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Are equities good inflation hedges? A frequency domain perspective
Review of Financial Economics 24 (2015) 12–17
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Are equities good inflation 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 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 classification: GO G1
a b s t r a c t By using industry level data, we examine the relation between equity returns and inflation in a frequency dependent framework. Our analysis shows that a positive relation in fact exists between equity returns and high frequency inflation shocks for commodity and technology related industries. Since higher frequency shocks are independent from trend and are transitory in nature, our findings imply a positive relation between stock returns and the unexpected component of inflation. Furthermore, we show that the results are robust to firm-level data by using a sample from the oil industry. Hence, our study provides a new look at the impact of inflation on equities by showing the sensitivity of conclusions in prior work to frequency dependence in data. © 2014 Elsevier Inc. All rights reserved.
Keywords: Inflation Stock returns Frequency domain
1. Introduction The relation between inflation and equity prices, motivated by the Fisher hypothesis, is one of the most frequently investigated topics in finance and economics. The underlying intuition of this hypothesis is that stocks represent claims on real assets and therefore, their valuations should increase with inflation. Thus, a positive relation is predicted between inflation and stock price movements, in which case it can be argued that equities provide a good hedge against the inflation risk. Unfortunately, empirical studies, beginning with the early work of Bodie (1976) and Fama and Schwert (1977), consistently report a negative correlation between stock returns and inflation. 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 finding is the “proxy” hypothesis of Fama (1981) and Kaul (1987). The argument of these authors is that the documented negative correlation with inflation is spurious. It arises because the stock market anticipates the negative impact of higher inflation on growth, which lowers the market valuations.1
☆ 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 significantly improved the paper. All remaining errors are mine. ⁎ Tel.: +1 910 962 7497. E-mail address: [email protected]. 1 Geske and Roll (1983) and Pearce and Roley (1988) provide discussions of alternative hypotheses on the negative correlation between inflation and stock returns.
http://dx.doi.org/10.1016/j.rfe.2014.12.001 1058-3300/© 2014 Elsevier Inc. All rights reserved.
In this paper our objective is to provide a further examination of the relation between stock returns and inflation by using a recently developed frequency domain decomposition method by Ashley and Verbrugge (2009). The principal advantage of this method is to allow us to examine whether there is persistency dependence in the stock return-inflation linkage, which could occur if higher and lower frequency inflationary shocks have different effects on stock price movements.2 We argue that differential effects of expected and unexpected inflationary shocks on stock valuations can be investigated by utilizing this method of analysis. Specifically, lower frequency shocks are those that tend to be persistent and are likely to represent a continuation of the trend in inflation. Thus, at least to some extent, these shocks can be anticipated by market participants. Higher frequency shocks, on the other hand, are those with less persistence and are, therefore, transitory in nature. These shocks are difficult to forecast by definition and hence, represent the unexpected component of inflation. Hence, our empirical method provides a novel approach to define unexpected inflation as those corresponding to higher frequencies on the spectra. Our primary hypothesis is that if equities are good inflation hedges then we should expect a positive relation between stock returns and unexpected inflation. Many studies in prior work have also examined the stock return– inflation linkage by obtaining proxies for expected and unexpected 2 While there are other frequency decomposition methods suggested in the literature, the Ashley–Verbrugge 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 inflation, which is plausible under the present value models of asset prices.
C. Ciner / Review of Financial Economics 24 (2015) 12–17
inflationary shocks. For example, Fama and Schwert (1977) use changes in the short term interest rate to infer the expected inflation. Bodie (1976) relies on ARIMA models to construct proxies for expected inflation. Hagmann and Lenz (2004) and Hess and Lee (1999) use vector autoregression (VAR) models to decompose inflation 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 inflation announcements. More recently, Wei (2009) uses a time series regression model that also includes lagged values of monthly unemployment rate to estimate the unexpected component of inflation. These studies in general support the conclusion of earlier papers that the relation between stock returns and unexpected inflation is also negative. Furthermore, in papers closely related to the present article, Lee and Ni (1996) use the Chebyshev filter to obtain estimates of unexpected inflation as the transitory component of inflationary shocks. These authors argue that there are differences in the relation between stock returns and inflation based on the frequency components of inflation. Kim and In (2006) rely on a multi-scale wavelet decomposition approach to examine the same relation. Interestingly, they detect a positive relation between inflation 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 Ashley–Verbrugge decomposition in the present paper rather than the abovementioned method of analyses.3 We also examine the stock return–inflation relation by relying on industry portfolios. This permits us to determine whether some sectors of the stock market may be considered better hedges against inflation. For example, Boudoukh et al. (1994) argue that non-cyclical stocks tend to be more positively correlated with inflation than cyclical stocks. Stocks of natural resource companies are usually considered as better inflation hedges because of the sensitivity of commodity prices to inflation. In the empirical analysis, therefore, we first calculate the conventional inflation betas using 48 industry portfolios by estimating conventional stock return–inflation 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 find that, in general, inflation betas are negative. Subsequently, we estimate the same model by replacing inflation with its frequency components obtained by the Ashley and Verbrugge (2009) decomposition. The results of this analysis lend support to the central claim of the paper, which is that the stock return–inflation relation shows dependency on the persistence of inflationary shocks. Specifically, we find that while long term, trend shocks, replicate the negative inflation betas obtained above as expected, inflation betas for unexpected (high frequency) shocks are in fact positive for 18 industry portfolios. These positive unexpected inflation 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. The first part of the empirical analysis utilizes value-weighted industry portfolios and hence, could simply be an artifact of data, since larger companies dominate value-weighted indices. To investigate the robustness of the findings to firm size, we conduct the analysis by using equally-weighted industry portfolios. We find largely similar results. Again, unexpected inflation betas for commodity-sensitive industries (gold, mines and oil) as well as technology-related industries (telecom, hardware and chips) have positive, and statistically significant, unexpected inflation 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 findings in Section 4. We provide the concluding comments of the paper in the final section of the study.
3
We thank an anonymous referee for recommending this discussion.
13
2. Statistical method of analysis Conventional time domain regressions are linear and force a fixed coefficient to describe the relation between the variables that is supposed to be constant at all frequencies. For instance, in the context of our paper, the conventional regression analysis suggests that the sensitivity of industry portfolio returns to transitory (high frequency) shocks in inflation is exactly the same as it is to permanent (low frequency) shocks. However, there is no a priori reason to expect this to always obtain and researchers have long recognized that estimating a frequency dependent regression model, in which the coefficient 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. For example, consider the following generalized linear regression model: 2 Y ¼ Xβ þ ϵ; ϵ N 0; σ j
ð1Þ
in which Y is T × 1 and X is 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 accomplished by pre-multiplying the regression by a T × T matrix A, whose (s,t)th element is given by
As;t
8 > 1 1=2 > > ; for s ¼ 1; > > T > > > 1=2 > > 2 πsðt−1Þ > > ; for s ¼ 2; 4; 6; …; ðT−2ÞorðT−1Þ cos < T T ¼ 1 > 2 2 πðs−1Þðt−1Þ > > ; for s ¼ 3; 5; 7; …; ðT−1Þor T; sin > > T T > > > 1 > > 2 1 tþ1 > > ð−1Þ ; for s ¼ T when T is even : T
AY ¼ AX β þ Aϵ A is an orthogonal matrix and the pre-multiplication gives: 2 Y ¼ X β þ ϵ ; ϵ n 0; σ I :
ð2Þ
In Eq. (2), the components of the variables now represent frequencies instead of time periods. Next, the T frequency components are partitioned into M frequency bands and dummy variables are created to define M vectors of length T, which can be written as D⁎1, ….. D⁎M. These dummy variables are used in a manner that for elements, which fall into the sth frequency band, D⁎s equals X⁎j and the elements are zero otherwise. Consequently, the regression equation can be rewritten as follows:
M
Y ¼ X f jg βf jg þ Σm¼1 β j;m D
m
þϵ
ð3Þ
in which X{j}⁎ is the X* with its jth column deleted and β{j} is the β vector with its jth component deleted. Hence, frequency-dependent coefficients βj,1 … … .. βj,M can be estimated and hypotheses tests can be conducted on the significance of these parameters. However, Ashley and Verbrugge (2009) argue that an important weakness exists in the above approach. In particular, since premultiplying with matrix A mixes past and futures values of the variables, the M frequency 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 finance and economics data. This would yield inconsistent estimates if the partitioned frequency components are used in an OLS regression. The main contribution of Ashley and Verbrugge (2009) is that they present a solution to this problem by applying a one-sided, rather
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C. Ciner / Review of Financial Economics 24 (2015) 12–17
than a two-sided bandpass filter. In essence, they suggest decomposing Xj into frequency components by applying the same transformation above in a moving M-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 signifies the longest persistency that will be considered. That is because shocks with greater than M-month persistency are considered long term trend shocks and are lumped together at zero frequency. In the present paper, we consider a 36-month window, which implies that all temporary inflationary movements should dissipate in 36-months. The Ashley–Verbrugge decomposition approach has been used in several recent papers in the literature. Both Ashley and Tsang (2013) and Yanfeng (2013) examine the frequency dependence in oil price–economic 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 consumer sentiment and stock return, while Ciner (2013) focuses on sensitivity of the oil price–stock return relation to frequency of shocks. Also, as mentioned in the Introduction, our paper is closely related to Lee and Ni (1996), who use the Chebyshev filter, and to Kim and In (2006), who use the wavelet theory, to similarly decompose inflation into its high and low frequency components. Thus, it is important to highlight why the Ashley–Verbrugge approach is preferred in the present study. In regards to the wavelet theory used by Kim and In (2006), while their approach is helpful in understanding time variation 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 methodology 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 difficult to interpret regression coefficients when the wavelet decomposition is used. This is perhaps the most important advantage of the Ashley–Verbrugge approach over the wavelet analysis. The estimated coefficients can be easily interpreted in the Ashley–Verbrugge method as reflecting the persistency of shocks in dependent variables.4 In regards to the Chebyshev filter used by Lee and Ni (1996), it should be mentioned that their analysis is a novel econometric approach and is consistent with the key points of the Ashley–Verbrugge decomposition method. First, the Chebyshev filter also uses only past values of input series; hence, when the decomposed parts are used in a regression, coefficients will not suffer from simultaneity bias if there is feedback between the variables. Secondly, the estimated coefficients have economically meaningful interpretations again similar to the Ashley–Verbrugge approach. On the other hand, Chebyshev filters do have an important disadvantage over spectral filters in that leakage in the filter 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 filter. Finally, one could also use a time series model, such as a VAR or an ARMA model, to conduct the filtering exercise. However, these models cannot be constructed with specific cutoff points determined by the researcher and hence, the frequency of the resulting filtered series will not be known. Again, this would make the economic interpretation of the regression results using the filtered series rather difficult. 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 inflation, giving rise to different conclusions. Note the separate models in Hagmann and Lenz (2004) and Wei (2009) as an example of this point. The Ashley–Verbrugge approach defines expected versus unexpected inflationary shocks as a measure of persistency and hence, avoids determining the correct forecasting model.
4
We thank Richard Ashley for providing this information in private conversation.
3. Data The data used in our study include the CPI, measured as a monthly series of annual percentage change in headline inflation, and the monthly returns on 48 stock industry portfolios. The series span the period between January of 1990 and December of 2012.5 The inflation 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 1 provides the summary statistics of monthly stock returns. It can be observed that the returns are positive and statistically significantly 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 inflation rate into its frequency components using the Ashley–Verbrugge approach. The 36-month window used in the application decomposes the inflation rate into 19 frequency components including the zero frequency. We could estimate the stock return–inflation regressions by substituting the inflation variable by its 19 frequency components. However, this would involve a substantial loss in degrees of freedom and, also, different findings across individual frequencies could make interpreting the results difficult. Therefore, we generate four new groups from the frequency components that have intuitive motivations. Specifically, we create four new 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 specification, Long represents the trend in inflation as the component with the greatest persistency. Medium1 represents inflationary shocks with persistency between 12- and 36-months, while Medium2 consists of shocks with persistency between 3- and 12-months. And finally, Short stands for the highest frequency component of inflation. These are shocks with persistency of less than 3-months and hence, by definition represent the most transitory components of inflation changes. Recall that, by construction, the sum of these variables equals the original inflation variable and can therefore be used in regressions to replace the inflation rate to test for frequency dependence in the stock return–inflation 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 component of inflation. 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. In Figs. 1–5 we provide graphs of these new variables. An examination of the inflation components suggests that the Ashley–Verbrugge approach achieves a decomposition of the aggregate inflation consistent with our expectations. The trend in inflation, captured by Long, closely replicates the inflation rate, which is expected because a majority of changes in monthly inflation rate are simply a continuation of the long term trend in data, especially for highly persistent macroeconomic data like the inflation rate. At the other end of the spectrum, high frequency shocks in inflation, captured by Short, have much greater volatility and do not resemble the overall inflation series. This is also expected because by construction these should be short term and hence, unpredictable shocks, which should not have a smooth pattern. 5 As discussed above, the Ashley–Verbrugge method to obtain the moving windows for the 36-month trend frequency results in a loss of the first 34 observations, hence the effective data cover the period between October of 1992 and December of 2012 for a total of 243 observations.
C. Ciner / Review of Financial Economics 24 (2015) 12–17
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Table 1 Summary statistics. Industry
Mean
Std. dev.
Skewness
Kurtosis
Agric Food Soda Beer Smoke Toys Fun Books Hshld Clths Hlth MedEq Drugs Chems Rubbr Txtls BldMt Cnstr Steel FabPr Mach ElcEq Aero Ships Guns Gold Mines Coal Oil Util Telcm Persv Bussv Hardw Softw Chips LabEq Paper Boxes Trans Whlsl Rtail Meals Banks Insur Real Fin
1.14 (.00) .74 (.00) 1.36 (.00) .84 (.00) 1.22 (.00) .47 (.24) 1.05 (.04) .63 (.08) .86 (.00) .87 (.03) .78 (.06) .85 (.00) .92 (.00) .94 (.01) .92 (.01) .56 (.30) .89 (.03) 1.08 (.01) .78 (.17) .48 (.36) 1.11 (.01) 1.25 (.00) 1.22 (.00) 1.42 (.00) 1.09 (.00) .82 (.25) 1.16 (.02) 1.81 (.02) 1.07 (.00) .77 (.00) .68 (.05) .61 (.12) .72 (.03) 1.32 (.02) 1.18 (.01) 1.09 (.05) .95 (.04) .77 (.02) .79 (.05) .86 (.01) .74 (.01) .88 (.00) .96 (.00) .83 (.04) .84 (.01) .68 (.17) 1.14 (.01)
6.43 3.97 7.67 4.93 7.23 6.42 8.03 5.59 4.25 6.83 6.61 4.82 4.57 5.82 6.05 8.53 6.53 7.12 8.86 8.32 6.99 6.56 6.33 7.58 6.48 11.24 8.10 12.47 5.53 4.13 5.42 6.20 5.25 8.80 7.75 8.78 7.23 5.31 6.36 5.30 4.78 5.01 4.87 6.33 5.40 7.79 7.39
.52 −.13 .24 −.41 −.14 −.23 −.23 .26 −.39 −.17 −.33 −.92 −.15 −.08 .06 1.14 −.10 −.38 −.29 −.07 −.49 −.31 −.93 .11 −.72 1.25 −.50 .11 −.04 −.60 −.23 −.19 −.69 −.33 −.01 −.46 −.28 .12 −.39 −.38 −.65 −.19 −.42 −.81 −.69 .94 −.49
1.84 1.68 3.59 2.03 2.38 1.19 3.57 4.70 2.34 1.86 1.04 2.23 .09 2.14 4.02 11.42 6.16 1.07 1.79 3.08 2.11 1.15 2.56 1.96 2.49 8.47 2.48 .89 .87 .91 1.24 .92 2.27 1.23 .86 1.26 1.19 2.72 1.15 .99 2.33 .53 .51 2.86 3.90 15.01 .89
Fig. 2. Long.
In which βconv stands for conventional estimates of inflation betas, Rit is monthly return of an industry portfolio and πt stands for monthly inflation rate. This is the standard model used in several papers in prior work including Ang et al. (2011) and Bekaert and Wang (2010) as recent examples. The conventional inflation beta, in this framework, measures the inflation hedging ability of a stock and it is expected to be positive if equities are good inflation hedges. As discussed above the central contribution of the present study is to decompose the rate of inflation into its frequency components and construct an enhanced model as follows: Rit ¼ α þ βLong πLong þ βMedium1 πMedium1 þ βMedium2 πMedium2 þ βShort π Short þ εt :
Note — This table provides the summary statistics of the data.
4. Empirical findings The primary model to estimate the relation between stock returns and inflation is the following equation: Rit ¼ α þ βconv πt þ εt
ð4Þ
Fig. 1. Aggregate CPI.
ð5Þ
Our primary argument is that that a frequency dependence on the inflation–equity return relation is likely to exist and, therefore, inflation betas will show variation across components of inflation. In particular, a good inflation hedge can be specified as a positive and statistically significant βShort coefficient in this framework as this would indicate a positive reaction to unexpected inflation shocks. We estimate both the conventional and frequency-dependent regression models using monthly industry return data and report the results in Table 2. We first observe that all of the estimated conventional inflation betas are negative and furthermore, are statistically significant 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, suggesting a negative covariance between the stock market movements and inflation. Even the commodity sensitive stocks, which are usually considered effective inflation hedges, have negative conventional inflation betas including coal, oil, gold and mines. In other words, the conclusion of this analysis is that equities do not provide protection against inflation risk at the industry level. We proceed to estimate the frequency dependent regression model depicted in Eq. (5) and report the inflation betas on the decomposed inflation series, also in Table 2. Consistent with our a priori expectation, the analysis now reveals the impact of different inflationary shocks on industry stock returns. Long term betas are largely consistent with conventional betas in that they are always negative and are statically significant for a majority of the industries in our sample. This is not
Fig. 3. Medium1.
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C. Ciner / Review of Financial Economics 24 (2015) 12–17
Fig. 4. Medium2.
Fig. 5. Short.
surprising because, as mentioned above, monthly inflation changes largely reflect 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 inflationary shocks, which are captured by short term betas in Eq. (5). Specifically, we detect that several industry indexes react differently to transitory inflation shocks. We find that unexpected inflation betas are positive and statistically significant for 18 industry portfolios. Moreover, while there are exceptions, there seems to be two groups of industries with positive unexpected inflation betas. The first 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 inflation, which is consistent with this finding. 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 inflation 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 inflationary shocks to their profits and ultimately, to their stock prices.6 The above analysis uses value-weighted portfolios, which can potentially be dominated by larger companies in an industry. In an attempt to determine whether the findings reported above can be generalized for a broader range of companies, we re-conduct the analysis using equallyweighted industry portfolio returns. These are, of course, more sensitive to the behavior of smaller companies within a given industry. We report the results of this analysis in Table 3, which show that the conclusions are largely robust to the company size effect. Conventional inflation betas continue to be negative without an exception. When the frequency dependent regressions are estimated, unexpected inflation betas are found to be positive and statistically significant for the same grouping 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 inflation. Finally, we conduct the analysis using firm-level data. Even the equally-weighted industry indices could mask the behavior of individual stocks. Moreover, some investors will rely on stand-alone stocks in their investments rather than portfolios; hence, the analysis could be useful in that aspect. We select our firm-level data from the oil and gas sector primarily because the above analysis shows that this industry is a candidate for providing a hedge against inflation 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 findings for this part of the analysis in Table 4 and, save for MUR, there is a positive and statistically significant relation between the unexpected component of inflation and these individual stock returns at the 10% level, suggesting that
6 To examine the robustness of our findings, we also used time series models to decompose inflation. Specifically, we estimated expected inflation using both VAR(1) and AR(2) models for three selected industries; reit, fin and gold. We chose those industries because they have positive and statistically significant unexpected inflation betas. The unexpected inflation betas are .31 (.79) for reit, .96 (.40) for fin and 1.93 (.27) for gold when a VAR(1) model is used. When, an AR(2) model is used, they are 1.01 (.17) for reit, 1.33 (.29) for fin and 2.86 (.13) for gold. These results are consistent with the view that time series models are unlikely to capture the dynamics uncovered by the Ashley–Verbrugge decomposition used in the paper and also, that it is difficult to determine the correct forecasting model to determine expected inflation. We thank an anonymous referee for suggesting this analysis.
Table 2 Inflation betas: value-weighted industry portfolios. Industry
Conventional
Long
Medium1
Medium2
Short
Agric Food Soda Beer Smoke Toys Fun Books Hshld Clths Hlth MedEq Drugs Chems Rubbr Txtls BldMt Cnstr Steel FabPr Mach ElcEq Aero Ships Guns Gold Mines Coal Oil Util Telcm Persv Bussv Hardw Softw Chips LabEq Paper Boxes Trans Whlsl Rtail Meals Banks Insur Real Fin
−.10 (.81) −.19 (.45) −1.03 (.03) −.29 (.36) .02 (.95) −.70 (.11) −1.59 (.01) −1.19 (.01) −.34 (.26) −.79 (.07) −.12 (.79) −.52 (.05) −.29 (.26) −.92 (.04) −.88 (.09) −1.20 (.22) −1.01 (.08) −.93 (.04) −1.04 (.08) −.56 (.30) −1.01 (.03) −1.02 (.02) −.75 (.06) −.81 (.14) .26 (.52) −.99 (.14) −1.61 (.00) −.94 (.27) −.39 (.28) −.10 (.69) −.80 (.01) −.21 (.59) −.64 (.04) −1.16 (.01) −.87 (.01) −.78 (.08) −.64 (.08) −.82 (.04) −.95 (.01) −.26 (.49) −.55 (.07) −.61 (.03) −.51 (.08) −.41 (.84) −.69 (.10) −1.39 (.06) −.94 (.03)
−.09 (.86) −.22 (.47) −1.19 (.02) −.45 (.18) .02 (.96) −.54 (.26) −1.89 (.00) −1.62 (.00) −.58 (.07) −.94 (.06) −.23 (.59) −.66 (.05) −.27 (.38) −1.05 (.04) −1.04 (.05) −1.47 (.13) −.98 (.11) −.69 (.21) −.85 (.26) −.78 (.28) −1.09 (.06) −1.05 (.04) −.70 (.13) −.75 (.22) .38 (.44) −.31 (.72) −1.33 (.06) −1.75 (.10) −.30 (.49) −.17 (.60) −.81 (.04) −.08 (.86) −.65 (.10) −1.45 (.01) −.95 (.06) −.78 (.20) −.72 (.16) −1.07 (.01) −1.00 (.01) −.43 (.29) −.57 (.14) −.65 (.06) −.40 (.24) −.64 (.21) −.73 (.12) −1.26 (.08) −.87 (.12)
−3.24 (.22) −.26 (.68) −1.69 (.25) −.25 (.73) −1.09 (.31) −.75 (.60) −.73 (.69) −1.36 (.34) .61 (.46) −.31 (.81) −1.91 (.10) −.83 (.32) −.56 (.46) −1.22 (.28) −1.03 (.52) −.93 (.73) −1.37 (.43) −2.03 (.16) −2.20 (.27) −1.60 (.38) −1.79 (.18) −.84 (.54) −.46 (.68) −.74 (.76) .03 (.97) −2.41 (.15) −2.97 (.07) −2.23 (.17) −1.71 (.07) −.30 (.68) −.99 (.33) −.62 (.61) −1.41 (.13) −.32 (.79) −1.06 (.30) −1.50 (.23) −1.69 (.12) −.85 (.48) −.96 (.40) .39 (.73) −1.05 (.22) −.84 (.33) .25 (.78) .04 (.97) −.45 (.73) −2.46 (.27) −2.34 (.07)
2.54 (.22) .17 (.85) .66 (.78) .82 (.43) .94 (.59) −1.74 (.41) −.06 (.97) 2.11 (.22) .67 (.54) −.18 (.92) 2.10 (.22) .89 (.55) −.13 (.90) .42 (.80) .42 (.78) .62 (.82) −.82 (.63) −1.67 (.37) −1.17 (.65) 1.88 (.41) .38 (.81) −.76 (.61) −1.25 (.39) −1.21 (.54) −.44 (.79) −4.42 (.16) −2.34 (.30) 6.23 (.05) .12 (.93) .59 (.56) −.40 (.75) −.82 (.58) .21 (.87) .36 (.83) .06 (.96) −.02 (.99) 1.00 (.56) 1.10 (.47) −.58 (.74) .54 (.71) .10 (.93) −.14 (.90) −1.92 (.20) .94 (.65) −.51 (.77) −1.20 (.63) −.13 (.94)
24.06 (.00) 4.20 (.46) −.68 (.94) −1.20 (.83) 6.15 (.48) 7.15 (.33) 8.65 (.42) 10.31 (.11) −1.26 (.79) −3.47 (.67) 4.72 (.59) 13.06 (.07) 5.33 (.32) 14.41 (.07) 4.44 (.51) 1.63 (.89) 9.51 (.20) 9.80 (.23) 29.50 (.00) 11.50 (.25) 19.53 (.01) 17.90 (.01) 8.16 (.30) 11.43 (.24) −3.46 (.70) 29.06 (.06) 20.95 (.04) 31.30 (.05) 18.56 (.00) 3.49 (.46) 14.47 (.02) 3.15 (.63) 12.88 (.02) 8.45 (.36) 19.17 (.03) 21.52 (.02) 22.10 (.00) 6.55 (.31) −.51 (.94) 6.97 (.31) 10.59 (.07) 2.43 (.69) −5.82 (.36) 4.00 (.64) 5.09 (.46) 22.98 (.03) 15.94 (.08)
Note — This table provides the inflation beta for value-weighted industry portfolios calculated by the conventional and frequency–decomposition approaches. Bold entries signify statistical significance.
C. Ciner / Review of Financial Economics 24 (2015) 12–17 Table 3 Frequency dependent regressions: equally-weighted industry portfolios. Industry
Conventional
Long
Medium1
Medium2
Short
Agric Food Soda Beer Smoke Toys Fun Books Hshld Clths Hlth MedEq Drugs Chems Rubbr Txtls BldMt Cnstr Steel FabPr Mach ElcEq Aero Ships Guns Gold Mines Coal Oil Util Telcm Persv Bussv Hardw Softw Chips LabEq Paper Boxes Trans Whlsl Rtail Meals Banks Insur Real Fin
−.42 (.43) −.73 (.02) −.94 (.04) −.71 (.05) .53 (.30) −1.24 (.02) −1.34 (.01) −2.49 (.00) −1.25 (.02) −1.25 (.02) −.53 (.19) −.92 (.02) −1.17 (.04) −1.15 (.02) −1.07 (.04) −1.32 (.09) −.84 (.09) −1.10 (.05) −.76 (.20) −.73 (.25) −.83 (.07) −.89 (.04) −.64 (.15) −.92 (.18) −.94 (.03) −2.35 (.00) −2.04 (.00) −.78 (.41) −.48 (.49) −.17 (.43) −1.66 (.00) −.99 (.02) −1.09 (.00) −1.42 (.00) −1.30 (.00) −1.26 (.01) −.83 (.05) −1.62 (.00) −.93 (.02) −.77 (.09) −1.09 (.02) −1.48 (.00) −1.24 (.01) −.06 (.85) −.68 (.09) −1.33 (.02) −.81 (.03)
−.52 (.38) −.72 (.06) −1.20 (.02) −.66 (.09) .90 (.17) −1.41 (.02) −1.50 (.01) −2.94 (.00) −1.59 (.00) −1.44 (.00) −.51 (.31) −1.09 (.03) −.94 (.18) −1.34 (.02) −1.46 (.01) −2.33 (.00) −.87 (.12) −.89 (.15) −.80 (.26) −.84 (.22) −1.06 (.07) −1.08 (.04) −.69 (.16) −.94 (.20) −.81 (.15) −1.85 (.10) −2.13 (.00) −1.75 (.14) −.63 (.46) −.25 (.37) −1.85 (.00) −.95 (.05) −1.15 (.02) −1.52 (.02) −1.51 (.01) −1.40 (.04) −1.10 (.04) −2.09 (.00) −1.03 (.04) −.84 (.09) −1.16 (.02) −1.56 (.00) −.1.22 (.02) −.15 (.68) −.54 (.22) −1.49 (.01) −.72 (.10)
−3.04 (.04) −1.45 (.10) −1.79 (.18) −.96 (.35) .63 (.74) −1.30 (.31) −2.06 (.19) −2.21 (.21) −1.24 (.45) −.69 (.66) −2.35 (.06) −1.84 (.07) −3.31 (.02) −1.27 (.33) −.08 (.96) −.41 (.85) −1.66 (.27) −3.02 (.08) −2.54 (.17) −1.59 (.40) −1.41 (.30) −1.96 (.13) −1.09 (.39) −1.36 (.52) −2.39 (.03) −6.40 (.00) −4.42 (.01) −1.09 (.54) −2.44 (.12) −.42 (.57) −2.28 (.10) −2.09 (.14) −2.42 (.01) −2.58 (.06) −2.28 (.06) −2.39 (.09) −1.91 (.11) −1.55 (.36) −1.17 (.32) −.91 (.51) −2.24 (.08) −2.16 (.71) −2.28 (.12) −.07 (.95) −1.04 (.41) −2.01 (.27) −1.85 (.09)
2.49 (.19) −.10 (.93) 1.67 (.40) −.77 (.58) −2.11 (.38) .12 (.94) .41 (.82) .64 (.78) 1.31 (.46) −.21 (.91) .82 (.63) 1.13 (.49) −.44 (.81) .45 (.81) .90 (.62) 5.20 (.02) .17 (.92) −.94 (.64) 1.15 (.62) .93 (.66) 1.44 (.40) 1.47 (.39) .19 (.90) −.10 (.96) −.78 (.68) −2.34 (.52) .73 (.77) 6.60 (.04) 2.46 (.29) .58 (.52) .40 (.83) −.38 (.81) .55 (.71) .48 (.80) 1.14 (.54) .89 (.66) 2.11 (.21) 1.78 (.36) −.02 (.98) −.10 (.95) .39 (.80) −.33 (.87) −.51 (.80) .58 (.68) −1.33 (.44) .48 (.83) −.55 (.71)
15.95 (.15) 4.93 (.44) 2.04 (.81) 6.12 (.31) 8.80 (.39) 12.21 (.14) 5.33 (.53) 11.15 (.28) 9.62 (.20) 6.42 (.47) 10.11 (.22) 11.41 (.20) 15.70 (.22) 14.42 (.09) .03 (.99) −2.32 (.79) 8.98 (.24) 12.75 (.19) 17.02 (.08) 23.88 (.01) 18.59 (.02) 17.86 (.03) 9.31 (.26) 24.48 (.01) −3.51 (.71) 33.27 (.02) 23.46 (.03) 19.87 (.28) 32.05 (.00) 3.56 (.38) 24.37 (.01) 7.68 (.30) 13.13 (.08) 20.19 (.07) 17.27 (.12) 22.33 (.04) 20.61 (.02) 9.41 (.28) −.49 (.95) 5.56 (.47) 8.14 (.30) 4.20 (.65) −1.20 (.89) 1.95 (.75) 6.09 (.33) 10.76 (.29) 10.33 (.14)
Note — This table provides inflation betas for equally-weighted portfolios using conventional and frequency decomposition approaches. Bold entries signify statistical significance.
the industry portfolio findings can be largely generalized to firm-level data at least for the oil and gas industry. 5. Conclusions Our findings suggest that significant frequency dependence exists in the relation between stock returns and inflation rate. Trend shocks, which are those with greater persistency, have a negative covariance Table 4 Inflation betas: oil company stocks.
CVX COP XOM HES MRO MUR
Conventional
Long
Medium1
Medium2
Short
−.29 (.43) −.35 (.45) −.14 (.61) −.33 (.61) −.37 (.47) −.81 (.31)
−.04 (.90) −.39 (.51) .19 (.56) −.56 (.46) −.03 (.96) −.62 (.35)
−1.26 (.27) −.83 (.55) −1.44 (.14) −2.72 (.02) −3.12 (.02) −1.72 (.17)
−1.11 (.53) .61 (.74) −1.40 (.32) 3.47 (.13) −.37 (.86) −1.30 (.55)
13.69 (.05) 23.24 (.00) 9.90 (.09) 26.77 (.01) 29.28 (.00) 16.93 (.13)
Note — This table provides the inflation beta for oil company stocks using the conventional and frequency domain approaches. Bold entries signify statistical significance.
17
with equity returns in all of the industries examined. However, we argue that this relation can be spurious if the impact of inflation on stock valuations is anticipated by market participants. If, for example, greater inflation leads to lower economic growth in the future as Fama (1981) has suggested, market valuations will be lowered in anticipation, generating negative inflation betas. This argument is particularly relevant for a highly persistent macroeconomic variable like inflation. Long term trend inflation betas are very similar to aggregate inflation betas because the majority of monthly changes in inflation is simply a continuation of the long term trend. On the other hand, higher frequency inflation shocks are transitory by nature, which implied that they cannot be anticipated. Therefore, a correct test of the sensitivity of stock returns to inflation should examine the link between high frequency inflationary shocks and equities, which is accomplished in this study. We find that commoditysensitive and technology-related equities do provide good inflation hedges in that they have positive and statistically significant links with unexpected inflation. 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 industry. Our study, overall, also has a noteworthy implication. When highly persistent macroeconomic data are used in financial research, accounting for frequency dependencies could yield richer results. References Ang, A., Brieri, M., & Signori, O. (2011). Inflation and individual equities. Working paper. Columbia Business School. Ashley, R. A., & Tsang, K. P. (2013). International evidence on the oil price–real output relationship: Does persistence matter? Available at SSRN 2185548 . Ashley, R., & Verbrugge, R. J. (2009). Frequency dependence in regression model coefficients: An alternative approach for modeling nonlinear dynamic relationships in time series. Econometric Reviews, 28, 4–20. Ashley, R., Tsang, K. P., & Verbrugge, R. (2011). Frequency dependence in a real-time monetary policy rule Available at SSRN 1543928 . Bekaert, Geert, & Wang, Xiaozheng (2010). Inflation risk and the inflation risk premium. Economic Policy, 25(64), 755–806. Bodie, Z. (1976). Common stocks as a hedge against inflation. Journal of Finance, 31, 459–470. Boudoukh, J., Richardson, M., & Whitelaw, R. F. (1994). Industry returns and the Fisher effect. Journal of Finance, 49(5), 1595–1615. Ciner, C. (2013). Oil and stock returns: Frequency domain evidence. Journal of International Financial Markets Institutions and Money, 23, 1–11. Ciner, C. (2014). The time varying relation between consumer confidence and equities. Journal of Behavioral Finance, 15, 312–317. Engle, R. F. (1974). Band spectrum regression. International Economic Review, 65, 1–11. Fama, E. F. (1981). Stock returns, real activity, inflation and money. American Economic Review, 74(4), 545–565. Fama, E. F., & Schwert, G. W. (1977). Asset returns and inflation. Journal of Financial Economics, 5, 115–146. Geske, Robert, & Roll, Richard (1983). The fiscal and monetary linkage between stock returns and inflation. Journal of Finance, 38, 1–33. Hagmann, M., & Lenz, C. (2004). Real asset returns and components of inflation: A structural VAR analysis (No. rp118). International Center for Financial Asset Management and Engineering. Hannan, E. (1963). Regression for time series. In M. Rosenblatt (Ed.), Time Series Analysis. New York: Wiley. Hess, P. J., & Lee, B. S. (1999). Stock returns and inflation with supply and demand disturbances. Review of Financial Studies, 12(5), 1203–1218. Kaul, Gautam (1987). Stock returns and inflation: The role of the monetary sector. Journal of Financial Economics, 18, 253–276. Kim, S., & In, F. (2006). A note on the relationship between industry returns and inflation through a multiscaling approach. Finance Research Letters, 3(1), 73–78. Lee, K., & Ni, S. (1996). Stock returns, real activities and temporary and persistent inflation. Applied Financial Economics, 6(5), 433–441. McQueen, G., & Roley, V. V. (1993). Stock prices, news, and business conditions. Review of Financial Studies, 6(3), 683–707. Pearce, D. K., & Roley, V. V. (1988). Firm characteristics, unanticipated inflation, and stock returns. The Journal of Finance, 43(4), 965–981. Tan, H. B., & Ashley, R. (1999). On the inherent nonlinearity of frequency dependent time series relationships. Nonlinear Time Series Analysis of Economic and Financial Data. US: Springer 129–142. Wei, C. (2009). Does the stock market react to unexpected inflation differently across the business cycle? Applied Financial Economics, 19(24), 1947–1959. Yanfeng, W. (2013). The dynamic relationships between oil prices and the Japanese economy: A frequency domain analysis. Review of Economics & Finance, 3, 57–67.
Contents lists available at ScienceDirect
Review of Financial Economics journal homepage: www.elsevier.com/locate/rfe
Are equities good inflation 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 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 classification: GO G1
a b s t r a c t By using industry level data, we examine the relation between equity returns and inflation in a frequency dependent framework. Our analysis shows that a positive relation in fact exists between equity returns and high frequency inflation shocks for commodity and technology related industries. Since higher frequency shocks are independent from trend and are transitory in nature, our findings imply a positive relation between stock returns and the unexpected component of inflation. Furthermore, we show that the results are robust to firm-level data by using a sample from the oil industry. Hence, our study provides a new look at the impact of inflation on equities by showing the sensitivity of conclusions in prior work to frequency dependence in data. © 2014 Elsevier Inc. All rights reserved.
Keywords: Inflation Stock returns Frequency domain
1. Introduction The relation between inflation and equity prices, motivated by the Fisher hypothesis, is one of the most frequently investigated topics in finance and economics. The underlying intuition of this hypothesis is that stocks represent claims on real assets and therefore, their valuations should increase with inflation. Thus, a positive relation is predicted between inflation and stock price movements, in which case it can be argued that equities provide a good hedge against the inflation risk. Unfortunately, empirical studies, beginning with the early work of Bodie (1976) and Fama and Schwert (1977), consistently report a negative correlation between stock returns and inflation. 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 finding is the “proxy” hypothesis of Fama (1981) and Kaul (1987). The argument of these authors is that the documented negative correlation with inflation is spurious. It arises because the stock market anticipates the negative impact of higher inflation on growth, which lowers the market valuations.1
☆ 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 significantly improved the paper. All remaining errors are mine. ⁎ Tel.: +1 910 962 7497. E-mail address: [email protected]. 1 Geske and Roll (1983) and Pearce and Roley (1988) provide discussions of alternative hypotheses on the negative correlation between inflation and stock returns.
http://dx.doi.org/10.1016/j.rfe.2014.12.001 1058-3300/© 2014 Elsevier Inc. All rights reserved.
In this paper our objective is to provide a further examination of the relation between stock returns and inflation by using a recently developed frequency domain decomposition method by Ashley and Verbrugge (2009). The principal advantage of this method is to allow us to examine whether there is persistency dependence in the stock return-inflation linkage, which could occur if higher and lower frequency inflationary shocks have different effects on stock price movements.2 We argue that differential effects of expected and unexpected inflationary shocks on stock valuations can be investigated by utilizing this method of analysis. Specifically, lower frequency shocks are those that tend to be persistent and are likely to represent a continuation of the trend in inflation. Thus, at least to some extent, these shocks can be anticipated by market participants. Higher frequency shocks, on the other hand, are those with less persistence and are, therefore, transitory in nature. These shocks are difficult to forecast by definition and hence, represent the unexpected component of inflation. Hence, our empirical method provides a novel approach to define unexpected inflation as those corresponding to higher frequencies on the spectra. Our primary hypothesis is that if equities are good inflation hedges then we should expect a positive relation between stock returns and unexpected inflation. Many studies in prior work have also examined the stock return– inflation linkage by obtaining proxies for expected and unexpected 2 While there are other frequency decomposition methods suggested in the literature, the Ashley–Verbrugge 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 inflation, which is plausible under the present value models of asset prices.
C. Ciner / Review of Financial Economics 24 (2015) 12–17
inflationary shocks. For example, Fama and Schwert (1977) use changes in the short term interest rate to infer the expected inflation. Bodie (1976) relies on ARIMA models to construct proxies for expected inflation. Hagmann and Lenz (2004) and Hess and Lee (1999) use vector autoregression (VAR) models to decompose inflation 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 inflation announcements. More recently, Wei (2009) uses a time series regression model that also includes lagged values of monthly unemployment rate to estimate the unexpected component of inflation. These studies in general support the conclusion of earlier papers that the relation between stock returns and unexpected inflation is also negative. Furthermore, in papers closely related to the present article, Lee and Ni (1996) use the Chebyshev filter to obtain estimates of unexpected inflation as the transitory component of inflationary shocks. These authors argue that there are differences in the relation between stock returns and inflation based on the frequency components of inflation. Kim and In (2006) rely on a multi-scale wavelet decomposition approach to examine the same relation. Interestingly, they detect a positive relation between inflation 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 Ashley–Verbrugge decomposition in the present paper rather than the abovementioned method of analyses.3 We also examine the stock return–inflation relation by relying on industry portfolios. This permits us to determine whether some sectors of the stock market may be considered better hedges against inflation. For example, Boudoukh et al. (1994) argue that non-cyclical stocks tend to be more positively correlated with inflation than cyclical stocks. Stocks of natural resource companies are usually considered as better inflation hedges because of the sensitivity of commodity prices to inflation. In the empirical analysis, therefore, we first calculate the conventional inflation betas using 48 industry portfolios by estimating conventional stock return–inflation 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 find that, in general, inflation betas are negative. Subsequently, we estimate the same model by replacing inflation with its frequency components obtained by the Ashley and Verbrugge (2009) decomposition. The results of this analysis lend support to the central claim of the paper, which is that the stock return–inflation relation shows dependency on the persistence of inflationary shocks. Specifically, we find that while long term, trend shocks, replicate the negative inflation betas obtained above as expected, inflation betas for unexpected (high frequency) shocks are in fact positive for 18 industry portfolios. These positive unexpected inflation 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. The first part of the empirical analysis utilizes value-weighted industry portfolios and hence, could simply be an artifact of data, since larger companies dominate value-weighted indices. To investigate the robustness of the findings to firm size, we conduct the analysis by using equally-weighted industry portfolios. We find largely similar results. Again, unexpected inflation betas for commodity-sensitive industries (gold, mines and oil) as well as technology-related industries (telecom, hardware and chips) have positive, and statistically significant, unexpected inflation 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 findings in Section 4. We provide the concluding comments of the paper in the final section of the study.
3
We thank an anonymous referee for recommending this discussion.
13
2. Statistical method of analysis Conventional time domain regressions are linear and force a fixed coefficient to describe the relation between the variables that is supposed to be constant at all frequencies. For instance, in the context of our paper, the conventional regression analysis suggests that the sensitivity of industry portfolio returns to transitory (high frequency) shocks in inflation is exactly the same as it is to permanent (low frequency) shocks. However, there is no a priori reason to expect this to always obtain and researchers have long recognized that estimating a frequency dependent regression model, in which the coefficient 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. For example, consider the following generalized linear regression model: 2 Y ¼ Xβ þ ϵ; ϵ N 0; σ j
ð1Þ
in which Y is T × 1 and X is 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 accomplished by pre-multiplying the regression by a T × T matrix A, whose (s,t)th element is given by
As;t
8 > 1 1=2 > > ; for s ¼ 1; > > T > > > 1=2 > > 2 πsðt−1Þ > > ; for s ¼ 2; 4; 6; …; ðT−2ÞorðT−1Þ cos < T T ¼ 1 > 2 2 πðs−1Þðt−1Þ > > ; for s ¼ 3; 5; 7; …; ðT−1Þor T; sin > > T T > > > 1 > > 2 1 tþ1 > > ð−1Þ ; for s ¼ T when T is even : T
AY ¼ AX β þ Aϵ A is an orthogonal matrix and the pre-multiplication gives: 2 Y ¼ X β þ ϵ ; ϵ n 0; σ I :
ð2Þ
In Eq. (2), the components of the variables now represent frequencies instead of time periods. Next, the T frequency components are partitioned into M frequency bands and dummy variables are created to define M vectors of length T, which can be written as D⁎1, ….. D⁎M. These dummy variables are used in a manner that for elements, which fall into the sth frequency band, D⁎s equals X⁎j and the elements are zero otherwise. Consequently, the regression equation can be rewritten as follows:
M
Y ¼ X f jg βf jg þ Σm¼1 β j;m D
m
þϵ
ð3Þ
in which X{j}⁎ is the X* with its jth column deleted and β{j} is the β vector with its jth component deleted. Hence, frequency-dependent coefficients βj,1 … … .. βj,M can be estimated and hypotheses tests can be conducted on the significance of these parameters. However, Ashley and Verbrugge (2009) argue that an important weakness exists in the above approach. In particular, since premultiplying with matrix A mixes past and futures values of the variables, the M frequency 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 finance and economics data. This would yield inconsistent estimates if the partitioned frequency components are used in an OLS regression. The main contribution of Ashley and Verbrugge (2009) is that they present a solution to this problem by applying a one-sided, rather
14
C. Ciner / Review of Financial Economics 24 (2015) 12–17
than a two-sided bandpass filter. In essence, they suggest decomposing Xj into frequency components by applying the same transformation above in a moving M-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 signifies the longest persistency that will be considered. That is because shocks with greater than M-month persistency are considered long term trend shocks and are lumped together at zero frequency. In the present paper, we consider a 36-month window, which implies that all temporary inflationary movements should dissipate in 36-months. The Ashley–Verbrugge decomposition approach has been used in several recent papers in the literature. Both Ashley and Tsang (2013) and Yanfeng (2013) examine the frequency dependence in oil price–economic 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 consumer sentiment and stock return, while Ciner (2013) focuses on sensitivity of the oil price–stock return relation to frequency of shocks. Also, as mentioned in the Introduction, our paper is closely related to Lee and Ni (1996), who use the Chebyshev filter, and to Kim and In (2006), who use the wavelet theory, to similarly decompose inflation into its high and low frequency components. Thus, it is important to highlight why the Ashley–Verbrugge approach is preferred in the present study. In regards to the wavelet theory used by Kim and In (2006), while their approach is helpful in understanding time variation 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 methodology 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 difficult to interpret regression coefficients when the wavelet decomposition is used. This is perhaps the most important advantage of the Ashley–Verbrugge approach over the wavelet analysis. The estimated coefficients can be easily interpreted in the Ashley–Verbrugge method as reflecting the persistency of shocks in dependent variables.4 In regards to the Chebyshev filter used by Lee and Ni (1996), it should be mentioned that their analysis is a novel econometric approach and is consistent with the key points of the Ashley–Verbrugge decomposition method. First, the Chebyshev filter also uses only past values of input series; hence, when the decomposed parts are used in a regression, coefficients will not suffer from simultaneity bias if there is feedback between the variables. Secondly, the estimated coefficients have economically meaningful interpretations again similar to the Ashley–Verbrugge approach. On the other hand, Chebyshev filters do have an important disadvantage over spectral filters in that leakage in the filter 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 filter. Finally, one could also use a time series model, such as a VAR or an ARMA model, to conduct the filtering exercise. However, these models cannot be constructed with specific cutoff points determined by the researcher and hence, the frequency of the resulting filtered series will not be known. Again, this would make the economic interpretation of the regression results using the filtered series rather difficult. 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 inflation, giving rise to different conclusions. Note the separate models in Hagmann and Lenz (2004) and Wei (2009) as an example of this point. The Ashley–Verbrugge approach defines expected versus unexpected inflationary shocks as a measure of persistency and hence, avoids determining the correct forecasting model.
4
We thank Richard Ashley for providing this information in private conversation.
3. Data The data used in our study include the CPI, measured as a monthly series of annual percentage change in headline inflation, and the monthly returns on 48 stock industry portfolios. The series span the period between January of 1990 and December of 2012.5 The inflation 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 1 provides the summary statistics of monthly stock returns. It can be observed that the returns are positive and statistically significantly 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 inflation rate into its frequency components using the Ashley–Verbrugge approach. The 36-month window used in the application decomposes the inflation rate into 19 frequency components including the zero frequency. We could estimate the stock return–inflation regressions by substituting the inflation variable by its 19 frequency components. However, this would involve a substantial loss in degrees of freedom and, also, different findings across individual frequencies could make interpreting the results difficult. Therefore, we generate four new groups from the frequency components that have intuitive motivations. Specifically, we create four new 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 specification, Long represents the trend in inflation as the component with the greatest persistency. Medium1 represents inflationary shocks with persistency between 12- and 36-months, while Medium2 consists of shocks with persistency between 3- and 12-months. And finally, Short stands for the highest frequency component of inflation. These are shocks with persistency of less than 3-months and hence, by definition represent the most transitory components of inflation changes. Recall that, by construction, the sum of these variables equals the original inflation variable and can therefore be used in regressions to replace the inflation rate to test for frequency dependence in the stock return–inflation 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 component of inflation. 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. In Figs. 1–5 we provide graphs of these new variables. An examination of the inflation components suggests that the Ashley–Verbrugge approach achieves a decomposition of the aggregate inflation consistent with our expectations. The trend in inflation, captured by Long, closely replicates the inflation rate, which is expected because a majority of changes in monthly inflation rate are simply a continuation of the long term trend in data, especially for highly persistent macroeconomic data like the inflation rate. At the other end of the spectrum, high frequency shocks in inflation, captured by Short, have much greater volatility and do not resemble the overall inflation series. This is also expected because by construction these should be short term and hence, unpredictable shocks, which should not have a smooth pattern. 5 As discussed above, the Ashley–Verbrugge method to obtain the moving windows for the 36-month trend frequency results in a loss of the first 34 observations, hence the effective data cover the period between October of 1992 and December of 2012 for a total of 243 observations.
C. Ciner / Review of Financial Economics 24 (2015) 12–17
15
Table 1 Summary statistics. Industry
Mean
Std. dev.
Skewness
Kurtosis
Agric Food Soda Beer Smoke Toys Fun Books Hshld Clths Hlth MedEq Drugs Chems Rubbr Txtls BldMt Cnstr Steel FabPr Mach ElcEq Aero Ships Guns Gold Mines Coal Oil Util Telcm Persv Bussv Hardw Softw Chips LabEq Paper Boxes Trans Whlsl Rtail Meals Banks Insur Real Fin
1.14 (.00) .74 (.00) 1.36 (.00) .84 (.00) 1.22 (.00) .47 (.24) 1.05 (.04) .63 (.08) .86 (.00) .87 (.03) .78 (.06) .85 (.00) .92 (.00) .94 (.01) .92 (.01) .56 (.30) .89 (.03) 1.08 (.01) .78 (.17) .48 (.36) 1.11 (.01) 1.25 (.00) 1.22 (.00) 1.42 (.00) 1.09 (.00) .82 (.25) 1.16 (.02) 1.81 (.02) 1.07 (.00) .77 (.00) .68 (.05) .61 (.12) .72 (.03) 1.32 (.02) 1.18 (.01) 1.09 (.05) .95 (.04) .77 (.02) .79 (.05) .86 (.01) .74 (.01) .88 (.00) .96 (.00) .83 (.04) .84 (.01) .68 (.17) 1.14 (.01)
6.43 3.97 7.67 4.93 7.23 6.42 8.03 5.59 4.25 6.83 6.61 4.82 4.57 5.82 6.05 8.53 6.53 7.12 8.86 8.32 6.99 6.56 6.33 7.58 6.48 11.24 8.10 12.47 5.53 4.13 5.42 6.20 5.25 8.80 7.75 8.78 7.23 5.31 6.36 5.30 4.78 5.01 4.87 6.33 5.40 7.79 7.39
.52 −.13 .24 −.41 −.14 −.23 −.23 .26 −.39 −.17 −.33 −.92 −.15 −.08 .06 1.14 −.10 −.38 −.29 −.07 −.49 −.31 −.93 .11 −.72 1.25 −.50 .11 −.04 −.60 −.23 −.19 −.69 −.33 −.01 −.46 −.28 .12 −.39 −.38 −.65 −.19 −.42 −.81 −.69 .94 −.49
1.84 1.68 3.59 2.03 2.38 1.19 3.57 4.70 2.34 1.86 1.04 2.23 .09 2.14 4.02 11.42 6.16 1.07 1.79 3.08 2.11 1.15 2.56 1.96 2.49 8.47 2.48 .89 .87 .91 1.24 .92 2.27 1.23 .86 1.26 1.19 2.72 1.15 .99 2.33 .53 .51 2.86 3.90 15.01 .89
Fig. 2. Long.
In which βconv stands for conventional estimates of inflation betas, Rit is monthly return of an industry portfolio and πt stands for monthly inflation rate. This is the standard model used in several papers in prior work including Ang et al. (2011) and Bekaert and Wang (2010) as recent examples. The conventional inflation beta, in this framework, measures the inflation hedging ability of a stock and it is expected to be positive if equities are good inflation hedges. As discussed above the central contribution of the present study is to decompose the rate of inflation into its frequency components and construct an enhanced model as follows: Rit ¼ α þ βLong πLong þ βMedium1 πMedium1 þ βMedium2 πMedium2 þ βShort π Short þ εt :
Note — This table provides the summary statistics of the data.
4. Empirical findings The primary model to estimate the relation between stock returns and inflation is the following equation: Rit ¼ α þ βconv πt þ εt
ð4Þ
Fig. 1. Aggregate CPI.
ð5Þ
Our primary argument is that that a frequency dependence on the inflation–equity return relation is likely to exist and, therefore, inflation betas will show variation across components of inflation. In particular, a good inflation hedge can be specified as a positive and statistically significant βShort coefficient in this framework as this would indicate a positive reaction to unexpected inflation shocks. We estimate both the conventional and frequency-dependent regression models using monthly industry return data and report the results in Table 2. We first observe that all of the estimated conventional inflation betas are negative and furthermore, are statistically significant 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, suggesting a negative covariance between the stock market movements and inflation. Even the commodity sensitive stocks, which are usually considered effective inflation hedges, have negative conventional inflation betas including coal, oil, gold and mines. In other words, the conclusion of this analysis is that equities do not provide protection against inflation risk at the industry level. We proceed to estimate the frequency dependent regression model depicted in Eq. (5) and report the inflation betas on the decomposed inflation series, also in Table 2. Consistent with our a priori expectation, the analysis now reveals the impact of different inflationary shocks on industry stock returns. Long term betas are largely consistent with conventional betas in that they are always negative and are statically significant for a majority of the industries in our sample. This is not
Fig. 3. Medium1.
16
C. Ciner / Review of Financial Economics 24 (2015) 12–17
Fig. 4. Medium2.
Fig. 5. Short.
surprising because, as mentioned above, monthly inflation changes largely reflect 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 inflationary shocks, which are captured by short term betas in Eq. (5). Specifically, we detect that several industry indexes react differently to transitory inflation shocks. We find that unexpected inflation betas are positive and statistically significant for 18 industry portfolios. Moreover, while there are exceptions, there seems to be two groups of industries with positive unexpected inflation betas. The first 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 inflation, which is consistent with this finding. 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 inflation 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 inflationary shocks to their profits and ultimately, to their stock prices.6 The above analysis uses value-weighted portfolios, which can potentially be dominated by larger companies in an industry. In an attempt to determine whether the findings reported above can be generalized for a broader range of companies, we re-conduct the analysis using equallyweighted industry portfolio returns. These are, of course, more sensitive to the behavior of smaller companies within a given industry. We report the results of this analysis in Table 3, which show that the conclusions are largely robust to the company size effect. Conventional inflation betas continue to be negative without an exception. When the frequency dependent regressions are estimated, unexpected inflation betas are found to be positive and statistically significant for the same grouping 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 inflation. Finally, we conduct the analysis using firm-level data. Even the equally-weighted industry indices could mask the behavior of individual stocks. Moreover, some investors will rely on stand-alone stocks in their investments rather than portfolios; hence, the analysis could be useful in that aspect. We select our firm-level data from the oil and gas sector primarily because the above analysis shows that this industry is a candidate for providing a hedge against inflation 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 findings for this part of the analysis in Table 4 and, save for MUR, there is a positive and statistically significant relation between the unexpected component of inflation and these individual stock returns at the 10% level, suggesting that
6 To examine the robustness of our findings, we also used time series models to decompose inflation. Specifically, we estimated expected inflation using both VAR(1) and AR(2) models for three selected industries; reit, fin and gold. We chose those industries because they have positive and statistically significant unexpected inflation betas. The unexpected inflation betas are .31 (.79) for reit, .96 (.40) for fin and 1.93 (.27) for gold when a VAR(1) model is used. When, an AR(2) model is used, they are 1.01 (.17) for reit, 1.33 (.29) for fin and 2.86 (.13) for gold. These results are consistent with the view that time series models are unlikely to capture the dynamics uncovered by the Ashley–Verbrugge decomposition used in the paper and also, that it is difficult to determine the correct forecasting model to determine expected inflation. We thank an anonymous referee for suggesting this analysis.
Table 2 Inflation betas: value-weighted industry portfolios. Industry
Conventional
Long
Medium1
Medium2
Short
Agric Food Soda Beer Smoke Toys Fun Books Hshld Clths Hlth MedEq Drugs Chems Rubbr Txtls BldMt Cnstr Steel FabPr Mach ElcEq Aero Ships Guns Gold Mines Coal Oil Util Telcm Persv Bussv Hardw Softw Chips LabEq Paper Boxes Trans Whlsl Rtail Meals Banks Insur Real Fin
−.10 (.81) −.19 (.45) −1.03 (.03) −.29 (.36) .02 (.95) −.70 (.11) −1.59 (.01) −1.19 (.01) −.34 (.26) −.79 (.07) −.12 (.79) −.52 (.05) −.29 (.26) −.92 (.04) −.88 (.09) −1.20 (.22) −1.01 (.08) −.93 (.04) −1.04 (.08) −.56 (.30) −1.01 (.03) −1.02 (.02) −.75 (.06) −.81 (.14) .26 (.52) −.99 (.14) −1.61 (.00) −.94 (.27) −.39 (.28) −.10 (.69) −.80 (.01) −.21 (.59) −.64 (.04) −1.16 (.01) −.87 (.01) −.78 (.08) −.64 (.08) −.82 (.04) −.95 (.01) −.26 (.49) −.55 (.07) −.61 (.03) −.51 (.08) −.41 (.84) −.69 (.10) −1.39 (.06) −.94 (.03)
−.09 (.86) −.22 (.47) −1.19 (.02) −.45 (.18) .02 (.96) −.54 (.26) −1.89 (.00) −1.62 (.00) −.58 (.07) −.94 (.06) −.23 (.59) −.66 (.05) −.27 (.38) −1.05 (.04) −1.04 (.05) −1.47 (.13) −.98 (.11) −.69 (.21) −.85 (.26) −.78 (.28) −1.09 (.06) −1.05 (.04) −.70 (.13) −.75 (.22) .38 (.44) −.31 (.72) −1.33 (.06) −1.75 (.10) −.30 (.49) −.17 (.60) −.81 (.04) −.08 (.86) −.65 (.10) −1.45 (.01) −.95 (.06) −.78 (.20) −.72 (.16) −1.07 (.01) −1.00 (.01) −.43 (.29) −.57 (.14) −.65 (.06) −.40 (.24) −.64 (.21) −.73 (.12) −1.26 (.08) −.87 (.12)
−3.24 (.22) −.26 (.68) −1.69 (.25) −.25 (.73) −1.09 (.31) −.75 (.60) −.73 (.69) −1.36 (.34) .61 (.46) −.31 (.81) −1.91 (.10) −.83 (.32) −.56 (.46) −1.22 (.28) −1.03 (.52) −.93 (.73) −1.37 (.43) −2.03 (.16) −2.20 (.27) −1.60 (.38) −1.79 (.18) −.84 (.54) −.46 (.68) −.74 (.76) .03 (.97) −2.41 (.15) −2.97 (.07) −2.23 (.17) −1.71 (.07) −.30 (.68) −.99 (.33) −.62 (.61) −1.41 (.13) −.32 (.79) −1.06 (.30) −1.50 (.23) −1.69 (.12) −.85 (.48) −.96 (.40) .39 (.73) −1.05 (.22) −.84 (.33) .25 (.78) .04 (.97) −.45 (.73) −2.46 (.27) −2.34 (.07)
2.54 (.22) .17 (.85) .66 (.78) .82 (.43) .94 (.59) −1.74 (.41) −.06 (.97) 2.11 (.22) .67 (.54) −.18 (.92) 2.10 (.22) .89 (.55) −.13 (.90) .42 (.80) .42 (.78) .62 (.82) −.82 (.63) −1.67 (.37) −1.17 (.65) 1.88 (.41) .38 (.81) −.76 (.61) −1.25 (.39) −1.21 (.54) −.44 (.79) −4.42 (.16) −2.34 (.30) 6.23 (.05) .12 (.93) .59 (.56) −.40 (.75) −.82 (.58) .21 (.87) .36 (.83) .06 (.96) −.02 (.99) 1.00 (.56) 1.10 (.47) −.58 (.74) .54 (.71) .10 (.93) −.14 (.90) −1.92 (.20) .94 (.65) −.51 (.77) −1.20 (.63) −.13 (.94)
24.06 (.00) 4.20 (.46) −.68 (.94) −1.20 (.83) 6.15 (.48) 7.15 (.33) 8.65 (.42) 10.31 (.11) −1.26 (.79) −3.47 (.67) 4.72 (.59) 13.06 (.07) 5.33 (.32) 14.41 (.07) 4.44 (.51) 1.63 (.89) 9.51 (.20) 9.80 (.23) 29.50 (.00) 11.50 (.25) 19.53 (.01) 17.90 (.01) 8.16 (.30) 11.43 (.24) −3.46 (.70) 29.06 (.06) 20.95 (.04) 31.30 (.05) 18.56 (.00) 3.49 (.46) 14.47 (.02) 3.15 (.63) 12.88 (.02) 8.45 (.36) 19.17 (.03) 21.52 (.02) 22.10 (.00) 6.55 (.31) −.51 (.94) 6.97 (.31) 10.59 (.07) 2.43 (.69) −5.82 (.36) 4.00 (.64) 5.09 (.46) 22.98 (.03) 15.94 (.08)
Note — This table provides the inflation beta for value-weighted industry portfolios calculated by the conventional and frequency–decomposition approaches. Bold entries signify statistical significance.
C. Ciner / Review of Financial Economics 24 (2015) 12–17 Table 3 Frequency dependent regressions: equally-weighted industry portfolios. Industry
Conventional
Long
Medium1
Medium2
Short
Agric Food Soda Beer Smoke Toys Fun Books Hshld Clths Hlth MedEq Drugs Chems Rubbr Txtls BldMt Cnstr Steel FabPr Mach ElcEq Aero Ships Guns Gold Mines Coal Oil Util Telcm Persv Bussv Hardw Softw Chips LabEq Paper Boxes Trans Whlsl Rtail Meals Banks Insur Real Fin
−.42 (.43) −.73 (.02) −.94 (.04) −.71 (.05) .53 (.30) −1.24 (.02) −1.34 (.01) −2.49 (.00) −1.25 (.02) −1.25 (.02) −.53 (.19) −.92 (.02) −1.17 (.04) −1.15 (.02) −1.07 (.04) −1.32 (.09) −.84 (.09) −1.10 (.05) −.76 (.20) −.73 (.25) −.83 (.07) −.89 (.04) −.64 (.15) −.92 (.18) −.94 (.03) −2.35 (.00) −2.04 (.00) −.78 (.41) −.48 (.49) −.17 (.43) −1.66 (.00) −.99 (.02) −1.09 (.00) −1.42 (.00) −1.30 (.00) −1.26 (.01) −.83 (.05) −1.62 (.00) −.93 (.02) −.77 (.09) −1.09 (.02) −1.48 (.00) −1.24 (.01) −.06 (.85) −.68 (.09) −1.33 (.02) −.81 (.03)
−.52 (.38) −.72 (.06) −1.20 (.02) −.66 (.09) .90 (.17) −1.41 (.02) −1.50 (.01) −2.94 (.00) −1.59 (.00) −1.44 (.00) −.51 (.31) −1.09 (.03) −.94 (.18) −1.34 (.02) −1.46 (.01) −2.33 (.00) −.87 (.12) −.89 (.15) −.80 (.26) −.84 (.22) −1.06 (.07) −1.08 (.04) −.69 (.16) −.94 (.20) −.81 (.15) −1.85 (.10) −2.13 (.00) −1.75 (.14) −.63 (.46) −.25 (.37) −1.85 (.00) −.95 (.05) −1.15 (.02) −1.52 (.02) −1.51 (.01) −1.40 (.04) −1.10 (.04) −2.09 (.00) −1.03 (.04) −.84 (.09) −1.16 (.02) −1.56 (.00) −.1.22 (.02) −.15 (.68) −.54 (.22) −1.49 (.01) −.72 (.10)
−3.04 (.04) −1.45 (.10) −1.79 (.18) −.96 (.35) .63 (.74) −1.30 (.31) −2.06 (.19) −2.21 (.21) −1.24 (.45) −.69 (.66) −2.35 (.06) −1.84 (.07) −3.31 (.02) −1.27 (.33) −.08 (.96) −.41 (.85) −1.66 (.27) −3.02 (.08) −2.54 (.17) −1.59 (.40) −1.41 (.30) −1.96 (.13) −1.09 (.39) −1.36 (.52) −2.39 (.03) −6.40 (.00) −4.42 (.01) −1.09 (.54) −2.44 (.12) −.42 (.57) −2.28 (.10) −2.09 (.14) −2.42 (.01) −2.58 (.06) −2.28 (.06) −2.39 (.09) −1.91 (.11) −1.55 (.36) −1.17 (.32) −.91 (.51) −2.24 (.08) −2.16 (.71) −2.28 (.12) −.07 (.95) −1.04 (.41) −2.01 (.27) −1.85 (.09)
2.49 (.19) −.10 (.93) 1.67 (.40) −.77 (.58) −2.11 (.38) .12 (.94) .41 (.82) .64 (.78) 1.31 (.46) −.21 (.91) .82 (.63) 1.13 (.49) −.44 (.81) .45 (.81) .90 (.62) 5.20 (.02) .17 (.92) −.94 (.64) 1.15 (.62) .93 (.66) 1.44 (.40) 1.47 (.39) .19 (.90) −.10 (.96) −.78 (.68) −2.34 (.52) .73 (.77) 6.60 (.04) 2.46 (.29) .58 (.52) .40 (.83) −.38 (.81) .55 (.71) .48 (.80) 1.14 (.54) .89 (.66) 2.11 (.21) 1.78 (.36) −.02 (.98) −.10 (.95) .39 (.80) −.33 (.87) −.51 (.80) .58 (.68) −1.33 (.44) .48 (.83) −.55 (.71)
15.95 (.15) 4.93 (.44) 2.04 (.81) 6.12 (.31) 8.80 (.39) 12.21 (.14) 5.33 (.53) 11.15 (.28) 9.62 (.20) 6.42 (.47) 10.11 (.22) 11.41 (.20) 15.70 (.22) 14.42 (.09) .03 (.99) −2.32 (.79) 8.98 (.24) 12.75 (.19) 17.02 (.08) 23.88 (.01) 18.59 (.02) 17.86 (.03) 9.31 (.26) 24.48 (.01) −3.51 (.71) 33.27 (.02) 23.46 (.03) 19.87 (.28) 32.05 (.00) 3.56 (.38) 24.37 (.01) 7.68 (.30) 13.13 (.08) 20.19 (.07) 17.27 (.12) 22.33 (.04) 20.61 (.02) 9.41 (.28) −.49 (.95) 5.56 (.47) 8.14 (.30) 4.20 (.65) −1.20 (.89) 1.95 (.75) 6.09 (.33) 10.76 (.29) 10.33 (.14)
Note — This table provides inflation betas for equally-weighted portfolios using conventional and frequency decomposition approaches. Bold entries signify statistical significance.
the industry portfolio findings can be largely generalized to firm-level data at least for the oil and gas industry. 5. Conclusions Our findings suggest that significant frequency dependence exists in the relation between stock returns and inflation rate. Trend shocks, which are those with greater persistency, have a negative covariance Table 4 Inflation betas: oil company stocks.
CVX COP XOM HES MRO MUR
Conventional
Long
Medium1
Medium2
Short
−.29 (.43) −.35 (.45) −.14 (.61) −.33 (.61) −.37 (.47) −.81 (.31)
−.04 (.90) −.39 (.51) .19 (.56) −.56 (.46) −.03 (.96) −.62 (.35)
−1.26 (.27) −.83 (.55) −1.44 (.14) −2.72 (.02) −3.12 (.02) −1.72 (.17)
−1.11 (.53) .61 (.74) −1.40 (.32) 3.47 (.13) −.37 (.86) −1.30 (.55)
13.69 (.05) 23.24 (.00) 9.90 (.09) 26.77 (.01) 29.28 (.00) 16.93 (.13)
Note — This table provides the inflation beta for oil company stocks using the conventional and frequency domain approaches. Bold entries signify statistical significance.
17
with equity returns in all of the industries examined. However, we argue that this relation can be spurious if the impact of inflation on stock valuations is anticipated by market participants. If, for example, greater inflation leads to lower economic growth in the future as Fama (1981) has suggested, market valuations will be lowered in anticipation, generating negative inflation betas. This argument is particularly relevant for a highly persistent macroeconomic variable like inflation. Long term trend inflation betas are very similar to aggregate inflation betas because the majority of monthly changes in inflation is simply a continuation of the long term trend. On the other hand, higher frequency inflation shocks are transitory by nature, which implied that they cannot be anticipated. Therefore, a correct test of the sensitivity of stock returns to inflation should examine the link between high frequency inflationary shocks and equities, which is accomplished in this study. We find that commoditysensitive and technology-related equities do provide good inflation hedges in that they have positive and statistically significant links with unexpected inflation. 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 industry. Our study, overall, also has a noteworthy implication. When highly persistent macroeconomic data are used in financial research, accounting for frequency dependencies could yield richer results. References Ang, A., Brieri, M., & Signori, O. (2011). Inflation and individual equities. Working paper. Columbia Business School. Ashley, R. A., & Tsang, K. P. (2013). International evidence on the oil price–real output relationship: Does persistence matter? Available at SSRN 2185548 . Ashley, R., & Verbrugge, R. J. (2009). Frequency dependence in regression model coefficients: An alternative approach for modeling nonlinear dynamic relationships in time series. Econometric Reviews, 28, 4–20. Ashley, R., Tsang, K. P., & Verbrugge, R. (2011). Frequency dependence in a real-time monetary policy rule Available at SSRN 1543928 . Bekaert, Geert, & Wang, Xiaozheng (2010). Inflation risk and the inflation risk premium. Economic Policy, 25(64), 755–806. Bodie, Z. (1976). Common stocks as a hedge against inflation. Journal of Finance, 31, 459–470. Boudoukh, J., Richardson, M., & Whitelaw, R. F. (1994). Industry returns and the Fisher effect. Journal of Finance, 49(5), 1595–1615. Ciner, C. (2013). Oil and stock returns: Frequency domain evidence. Journal of International Financial Markets Institutions and Money, 23, 1–11. Ciner, C. (2014). The time varying relation between consumer confidence and equities. Journal of Behavioral Finance, 15, 312–317. Engle, R. F. (1974). Band spectrum regression. International Economic Review, 65, 1–11. Fama, E. F. (1981). Stock returns, real activity, inflation and money. American Economic Review, 74(4), 545–565. Fama, E. F., & Schwert, G. W. (1977). Asset returns and inflation. Journal of Financial Economics, 5, 115–146. Geske, Robert, & Roll, Richard (1983). The fiscal and monetary linkage between stock returns and inflation. Journal of Finance, 38, 1–33. Hagmann, M., & Lenz, C. (2004). Real asset returns and components of inflation: A structural VAR analysis (No. rp118). International Center for Financial Asset Management and Engineering. Hannan, E. (1963). Regression for time series. In M. Rosenblatt (Ed.), Time Series Analysis. New York: Wiley. Hess, P. J., & Lee, B. S. (1999). Stock returns and inflation with supply and demand disturbances. Review of Financial Studies, 12(5), 1203–1218. Kaul, Gautam (1987). Stock returns and inflation: The role of the monetary sector. Journal of Financial Economics, 18, 253–276. Kim, S., & In, F. (2006). A note on the relationship between industry returns and inflation through a multiscaling approach. Finance Research Letters, 3(1), 73–78. Lee, K., & Ni, S. (1996). Stock returns, real activities and temporary and persistent inflation. Applied Financial Economics, 6(5), 433–441. McQueen, G., & Roley, V. V. (1993). Stock prices, news, and business conditions. Review of Financial Studies, 6(3), 683–707. Pearce, D. K., & Roley, V. V. (1988). Firm characteristics, unanticipated inflation, and stock returns. The Journal of Finance, 43(4), 965–981. Tan, H. B., & Ashley, R. (1999). On the inherent nonlinearity of frequency dependent time series relationships. Nonlinear Time Series Analysis of Economic and Financial Data. US: Springer 129–142. Wei, C. (2009). Does the stock market react to unexpected inflation differently across the business cycle? Applied Financial Economics, 19(24), 1947–1959. Yanfeng, W. (2013). The dynamic relationships between oil prices and the Japanese economy: A frequency domain analysis. Review of Economics & Finance, 3, 57–67.