Inflation and stock returns: Evidence from China

Inflation and stock returns: Evidence from China Jingjie Wang 10226354 Supervisor: Liang Zou

Content Inflation and stock returns: Evidence from China... 1 1. Introduction... 2 2. Literature Review... 5 3. Data and methodology... 10 3.1 Objectives... 10 3.2 Background and Data... 10 3.3 Methodology:... 16 4. Empirical Results... 20 5 Conclusion... 27 Bibliography... 29 2

Abstract This Paper investigates the relation between common stock returns and inflation in the Chinese Stock Market. The evidence shows that the Fisher Effect Hypothesis which states that the real rates of return on common stock and expected inflation rates are independent is rejected within the data we considered. Instead, the Fama s proxy hypothesis which implies the negative relation between stock returns and inflation can be explained by the negative relation between inflation and expected real economy and the positive relation between expected real economic activities and real stock returns, is supported in our data. Further we test the relation between inflation and stock returns in different time periods and test the Chinese market is influenced by the government policy and economic environment. 1

1. Introduction In the last 20 years growth, Chinese Stock Market has become a relatively mature market that provides the equity financing function to firms, investment opportunities to investors. The importance of stock market in economic development has been gradually recognized by the policy makers. People have been becoming more willing to participate in the stock market. The high inflation rates in recent years draw citizens attention and the relation between inflation rate and stock return has become a hot topic in China again. This paper investigates the relation between inflation and stock returns in the Chinese Stock Market. Policy makers and investors may find some evidence that can solve their questions about stock market and inflation. For example, whether the inflation risk is perfectly hedged by the stock returns in the Chinese Stock Market and whether there is a positive relation between stock returns and inflation and how they affect each other. In the historical bull market in 2007 and the bear market in 2008, some of the investors made great profits and some of them suffered great losses. More investors have participated in the stock market. One reason is that the new investors notice the great success of some investors and they want to get high returns in stock market. Moreover in the past two years which is 2010 and 2011, the CPI kept stable at a very high level and continues high inflation rate appeared. The food price which is closer to citizens lives grew quicker than any other prices. Medias report the change in CPI month by month. Citizens always talk about the growth in prices. Stock returns and inflation become two hot topics in China. This paper will explore the relation between stock returns and inflation in the Chinese stock market. Investors in western countries began their research on the inflation risk and stock returns in 1970s during which the inflation rate was high. Whether their portfolio could restrain the loss of currency purchasing power from inflation was the most important question. Previous literatures mainly focus on testing fisher effect hypothesis in different countries. Fisher (1930) asserts that asset nominal return is the sum of expected real return and expected inflation where the expected return remains constant, so the nominal stock returns vary in a one-to- 2

one correspondence with expected inflation. According to Fisher effect hypothesis, asset real return is constant and will not change systematically although there is a change in inflation. So the loss in currency purchasing power can be made up by asset investment. As holding a stock equals owning the ownership of the real asset, people conduct Fisher effect hypothesis into stock markets. They hold the opinion that the expected nominal return of a stock is the sum of expected real return and expected inflation. Therefore the currency devaluation risk can be perfectly hedged by stocks. Fisher effect hypothesis was widely proved before 1970s. According to his theory, there is a positive relation between nominal returns and inflation. The real interest rate is independent from inflation rates, for the stocks represent the ownership of tangible assets or real assets. When inflation happens and the currency purchasing power decreases, people will invest their money into stock market to avoid currency devaluation. Both the stock price and the stock returns will increase. Therefore stock is supposed to be a financial asset that can perfectly hedge the risk from unexpected inflation. After 1970s, however, large number of analysis document that there is a negative and significant relation between real returns and inflation. Bodie(1976), Jaff and Mandelker(1976) empirically analyze the relation between stock returns and inflation using the American post-war data including Stock index and CPI, and find that there is a negative and significant relation between nominal stock return and inflation. Cohn and Lessard(1981) investigate the relation in other countries and conduct similar result which is contrary to Fisher effect hypothesis. Fama and Schwert(1977) investigate the relation by analyzing unexpected inflation and expected inflation separately and conduct a negative relation between inflation and stock returns. More researches after 1970 also show that stock did not perfectly hedge the risk of inflation using different evidence. In China, some economists explore the relation between inflation and stock returns and explain the puzzle between theory and empirical analysis. But there is no widely approved conclusion. Contrary to developed western countries stock market, Chinese stock market is young and not very efficient. It is interesting to 3

discover the relationship between inflation and stock return considering the unique characteristics of Chinese stock market. One reason why this topic is interesting is that investors are uncertain about whether the relation is positive or negative and whether their investments on stocks can restrain the inflation risk. Another reason is that policy makers whose primary mission is to stabilize the price level are uncertain about whether they can achieve information of inflation from high stock return. In this thesis, we will try to find more detailed relationship between inflation and stock returns using Chinese data. Moreover, it is meaningful to test whether the western theory is still work in Chinese Stock market. Furthermore, this thesis may provide more rational thoughts to some irrational investors who always follow some institutional investors and easy to be affected by inflation announcement. In addition, lack of relevant papers in this area analyzed Chinese market in recent years. My thesis may fill the vacancy in analyzing the relationship between inflation rate and the stock returns using newest data. The research question is stated below: What is the relation between inflation and stock return in China? This thesis mainly investigates two issues. The first one predicts the effectiveness of Chinese Stock Market, by supposing that the stock market reflect the impact of change of inflation rate. The second one investigates the relation and some other factors will be taken into account. This paper divided into five sections. Section 1 describes the background of writing this paper. Section 2 reviews the theories. Section 3 contains a description of data and methodology that will be used. The empirical results of testing Fisher hypothesis and Fama proxy hypothesis are presented in section 4. Then we will conclude in part five. 4

2. Literature Review Fish (1930) differentiates interest rate into nominal interest rate and real interest rate. He suggests that the nominal interest rate emerged from debit and credit sides and measured by currency. He also suggests that the real interest rate is the rate that can get rid of currency factors or price level fluctuations. Keeping the currency value or the price level constant, he holds the opinion that the nominal interest rate equals to real interest rate. However, the nominal interest rate will different from real interest rate when the value of currency or the price level changes. He indicates that if depositors and lenders are rational, they will adjust the interest rate based on the future expectation to avoid the influences from the fluctuation of currency value and price level. So the nominal interest rate will adjust according to expected inflation rate and normal price level. There is a long term positive relation between nominal interest rate and inflation rate. The real interest rate, however, only affected by the real economy, will keep constant. The following equations present the Fisher effect hypothesis: 1+R t =(1+r t )+(1+π t e ) Or R t =r t +π t e where R t is the nominal interest rate at time t, r t is the real interest rate at time t, e π t is the expected inflation rate at time t. As holding a stock represent owning the ownership of a certain asset, when using Fisher s Theory into financial market, we have stock return equals to real return plus inflation. That is: SR t =Sr t +π t e where SR t is the nominal stock return at time t, Sr t is the real stock return at e time t, π t is the expected inflation rate at time t. Fisher effect theory implies that when inflation rate changes, the nominal return of stocks will also change. That is when the inflation rate increase, stock returns will 5

increase, when the inflation rate decrease, the stock return will decrease. Therefore, stock market is a useful tool to hedge against the currency devaluation caused by inflation. After 1970, many researchers suggest that the correlation of inflation and stock returns is negative or non-existent. Fama and Schwert (1977), Bodie (1976), Schwert (1981) analyze the relation between stock returns and inflation using American after-war statistics and they find that there is a negative relation between stock returns and inflation. Also Jaffe and Mandelker (1976), Nelson (1976), show evidence that there is a negative relation between inflation and stock returns. Cohn and Lessard (1981), Solnik and Gultekin (1983) analyze the relation using data from other countries also strengthen the opinion that the negative relation between stock returns and inflation do exist. Different from Fama (1977), Maik Schmeling and Andreas Schrimpf (2011) show that the correlation of inflation and stock returns exists or negative and somehow can be positive in some situations. However, they did not consider the cause of the effects especially in monetary policy and interest rate policy. Fatma Lajeri and Jean Dermine (1999) evaluate the impact of unexpected inflation on the stock returns of a sample of French banks. It offers an empirical test of theories to predict the impacts of inflation on the stock returns of banks. Lifang Li, Paresh Kumar Narayan, Xinwei Zheng (2010) also consider the impacts of unexpected inflation on stock returns of a sample of UK stock market. In this thesis, they use ARIMA model to predict the expected inflation rate and compare the different effects made by expected and unexpected inflation rate. This method will be adopted in my thesis to predict the expected inflation rate. Glenn W. Boyle and Lesile Young (1992) investigate the relationships between ex ante stock returns and ex ante inflation from regressions of ex post stock returns on nominal interest rates. Lifang Li, Paresh Kumar Narayan, Xinwei Zheng (2010) analyze the impacts the inflation rate made on stock returns around the inflation announcement days. They find that unexpected inflation announcements negatively affect stock returns while expected inflation has little impacts in the 6

announcement study. Further, a positive relationship between expected inflation and stock returns and a negative relationship between unexpected inflation and stock returns are found in the medium-term study. Christophe Boucher (2006) considers a new perspective on the relationship between stock prices and inflation, by estimating the common long-term trend in the earning price ratio and inflation. Plenty of researchers indicate that there is a short-term negative relation between stock returns and inflation and there is a long-term positive relation between stock returns and inflation. Analysts try to explain this relation in different ways. Fama (1981) uses proxy hypothesis to explain this relation. He suggests that the negative relation between real stock return and expected inflation rate is spurious which means both of them affected by the real economy and there is no direct causal relation between these two. He also indicates that the negative relation between stock returns and inflation can be explained by the negative relation between inflation and expected real economy and the positive relation between expected real economic activities and real stock returns. Schotman and Schweitzer (2000) and Gallagher and Taylor(2002) sustain the proxy hypothesis. But Song (1997) show evidence that the relation between real stock returns and unexpected inflation cannot be explained by the real economic activities and stock returns using Indian statistics. Furthermore, Ram and Speneer (1983), do not accept the hypothesis. They discover that inflation is the one-way Granger reason of stock returns by using Granger-Causality test. In addition, Wahlroos and Berglund reject the proxy effect by testing the relation between inflation and stock returns using Finland data. Najand and Seifert (1990) deny the proxy hypothesis by finding that although the negative relation between inflation and real economic activities do exist, the positive relation between real stock returns and real economic activities does not correct. It is apparent that the proxy hypothesis is not fully acceptable. Kevin and Perry (1998) try to explain this relation using volatility hypothesis. They suggest that there is a positive relation between inflation and the fluctuation of inflation, and high inflation fluctuation leads to a low stock returns, this, in turn, 7

leads to the negative relation exist between inflation and stock returns. Friedman (1977) indicates that inflation will cause inflation uncertainty. Cukierman and Meltzer (1986) investigate the relation and they find that the increase in money supply and inflation uncertainty will lead to an increase in the optimal inflation rate. Grier and Perry (1998) estimate the inflation uncertainty by using GARCH(1,1) model based on seven industrial countries data and run the Granger causality test and find that inflation is the reason of inflation uncertainty. Hu and Willett (2000), in their research on American monthly stock returns and inflation from January 1955 to December 1995, suggest that when it is in a high inflation period, inflation fluctuation increases and so is inflation uncertainty, this, in turn, influences real economic activities and decrease the stock returns. Gautam Kaul (1986) indicates that the negative stock return-inflation relations are caused by money demand and counter-cyclical money supply effects. Mohammad Najand Gregory Noronha (1998) suggests that inflation appears Granger-causally prior and helps explain negative stock returns in Japan and inflation predicts interest rates. Interest rate has been considered as an important component between inflation and stock returns. But less literature analyze the relationship between inflation monetary policy and stock returns using Chinese statistics. The increase in money supply will affect the price of financial market through some transmission mechanism. The main mechanism in financial market contains Tobin s Q (1969), the company balance sheet effects (Ben Bernanke1995), the Household Wealth Effects (Modigliani1971) and the Residents Liquidity Effects. As the Chinese Stock Exchange starts at a very late time, lack of related literatures and researches discussed Chinese issue. Hou (1994) and Li (1999) discuss theoretically about the relationship between inflation and stock price. Jin and Yu (1998) run regression to analyze the relation using monthly data from 1993 to 1996 and accept the negative relation between inflation and stock price. But considering the time period they have chosen is in a high inflation period and stock market is in chaos, the result is not acceptable. Zhao (1999) investigates the relation between 8

nominal stock returns, inflation, and nominal output using monthly data from Jan 1993 to Mar 1998 and indicates that the negative relation between stock returns and inflation is significant and also the positive relation between nominal output and stock returns. The Fama s proxy hypothesis has been proved in his paper. Li (2001) simply compares the stock price index and CPI and concludes that there is a long term positive relation between inflation and stock price. Gang and Chen (2003) prove proxy hypothesis in Chinese Stock Market and find that the negative relation between stock returns and inflation is stable. Liu and Wang (2004) build GARCH model to test the volatility hypothesis using monthly data from Jan 1991 to Mar 2002 and conclude that fluctuation hypothesis accepted in Chinese Stock Market. My paper will make contributions to existing literatures mainly in two folds: First, the relationship between inflation interest rate and stock returns in China has not been analyzed using full data of the Chinese Stock Market. Second, as Chinese government changes interest quite often in recent years, it is more meaningful to explore whether the changes in interest help restrain inflation and how China s economy perform based on the change in interest rate. 9

3. Data and methodology 3.1 Objectives Analyze the relationship between inflation and stock returns based on China s circumstance. Test Fisher effect hypothesis and Fama s proxy hypothesises which explain the paradox between theory and actual. 3.2 Background and Data 3.2.1 Background The main research object of this paper is the Shanghai Stock Exchange which was founded in Dec 1990 approved by China Central Bank. After 20 years construction, the Stock exchange has become a relatively matured market. However, the Chinese Stock Exchange is still a young market and there are many aspects wait to be improved, for instance, information asymmetry, randomness in market competition, and lack of standardization in operation mechanism. In addition, since large part of the participators of China Stock Market are irrational investors and the contradiction of supply and demand as well as the contradiction of the market structure, the price mechanism failures always occur which lead to a low resource allocation efficiency. Chinese researchers discuss the efficiency of China Stock Market but they don t have a completely consistent conclusion, but the basic conclusion is that the market is becoming efficient. Yu(1994) asserts that the price of the China Stock Market is strongly serial correlated by using Box-Pierce test and run test. Chen(1997) indicates that the Shanghai Stock Exchange and Shenzhen Stock Exchange satisfy the weak form of efficient market hypothesis using Dickey- Fuller test. To conclude, although the Chinese Stock Market is not well standardize and abnormal fluctuations reflect the inefficiency of the stock market, the efficiency of China capital market has been improved significantly. 3.2.2 Data The monthly data of index of Shanghai Exchange will be collected from Resset Database and some Chinese stock trading software such as TONGHUASHUN system. The actual inflation rate data will be collected from inflation announcements 10

analysis which posted every month in some Chinese official newspapers and statistical yearbook and finance.yahoo.com by simply using data of CPI. The expected inflation rate will be estimated from an auto regressive integrated moving average model of the actual inflation rate while controlling for seasonality. Announcement date will be hand-collected from the public press (particularly from China daily) and www.ce.cn which is the most important and official website publishing economy data and economy regime. All data will be collected from Jan 1991 to Dec 2011. High inflation period(1993-1994) and two financial crisis(1998 and 2008) are included in this time period. It will be worth to discuss the policy of Chinese government on the market since the Chinese government is more active by frequently changing the policy based on the economic development in this time period. 3.2.3 Definition of variables a. Real stock return There are two stock exchange markets in China which is Shanghai Stock Exchange and Shenzhen Stock Exchange. As the value of Shanghai Stock Exchange is higher than that of Shenzhen and more firms listed on Shanghai Stock Exchange, in this thesis, the monthly closing price of Shanghai Stock Exchange (SZZS) will be collected to compute the real stock return. The nominal stock return is: R t = (SZZS t SZZS t 1 ) /SZZS t 1 where SZZS t is the closing price of the last trading day at month t. Then the real stock return r t is r t = R t π t. b. inflation rate In this thesis, we will use the month-to-month ratio of CPI to represent the inflation rate. But when we collect the CPI data from the government website and China Yearbook, we find that only the CPI ratios on year-to-year basis are available. Chinese government began to use month-to-month ratio in 2000, that means the CPI ratios from 1991-2000 are missing. In order to get the month-to-month ratio of CPI and avoid the mismatching in data, therefore, we compute the month-to- 11

month ratios based on the year-to-year basis and the month-to-month data of 2001 as the following show. 1. Assuming the consumption price in Jan 2002 is 100, we can compute the consumption price in 2001 from Jan-Dec by dividing the consumption price 100 by the month-to-month data of 2001 we already have gradually. For example: CP dec = 100/CPI m m(jan 2002 ) CP nov = CP dec /CPI m m(dec 2001 ) 2. Divide the consumption price by the CPI year-to-year basis CPI, we can have the consumption price of the previous year. For example: CP dec 2000 = CP dec 2001 / CPI y y(dec 2001 ) 3. The month-to-month CPI data can be computed by calculate the month-tomonth difference in consumption price of 2000. For example: CPI m m(dec 2000 ) = (CP dec CP nov )/CP nov 4. The month-to-month CPI data can be collected by using this method consecutively. c. Rate of currency supply and rate of output growth In China, the GDP announcements only take place quarterly. So I will use industrial output growth which reflects large part of the growth of GDP to represent the output growth. The industrial output growth will be collected from China year book. I t = (G t G t 1 ) /G t 1 where G t is the monthly industrial growth at time t. I t is the change of industrial output growth. 12

3.2.4 Descriptive statistics of the variables Table 1 Variable Obs Mean Std. Dev. Min Max r t 251 0.0223359 0.1790286-0.3115295 1.772262 I t 252 0.0173762 0.1064476-0.334 0.3292 CPI t 253 0.4051385 1.312823-3.00003 5.599998 Table 1 displays the descriptive statistics of variables. From this table we notice that China s industrial growth keeps a monthly average pace of approximately 1.7% and the monthly average stock return is 2.2%. Meanwhile, the CPI monthly average growth rate is 0.4 with a relatively high standard deviation of 1.31. Thus, the fluctuation of CPI is supposed to be more drastic than other variables preliminarily. The following three graphs below illustrate the variation trend of the five variables. 13

14 Graph 1 Graph 2-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 Jan-91 Dec-91 Nov-92 Oct-93 Sep-94 Aug-95 Jul-96 Jun-97 May-98 Apr-99 Mar-00 Feb-01 Jan-02 Dec-02 Nov-03 Oct-04 Sep-05 Aug-06 Jul-07 Jun-08 May-09 Apr-10 Mar-11 Rt Rt -10.0-5.0 0.0 5.0 10.0 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 cpi cpi

Graph 3 0.4000 I 0.3000 0.2000 0.1000 0.0000 I -0.1000-0.2000-0.3000-0.4000 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 The graph 1 shows the variation trend of stock return in previous 20 years. The abnormal high return in Oct 1991 May 1992 and Aug 1993 can be explained by the historical policy events. In Aug 1991, Shenzhen Stock Exchange established policy to rescue the market. After the National Day 1991, stocks that listed on Shenzhen Stock Exchange started to grow dramatically. Shanghai Stock Index influenced by the rescue policy in Shenzhen also rocketed to 1429 with an absolute growth rate of 140%. In May 21th 1992, Shanghai Stock Exchange released share price limit. On that day the index grew from 617 to 1266. After the index reached 1420.79 on 25 th May 1992, it began to decline substantially. In July 30 th 1994, Chinese government made a decision to stop issuing new stock, to strictly control the rights issue of listed firms, and to extend the range of the market entering capital. This decision made the index to increase by 111.72(33.46%) at the announcement day. The continued negative return in 2008 reflects the persistently decrease in 2008 and the financial crisis 2008. 15

In our analysis, the abnormal changes that caused by the government policy will be treated as outliers in order to keep the consistent of regression. Graph 2 illustrates the change of CPI precisely. Two high inflation periods have been presented (1993-1994, 2007-2008). This graph shows the rate of industrial growth. But we can easily notice that seasonality exists. We will eliminate the seasonality by using X-11 seasonal adjustment before the empirical analysis. 3.3 Methodology 3.3.1 Data stationary and unit root test As stock returns which I will collect is a time series, first I will use Augmented Dickey and Fuller test to check for the non-stationarity of series. The test of this non-stationarity of series can be obtained from the estimates of the following regression model. RR tt = αα + ββββ + γγrr tt 1 + δδ 1 RR tt 1 + + δδ pp 1 RR tt pp+1 + εε tt where αα is a constant, ββ is the coefficient on a time trend and p is the lag order of the autoregressive process, RR tt is the stock returns. 3.3.2 Test of Fisher effect hypothesis Like previous empirical research on this topic, here we test the generalized Fisher hypothesis, which states that the market is efficient and that the expected real return on common stocks and the expected inflation rate vary independently so that, on average, investors are compensated for changes in purchasing power. As the expectations of nominal return, real return and inflation rate are unobservable, here we test the Fisher hypothesis using actual value of return and inflation like previous research do. The tests of this joint hypothesis can be obtained from the estimates of the following regression model. R t =α+βcpi t + є t (a) 16

where CPI t is the inflation rate at time t, R t is the nominal stock return at time t. The time subscript t denotes returns between the end of time period t-1 and the end of time period t. E is the mathematical expectations operator. 3.3.3 The expected inflation rate It is possible that the regression results may be more favourable to the Fisher hypothesis if we have a better proxy for expected inflation than the contemporaneous rate. Furthermore, one can investigate the adjustment of the market to changes in the unexpected inflation rate if actual changes in inflation rates could be decomposed into unexpected and expected components. Here we use ARIMA models to generate expected and unexpected components of inflation by using procedures developed by Box and Jenkins. Inflation forecasts from ARIMA models are used as estimates of expected inflation, and the difference between expected inflation and actual inflation are used as the unexpected component of inflation rates Formally we estimate the expected inflation rate using following ARIMA model. ARIMA model: PP tt ee PP tt 1 =μ+σ(pp tt 1 -PP tt 2 ) (b) where PP ee tt is the expected inflation rate estimated from the actual inflation rate by using auto regressive integrated moving average model(arima). In ARIMA model, we will run a regression based on the actual inflation rate to get the predict ratio of the expected inflation rate. PP μμ tt is the unexpected inflation rate equals to the difference between the actual inflation rate and the expected inflation rate. Using ARIMA, we estimate the expected inflation rate at each date and obtain the unexpected inflation rate simply using the difference between expected inflation rate and actual inflation rate, then apply to OLS regression. 3.3.4 The relation between stock return and expected inflation rate and unexpected inflation rate To estimate the relation above, we use the following regression model. R t = α + β 1 CCCC tt ee + β 2 CCCCCC tt uu + εε 17 (c)

3.3.5 Fama s proxy hypothesis Some researchers tried to explain the anomaly relation between stock return and inflation. Here we test Fama s proxy hypothesis. First the inflation rate is regressed on the lagged, contemporaneous and leading levels of growth in industrial growth to purge the effect of output from the inflation as specified in Eq. R t CPI t = α 0 + α 1 є t + kk β j+k+1 jj = k g t+j + ϑt In eq. (d), the finding of α 1 =0 would support the hypothesis that the real stock return is independent of inflation once the impact of real output has been taken out. Once this has been established then we need to test for the two propositions of Fama s to validate his hypothesis. Eq. Tests the relationship between real stock return and growth of real output and Eq. Tests the relationship between real stock return and inflation. R t CPI t = α + β j+k+1 g t+j + ϑt kk jj = k (d) (e) kk CPI t = α + β j+k+1 g t+j + ηt jj = k A significant positive βs in eq.(e) and negative βs in Eq.(f) can up hold Fama s hypothesis. Considering Chinese stock market has just been founded and the change in inflation rate and stock return presents that they were influenced by the government policy. We test the relation between inflation rate and stock return in different time period. We will divide 20 years into four periods. Firstly, time from Jan 1991 to Dec 1995 will be treated as the first time period. The reason why we choose Dec 1995 as the separation is that the price of the common stocks lay on the demand supply relation at the beginning of the stock market foundation. Jul 2007 will be the second point of division because before Jul 2007, Chinese stock market experienced a 11 year development and then went into a historical bull market after that time. Another point would be Aug 2009. This time point can be treated as the end point of the bear market in 2008. (f) 18

First we will test the general relation between stock return and inflation rate in different time period using the model below R t =α+βcpi t + є t (g) where CPI t is the inflation rate at time t, R t is the nominal stock return at time t. The time subscript t denotes returns between the end of time period t-1 and the end of time period t. E is the mathematical expectations operator. Further we will divide the inflation rate into expected inflation and unexpected inflation rate also using ARIMA and test the relation with stock return. The formula below will be used to test the relation. R t = α + β 1 CCCCCC ee tt + β 2 CCCCCC uu tt + εε (h) ee where R t is the stock return at time t, CCCCCC tt is the expected inflation rate at time t uu and CCCCCC tt is the unexpected inflation rate computed by the difference between real CPI and expected inflation rate. As Chinese government perform more actively in this period by changing interest rate frequently, we will whether the interest rate have effect on stock return using short term interest rates as predictors of inflation. Fama has shown that Treasury Bill returns can be used as predictors of inflation in the U.S. Here we employ Fama s technique to predict monthly inflation rates from 1-year fixed deposit. We assume that one year fixed deposit yield observed at the end of a quarter contains the market s assessment about the expected inflation during the next quarter. Formally we estimate the expected inflation and unexpected inflation from the following regression model. RCPI t =α+βinterest t + є t (m) where interest t is the one-year fixed deposit and RCPI t is the inflation rate. Some rational explainations will be given on the different result from the regressions based on four different time period according to Chinese unique circumstance. 19

4. Empirical Results The two tables below show the result of ADF-test. From the statistics, we conclude that all the null hypothesises is rejected at the 99% significance level. The variables have no unit-root and the time series are stationary. Table 2 First ADF test RR tt = αα + ββββ + γγrr tt 1 + δδ 1 RR tt 1 + + δδ pp 1 RR tt pp+1 + εε tt variable Test statistic 1% Critical Value 5% Critical Value 10% Critical Value Rt -11.358-3.99-3.43-3.13 CPI -11.117-3.99-3.43-3.13 It -18.428-3.99-3.43-3.13 Table 3 ADF test after eliminate the abnormal change variable Test statistic 1% Critical Value 20 5% Critical Value 10% Critical Value Rt -8.384-3.99-3.43-3.13 CPI -11.562-3.99-3.43-3.13 It -16.752-3.99-3.43-3.13 The regression results of testing Fisher hypothesis are shown in table 4. Regression coefficient is negative and significant. That means stock return and inflation in the Chinese stock exchange are negative correlated. In long term, the increase in inflation rate leads to a decrease in stock return. The common stocks cannot be a good hedge against inflation. Thus, the Fisher hypothesis is rejected at the first step in China. It is possible that the regression results may be more favourable to the Fisher hypothesis if we have a better proxy for expected inflation than the contemporaneous rate. Furthermore, one can investigate the adjustment of the market to changes in the unexpected inflation rate if actual changes in inflation

rates could be decomposed into unexpected and expected components. We experimented with ARIMA models to generate expected and unexpected components of inflation by using procedures developed by Box and Jenkins. Inflation forecasts from ARIMA models are used as estimates of expected inflation. The difference between actual inflation rate and expected inflation rate is used as estimates of unexpected inflation. Table 5 shows the results of ARIMA process. Table 4 R t =α+βcpi t + є t Rt Coef. Std.Err t P> t cpi -0.02027-0.00864-2.35 0.02 _cons 0.014486 0.011689 1.24 0.216 Table 5 Result of ARIMA PP ee tt PP tt 1 =μ+σ(pp tt 1 -PP tt 2 ) D.cpi Coef. Std.Err. T P> t _cons -0.0008539 0.0138389-0.06 0.951 AR(1) 1.039034 0.06010 17.29 0.000 AR(2) -0.4270661 0.0747273-5.71 0.000 MA(1) -1.793062 0.0533159-33.63 0.000 MA(2) 0.8551786 0.0499122 17.13 0.000 Table 6 R t = α + β 1 CCCC ee tt + β 2 CCCCCC uu tt + εε Rt Coef. Ste.Err. t P> t ecpi 0.0328472 0.0150223 2.19 0.030 uncpi -0.021012 0.008672-2.42 0.016 _cons 0.014097 0.0116942 1.21 0.229 21

The results of testing the relation between stock return and expected inflation rate and unexpected inflation rate are shown in table 6. According to the results, we estimate the formula as follows. R t = 0.014097 + 0.0328472CCCCCC ee uu tt 0.0210123CCCCCC tt (1.21) (2.19) (-2.42) R-squared=0.25 The evidence here suggests that the relation between expected inflation and stock return is positive and significant, the relation between unexpected inflation and stock return is negative and significant. The Fisher effect hypothesis is rejected by the data we use in China. The result is consistent with Nelson(1976), Bodie(1976), Gultekin(1980), Fama(1975), Jaffe and Mandelker(1976), Fama and Schwert(1977), Fama and Gibbons(1984), Adrangi, Chatrath and Raffiee(1999), the change of unexpected inflation rate has a negative significant effect on stock return. Fama s proxy hypothesis explains the negative relation between stock returns and inflation using two propositions that the negative relation between inflation and expected real economy and the positive relation between expected real economic activities and real stock returns. We checked the two propositions of Fama by estimating equations (e) (f). A positive significant coefficient between real stock return and growth of real output and a negative coefficient between inflation rate and growth of real output satisfy Fama s propositions. The estimation from (e) (f) shows exactly the same. Both equations are estimated with only the contemporary growth in real output. Table 7 and 8 present the results. Here we prove that the anomaly of negative relation between stock return and inflation can be expressed by Fama s proxy hypothesis. Table 7 Real return and industrial growth rt Coef. Std.Err t P> t I 0.2055837 0.0754596 2.72 0.007 _cons -0.040177 0.0081186-4.95 0.000 22

Table 8 Cpi and industrial growth Cpi Coef. Std.Err t P> t I -0.220768 0.0767888-2.88 0.004 _cons 0.04391549 0.0082661-4.95 0.000 The regression result of the first time period is shown in table 9. Evidence from the first step regression show that there is a negative relation between inflation rate and stock return but it is not significant. When we apply to the second regression we find a positive relation between expected inflation rate and the stock return and a negative relation between unexpected inflation rate and the stock return. Both are insignificant. The negative relation between inflation rate and stock return can be explained by the demand-supply relation at the beginning of the stock market. The result is consistent with Han(2008). Han(2008) states that in this time period, the supply shock is larger than demand shock which lead to the negative relation between inflation and stock return. Evidence shown in table 10 proves that the relation between stock return and inflation is positive but insignificant from Dec 1995 to Jul 2007. The relation between expected inflation and stock return is positive and significant and the unexpected inflation has a significant negative effect on stock return. This finding is consistent with the result when we test the relation using whole statistics before. The result shown in table 11 is about the third time period. The negative relation and no significant results found in this time period can be explained by the financial crisis. Start from Dec 2006, Shanghai Stock Exchange experienced a dramatic increase, rocketing from 2675 to 6158 in Jan 2008.Then the stock price influenced by the financial crisis 2008, and went down by 3000 to the end of 2008. Meanwhile, the inflation rate kept stable with around 105 on year-year basis. The result in table 12 shows weak evidence on the relation between stock return and inflation rate. When we estimate inflation using short term interest rates as predictors, we find different result. Evidence shown in table 13 suggests that there is a negative relation between inflation and interest rate which is significant at 10% 23

significance level. Apparently, interest rate is a useful tool in China to restrain high inflation. Table 13(b) shows that there is a positive relation between expected inflation and stock return and a negative relation between unexpected inflation and stock return. Comparing with the previous regression result, when we use short term interest rates as the predictors of inflation rate, we receive a more significant result (an improvement in t-statistics). Table 9 Period 1(Jan 1991-Dec 1995) R t =α+βcpi t + є t Rt Coef. Std. Err t P> t Cpi -0.024671 0.0232883-1.06 0.294 _cons 0.0338292 0.0501452 0.67 0.503 R t = α + β 1 CCCCCC ee tt + β 2 CCCCCC uu tt + εε Rt Coef. Std. Err. T P> t Ecpi 0.0279886 0.0230907 1.21 0.231 Uncpi -0.060939 0.0591426-1.03 0.307 _cons 0.1269133 0.0772107 1.64 0.106 Table 10 Period 2(Jan 1996-Jul 2007) R t =α+βcpi t + є t Rt Coef. Std. Err t P> t Cpi 0.0077646 0.0061986 1.25 0.212 _cons 0.015877 0.0066819 2.38 0.019 R t = α + β 1 CCCCCC ee tt + β 2 CCCCCC uu tt + εε Rt Coef. Std. Err. T P> t Ecpi 0.015496 0.0062727 2.39 0.019 Uncpi -0.053523 0.019184-2.79 0.005 _cons 0.0124669 0.0076607 1.63 0.106 24

Table 11 Period 3(Aug 2007-Aug 2009) R t =α+βcpi t + є t Rt Coef. Std. Err t P> t Cpi -0.017521 0.0360113-0.49 0.631 _cons -0.008740 0.0274799-0.32 0.753 R t = α + β 1 CCCCCC ee tt + β 2 CCCCCC uu tt + εε Rt Coef. Std. Err. T P> t Ecpi 0.0247254 0.0391614 0.63 0.534 Uncpi -0.045376 0.0634357-0.72 0.482 _cons -0.000387 0.0301291-0.01 0.990 Table 12 Period 4(Sep 2009-Dec 2011) R t =α+βcpi t + є t Rt Coef. Std. Err t P> t Cpi 0.0221712 0.0230235 0.96 0.344 _cons -0.013224 0.0138346-0.96 0.348 R t = α + β 1 CCCCCC ee tt + β 2 CCCCCC uu tt + εε Rt Coef. Std. Err. T P> t Ecpi 0.0218338 0.0236577 0.92 0.365 Uncpi 0.0100726 0.0821225 0.12 0.903 _cons -0.010762 0.030666-0.35 0.729 25

Table 13(a) RCPI t =α+βinterest t + є t Cpi Coef. Std. Err t P> t interest -10.79633 1.631219-1.89 0.089 _cons 0.6657551 0.473139 1.41 0.174 Table 13(b) Rt Coef. Std. Err. T P> t Ecpi 0.0271006 0.023546 1.53 0.144 Uncpi -0.097696 0.019855-1.64 0.119 _cons -0.010762 0.030666-0.35 0.729 26

5. Conclusion This paper investigates the relation between stock returns and inflation in China from 1991 to 2011. We test the generalized Fisher hypothesis, which states that real rates of return on common stocks and expected inflation rates are independent and that nominal stock returns vary in a one-to-one correspondence with expected inflation. Using time series regression, we find a strong negative relation between inflation and stock return which evidently prove that the Fisher hypothesis is rejected in Chinese market in long term. We also test the fama proxy hypothesis. After checking the two propositions of Fama hypothesis, we find that Fama's hypothesis is satisfied by Chinese market. A positive significant coefficient between real stock return and growth of real output and a negative coefficient between inflation rate and growth of real output has been found. Then we divide inflation rate into expected inflation rate and unexpected inflation rate using ARIMA model. We find that unexpected inflation rate negatively affect the stock return and expected inflation rate positively affect it. In addition, the impact from unexpected inflation is larger than that from expected inflation rate. Furthermore, based on Chinese unique situation, we explore the relation between stock return and inflation rate by dividing the sample into four parts according to different time. For the first step, we use general time series regression to find the relation. For the second step, we investigate the relation by dividing inflation rate into unexpected inflation rate and expected inflation rate. From 1991 to 1995,no significant result has been found since the demand-supply relation played a key role at the beginning of the stock exchange. From 1996 to 2007, the result is consistent with other researchers that the unexpected inflation negatively affects the stock return and expected inflation positively affects it. The regression coefficients are significant. In the third time period, influenced by the financial crisis, it is hard to find an exact relation between inflation and stock return. In the fourth period, no significant result found at the first step. Considering Chinese government change the interest rate in 2008 and 2010 for several times, we 27

introduce short term interest rate to be the predictors of inflation rate. A strong and significant relation between interest rate and inflation has been found. Thus we suggest that interest rate is a useful tool to restrain the inflation rate in China. Also, the regression result has been improved when using interest rate to predict the expected and unexpected inflation rate. We further suggest that, in this period, interest rate is a intermediary that connect inflation and stock return. In other words, Chinese government announced powerful policy to restrain the inflation rate and control the stock market. Finally, our findings suggest that the Chinese common stocks did not provide a perfect hedge against inflation. Chinese stock market is influenced widely and deeply by the inflation and other factors such as government policy. Chinese stock market is still a strong policy market. Thus, stockholders and other investors can change the portfolio according to the government policy. 28

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