 1217

7/25/2019 Are Equities Good Inflation Hedges- A Frequency Domain Perspective10.1016@j.rfe.2014.12.001

6/6

the industry portfoliondings can be largely generalized to rm-level

data at least for the oil and gas industry.

5. Conclusions

Our ndings suggest that signicant frequency dependence exists inthe relation between stock returns and ination rate. Trend shocks,

which are those with greater persistency, have a negative covariance

with equity returns in all of the industries examined. However, we

argue that this relation can be spurious if the impact of ination on

stock valuations is anticipated by market participants. If, for example,

greater ination leads to lower economic growth in the future as

Fama (1981) has suggested, market valuations will be lowered in antic-

ipation, generating negative ination betas. This argument is particular-

ly relevant for a highly persistent macroeconomic variable like ination.

Long term trend ination betas are very similar to aggregate ination

betas because the majority of monthly changes in in

ation is simply acontinuation of the long term trend.

On the other hand, higher frequency ination shocks are transitory

by nature, which implied that they cannot be anticipated. Therefore, a

correct test of the sensitivity of stock returns to ination should exam-

ine the link between high frequency inationary shocks and equities,

which is accomplished in this study. We nd that commodity-

sensitive and technology-related equities do provide good ination

hedges in that they have positive and statistically signicant links

with unexpected ination. This conclusion is largely robust to using

value-weighted and equally-weighted industry portfolios as well as

for a set of individual company share prices selected from the oil indus-

try. Our study, overall, also has a noteworthy implication. When highly

persistent macroeconomic data are used in nancial research, account-

ing for frequency dependencies could yield richer results.

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Table 3

Frequency dependent regressions: equally-weighted industry portfolios.

In du str y Co nvent iona l L ong Med iu m1 Medium2 Shor t

Agric .42 (.43) .52 (.38) 3.04 (.04) 2.49 (.19) 15.95 (.15)

Food .73 (.02) .72 (.06) 1.45 (.10) .10 (.93) 4.93 (.44)

Soda .94 (.04) 1.20 (.02) 1.79 (.18) 1.67 (.40) 2.04 (.81)

Beer .71 (.05) .66 (.09) .96 (.35) .77 (.58) 6.12 (.31)

Smoke .53 (.30) .90 (.17) .63 (.74) 2.11 (.38) 8.80 (.39)

Toys 1.24 (.02) 1.41 (.02) 1.30 (.31) .12 (.94) 12.21 (.14)

Fun 1.34 (.01) 1.50 (.01) 2.06 (.19) .41 (.82) 5.33 (.53)Books 2.49 (.00) 2.94 (.00) 2.21 (.21) .64 (.78) 11.15 (.28)

Hshld 1.25 (.02) 1.59 (.00) 1.24 (.45) 1.31 (.46) 9.62 (.20)

Clths 1.25 (.02) 1.44 (.00) .69 (.66) .21 (.91) 6.42 (.47)

Hlth .53 (.19) .51 (.31) 2.35 (.06) .82 (.63) 10.11 (.22)

MedEq .92 (.02) 1.09 (.03) 1.84 (.07) 1.13 (.49) 11.41 (.20)

Drugs 1.17 (.04) .94 (.18) 3.31 (.02) .44 (.81) 15.70 (.22)

Chems 1.15 (.02) 1.34 (.02) 1.27 (.33) .45 (.81) 14.42 (.09)

Rubbr 1.07 (.04) 1.46 (.01) .08 (.96 ) .90 (.62) .03 ( .99 )

Txtls 1.32 (.09) 2.33 (.00) .41 (.85) 5.20 (.02) 2.32 (.79)

BldMt .84 (.09) .87 (.12) 1.66 (.27) .17 (.92) 8.98 (.24)

Cnstr 1.10 (.05) .89 (.15) 3.02 (.08) .94 (.64) 12.75 (.19)

Steel .76 (.20) .80 (.26) 2.54 (.17) 1.15 (.62) 17.02 (.08)

FabPr .73 (.25) .84 (.22) 1.59 (.40) .93 (.66) 23.88 (.01)

Mach .83 (.07) 1.06 (.07) 1.41 (.30) 1.44 (.40) 18.59 (.02)

ElcEq .89 (.04) 1.08 (.04) 1.96 (.13) 1.47 (.39) 17.86 (.03)

Aero .64 (.15) .69 (.16) 1.09 (.39) .19 (.90) 9.31 (.26)

Ships

.92 (.18)

.94 (.20)

1.36 (.52)

.10 (.96) 24.48 (.01)Guns .94 (.03) .81 (.15) 2.39 (.03) .78 (.68) 3.51 (.71)

Gold 2.35 (.00) 1.85 (.10) 6.40 (.00) 2.34 (.52) 33.27 (.02)

Mines 2.04 (.00) 2.13 (.00) 4.42 (.01) .73 (.77) 23.46 (.03)

Coal .78 (.41) 1.75 (.14) 1.09 (.54) 6.60 (.04) 19.87 (.28)

Oil .48 (.49) .63 (.46) 2.44 (.12) 2.46 (.29) 32.05 (.00)

Util .17 (.43) .25 (.37) .42 (.57) .58 (.52) 3.56 (.38)

Telcm 1.66 (.00) 1.85 (.00) 2.28 (.10) .40 (.83) 24.37 (.01)

Persv .99 (.02) .95 (.05) 2.09 (.14) .38 (.81) 7.68 (.30)

Bussv 1.09 (.00) 1.15 (.02) 2.42 (.01) .55 (.71) 13.13 (.08)

Hardw 1.42 (.00) 1.52 (.02) 2.58 (.06) .48 (.80) 20.19 (.07)

Softw 1.30 (.00) 1.51 (.01) 2.28 (.06) 1.14 (.54) 17.27 (.12)

Chips 1.26 (.01) 1.40 (.04) 2.39 (.09) .89 (.66) 22.33 (.04)

LabEq .83 (.05) 1.10 (.04) 1.91 (.11) 2.11 (.21) 20.61 (.02)

Paper 1.62 (.00) 2.09 (.00) 1.55 (.36) 1.78 (.36) 9.41 (.28)

Boxes .93 (.02) 1.03 (.04) 1.17 (.32) .02 (.98) .49 (.95)

Trans .77 (.09) .84 (.09) .91 (.51) .10 (.95) 5.56 (.47)

Whlsl 1.09 (.02) 1.16 (.02) 2.24 (.08) .39 (.80) 8.14 (.30)

Rtail 1.48 (.00) 1.56 (.00) 2.16 (.71) .33 (.87) 4.20 (.65)Meals 1.24 (.01) .1.22 (.02) 2.28 (.12) .51 (.80) 1.20 (.89)

Banks .06 (.85) .15 (.68) .07 (.95) .58 (.68) 1.95 (.75)

Insur .68 (.09) .54 (.22) 1.04 (.41) 1.33 (.44) 6.09 (.33)

Real 1.33 (.02) 1.49 (.01) 2.01 (.27) .48 (.83) 10.76 (.29)

Fin .81 (.03) .72 (.10) 1.85 (.09) .55 (.71) 10.33 (.14)

Note Thistableprovides ination betasfor equally-weighted portfolios using conventional

and frequency decomposition approaches. Bold entries signify statistical signicance.

Table 4

Ination betas: oil company stocks.

Conventional Long Medium1 Medium2 Short

CVX .29 (.43) .04 (.90) 1.26 (.27) 1.11 (.53) 13.69 (.05)

COP .35 (.45) .39 (.51) .83 ( .5 5) .61 ( .7 4) 23.24 (.00)

XOM .14 (. 61) .19 (.56) 1.44 (.14) 1.40 (.32) 9.90 (.09)

HES .33 (.61) .56 (.46) 2.72 (.02) 3.47 (.13) 26.77 (.01)

MRO .37 (.47) .03 (.96) 3.12 (.02) .37 (.86) 29.28 (.00)

MUR .81 (.31) .62 (.35) 1.72 (.17) 1.30 (.55) 16.93 (.13)

Note This table provides theination beta foroil company stocks using theconventional

and frequency domain approaches. Bold entries signify statistical signicance.

17C. Ciner / Review of Financial Economics 24 (2015) 1217

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