For testing the stationary of the market return, it is obvious that market return is not simply following the random walk theory. Moreover, the stock price can reflect the functions of the economic system such as policy making, risk management and financial market valuation.
In Dr Nishat`s research, with using the 30 years data, and transferring the non-stationary data into stationary by unit root technique, he indicates industrial production index is a significant important macroeconomic variable to the change in the stock price. 未完
Macroeconomic variables and stock price
In financial economic theory, under the long term equilibrium condition, the stock market always reflects the risk of the investment. If the investors are seeking for high return, they have to face the higher risk, but if they want to be safe, the low return has to be accepted. Unless the decision makers are able to get some private information, otherwise, in reality, higher return always comes with higher risk. Therefore, it is very important to set up a model about testing the risk level.
Sharpe, Lintner and Mossin have set up the Capital Asset Pricing Model (CAPM) to illustrate the relationship between risk and return. The equation (1) is the regression of CAPM.
E(RI) = Rf+β*(E(Rm)-Rf) , β = (1)
Where
E(RI)= stock required expected return,
Rf = the risk free interest rate (3 month treasure-bill rate),
E(Rm)= expected market expected return, and
E(Rm)-Rf=the risk premium
CAPM indicate the relationship between stocks required return, risk free rate and risk premium for one period with using the term beta β. Beta describes the volatility of a stock to the stock market index. If a stock has a zero beta, which means it is independently related to the changes of the stock market. Risk free interest rate is the rate of return generated from the risk free investment and independent from the market. As long as the investors take more risk into the business, the required expected return will goes up. Therefore, the changes in the interest rate will directly affect the required return of the stock and also affect the asset holders to make investment decision.
In CAPM, the stock market return has been treated as a source of risk, but CAPM does not explain how the overall market establishes the mechanism of generating profit. In this case, the Asset Pricing Theory has been introduced by Ross.
Equation (2) is the expression of the APT model,
Ri,t-Et-1(Ri,t) =∑J βi,jFj,t+εi,t
Fj,t = the jth stock return under the systematic risk at time t,
Et-1(Ri,t) = constant stock return
βi,j = the sensitivity of stock j to Fj,t, and
εi,t = disturbance term
The APT model has expanded the one factor CAPM model to the various-factors model and it establishes the linear regression between various macroeconomic variables and stock market return. With macroeconomic factor, APT model not only explain the return of individual asset but also the whole market.
There is a question emerged, which macroeconomic variables should be used as the systematic factors for the analysis.
(3)
Equation (3) is the Dividend Discount Model (DDM),
Where,
=the dividend at time t+j
=the capitalization rate from time t to time t+j, and
Et = the expected return at time t,
In the DDM model, every macroeconomic variable can be the systematic factor which may influence the stock price in the future, but the more specific test has to be conduct to pick out which variables are more significant.
It is very important of establishing the relationship between stock return and macroeconomic variables. Firstly, with knowing the relationship, the investors can improve the performance of the portfolio. As long as there is a new announcement released, the investor could do the forecast about the trend of the stock market. If they predict the stock price will go up, they can put more weight on that stock and conducting the portfolio in advance. Moreover, it improves the portfolio return with taking lower risk. Secondly, from the macroeconomic variables, it is possible to making the long term equilibrium stock pricing. If the stock market has the unexpected big rise or fall without the corporation of macroeconomic variables, it should be doubtful. The investor should be able to avoid the irrational behavior to interrupt the stock market and have positive attitude to make more profit.
However, the stock market is the most unstable market in the world. No matter in the developed countries or the emerging market, there are many examples that the economy and the stock market goes opposite direction in one period. For example, from year 2000 to year 2002, the United States economy was obviously recovering, however, at the same time the Dow Jone index have dropped about 30%, and also the decade from 1997 to 2007 is the fastest developing period of Chinese economy, however, it is also the ten-years for the bear market as well. For the entire macroeconomic variables, McQueen and Roley（1993）found for an individual macroeconomic variable, it could have different effect on the stock market or even opposite. (McQueen & Sim, 2001) Boyd,Jagannathan and Hu（2001）indicate that it is very hard to get the coefficient correlation between macroeconomic variables and stock market return, because they are changing all the time. (Boyd, Jagannathan, & Hu, 2001)
In conclude, due to the complexity of the relationship between the macroeconomic variables and the stock market, this paper will analyze the variables individually and study about how the variables are connected with each other.
Interest rate and stock price
(Alam & Uddin, 2009)
Based on the analysis both on developed and developing countries, Alam and Uddin emphasis the significance of the relationship between stock price and interest rate. They indicated that, "interest rate is considered as the cost of capital, means the price paid for the use of money for a period of time". For a company, it has to generate enough profit to cover the cost of capital. If the interest rate is high and plus the high inflation rate, although the company works hard to generate as much as possible profit, it still faces the risk of low cash inflow and cannot pay off the debts. As a result, the company may go bankrupt.
Some researchers try to establish the linear regression between stock price and interest rate.
Y1 I,t= δ1+α1X1i,t + μi,t (4)
Y2 I,t= δ1+α1X2i,t + μi,t (5)
In the equation (4), Y1 represents the stock price and X1 represents the interest rate, the equation is testing whether there is a linear relation between interest rate and stock or not.
In the equation (5), Y2 represents the changes in the stock price and X2 represents the changes in interest rate. The regression aims to test whether there is stable linear relationship between the changing variables.
Alam and Uddin found that both the developed and developing countries` interest rate is not efficiently affect the stock price, however, the changes of interest rate are significantly affect the changes in stock price and could establish a significant negative relationship. Therefore, to some extent, they consider that the interest rate is an efficient way for governments to control and regulate the economy, namely, by adjusting the interest rate, the governments could affect the stock price and attract more people to invest and spend. For example, good investors are always seeking to get more extra profit from the financial market, if the government increase the interest rate, which means the banks will pay more for their depositors, therefore, the investors would like to invest less in the stock market and put more money into bank account with getting higher interest and lower risk of losing money. However, for the whole economy it is very bad of losing investment and decrease of share price. (Alam & Uddin, 2009)
Fama(1981) specificly argues that the short term interest rate is negatively related with the stock market return, however, due to discount rate, it is very hard to establish the linear relation between long term interest rate and short term interest rate. (Fama, 1965) Campbell`s 1987 research has provide the academic evidence for that interest rate is an effective variable in predicting the excess return of the stock market. (Campbell, 1987) By using regression analysis, Zhou (1996) states that by analyzing the long horizon data, although the interest rate is proved to be significant to the changes in stock price, the stock market still do not move will interest rate in one-for-one model. (Zhou, 1996) Lee (1997) has forecast the excess return with using the three years rolling regression on the short term interest rate (including the overnight interest rate and treasure bill interest rate, in addition, he found the relationship is not stable enough to do the accurate forecast. The relationship changes from the significant negative to no relation or insignificantly positive. (Lee, 1997) Arango (2002) has test the relationship by using another type interest rate-inter bank loan interest rate. Due to the inter bank loan interest rate is most heavily depend on the monetary policy, therefore, nonlinear relation exist here. (Arango, Gonzalez, & Posada, 2002)
Some economist has indicated that the discount rate has played a very important role in the interest rate-stock price relationship. In literature, discount rate represents the time value of money. According to Chen, Mohan, and Steiner (1999) research, stock return is always negatively and significantly respond to the unexpected announcement or information. The unexpected Federal Reserved discount rate change is representing the unexpected announcement or economic policy. Therefore, they emphasis "the discount rate can be a signal" it influences other markets` interest rate which in turn will change the stock price in the foreseeable future. (Chen, Mohan, & Steiner, 1999)
Bank of England states that, Interest rate and inflation rate are bounded to stimulate the market demand and the demand will determine the stock price eventually. When these two rates are too low, it may build up the inflationary pressure, when these two rates are too high, the first reaction is to control the inflation rate.
Money supply and stock price
Some economists has emphasized that monetary policy is the most important and efficient macroeconomic policy for the central bank to control the overall economy. Through adjusting the monetary policy frequently, it will lead the significant changes in the stock market. In addition, money supply seems like the most crucial components of the monetary policy. Biniv Maskay illustrates that "changes in money supply can be either anticipated or unanticipated by the people". (Maskay, unknow) Some economist indicate that because all the information is available on the market and not embedded in the stock price, both anticipated and unanticipated changes in money supply would affect the stock price; however, some others argue that only the unanticipated money supply matters, the anticipated money supply has no influence on the stock price because all the valuable information is already embedded in the stock price in efficient market. (Corrado & Bradford, 2005) With analyzing the data of Pakistan, Husain and Mahmood (1999) has proved monetary policy will affect the changes in stock prices both in long run and short run. (Husain & Mahmood, 1999)
With comparing the turning point of stock price and growth rate of money supply, Sprinkel (1964) found that a peak growth rate of money supply was always followed by approximately fifteen month bear stock market, and the bull market can be predicted to emerge after two-month trough point of money supply. (Sprinkel, 1964) Gupta (1974) used over 23-year period monthly data and found that 59% of the peaks in the stock market could be accurately predicted. (Gupta, 1974)
The changes in money supply affect the market through the interest rate and discount rate. Some economists state that the causal relation between money supply and stock price can be separated into two parts. First is the negative causal relation between money supply and interest rate, and the second is the negative causal relation between interest rate and stock price. But Alatiqi and Fazel (2008) holds different view, they argue there is no reliable causal relation between these three variables. In theory, the analyzing of relationship between money supply and interest rate are normally based on the short-term liquidity effect. In order to keep the money market equilibrium, interest rate has to decrease due to the increase of money supply. However, when the money supply increase, assuming the money demand curve began to move to right as well, at the equilibrium point, the interest rate might be same as the old one or even higher. The uncertainty of the causal relationship between money supply and interest rate also exists in the relationship between interest rate and stock price. Normally, the decrease of interest rate gives an opportunity for companies to retain more profit, so achieve the higher stock price. Nevertheless, the stock price may not change due to other cost may increase besides cost of capital, at this point, the profit still low and the stock prices are unable to raise. (Alatiqi & Fazel, 2008)
Some economist concerns about the tightening monetary policy. Bernanke and Kuttner (2005) describe the situation of tightening monetary policies; they emphasize the significance influence of the monetary value and perceived risk on the stock market. If the money supply decrease, the interest rate will rise and which in turn lead the discount rates increase, therefore, the actual present value of the stock decreases. Also, tightening monetary policies would increase the risk premium to compensate the risk of holding riskier stocks. Normally, the investors would take the tightening money supply as a signal which the stock market or economy is going to the lower point. (Bernanke & Kuttner, 2005)
Sellin(2001) states that changes in money supply will changes peoples` expectation about future monetary policies and which in turn lead the stock price changes. One significant argument in his paper is if the central bank increases the money supply to give the market a positive shock, it will lead the people to anticipate a tightening monetary policy will come out following. As the interest rate goes up, the discount rates will be driven up as well. The consequence is the present value of the stock goes down which lead the stock prices go down. However, some others also argue that the positive shock may lead to the stock price increase. If the money supply increases, the money demand will increase anyway, and the economy will have more economic activities operating. With the higher cash flow in the stock market, the stock price will rise. (Sellin, 2001)
Some research indicated the money supply problem from the individual`s or business`s point view. If the government reduces the growth rate of money supply, the company has to limit or reduce the fund for working capital which would in turn limit the expansion of the business. Also, with the interest rate goes up, namely, the cost of capital goes up, the retained profit will decrease. Moreover, a higher interest rate means more expansive when apply mortgage from the bank. However, some argument states the decrease in money supply may lead the inflation rate go down, so it still has opportunity to increase stock price with the lower nominal interest rate.
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Inflation and stock price
In theory, the stock market could operate well under the strong economy growth and low inflation condition. Therefore, when analyzing the stock valuation, it is reasonable to consider the influence of inflation on stock price.
In 1930, Fisher concluded the approximately linear relationship between inflation rate, nominal interest rate and expected return from the exact relationship.
r ≈ Ï+ E(I) (6)
(1+r)=(1+Ï) * (1+E(I)) （7）
Where,
r= nominal interest rate,
Ï=sum of expected real return, and
E(I)= expected inflation rate
Fisher (1930) argued that "the expected real return is determined by real factors, and is unrelated to expected inflation." When analyzing the relationship, the real interest rate cannot be observed which is determined by real factors and it normally assumed to be stable over time. At this stage, the only reason for the fluctuation of nominal interest rate is expected inflation rate. If following the negative causal relation theory of interest rate and stock price, as the inflation rate increases, it would lead the nominal interest rate increase and which in turn the stock price goes down.
Moreover, by analyzing with using simple regression and Granger causality test, Farsio and Fazel(2008) indicated there is no stable causal relation between inflation rate and stock price. In different time period, for the same group of companies, the causal relation can be either negative or positive. In no debt companies, they are not bothered by the interest rates; the only cost they may concern is the input good cost which changes keeping in line with the inflation rate. As the inflation rate goes up, the company cash flow will goes up and consequently, the stock price would rise. (Farsio & Fazel, 2008) Nevertheless, Gultekin(1983) has tested Fisher`s hypothesis with using twenty six countries data from 1947 to 1979 and could not find any reliable positive relation between nominal interest rate and inflation rate. (Gultekin, 1983)
So far, most research has indicated the negative causal relation between inflation rate and stock price. With using 1953-1971 monthly data of UK and US stock market, Fama and Schwert (1977) illustrated both expected and unexpected inflation rates are negatively correlated with the stock return. (Fama & Schwert, 1977) In addition, Boudoukh and Richardson (1993) did the same test with using UK and US short term and long term data, they conclude, at the short term horizon, the inflation and stock return are uncorrelated, however, at the long term, the relationship is following the Fisher`s hypothesis. In emerging market, Lee (1998) tested the data from Hong Kong, Tai Wan, Korea and Singapore, and found the negative correlation. (Lee B. , 1998)
With analyzing the empirical evidence of MENA countries, Al-Rjoub indicates a significant negative relationship between unexpected inflation rate and stock return with the absence of asymmetric information. (Al-Rjoub, unknow) By analyzing 10 different types companies in Jordan, Mousa, safi, Hasoneh & Abo-orabi found that some companies` stock prices are negatively correlated with the inflation rate, however, some others are slightly positive correlated. (Mousa, Safi, Hasoneh, & Abo-orabi, 2012)
Feldstein (1983) argued the crucial relationship between inflation rate and stock price from two aspects. On one side, he illustrate that with a higher steady state inflation rate, the stock price would increase as a faster rate. On the contrary, if the expected future inflation rate is going up, it would cause the stock pricing falling at the same time. Although after the falling period, the stock price will start rising again under the higher inflation, the fundamental stock price is still lower. (Feldstein, 1983)
Fama (1981) has suggested a "proxy hypothesis" about the relationship between inflation rate and stock return. He emphasized that the negative causal relation is spurious, because this relationship is set up on assumption of inflation and real activities. In Fama`s new hypothesis, he predicted the increasing inflation rate might cause decreasing on real economic activities and money demand. (Fama E. , 1981) The worse is the reduction of real activity may lead to even worse fiscal deficit. (Geske & Roll, 1983) some economist find strong evidence to support the proxy hypothesis such Kual(1987), but some others such as Cochran and DeFina (1993) still argue the unreliability of the proxy Hypothesis.
å¯ä»¥å†åŠ 一些关于CPI and PPI 的论述
Exchange rate and stock price
First economists pay attention on the relationship between exchange rate and stock price is Franck and Young in 1972. They test six different exchange rates but found no relation existing at that time. (Franck & Young, 1972)
As one of the classical economic theory, Dornbusch and Fisher (1980) has introduced the "flow oriented" model, which indicated that exchange rate would have influence on the international competitiveness and the balance of trade position, as a consequence, the real output of the country would change and also affect the current and future company`s cash flow, and all these will lead the movement of the stock price. (Dornbusch & Fisher, 1980)On the other hand, Gavin (1989) argue this relationship is bi-directional --- the movement of stock price also affects the exchange rate through the changes in money demand in short-run. (Gavin, 1989) Yu (1997) has done the Granger Causality test on Hong Kong, Tokyo and Singapore financial market and found only Tokyo financial market existed bi-directional causal relation between exchange rate and stock price and no causal relation in Singapore market. (Yu, 1997)
By analyzing the US data, economists found different relation between exchange rate and stock market. Aggarwal (1981) found the positive relation between US dollar and stock price; (Aggarwal, 1981) however, with using the different period data 1980-1986, Soenen and Hennigar(1988) indicated the relation should be negative during that period. (Soenen & Hennigar, 1988) If changing the data to daily base, Roll (1992) argued the there exist positive relation between exchange rate and stock price. (Roll, 1992) When Chow et al (1997) used monthly data from 1977 to 1989 to test the relation between excess stock return and real exchange rate of return, the result was very debatable which is no relation existing. (Chow, Lee, & Solt, 1997)
By using the Portfolio Balance Model, Smith (1992) figured out the equity value is the most significant determinate of exchange rate. Other variable such as government bonds and money were not that much important. (Smith, 1992)
It is also reasonable to discuss about the exposure of domestic companies to foreign currency risk. When exchange rate fluctuated, it will affect firms` discounted cash flow. The transaction cost might increase and the company profit would decrease. By analyzing the data of US, UK, Japan and Germany with conditional international asset pricing model, Dumas and Solink (1995) proved the exchange rate does matter. (Dumas & Solnik, 1995)
Phylaktis and Ravazzolo studied on both the long run and short run relationship between exchange rate and stock price. With considering the affect of the exogenous shock impact, they indicate the positive causal relation between exchange rate and stock price in long run. In addition, they also found evidence to prove that the financial crisis definitely has long term influence on the stock market. (Phylaktis & Ravazzole, Unknown)
In different from the long run relation, Bahmani- Oskooee and Sohrabian found the dual causal relation between stock price and exchange rate in short run by conducting the Granger Causality test in monthly data of S&P 500 in 1973 -1988. (Bahmani- Oskooee & Sohrabian, 1992)
Additionally, Caporale and PIttis (1997) summarized that reason for no causal relation between exchange rate and stock market is omission of an important variable from the system.-"which acts as a conduit through which the real exchange rate affects the stock market". Currently, each individual country`s economy is becoming increasing correlated with each other. As the local market has to set up the relationship around the world to expand the business scale, the linkage between foreign exchange and stock market are becoming tight. To some extent, US stock market plays a significant role in the financial system. They also showed an exam of invalid relationship in an incomplete system which lack the US market as a variable. (Caporale & Pittis, 1997)
Muhammad and Rasheed assumed the relationship is negative and each individual holds both foreign and domestic asset in their portfolio. As the domestic assets price increasing, the demand for the domestic also goes up. In order to generate more money to buy the domestic assets, local individual has to sell the foreign assets which cause the foreign assets price decreases and the local currency appreciation. Because the domestic assets price is increasing, the wealth value of local assets holder is also going up which in turn lead the domestic interest rate increase. With doing the empirical analysis, Muhammad and Rasheed found no causal relation between exchange rate and stock price to support their hypothesis. It can be explained as "treating the exchange rate as the price of an asset (price of one unit of foreign currency). Therefore, like prices of other assets, the exchange rates are determined by expected future exchange rates." At this stage, the expected future exchange rates could be determined by any news or information which also affect current exchange rate. (Muhammad & Rasheed, unknown)
Bartov and Bodnor (1994) emphasized the contemporaneous exchange rate only has little influence on the abnormal return, however, the lagged change in exchange rate could be negatively correlated with the abnormal return. (Bartov & Bodnar, 1994)
Real economy and stock price
When examining the causal relationship between real economy and stock price, the industrial production index normally delegated the real economic activities. As a measurement of the industrial sectors of the economy, although industrial production is only take small proportion of the Gross Domestic Production, it is quite sensitive to the changes in interest rate and consumer demand. To some extent, the central banks also pay attention to the industrial production to avoid the uncontrolled level of inflation rate. Furthermore, many literatures has proved the annual stock return variance is a good indicator of forecasting the variance of significant determinates of companies cash flow such as Gross National Product and industrial production index. (Fama E. , 1990)
Pearce (1982) discussed about a model which treat the stock price as the present or discounted value of the expected future dividends. In this model, if the investors use a low required return to discount their future earnings, the stock price would increase, however, if the overall economy suffers a recession or grow slowly, the stock price would fall as the lower expectation about future corporate profits which might lead to a economic vicious cycle. (Pearce, 1983)
Pearce (1983) also indicated that a strong economy recovery is always following the increasing of the stock price in US. He believes the stock price could be one of the most reliable indicators of the economic activities. Therefore, the stock price can be seen as a signal of the changes in the economy. Specifically, with the stock prices increasing, the wealth of the householders are raising which might lead the householders believe they have stronger purchasing power and are willing to spend more. Arising spending would significantly speed up the economy recovery. (Pearce, 1983)
By examining the 1953-1987 US stock market data in ordinary least-square (OLS) regression, Fama (1990) indicated the changes in the stock return can be explained by the expected return and forecast of the real economy activities, (Fama E. , 1990) however, Foresti (2006) hold an opposite view to Fama`s. Foresti only admit that the investors could predict the growth trend of the economy by observing the stock price and emphasize the opposite hypothesis would be rejected. (Foresti, 2006)Actually, the methodology Fama used to test the relation has the limitations in the OLS regression which is selecting the explanatory variables based on the goodness of fit. In the research of Nardari and Scruggs, they believe the fluctuation of the stock market is due to the "volatility of news about future returns". Some economist has done the Granger Causality test with different countries data in same time period, the result shows only few countries industrial production growth could granger cause the changes in stock market. (Errunza & Hogan, 1998)
Choi et al (1999) examined the G-7 countries(US, UK, Japan, Canada, Germany, France and Italy) monthly, quarterly and annual causal relation between stock return and industrial production and found US, UK, Japan, Canada and Germany could show significant correlation in short run which industrial production is granger caused the volatility of stock market; the causal relation only exist in France quarterly data and no relation exist in Italy. These researchers also indicated the significance of the stock market information. It seems the information available in stock market does not affect the forecasting of the industrial that much. Compared to the stock market, the industrial production growth are more stable and much easier to be forecast, the information on stock market is too volatile and not that much reliable. (Choi, Hauser, & Kopecky, 1999)
Some economists explain the relationship between real economic activity and stock price through the oil price shocks. Sadorsky (1999) indicated the volatility of oil price would asymmetrically affect the US economy. He shows after 1986 the oil price could explain more volatility in stock price than the interest rate. As a consequence, a positive relation can be set up -the increasing oil price would lead to the down turn of stock market and the shocks in the stock market would have positive related with interest rate and industrial production. (Sadorsky, 1999)
In emerging markets, Nishat and Shaheen (2004) proved the positive causal relation between industrial production and stock price in Pakistan. (Nishat & Shaheen, 2004)Naka, Mukherjee and Tufte (1998) also found the industrial production could positive affect the stock prices significantly in India. (Naka, Mukherjee, & Tufte, 1998) Some other literatures also proved the above positive relation in the stock market such as Singapore, Brazil and Chile. However, in the countries such as Argentina and Mexico, the influence of industrial production on the stock price is no longer significant. (Abugri, 2008)
Financial Crisis， economic announcement and stock price
At the second half of year 2007, the housing bubble in US had got to the peak, as a consequence, the delinquencies in the subprime sector finally spread to the prime mortgage sector. All these changes leaded the real estate prices started to drop down dramatically. The crisis happening in housing market firstly affected the financial stock market especially the banking sector such as American Express, JP Morgan Chase, and Citigroup and so on. During 2007-2008, S&P 500 has lost 36.31% while average loss of the banks` value is 62.54% compared to the past average loss 21.07%. (Chaudhury, 2011)
The primary reason of the subprime crisis is the continuous increasing demand for houses in the US. Since from the bull market of 1990`s, due to the economic expansion and the technology boom, people have increasingly confidence about their career and income, additionally, the continuous increasing of housing value and lower Federal Funds rate also encourage people to invest in house with high Loan to Value (LTV) mortgages. (Chaudhury, 2011)
To some extent, at the beginning of 1990`s, the US government used to fully support the expansion of Mortgage to meet the strong demand of mortgage loan with relaxing standards, such as making the Federal Housing Enterprises Financial Safety and Soundness Act of 1992 and the1995 Community Reinvestment Act which allowed the Government Sponsored Enterprises (GSE) Fannie Mae and Freddie Mac to supply the a minimum proportion of subprime loan as the mortgage to trade the affordable housing. Actually, the lenders were eager to get the higher net interest margin (NIM) by lending the subprime mortgage at a higher interest rate than the prime mortgage even relaxing, bending or ignoring the conventional underwriting standards . However, due to the low credit rating and low income level of the borrowers, they were only able to pay back the interest when the house value kept increasing. (Chaudhury, 2011)
Almost at the same time, the over the counter derivatives trading were becoming increasingly no oversight. The Wall Street bankers found a way to make more money through designing, selling and investing in the more complex derivatives of the subprime mortgage--collateralized debt obligations (CDO) and credit default swaps (CDS). Under the lenient policies of the subprime market, the selling volume of the CDOs and CDSs were keeping raising speedily and they became the key drive of the subprime mortgage. Eventually, at the 2005, 20 percent of the new mortgage loans were subprime compared to 1994 which was only 5 percent. (Braunstein, 2007) The other statistic data showed the dollar amount of subprime loan outstanding rose from $332 billion in 2003 to $1.3 trillion by the end of June, 2007 (BBC, 2007)
In 2006, the US real estate market began to slip, and the interest rates have also risen several times, the borrowers cannot afford to pay back the mortgage, which made subprime mortgage default and bad debt increase. Moreover, the price of the CDOS and CDSs began to fall which lead relative financial institutions were facing the liquidity problem in both US and European. As a result, the citizen`s credit was becoming even lower, and the evaluation of the housing relative bonds price went down. Once the mortgage assets value shrink there is a crisis and it will spread to the whole relative chains. (Chaudhury, 2011)
Although the reasons for formation of the sub-prime crisis are multiple, the United States government cannot deny their slow response and inefficiency at making policies to reduce the damage of the financial crisis which accelerate the stock market loss and the speed of spreading to the world wide. (Buiter, 2007) Recently, the impact of the 2007 financial crisis is still existing, in United States, although the government and banking system have made some announcements to gain the positive shock to the economy, the high unemployment, low consumer confident, decline of house value and personal bankruptcy are still primarily significant problems. (Gerry, 2011)
S&P 500
Standard & Poor`s 500 index is a US stock market index which records the behavior of top 500 listed US companies. This index was first set up and operated by the Standard & Poor`s Index Committee in 1957. At beginning, the S&P 500 contained 425 kinds of industrial stocks, 15 kinds of rail stocks and 60 kinds of public utilities stocks. From 1st of July,1976, the new S&P 500 were consist of 400 kinds of industrial stocks, 20 kinds of transportation stocks, 40 kinds of public utility stocks and 40 kinds of financial stocks. All of the 500 listed companies covered by the S&P 500 are also list in the New York Stock Exchange (NYSE) and Nasdaq Stock Exchange. Moreover, S&P 500 used to be a market-value weighted index, which means "each stock's weight is proportionate to its market value", the stock with higher market capitalization has more influence on the index trend. With conducting the two-steps transition in 2005, the S&P 500 now is float weighted index which is only concerns about the number of shares trading in the public. Compared to the Dow Jone Index, S&P 500 contains more companies and is more representative and accurate; therefore, the risk is more dispersion and S&P 500 could reflect more extensive market change. In US, the past statistic states" an estimated $625 billion is "passively" invested in index funds tracking the S&P 500", it becomes the favorite index for the passive investors and majority of active portfolio are taking it as the benchmark as well.
Recently, many index funds and exchange-traded funds (ETF) are trying to tracking the performance of S&P 500 index, which are containing same stocks in same proportion. Vanguard's S&P 500 Index Fund (VOO), iShares S&P 500 ETF (IVV) and SPDR's S&P 500 ETF (SPY) are the examples of taking S&P 500 as their benchmark. Moreover, in the derivatives market, the company such as Chicago Mercantile Exchange (CME) and Chicago Board Options Exchange (CBOE) also offer the future or option contracts which are tracking the S&P 500.
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Methodology
Granger (1969) and Sims (1972) developed the testing method for the causal relation. At that time, many economists have testing the causal relationship between money and income with applying this technique. In order to test the bi-direction causal relationship between the macroeconomic variables and S&P 500 in the VAR model, the granger causality test will be conducted. It controls the expected patterns of the auto dependence in the dependent variables, then set up the causal relation within the independent variables. Additionally, the granger causality test does not follow the assumptions of the OLS, with the involving of the lag term, it could set up causal relation without knowing the exactly coefficients, therefore, it only can be used as the significant test.
A time series data X might cause a time series Y if and only if the expectation of Y given the history of X is different from the unconditional expectation of Y. The X and Y have to be stationary time series data with zero mean. Therefore, the unit root test must be conducting before the granger causality test.
E (Y|Yt-j, Xt-j)≠E (Y|Yt-j) (8)
The model is
Yt=β0+β1Yt-1+…+βjYt-j+φ1Xt-1+… +φjXt-j+εt (9)
Xt=β0+β1Xt-1+…+βjXt-j+φ1Yt-1+… +φjYt-j+μt (10)
The t is the time and j is the appropriate lags term.εt andμt are the two uncorrelated white noise term. All the related variables are transferred into Logarithms.
In the equation (9) and (10), if the testing result shows the φs are jointly significant, the causal relation established; if theφs are jointly zero, there is no causal relation existing.
The Hypothesis is
H0: the macroeconomic variables do not granger cause the S&P 500
H1: the macroeconomic variables do granger cause the S&P 500.
If the granger testing result rejects the null hypothesis, then the macroeconomic variables could granger cause the stock index.
Data description
In the past literatures, economist were using various economic series to attempt the primary determinates of the relationship between macroeconomic variables and stock prices. This paper will conduct the econometrics testing on industrial production index (IPI), producer price index (PPI) and consumer price index (CPI) which proxy the goods market, the money supply (M1 and M2), the nominal interest rate (overnight interest rate (OIR) and treasure bill interest rate(TIR)) which proxy the money market. Based on the past research, the money supply mainly affects the stock returns by CPI and OIR. The stock market index is delegated by the S&P 500.
Although since from the 1990s, the problem of the subprime mortgage sector has already grown up, the significance serious negative shock in the US real estate market was emerging in 2007. This paper will mainly focus on situation of financial market during the period of the latest 11 years 2001:01-2011:12 with using monthly data. With the both macro and micro economy environment changed and the new government announcements came out, the financial system has to rebuild the relationship between the macroeconomic variables and stock market index. In order to compare the different performance of the macroeconomic variables and S&P 500, the time series data will be split into two periods, one is delegated the period before the subprime 2001:01-2006:12, the other one is the period of the financial crisis 2007:01-2011:12. All the variables will be taken as the logarithmic from.
Now US are following the floating exchange rate policy. As stated by the relevant law, the US government could intervene the foreign exchange market if necessary. Normally, the floating exchange rate is decided by the market demand and supply. As the European is one of the largest financial markets in the world, and Euro, pound and US dollar are three most powerful currencies when doing the international trading, this paper will study on exchange rate of Euro to US dollar and GBP to US dollar. This is a limitation of this study which cannot concern all the other foreign currencies worldwide which may affect the changes in stock index.
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Exchange rate 美国现在的å¤-汇政ç-
However, in 2010 US government declared they will start to print money again which will accelerate the worldwide liquidity problem (the interest rate was too high) and get the inflation and money market to a even worse situation.
Average stock return
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2001:01-2011:122001-2011L.png
2001-2011D.png
2001:01-2006:122001-2006L.png
2001-2006D.png
2007:01-2011:122007-2011L.png
2007-2011D.png
Observing the descriptive statistic result of the 11 years, the average monthly returns of stocks is -0.0451%. Although it quite small, it still reveal the S&P 500 did not perform very well during this 11 years period, which may due to the high inflation in the second half of 2000s. In 2008, US Inflation rate got to 9.8% which was the highest during the latest 17 years, at the same time the housing price was falling down to the lowest point. The average stock return during the period 2001-2006 is positive 0.2% and negative -0.2% during2007-2011 could also prove the US subprime crisis did have negative shock on the stock market .
Unit root test
In literature, the classical regression model implies an important hypothesis-the time series data is stationary. If the time series data is non-stationary, for example, the time series data can be keeping increase or circle or random walking, the rule of big sample statistic "consistency" will be broken in any of these three cases, which in turn increase the danger of being Spurious regression. The Spurious regression is two independent variables are highly auto correlated (R2 is relatively high), if doing the regression model of these two, the coefficient of the determinants can be relatively high.
In real economy, the time series data such as consumption, income and price level are always going with the same direction which indicated they are non-stationary data. Due to the spurious regression, analyzing the time series data with the classic causal regression model might not get significant economic results. Therefore, it is reasonable to do the Unit Root Test which indicate whether the time series data stationary or not. The stationary time series data must satisfy some key requirements. First one is the mean, variance, autocorrelation should be constant over all period; second is the series data is easy to be forecast, namely, the future of the data should be proximately same as the past.
Normally, the non-stationary time series data could be transferred into stationary time series data by conducting the mathematical transformation -- first-difference or even second-difference. By differencing the time series data, a new time series data has been created. The value of the differenced time series data is the current value of data subtracts the foregoing period value. Before doing the differential part, the time series variables have to be determined whether stationary or not by conducting the unit root test. Dickey Fuller test is a very popular way to do the init root test.
In the case of Dickey Fuller test, the problem of autocorrelation is still not solved. In order to solve the hidden trouble of the autocorrelation problem, Dickey Fuller has developed a test called Augmented Dickey Fuller test which has three types of models.
ΔYt=δYt-1 ++εt without constant(intercept) and trend(none)
ΔYt=α+δYt-1 ++εt with constant(intercept)
ΔYt=α+βTrend+δYt-1 ++εt with constant(intercept) and trend
In probability of occurring autocorrelation, before conducting the test, it is necessary to observe the line chart of each individual time series data and select the best model for the test. Additionally, all the variables are in logarithmic terms.
The hypothesis is
H0: δ=0, (there is a unit root in the variable, and the time series data is non-stationary.)
H1: δ≠0, (there is not a unit root in the variable , and the time series data is stationary. )
If the ADF testing result shows the t statistic > ADF critical value, the null hypothesis cannot be reject, which indicate the unit root exists, and the first difference need to be conduct.
If the t statistic < ADF critical value, the null hypothesis can be rejected and the time series data is stationary.
2001:01-2011:12
LOG
T-statistic
PROB
H0:
LSP500
-1.962558
0.0518
NOT REJECT(T=-2.88(α=5%))
LDJ
-1.738051
0.0846
NOT REJECT(T=-2.88(α=5%))
LPPI
-2.763104
0.0066
NOT REJECT(T=-3.44(α=5%))
LCPI
-1.890673
0.1117
NOT REJECT(T=-2.88(α=5%))
LOIR
-2.791293
0.0061
NOT REJECT(T=-2.88(α=5%))
LTIR
-2.09587
0.0381
NOT REJECT(T=-3.44(α=5%))
LM0
0.086123
0.9635
NOT REJECT(T=-2.88(α=5%))
LIPI
-0.964419
0.3369
NOT REJECT(T=-2.88(α=5%))
LM1
0.774234
0.4402
NOT REJECT(T=-3.44(α=5%))
LM2
-2.185868
0.0306
NOT REJECT(T=-3.44(α=5%))
LEROUSD
-1.697053
0.0921
NOT REJECT(T=-2.88(α=5%))
LGBPUSD
-1.656333
0.1001
NOT REJECT(T=-2.88(α=5%))
LIMP
-2.0078
0.5911
NOT REJECT(T=-3.44(α=5%))
LEXP
-2.7218
0.2298
NOT REJECT(T=-3.44(α=5%))
1ST DIFFERENCE
T-statistic
PROB
H0:
DLSP500
-8.4987
0.0000
REJECT(T=-2.88(α=5%))
DLDJ
-8.463053
0.0000
REJECT(T=-2.88(α=5%))
DLPPI
-6.687588
0.0000
REJECT(T=-3.44(α=5%))
DLCPI
-7.884645
0.0000
REJECT(T=-2.88(α=5%))
DLOIR
-11.94961
0.0000
REJECT(T=-2.88(α=5%))
DLTIR
-9.081239
0.0000
REJECT(T=-3.44(α=5%))
DLM0
-7.1157
0.0000
REJECT(T=-2.88(α=5%))
DLIPI
-4.737566
0.0000
REJECT(T=-2.88(α=5%))
DLM1
-7.677614
0.0000
REJECT(T=-3.44(α=5%))
DLM2
-6.360086
0.0000
REJECT(T=-3.44(α=5%))
DLEROUSD
-8.041686
0.0000
REJECT(T=-2.88(α=5%))
DLGBPUSD
-7.343013
0.0000
REJECT(T=-2.88(α=5%))
DLIMP
-4.815
0.0007
REJECT(T=-3.44(α=5%))
DLEXP
-4.562
0.0018
REJECT(T=-3.44(α=5%))
2001:01-2006:12
LOG
T-statistic
PROB
H0:
LSP500
-1.041312
0.3014
NOT REJECT(T=-2.90(α=5%))
LDJ
-0.650298
0.5177
NOT REJECT(T=-2.90(α=5%))
LPPI
-2.602385
0.0114
NOT REJECT(T=-3.47(α=5%))
LCPI
-2.142996
0.0357
NOT REJECT(T=-3.47(α=5%))
LOIR
-4.839883
0.0000
REJECT(T=-2.90(α=5%))
LTIR
-0.642097
0.5229
NOT REJECT(T=-2.90(α=5%))
LM0
-1.602745
0.4759
NOT REJECT(T=-2.90(α=5%))
LIPI
-3.207963
0.0023
NOT REJECT(T=-3.47(α=5%))
LM1
-1.079417
0.2842
NOT REJECT(T=-3.47(α=5%))
LM2
-2.939257
0.0045
NOT REJECT(T=-3.47(α=5%))
LEROUSD
-1.711038
0.0916
NOT REJECT(T=-3.47(α=5%))
LGBPUSD
-2.442743
0.0172
NOT REJECT(T=-3.47(α=5%))
LIMP
0.737098
0.9922
NOT REJECT(T=-2.90(α=5%))
LEXP
1.345468
0.9987
NOT REJECT(T=-2.90(α=5%))
1ST DIFFERENCE
T-statistic
PROB
H0:
DLSP500
-5.836848
0.0000
REJECT(T=-2.90(α=5%))
DLDJ
-5.868534
0.0000
REJECT(T=-2.90(α=5%))
DLPPI
-7.392426
0.0000
REJECT(T=-3.47(α=5%))
DLCPI
-6.982882
0.0000
REJECT(T=-3.47(α=5%))
DLOIR
-9.883419
0.0000
REJECT(T=-2.90(α=5%))
DLTIR
-3.549948
0.0000
REJECT(T=-2.90(α=5%))
DLM0
-6.009093
0.0000
REJECT(T=-2.90(α=5%))
DLIPI
-5.735066
0.0000
REJECT(T=-3.47(α=5%))
LM1
-7.662239
0.0000
REJECT(T=-3.47(α=5%))
LM2
-5.452556
0.0000
REJECT(T=-3.47(α=5%))
DLEROUSD
-6.660449
0.0000
REJECT(T=-3.47(α=5%))
DLGBPUSD
-7.219346
0.0000
REJECT(T=-3.47(α=5%))
DLIMP
-6.075397
0.0000
REJECT(T=-2.90(α=5%))
DLEXP
-9.293342
0.0000
REJECT(T=-2.90(α=5%))
2007:01-2011:12
LOG
T-statistic
PROB
H0:
LSP500
-1.507999
0.1371
NOT REJECT(T=-2.91(α=5%))
LDJ
-1.503466
0.1382
NOT REJECT(T=-2.91(α=5%))
LPPI
-1.060077
0.2936
NOT REJECT(T=-2.91(α=5%))
LCPI
-1.491832
0.1413
NOT REJECT(T=-2.91(α=5%))
LOIR
-1.390337
0.1714
NOT REJECT(T=-2.92(α=5%))
LTIR
-1.560424
0.1242
NOT REJECT(T=-2.91(α=5%))
LM0
-0.770880
0.8197
NOT REJECT(T=-2.91(α=5%))
LIPI
-0.86859
0.3887
NOT REJECT(T=-2.91(α=5%))
LM1
-1.871842
0.0665
NOT REJECT(T=-3.48(α=5%))
LM2
-1.070559
0.2890
NOT REJECT(T=-3.48(α=5%))
LEROUSD
-2.316478
0.0241
NOT REJECT(T=-2.91(α=5%))
LGBPUSD
-1.313591
0.1942
NOT REJECT(T=-2.91(α=5%))
LIMP
-1.988345
0.2910
NOT REJECT(T=-2.91(α=5%))
LEXP
-1.904858
0.3278
NOT REJECT(T=-2.91(α=5%))
1ST DIFFERENCE
T-statistic
PROB
H0:
DLSP500
-5.716832
0.0000
REJECT(T=-2.91(α=5%))
DLDJ
-5.673569
0.0000
REJECT(T=-2.91(α=5%))
DLPPI
-3.504969
0.0000
REJECT(T=-2.91(α=5%))
DLCPI
-5.225588
0.0000
REJECT(T=-2.91(α=5%))
DLOIR
-9.967206
0.0000
REJECT(T=-2.93(α=5%))
DLTIR
-6.16314
0.0000
REJECT(T=-2.91(α=5%))
DLM0
-4.510640
0.0006
REJECT(T=-2.91(α=5%))
DLIPI
-3.070384
0.0000
REJECT(T=-2.91(α=5%))
DLM1
-5.38463
0.0000
REJECT(T=-3.48(α=5%))
DLM2
-3.887612
0.0003
REJECT(T=-3.48(α=5%))
DLEROUSD
-4.893655
0.0000
REJECT(T=-2.91(α=5%))
DLGBPUSD
-4.07409
0.0002
REJECT(T=-2.91(α=5%))
DLIMP
-3.152064
0.0286
REJECT(T=-2.91(α=5%))
DLEXP
-5.228582
0.0001
REJECT(T=-2.91(α=5%))
The second column of the table is the significant t statistic value for the test. The PROB tells whether the t- statistic test result is significantly meaningful.
For the 11-year period data sample, at the log level, the unit root null hypothesis cannot be rejected because the t statistic values of all variables are bigger than the critical value at the 5% confidence interval. So there is a unit root in each original variable data, namely they are not stationary data. The t statistic value of the first difference variables are all smaller than the critical value which indicate the null hypothesis could be rejected at 95% confidence level and the differential time series data are stationary.
Moreover, for the period 2001 to 2007, in the log level, all the variables cannot reject the null hypothesis at 95% confidence level except for variables the overnight interest rate and foreign net long term sales. But after the differential transformation of the data, all the economic variables could not find the evidence to show the existence of the unit root. Therefore, at the first half of 2000s, the first differential time series data are stationary.
For the period 2007-2011, the log level economic variables cannot find evidence to reject the null hypothesis, but again, the first differential time series are prove to be stationary over 5 years.
Correlation coefficient
A correlation coefficient is an important measurement of relationship between two variables. It could indicate whether the two variables have linear relation and how strong the relation is. In literature, the correlation coefficient of two variables should range from -1 to +1. The closer to 1 the absolute value of the coefficient, the stronger the relationship is. Otherwise, the zero coefficient means no linear relationship exist between the two variables. Usually, the economist would like to observe the scatter chart before the correlation coefficient. The distribution of the scatter could visually indicate whether the two variables go same direction or not. Additionally, the positive coefficient means the two variables have positive linear relationship and go same direction; the negative means negative linear relationship and go different direction.
Karl Pearson developed a precise mathematical way to accurately calculate the correlation coefficient. He stated "the correlation coefficient r is the covariance of two variables (Cov(X, Y)) divided by the product of their sample standard deviation (SX, SY)."
Where,
r= the correlation coefficient of two variables,
Cov(X, Y)=the covariance of the two variables,
SX= the standard deviation of the variable X
SY= the standard deviation of the variable Y.
However, there is an important limitation about the correlation coefficient. The correlation could only indicate the two variables are related to each other, but it does not mean the causation. It is impossible to conclude one variable could cause the other one from the observation of the correlation coefficient. What the correlation coefficient is able to do is to show "one variable changes, the others seems to move in a predictable way-either same or different direction."
Moreover, it is reasonable to mention the significant test which could indicate whether the estimated correlation coefficients show a random or a real relationship. If the correlation coefficient is not significantly real, the result will be worthless. Therefore, here will test the estimation which is the correlation coefficient is significantly different from zero and proposed the null and alternative hypothesis:
H0: there is no linear relationship; the correlation coefficient r is equal to 0,
H1: there is linear relationship; the correlation coefficient r is not equal to 0.
This is a two-tail significant test. The formula of the significant test is
Where,
n is the sample size,
r is the correlation coefficient.
If the absolute value of t statistic is bigger than the critical value 1.81 at 5% confidence level, the null hypothesis will be rejected, but if the absolute value of the t statistic is smaller than the critical value, the null hypothesis cannot be rejected at this level and the t statistic would have a t distribution with n-2 degrees of freedom.
The result shows the relationship between S&P 500 and macroeconomic factor during the three time periods.
2001:01-2011:12
Dependent Variable: LSP500
Dependent Variable: DLSP500
Variables
Correlation
Coefficient
S&P 500
t-Statistic
H0
Hypothesis
Variables
Correlation
Coefficient
S&P 500
t-Statistic
H0
Hypothesis
LDJ
0.9891
76.5897
Reject
DLDJ
0.9944
106.8700
Reject
LPPI
0.4861
6.3421
Reject
DLPPI
-0.0985
-1.1242
Not Reject
LCPI
0.4392
5.5740
Reject
DLCPI
0.1123
1.2836
Not Reject
LOIR
0.4100
5.1253
Reject
DLOIR
-0.0799
-0.9104
Not Reject
LTIR
0.3243
3.9088
Reject
DLTIR
0.1736
2.0021
Reject
LM0
-0.2043
-2.3792
Not Reject
DLM0
-0.2487
-2.9167
Not Reject
LM1
0.1652
1.9098
Reject
DLM1
0.0661
0.7524
Not Reject
LM2
0.3366
4.0757
Reject
DLM2
-0.1412
-1.6200
Not Reject
LIPI
0.8441
16.6605
Reject
DLIPI
0.0307
0.3236
Not Reject
LEROUSD
-0.6077
-8.7247
Reject
DLEROUSD
-0.0655
-0.7455
Not Reject
LGBPUSD
-0.7496
-12.9126
Reject
DLGBPUSD
-0.1000
-1.1415
Not Reject
LIMP
0.5638
7.7826
Reject
DLIMP
0.2119
2.4633
Reject
LEXP
0.4543
5.8146
Reject
DLEXP
0.2729
3.2223
Reject
2001:01-2006:12
Dependent Variable: LSP500
Dependent Variable: DLSP500
Variables
Correlation
Coefficient
S&P 500
t-Statistic
H0
Hypothesis
Variables
Correlation
Coefficient
S&P 500
t-Statistic
H0
Hypothesis
LDJ
0.9991
197.0695
Reject
DLDJ
0.9921
66.1661
Reject
LPPI
0.9198
19.6122
Reject
DLPPI
-0.2550
-2.2064
Reject
LCPI
0.9089
18.2354
Reject
DLCPI
-0.3352
-2.9767
Reject
LOIR
0.5977
6.2375
Reject
DLOIR
0.0081
0.0678
Not Reject
LTIR
0.7769
10.3236
Reject
DLTIR
0.0224
0.1875
Not Reject
LM0
-0.0787
-0.6604
Not Reject
DLM0
-0.0874
-0.7289
Not Reject
LM1
0.9156
19.0516
Reject
DLM1
0.2854
2.4915
Reject
LM2
0.9417
23.4173
Reject
DLM2
-0.1408
-1.1899
Not Reject
LIPI
0.9128
16.1170
Reject
DLIPI
0.0587
0.4199
Not Reject
LEROUSD
-0.8224
-12.0945
Reject
DLEROUSD
-0.3061
-2.6901
Reject
LGBPUSD
-0.8574
-13.9386
Reject
DLGBPUSD
-0.3226
-2.8515
Reject
LIMP
0.5696
5.7982
Reject
DLIMP
-0.0061
-0.0514
Not Reject
LEXP
0.7035
8.2835
Reject
DLEXP
0.2587
2.2246
Reject
2007:01-2011:12
Dependent Variable: LSP500
Dependent Variable: DLSP500
Variables
Correlation
Coefficient
S&P 500
t-Statistic
H0
Hypothesis
Variables
Correlation
Coefficient
S&P 500
t-Statistic
H0
Hypothesis
LDJ
0.9943
71.0230
Reject
DLDJ
0.9966
92.1191
Reject
LPPI
-0.1123
-0.8607
Not Reject
DLPPI
0.1384
1.0643
Not Reject
LCPI
-0.0144
-0.1097
Not Reject
DLCPI
0.1870
1.4497
Not Reject
LOIR
0.2748
2.1766
Reject
DLOIR
-0.1395
-1.0729
Not Reject
LTIR
0.6159
5.9538
Reject
DLTIR
0.2262
1.7685
Not Reject
LM0
-0.5124
-4.5447
Reject
DLM0
-0.2993
2.3679
Reject
LM1
-0.4279
-3.6055
Reject
DLM1
-0.0087
-0.0663
Not Reject
LM2
-0.5117
-4.5358
Reject
DLM2
-0.1332
-1.0235
Not Reject
LIPI
0.8817
14.2320
Reject
DLIPI
-0.0004
-0.0030
Not Reject
LEROUSD
-0.2763
-2.1895
Reject
DLEROUSD
0.1519
1.1704
Not Reject
LGBPUSD
-0.7904
-9.8263
Reject
DLGBPUSD
0.1955
1.5182
Not Reject
LIMP
0.7550
8.7697
Reject
DLIMP
0.3154
2.5089
<>
