Generalized Fisher Hypothesis Validity for Canada, UK, and Suisse Stock Markets: Evidence from ARDL Models

The original hypothesis that is attributed to the monetarist, Irvin Fisher offers the first preliminary study towards formalizing the relationship between asset returns and inflation. Fisher hypothesis assumes that nominal interest rate is expressed as the sum of real return and inflation rate2. Fisher (1930) hypothesized that the expected real interest rate is determined by real factors and is independent of the expected inflation rate. This hypothesis was generalized to asset in the efficient stock markets context (Fama & Schwert, 1977).

The generalized Fisher hypothesis (GFH) assumes independence between the expected real return and inflation. Invalidity of the GFH, that real returns on financial assets are likely to be dependent of inflation rates, has some implications. The more important implication is the uncertainty creation across financial markets, thereby adversely affecting investment and saving decisions in an economy. According to the GFH, in an efficient market, investors should be fully compensated for the increased price levels even if inflation decreases the value of money. Associated with perfectly competitive and informationally efficient capital markets in which investors are rational, the GFH postulates that stock prices should move one-for-one with goods prices to compensate investors for prices growth (inflation). This implies that stock returns should serve as a hedge against inflation, that is, real stock returns and inflation are independent. Consequently, we should observe a positive and one-to-one relationship between nominal stock returns and inflation rates.

The Fisher hypothesis has become the workhorse for motivating the inflation hedging question of any asset class including commodities (Arnold & Auer, 2015). However, existing empirical research on the relationship between stock returns and expected inflation hasn't reached a consensus yet. During the 1970s, new evidence contradicted the economic GFH. More specifically, (Nelson, 1976; Bodie, 1976; Fama & Schwert, 1977; Modigliani & Cohn, 1979) reported a negative relationship between stock returns and inflation. Later, from the consequence of proxy hypothesis effects, Fama (1981) concluded also for the negative correlation between stock returns and inflation. This proxy hypothesis garnered substantial support in some subsequent papers (Gultekin, 1983; Geske & Roll, 1983; Erb, et al. 1995).

The negative relationship between real stock returns and inflation rates has also been explained by four theories based on four hypotheses including Money Illusion Hypothesis (MIH), Tax Effect Hypothesis (TEH), Proxy Effect Hypothesis (PEH), and Reverse Causality Hypothesis (RCH) (Tiwari, et al. 2019).

The positive relationship between nominal stock returns and inflation rates can also be explained by the Wealth Effect Hypothesis (WEH) since real stock returns can affect inflation rates through their impact on consumption and then on aggregate demand (Ando & Modigliani, 1963). According to WEH, there are different channels through which stock prices can affect consumption such as the realized gain (higher future income and wealth) via the expectation that raising the current stock price, the liquidity constraint effect, and the stock option value effect. Based on these two hypotheses (GFH and WEH), a positive relationship between nominal stock returns and inflation rates can be observed in the data.

Empirically, the relationship between (nominal or real) stock returns and inflation has been analyzed in the literature for short or long horizons. For short-run, many have found a negative correlation (Bodie, 1976; Fama & Schwert, 1977; Fama, 1981; Ghazali & Ramlee, 2003; Koustas & Lamarche, 2010; Tsong & Lee, 2013), while for long-run, the results are more likely to support the Fisher hypothesis (Schotman & Schweitzer, 2000; Lothian & McCarthy, 2001).

Two other important questions on the correlation between real stock returns and inflation rates are treated in the literature. The first is about the sign and the strength of the correlation that may depend on the frequency scale (price level vs index level). The second is about how the correlations can evolve heterogeneously overtime (Valcarcel, 2012; Antonakakis, et al. 2017).

Previous studies have dealt with different models and inferential (estimation and test) approaches in order to detect and explain the hedging inflation ability. Recently, for robustness question, the panel data-based approach was used in a few numbers of papers (Afees, et al. 2019, 2020; Halit, 2016). For example, Afees, et al.(2019) found that the GFH test results based on panel data (the price level data for the individual constituents of US stock returns) were opposite to those based rather on the index level data (univariate time series).

In this paper, GFH test will be verified within the univariate time series type data. We consider three developed countries having in common a monetary policy based on inflation rate targeting stabilization including Canada, the UK, and Suisse stock markets for the period from 1999M01 to 2018M04 covering 2008 GF crisis. The objective is to examine the inflation-hedging ability within each stock market. We want to know if hedging ability results from each stock markets may be different from ones of the portfolio asset from the three stock markets. In addition, since the long run relationship between stock return and inflation can be instable through time, the analysis will be done for the following four periods: the full data set and the three sub periods: Pre the Global Financial Crisis (GFC), during the GFC period, and Post the GFC period. To the best of our knowledge, our paper is the first which uses a univariate ARDL approaches to explore the stability of the GFH relationship that examining the inflation- hedging ability.

This study is organized as follows: after introduction, we give an empirical literature review; we mention then the required data and their sources and we give some descriptive analysis and present data analysis; after that, we outline the methodology used and we provide the empirical results and analysis; concluding remarks will be given at the end.

The generalized Fisher hypothesis assumes the independence between the expected real return and inflation and a positive relationship between nominal stock returns and expected inflation. These conditions have also been extensively explored for developing and advanced economies over the past three decades (Lintner, 1973; Fama, 1981; Geske & Roll, 1983; Basse & Reddemann, 2011; Arnold & Auer, 2015; Baker & Jabbouri, 2016; Baker & Jabbouri, 2017; Adekoya, et al. 2021; Simpson, et al. 2007). Some studies highlighted the existence of positive and/or negative associations (Hardin, et al. 2012; Hoesli, et al. 1997; Barnes, et al. 1999; Lee & Lee, 2012), while others have detected only a negative relationship (Chatrath, 1997; Maysami & Koh, 2000).

More recent studies are based on recent models and techniques in order to detect the hedging inflation ability such as the NARDL model (Thi, et al. 2016), the time variation investigation (Salisu, et al. 2019; Kuang, 2017), the cointegration tests (Al-Nassar & Bhatti, 2019), the comparative analysis (Akinsomi, 2020), the ARDL model (Afees, et al. 2020), the VAR model (Sangyup & Junhyeok, 2022), etc.

Based on Markov-switching GRG copula model, Kuang (2017) explored tail quantile dependences between the inflation rate and the real estate investment trust (REIT) return. Finding say that the positive and negative co- movements coexist. In the negative co-movement state, the REIT cannot hedge inflation risk, while in the positive co-movement state, the REIT has a partially hedging ability.

Recently, Salisu, et al. (2019) examined the inflation hedging potential of the two most valuable precious metals namely gold and palladium. They employed both time series and panel data techniques for country-specific and group analyses. They concluded that both gold and palladium provide hedge against inflation in OECD countries notwithstanding the varying results across the individual countries. While the inflation-hedging potential of gold has been sustained, it only improves for palladium after the Global Financial Crisis. Their conclusions are sensitive to data frequency. Also, in order to investigate the relationship between property returns and inflation hedging ability, Akinsomi (2020) used a comparative analysis of the year-to-date (YTD) returns of global returns index and REITs sectors in the United States. Finding reveal that most sector REITs during the pandemic have lost considerable value based on YTD returns as at May 2020. Flight to quality is expected during this uncertain period to REITs such as data REITs, grocery-anchored REITs and storage REITs. These REITs are not as adversely affected by COVID-19 in comparison to other REITs.

Afees, et al. (2020) analyzed asset-inflation hedging nexus for the US with the aim of determining inflation hedging characteristics of selected assets; stocks, gold, and real estate’s using the bivariate and multivariate modelling frameworks that taking into account of the asymmetry, the time-variation and the structural breaks. Founding says that inflation hedging tendencies of assets are heterogeneous across the considered assets. The real estates and stocks are proved to be good hedges against inflation, while gold investment defied Fisher’s hypothesis. However, even the results are robust to alternative data frequencies, they are sensitive to the decomposition of data for pre- and post-GFC periods, indicating that asset-inflation hedging relationship for the US is time-varying.

Sangyup & Junhyeok (2022) used a Vector Autoregression (VAR) model. They provide systematic evidence on the relationship between inflation, uncertainty, and Bitcoin. Bitcoin appreciates against inflation (or inflation expectation) shocks, confirming its inflation-hedging property claimed by investors. The main findings hold with or without the COVID-19 pandemic episode.

To the best of our knowledge, only one study in the above literature has consider the ARDL model (Afees, et al. 2020) and only one which consider both univariate time serie and panel data analysis (Salisu, et al. 2019).

In this paper, we’ll conduct an analyses on three developed countries including the United Kingdom, Canada and Switzerland for a period spanning from 1999 to 2018 covering the 2008 GFC period using univariate ARDL models. We which to see if the asset-inflation hedging relationship for the considered sample is time-varying or not (say if results are sensitive to the decomposition of data for pre- during and post- GFC periods).

GFH verification can be implemented in different specifications (static or dynamic). Dynamic specifications are considered and applied in the following sub-sections.

To explore the long- and short-run linear relationships between stock market returns and inflation, the following equation in the ARDL form will be used:

where $\mathrm{R}=\Delta \log (\mathrm{SP})$ and $\mathrm{INF}=\Delta \log (\mathrm{CPI}), \mathrm{SP}$ is the stock price, and CPI is the consumer price index. $\mathrm{C}_1$ is the intercept, $\delta_1$, and $\delta_2$ represent long-term relationship (all are real parameters), $\alpha_i$ and $\beta_i$ represent shortterm relationship, $p$ and $q$ are the optimal lags to be used, $\Delta=1-B, B$ is the lag operator, and $\varepsilon_t \sim W N(0$, $\left.\sigma^2\right)$.

To resolve null hypothesis of no cointegration in the ARDL framework, Pesaran, et al. (2001) provided the bound test based on F_PSS Fisher type statistic that can be applied regardless of whether the series are I (0), I (1) or fractionally integrated (but not I(2)). If cointegrating relationship is established between stock returns and inflation, Granger causality test can be done in the following error correction model (ECM):

where: $\mathrm{ECT}_{\mathrm{t}-1}=R_{t-1}-\gamma_2 I N F_{t-1}+c$ is the error correction term representing the long-run relationship between stock returns and inflation, $\delta_1$ captures the sensitivity of the error correction term.

A negative and significant coefficient of the error correction term, the speed of adjustment 𝛿₁, indicates that there is a long-run causal relationship between stock returns and inflation. Precisely, the unidirectional causality from inflation to stock returns hints an inefficiency of the stock market which suggests that information on past values of inflation could provide opportunities for abnormal gains from the return R.

The positive relationship between inflation and stock market returns in long run ($\gamma_2$ > 0) is the Fisher hypothesis. It suggests that as inflation rises, investors on stock market are compensated for it in the long run.

Theoretically, negative relationship in short-run (𝛽_𝑖 < 0 or ∑^𝑝 𝛽_𝑖 < 0) is in tandem with (Fama, 1981) proxy hypothesis (and the standard stock valuation model which predict a negative relationship between inflation and stock market returns).

The paper uses a dataset for three (N=3) countries, including Suisse, UK, and Canada over the period from 1999M01 to 2018M04 (T=232). The stock price SP data is obtained from the investiong.com while the consumer price CPI series is obtained from OCDE. We use a large sample that includes both the pre- and post-2008-2010 periods of the Global Financial Crisis (GFC).

In order to implement the ARDL model, we determine the appropriate lags length. All lags selections are based on the lowest value of the Akaike Information Criterion (AIC). All these results are reported at Table 2 (see note). We consider then the question of cointegrating relationship test between stock return (R) and Inflation (INF). The results of F_PSS test-statistic are reported in Table 1. The F_PSS -statistics for joint significance are above the upper bound critical value at 5% level of significance (4.16). This result confirms the existence of long-run equilibrium relationship among the variables used for each of the three considered stock markets and for the full period as well as for the three sub-periods (pre, during, and post crisis). Then, we can investigate whether the stock return responds positively or negatively, completely or partially to changes in inflation.

We further go to the long-run stability relationships. The results of the long run coefficients are presented in Table 2. The negative and statistically significant coefficients of the Error Correction Terms (ECT_t−1) suggests that there is a unidirectional causality running from inflation to stock market returns for each country and for all considered periods.

From Table 2, it is clear that the long run relationship between R and INF is ‘significantly’ positive only for Suisse stock market (during the GFC crisis) and Canadian stock market for all considered sub-periods. The positive long run relationship is in a chord with Fisher hypothesis. It suggests that as inflation rises, investors on the Suisse or Canadian stock market are compensated for it in the long run. Moreover, the unidirectional causality from inflation to stock returns hints of inefficiency of the Suisse and Canadian stock markets which suggests that information on past values of inflation could provide opportunities for abnormal gains from the Suisse and Canadian stock markets.

Besides, for the UK stock market, negative relationship implies that the Fisher effect is not only not valid in the long run but can be connoted by a worse hedging against inflation. This result is not surprising since UK stock return is the lowest in mean while the UK inflation rate on average is negative. Based on the theories mentioned in the introduction, we conclude that for post or pre GFC period, the Fisher and the Wealth Effect Hypothesis could be rejected in favor of the Money Illusion, Tax Effect, Proxy Effect and/or Reverse Causality Hypotheses.

Looking at different considered periods, Suisse stock market seems to be inefficient for only during crisis period. Indeed, between 2008M01 and 2009M12 (crisis period), Suisse stock market has superior performance as $\hat{\beta}$ = 2.082296 >> 1. However, Canadian stock market is found to be inefficient for all considered periods. Results support partial Fisher effects Pre crisis period ($\hat{\beta}$=0.67395 < 1), full hedge hypothesis for post crisis period ($\hat{\beta}$=0.98384 ≈ 1), and a superior performance ($\hat{\beta}$=2.328087 >> 1) during crisis period.

Diagnostic tests (in Table 3) suggest adequate specifications for all countries and for all considered periods since the models show free autocorrelation errors and free conditional heteroscedasticity. The structural stability test is conducted by employing the cumulative sum of squares recursive residuals (CUSUMSQ). The stability tests confirm the stability of the estimated coefficients during crisis and post crisis periods.

For the Suisse market case, the selected model by AIC criteria is ARDL(1, 0) for the full period and for the three considered sub-periods (Pre, during, and Post crisis). For the UK stock market, we get the ARDL(5, 0) for full period and ARDL(1, 0) for the 3 sub-periods. For the Canada stock market, we get the ARDL (2, 1) for full period, ARDL(1, 0) for pre and during crisis and the ARDL(2, 0) for the post crisis period. $\gamma_2$ is the long run effect of INF in equation (2). The positive relationship between inflation and stock market returns in long run ($\gamma_2$ > 0) suggests that as inflation rises investors on stock market are compensated for it in the long run. $\delta_1$ is the coefficient of ECM_t−1 in equation (2). A negative and significant coefficient of the error correction term, $\delta_1$, indicates that there is a long-run causal relationship between stock returns and inflation. Precisely, the unidirectional causality from inflation to stock returns hints an inefficiency of the stock market which suggests that information on past values of inflation could provide opportunities for abnormal gains from the return R.

As mentioned earlier, there is no general consensus among empirical research on the validation of GFH (Antonakakis, et al. 2017). This paper intends to make some contributions to the empirical literature on the Generalized Fisher Hypothesis (GFH) and the inflation-hedging ability of countries commons stocks market. As well, it is of great importance to see if the long run relationship between stock return and inflation can evolve heterogeneously overtime. To this end, we consider the three democratic countries, including Canada, UK, and Suisse from 1999M01 to 2018M04 covering the 2008 GFC period.

Based on univariate ARDL time series data models, we conclude that Canadian (UK) stock return is (not) a hedge against inflation for the three sub-periods, while Suisse market return is a hedge against inflation only during GFC crisis. During crisis both Suisse and Canadian stock returns are superior hedge against inflation. Post crisis, the Canadian stock market is unique to be full hedge against inflation (this result is in accordance with (Richard & Ran, 2021)). No significant relationship is found in the UK context during crisis period (period of deflation). In addition, post and Pre crisis, UK stock market is found to be worse hedge against inflation. Then, it would mean that being on the UK stock market, investors would be better off in reducing their stock market investments in times of high inflation rates. During crisis period (deflation period), being on either Suisse or Canadian stock market, investor can have important abnormal gains.

Findings confirm that GFH tests give different conclusions over considered sub-periods. Results are sensitive to the decomposition of data for pre- and post-GFC periods, indicating that asset-inflation hedging relationship for the considered sample is time-varying. Table 4 gives a sum up of all the previous results (from Table 2). Looking at Table 4, hedging ability is unchanged for the UK and the Canadian stock market, while Suisse case reveal unambiguous instability.