Interaction Between Mutual Funds And Macro-economic Variable; A Ghanaian Context

INTERACTION BETWEEN MUTUAL FUNDS AND MACRO-ECONOMIC VARIABLES: A GHANAIAN CONTEXT MSc FINANCIAL ECONOMICS STUDENTS ID: 129045821 SUPERVISOR: PROF WOJCIECH CHAREMZA



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ABSTRACT This paper analyses the interaction between mutual fund prices, exchange rates and inflation in Ghana. The study focuses on the first and the largest equity mutual fund in Ghana known as the Databank EPACK Investment Fund. With over 50 million shareholdings and investments in 12 African countries, the fund is arguably the leading Pan African mutual fund. A total of 190 observations were obtained for the period between January 1997 and December 2012 of monthly prices of the fund, exchange rates and inflation rate in Ghana. The vector autoregressive model is employed on the stationary series of the variables. The stationarity of the variables were tested using the Augmented Dickey Fuller (ADF) unit root test and found that variables are in the same order of integration. Long run relationships are tested with Johansen cointegration and it was revealed that variables were not cointegrated at 5% significance. The result suggests that the price of the fund and exchange rates do not interact significantly.

Keywords: Mutual Funds, Exchange Rates, Inflation, Augmented Dickey Fuller Test, Grange Causality, Impulse Responses and Variance Decomposition



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TABLE OF CONTENT 1.0

Introduction

2.0

Review of Relevant Literature

2.1

Ghana’s Macroeconomic Environment

2.2

Mutual Funds and Flow Performance

2.3

Stocks and Macro-economic Variables

3.0

Methodology

3.1

Data Sources and Specification of the Model

3.2

Descriptive Statistics

3.3

Vector Auto Regressive Model

3.3.1 Arguments for and against the VAR Model 3.3.2 Stationarity and Unit Root Test 3.3.3 First Differences 3.3.4 Cointegration & Serial Correlation 3.3.5 Granger Causality 3.3.6 Impulse Responses 4.0

Analysis of Results and Interpretation Findings

4.1

Results from Vector Auto Regression Estimates

4.2

Causality Analysis

4.3

Analysis of Impulse Responses

4.4

Variance Decomposition

5.0

Conclusion

5.1

Summary of Findings

5.2

Policy Implications

5.3

Limitation References Appendices



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1.0 INTRODUCTION The mutual fund industry has seen a robust growth over the past decade with increasing number of global fund managers operating within African markets and the introduction of new product lines and services. It is undoubtedly so that they are becoming an attractive investment avenue for investor’s in respect of diversification, tax exemption, flexibility, divisibility, economies of scale and active management by professionals. Like every other investment, mutual funds are subject to certain risk factors and conditions pertinent to economic and market conditions. The past few years have exposed this asset class to various global and macro-economic factors. Among these factors include liquidity risk, credit risk, interest rate risk, exchange rate risk, inflation, and sovereign or country risk. The interaction between currency and stocks markets has been the subject of many academic debate and empirical analysis over the past two decades. This is quite considerate given the important role that equity and currency markets play in facilitating economic activity. This study seeks to reveal the impact of foreign currency movements and inflation on the monthly prices (net asset values) of a major fund within the Ghanaian mutual fund industry. The motivation behind the study is to establish causal relationships between the price of the mutual fund, exchange rates and inflation. The objective of the study is to identify and ascertain the strength and direction of causation between these variables particularly between the movement in price of fund and exchange rates as quoted as Ghana cedi per dollar. The chosen period was characterized by immense volatility and co-movement in macro-economic variables particularly exchange rates and inflation.



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Commencing with just 5 shareholders, the fund has seen quite a significant growth in performance over the period with its shareholding increasing to 79,826 in 2012. The yield to date of the fund has also experienced a significant growth over the years coupled some immense volatilities. With a composition of 80% of its investment in equity stocks and 20% in fixed income products, the fund is arguably one of the most volatile and high yielding investments in Africa. The figure below shows the historical yield to date performance of the fund.

Figure 1.0 DATABANK EPACK INVESTMENT FUND (GHC, YTD) 1.5 1 0.5

-0.5

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

0

(Source Databank Research 2013)

The study employed pair wise Granger causality test and discovered that there was no causal relationship between exchange rates and price of the fund in either direction. There was a unidirectional causality between exchange rates and inflation with causality running from exchange rate to inflation which was significant at both 1 and 5 percent level. Furthermore there seemed to be a unidirectional causality between inflation and price with causality running from inflation to prices. The results of this study is significant for policy makers and market practitioners in that it sheds light on the nature of the co-movement between mutual fund prices and macro-economic variables.



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The paper is organized as follows; Section II provides a global overview of mutual funds as well as the current Ghanaian Macroeconomic scenario and highlights within the Ghanaian mutual fund industry. It also provides a detailed review of relevant literature on the area under study and examines the economic theory surrounding stocks and currency movements. Section III provides a description of data and the methodology employed in the study. Section IV gives the analysis and interpretation of findings of the study. Lastly, Section V sums up the entire an analysis and provides some policy conclusions and some limitations based on the results and findings from the study.



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2.0

REVIEW OF RELEVANT LITERATURE

There has been a remarkable growth in mutual funds since the 1980s. Previous studies have focused on the micro-level relation between individual fund performance and the flow of money into or out of a mutual fund. Sirri and Tufano (1998) analyze the relationship between annual fund flow and performance-flow relationship. Their results suggest that “Mutual fund consumers chase returns, flocking to funds with the highest recent returns, though failing to flee from poor performers.” Ippolito (1992) also concludes that mutual fund investors move cash into funds that had the best performance and are less sensitive to stock market volatilities in the preceding year. Coval and Stafford (2006) study asset sales and institutional price pressure by accessing stock transactions of mutual funds. They find supporting evidence that widespread selling by financially distressed mutual funds leads to a reduction of prices below the fundamental value.

Mutual funds are a pool of funds from several investors which are invested in stocks, shortterm money-market instruments, bonds, other securities or assets, or some combination of these investments. A mutual fund is an investment vehicle that pools capital from clients purchasing its shares to invest in a portfolio of securities (Reilly & Brown 2003). Each share represents a proportionate ownership of the fund’s holdings and the income those holdings generate. It represents a professionally managed collective investment scheme that pools money from many investors and invests it in stocks, bonds, and other securities. Collective investment schemes are ideally medium to long-term commitments to certain assets which are expected to provide some income or capital appreciation or a mixture of both. Mutual funds are usually referred to as open ended funds because, as more people invest, the fund issues more units of shares.



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Investors usually purchase shares from the funds itself or through a broker in a secondary market. The price that the investors pay per share is the funds per share Net Asset Value (NAV) in addition to any commission fees that the fund imposes. Investors make profits when they sell their shares at prices higher than the initial purchase price. Alternatively, shareholders may incur capital loss with selling price lower than purchase price (Koh,1999). Mutual funds are mostly redeemable in the sense that the investor can liquidate their shares back to the fund or to the broker. Portfolios in these mutual funds are managed by a separate entity known as investment advisors or representatives and registered with the Security and Exchange Commission (SEC). Today, mutual funds form a major part of financial activity in American life. Clifford E. Kirsch & Bibb L. Strench (2011) established that about one-third of the families in the United States invest in mutual funds from 1980 through 2008, the total net assets invested in mutual funds in the US grew from $134 billion to over $9 trillion. Households owning mutual funds grew from 4.6 million to 52.5 million with the same period. Shares in the funds now represent a major part of household wealth, and the funds themselves have become important intermediaries for savings and investments. In the United States, more than 4,000 mutual funds currently hold stocks and bonds worth a total of more than $2 trillion. Household investment in these funds increased more than fivefold in the last ten years, making it the fastest growing item on the household financial balance sheet. Most of this growth came at the expense of more traditional forms of savings, particularly bank deposits. Mutual funds operate as tax-exempt financial institutions that pool resources from numerous shareholders to invest in a diversified portfolio of securities. Mutual fund investments, which are generally considered to be less risky than other financial instruments such as shares and debentures, have also suffered in the general atmosphere of volatility.



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Most of the works on mutual funds have been done on the issue of fund flow and performance. Keswani (2011) suggests that there is no significant relationship between fund sizes performance for small and large Balanced Mutual Funds. Shares in mutual funds now represent a major part of household wealth, and the funds themselves have become important intermediaries for savings and investments. 2.1

GHANA’S MACROECONOMIC ENVIRONMENT

Located in West Africa, the Republic of Ghana was formerly a British colony. It attained its independence on March 6, 1957 and became the first African nation to do so. Ghana’s official language as English and predominantly used in business and government communications, but there are about 250 native languages and dialects spoken. Ghana as a developing country has aspirations for economic growth, poverty reduction and the enhancement of the economic conditions of its indigens. However domestic saving in most developing countries, including Ghana, is very low. Gross domestic savings in Ghana from 1983 to 1990 averaged 7.4 percent of GDP (Kapur et al, 1991). Ghana’s economy ranks 77th in 2013 with an economic freedom score of 61.3. The country’s overall score increased by 0.6 over the previous year due to improvements in investment freedom, the control of government spending, and fiscal freedom. Ghana ranks 7th out of 46 countries in the Sub-Saharan Africa region, and its overall score have risen above the world average. Ghana’s economy grew by 7.9% in 2012 led by the immense growth in the services sector recording the highest growth of 10.2%, followed by industry 7%, with agriculture recording the lowest growth of 1.3% (Ghana Statistical Service (G.S.S) 2012). The notable economic growth rate of 8% over the past five years has been supported by strong improvements in economic freedom, with reforms focused on spurring private sector-led development. Ghana is considered as a model for democracy as well as political and economic reforms.

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The country is rich in natural resources, including gold, diamonds, manganese ore, bauxite, and oil production which began in 2010. High prices for gold and cocoa helped to sustain economic growth from 2008–2011 (Index of Economic Freedom, 2013). The industrial sector (contributed 30 percent of GDP in 2007) is more developed than in many other African countries, nonetheless agriculture continues to be its economic pillar accounting for 50 percent of employment and 39 percent of exports in 2007 (Index of Economic Freedom 2013). Bank of Ghana (BoG) has a monetary policy framework with the sole objective of maintaining price stability respect of inflation, exchange rates and interest rates. Inflation in May 2013 was 11.10 percent, up from 10.6 percent in April and 8.8 percent in January (G.S.S, 2012). The current interest rate was recorded at 17.2% and the exchange rate between the US Dollar and the Cedi at USDGHS 1.9870 as of June 2013 (BoG 2013) representing an average of 5% depreciation. Analysts have projected an end of year depreciation of 9% percent plus or minus two against the dollar against an earlier prediction of 6% during the first quarter of the fiscal year. (Databank Research 2013) However the Ghanaian economic conditions seemed stagnate, with an overall slow-down in economic growth, coupled with pressures of increasing crude oil prices and increasing inflation. Prior to the financial crisis, Ghana recorded high sustained GDP growth, a stable exchange rate, and a favourable balance of payments position. However, in the run up to the 2012 elections, the macroeconomic environment deteriorated rapidly, reflecting a confluence of a food and energy crisis and an expansionary fiscal policy (International Monetary Fund Report, 2011).



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Figure 2.1a AVERAGE MONTHLY DATA ON GHANA’S INFLATION, INTEREST RATES AND EXCHANGE RATES Average Monthly Inflation Interest 2000-2013 Average Monthly Interest 2000-2013

(Source Bloomberg 2013)

(Source Bloomberg 2013)

Average Monthly Exchange Interest 2000-2013

(Source Bloomberg 2013)

The mutual fund industry of Ghana has experienced remarkable growth during the last decade because of the return it offers to individual and institutional investors. The industry envisaged to bridge the wide gap which until the early 1990’s existed large investment programs and a shortage in savings level. The increased level of assets under management (AUM) and a number of new funds being launched is also significant contribution to the industries growth. Investors who committed their funds for more than 5 years earned exceptionally high returns. These abnormal returns have motivated many investors to participate in investing in these mutual funds. To throw more light on this immense growth in the industry, the Security and Exchange commission of Ghana has successfully registered over 22 mutual funds managed by over 15



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different financial Institutions and investment banks. These funds comprises of short term money market instruments, long term equity funds, balanced funds (a hybrid of both short and long term instruments) and ethical funds. Despite the growing interest of researchers in mutual funds over the world, Ghana’s mutual fund industry has failed to attract the attention of researchers. Limited research has been done on Ghanaian mutual. The Ghanaian mutual funds have become major players in the capital markets (equity and debt) and stock markets are being driven by the global economic factors. As such fund managers require understanding the linkages and accordingly planning their strategies of new investments. 2.2

Mutual Funds and Flow Performance

Classical theories hypothesise that stock prices and exchange rates can interact. The first approach encapsulates the ‘flow oriented’ models was pioneered by Dornbusch and Fisher 1980, which postulate that exchange rate movement can cause stock price movements. This is described by Granger-Sim causality as ‘unidirectional’ causality running from exchange rates to stock prices, or that exchange rate ‘Granger-cause’ stock price. This model is rooted from the macro perspective that as stock prices represent the discounted present value of a firm’s expected future cash flows. Conclusively, any factor that affects a firm’s cash flow should reflect in that firm’s stock price if the market is efficient as the Efficient Market Hypothesis suggests. Warther (1995) as well as Edelen and Warner (2001) pioneered the study of security returns and aggregate mutual fund cash flows. They ascertained whether there was a correlation between security returns net inflows using monthly data for the period January 1984–June 1993. The net money inflows were categorized into expected and unexpected components. The expected fund flows were estimated by running a regression of current flows on past flows. The residual from the expected fund flow regression was found to be the unexpected

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funds flow. Their results suggests there was evidence to show that security returns were highly correlated with concurrent unexpected cash flows into mutual funds but unrelated to concurrent expected flows. This result is consistent with the popular belief that fund inflows and returns are positively related. Their findings further purports to show that security returns does not lead nor lag flows in mutual fund. This sought to reject either sides of the feedback trading model. There have been several advancements in the work of Warther (1995). A notable example is that of Remelona et al., (1997). They employed a similar methodology like that of Warther’s (1995) and examined the effects and impact of markets returns on aggregate fund flows. Their improvement in the work of Warther’s (1995) can be viewed in respect of the inclusion of the returns of securities not held by the fund. They also employed the use of instrumental variables in their regression model rather than Ordinary Least Squares. Their results revealed that unexpected equity funds flow were affected by coeval bond returns but not by lagged returns. Fortune (1998) used VAR models to examine the relationship between fund flows and returns. This was done with use of seven variables and monthly data spanning across January 1984 through December 1996. The result obtained suggested a positive correlation between fund flows and contemporaneous returns. However, the results show that feedback do exists contrary to the findings of Warther (1995) and that of Remelona et al., (1997). Security returns do affect future fund flows and some fund flows do affect future security returns. Overall, there exists a mix of evidence on causal relationship between stock returns and mutual fund flows.



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Most works on mutual funds have been done in relation to fund flow and performance. Pollet and Wilson (2008) established that, though asset growth has minimal effect on the behaviour of the fund, both small and large funds diversified their portfolio in response to diversification and growth were associated with better performance of small-cap funds. Empirical studies have been conducted under this subject matter. Notable among them is the study conducted by Alexakis et al. (2005) employing the use of data from the Greek Money Market industry to establish a relationship between stock returns and investment fund flows. The study tested causality mechanism and established that mutual funds flows are affected by stock returns and vice versa. Mutual fund flows were found to cause high or low stock returns trends and cash outflows in equity funds in the Greek stock market. In this study, they mined the possibility of a causal relationship between mutual fund flows and stock returns for the Greek market. The statistical evidence showed that there was bidirectional causality between mutual fund flows and stock returns. This implied that lagged stock returns granger cause the mutual fund flows and vice versa. Evidence from the error correction models employed showed that variables were cointegrated. Their results were believed to be explained within the framework of investor’s sentiments. Thus investor psychology was an important factor influencing investment behaviour and more importantly in the case of emerging markets. They conclude that investors monitor and extrapolate trends in stock prices to enable them anticipate whether the prices would rise or fall and hence purchase or redeem shares. The determinants of mutual fund performance and returns have been viewed various studies across different countries and with different research approaches and techniques. Goetzmann and Massa (2003) extended their study by analysing the relationship between daily index fund flows and asset prices. The other objective was to examine whether shocks to prices were originated from demand flows into index funds. The results suggested a strong correlation between fund inflows and S&P market returns.



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Their results provide evidence that the market responds to daily demand. They also established that negative reactions occur due to the past returns and that investors' behaviour appears to be mainly induced by risk aversion rather of return. A.B.M. Munibur Rahman and Md. Salah Uddin Rajib (2013) performed an extensive search on the mutual fund industry of Bangladesh establishing the mutual fund dynamics in relation to stock market using a vector autoregressive causality analysis. A total of 714 days observation from January 2008 to December 2010 of four variables; Dhaka Stock Exchange (DSE ) general index turnover, DSE general index return, mutual funds’ turnover and mutual funds’ returns. They also found a bidirectional causality moving from DSE general index turnover to DSE general index return. They further conclude that demand for equity shares drives the demand for mutual fund shares but fails to raise the demand for its own price unless the price of the underlying value of the mutual fund changes. Consequently investors respond to changes in the value of the funds and are not attracted to mutual funds unless a positive externality drives the demand of mutual funds. Burucu and Contuk’s (2011) performed granger causality test findings and revealed a relationship between investment funds flow and earnings of market stock based on Turkey stock market. There is no causal relationship between investments funds flow and earnings of market stock in their analysis result.

2.3

Stocks and Macro-Economic Variables

Most of the empirical literature that analysed the relationship between stock prices and exchange rate mainly examined cases for the developed countries with very little or no attention on the developing countries. The results of these studies are, however, inconclusive. Some studies established a significant and positive relationship between stock prices and exchange rates (Solnik (1987), Smith (1992), and Aggarwal(1981)) while others have



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reported a significant negative relationship between the two (e.g., Soenen and Henniger (1988)). Solnik (1987) for instance examined the impact of several variables (exchange rates, interest rates and inflationary expectation) on stock prices. He employed the use of monthly data from nine western markets (Germany, U.S., Canada, Japan, U.K., France, Netherlands, Switzerland, and Belgium). He found that depreciation had a positive but insignificant influence on the U.S. stock market compared to changes in inflationary expectation and interest rates. Soenen and Hanniger (1988) used monthly data on effective exchange rates and stock prices for the period 1980-1986. They discovered a strong negative relationship between the value of the U.S. dollar and the change in stock prices. However, when they analyzed the above relationship for a different period, they found a statistically significant negative effect of revaluation on stock prices. On the other hand, there are some studies that have found very weak or no association between stock prices and exchange rates (Eli Bartov and Gordon M.Bodnor (1994), Franck and Young (1972)).

Eli Bartov and Gordon M.Bodnor (1994) concluded that

contemporaneous changes in the dollar had minimal effect in explaining abnormal stock returns. They also, found a lagged change in the dollar is negatively associated with abnormal stock returns. The regression results showed that a lagged change in the dollar had explanatory power in respect of errors made in analyst's estimates of quarterly earnings. In respect of causation, there is a mix of evidences. Some studies have revealed causation runs from exchange rates to stock prices (for instance, Abdalla and Murinde (1997)) . Conversely, Ajayi and Mougoue (1998) reported a reverse causation. They show that an increase in aggregate domestic stock price has a negative short-run impact on the domestic currency value but have a positive effect on domestic currency value in the long-run as stock



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prices increased. However, currency depreciation has a negative short-run effect on the stock market. Bahmani-Oskooee and Sohrabian (1992), also claim there is a bi-directional causality between stock prices and exchange rates in the short-run but not in the long-run. In theory, there is no consensus on the relationship between stock prices and exchange rates. For example, the portfolio balance model of exchange rate determination suggests a negative relationship between stock prices and exchange rates and that the causation runs from stock prices to exchange rates. The model suggests that individuals hold domestic and foreign assets, including currencies, in their portfolio. Consequently exchange rates play a vital role in balancing the demand for and supply of assets. As domestic stock prices increases, individual demand for domestic assets also increases. In order to buy more domestic assets, local investors would have to sell foreign assets (since they are relatively less attractive now), causing local currency appreciation. An increase in wealth as a result of a rise in domestic asset and commodity prices may lead to an increase in investors demand for money causing the domestic currency to appreciate in value. This in turn raises domestic interest rates. Another channel that results in the same negative relationship is an increase in foreign demand for domestic assets due to stock price increase. This would also cause a domestic currency appreciation. Note that the above scenarios defines exchange rate as the price of one unit of foreign currency in local currency terms. Thus currency appreciation means lowering or decrease in exchange rate. Hence, the relationship between stock prices and exchange rates is negative. Investors can use this information to form a trading strategy to hedge their return on foreign investment. In contrast, there exists a positive relationship between stock prices and exchange rates with direction of causation running from exchange rates to stock prices when the domestic currency depreciation makes local firms more competitive, leading to an increase in their exports. This in turn raises their stock prices. However this relationship would be negative if



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many firms use lots of imported inputs in their production. Increase in their cost of production due to currency depreciation might reduce firms’ sales and profits that might lead to a fall in their stock prices. The above discussion clearly shows that there is no empirical theoretical consensus on the issue of whether there exists a definite relationship between stock prices and exchange rates and the direction of causation if they are related. Further studies have been conducted on the impact of macro-economic variable on mutual funds. The impact of exchange rates on stock market volatility has seen much attention especially after the recent Financial Crisis. Many literatures have supported the phenomenon of traditional approach that exchange rates’ fluctuation lead to stock prices movement. The major causes of Asian Financial Crisis were the devaluation of local currencies, the shortterm external debts and high interest rates and financial imbalances (Kamin (1999), Mishkin (1999) and Kwack (2000)). In retrospect, there are quite a number of studies that attempted to determine the impact on stock prices and exchange rates changes. The findings, however, are not uniform and present a mix of evidences across the various studies. According to Dornbursh and Fisher (1980), changes in exchange rates affect firm’s earning and hence impact its stock price. Aggarwal (1981) on the hand argued that a change in exchange rates could directly affect stock prices of multinational firms and indirectly affect stock prices of domestic firms. Kearney (1998) found that exchange rates volatility is more significant in determining the volatility of stock prices than interest rates volatility. An increase in exchange rates volatility is followed by a decline in correlation between bonds and to a smaller extent, the stock market (Bodart and Reding (1999). Phylaktis and Ravazzolo (2000) analysed the stock prices and exchange rates dynamics and found that the US stock market acts as a channel through which stock market and foreign exchange market were linked. In addition, Pan et al. (2000) advanced earlier studies using



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seven Asian emerging markets and concluded that in general, exchange rates granger-cause stock prices. They also found that for countries with higher trade to GDP ratio, exchange rate fluctuations tend to exhibit significant influence on the stock market, regardless of the degree of capital control. Despite the proposition of causal relationships between exchange rate volatility and stock prices in the above studies other studies conclude that there is no significant relationship between exchange rates and stock price movement. Notable among them include (Solnik 1984), Jorion (1990, 1991), Bodnar and Gentry (1993), Amihud (1993) and Bartov and Bodnar (1994). Their work failed to establish any relationship between movements in the US dollar and stock returns of US firms using monthly exchange rates. Griffin and Stulz (2001) sought to advance earlier studies by employing weekly exchanges rates rather than monthly data. Their results however saw a negligible impact of exchange rate volatility and prices. Ma and Kao (1990) also established that currency appreciation positively affected domestic stock market for an import-dominant country while it negatively affected the domestic stock market for an export-dominant country. Their results was however consistent with the goods-market theory. Furthermore, stock price exchange rates have been found to be different across countries (Qiao 1996). He employed daily stock price indices and spot exchange rates obtained from the financial markets of Hong Kong, Japan, and Singapore over the period from January 3, 1983 to June 15, 1994 and examine the interaction between these financial variables. His results, based on the Granger causality test, show that the changes in stock prices are caused by changes in exchange rates in Tokyo and Hong-Kong markets. To be specific, his analysis on three Asian countries established that the direction of causation was bi-directional for Japan, unidirectional from exchange rates to stocks returns for Hong Kong and was noncausal for Singapore. He also indicated that there existed a strong long-run relationship and



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cointegration among these three countries. He uses a vector autoregressive model to analyze a long-run stable relationship between stock prices and exchange rates in the above Asian financial markets. His results found a strong but stable long-run relationship between stock prices and exchange rates on levels for all three markets. Employing daily data for eight countries, Ajayi and Mougone (1996) revealed significant interaction between exchange rates and stock prices. Their observations were based on the emerging markets of Pakistan, India, Korea and the Philippines. Bahmani-Oskooee and Sohrabian (1992) also employed monthly data from July 1973 to December 1988, to evaluate the interactions between the Standard and Poor’s (S&P) Composite Index and the effective exchange rate of the dollar and found the bi-directional causality between them. However, there was no long run relationship or no cointegration between the two variables. Abdalla and Murinde (1997) suggested unidirectional causality from exchange rates to stock prices in all countries, with the exception of Philippines, whose case stock prices granger caused the exchange rates. Moreover, they found that there was long run relationship or cointegration between Pakistan and India. Malliaris and Urrutia (1992) examined the impact of 1987 crash on six stock market indices and found no lead-lag relationships for the period before and after the market crash. There however seemed to be feedback relationships and unidirectional causality during the month of crash. In recent past, Granger et al. (2000) also advocated that different countries have different affinities between exchange rates and stock prices. They found that the Philippines were under portfolio approach with negative correlation. Hong Kong, Thailand, Malaysia, Singapore, and Taiwan indicated strong feedback relations, whereas those of Indonesia and Japan failed to reveal any recognizable pattern.



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The above literature suggests that mutual funds have been viewed from several perspectives. Notable among them includes performance and funds flow, volatility and sensitivity to macro-economic variables. In respect of performance there are evidences from literature suggesting that mutual fund flows and returns are correlated with each other. Other studies hold the view that mutual funds returns were not correlated with concurrent or lagged flows contrary to the earlier mentioned position. Some views suggest no relationship between mutual fund returns and concurrent or lagged flow.

The novelty behind this study is to view the mutual fund industry and the macro-economic environment from a newer perspective by focusing on a developing economy distinguishing it from what the previous studies have done. Ghana as a choice of study is in no doubt a good starting point considering its global recognition as one of the fastest growing economies within the Sub-Saharan region. By situating the study in an African context, the search would seek to paint a much clearer picture and an add on to what has already been established in literature by focusing on the impact of foreign exchange rates on mutual fund prices with much emphasis on the US dollar as the main currency exchange in Ghana.



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3.0

METHODOLOGY

3.1

Data Sources and Specification of the Model

The study employed the use of the vector autoregressive model to establish causal relationship between mutual fund prices exchange rate and inflation. The data that are used in this model are average monthly prices of the largest mutual fund in Ghana, monthly exchange rates quoted as Ghana Cedis per US dollar as well as monthly inflation rate. The data span for the period between Jan 1997 to Dec 2012 representing a period of 16 years. The choice of the number of years was intended to capture diverse occurrence within the economic history of Ghana particularly the period of the global economic and financial crises. The intuition behind the adoption of monthly data was rooted from the fact that most of the researches in this area of study employed monthly data and as a result the object was to obtain some level of consistency and a basis for comparison with what earlier studies had already established. Furthermore, there were certain challenges as to the availability of a more detailed data such as daily or weekly information. The monthly fund prices were obtained from Databank Financial Services while other macroeconomic data in respect of monthly exchange rates and inflation were obtained from Bloomberg and Ghana Statistical Service. 3.2

Descriptive Statistics

A total of 190 observations were used in the study. The average return on the prices on the fund was GHS 0.43 per share while the average exchange rate for the cedi per dollar was recorded as 0.909 Ghana Cedis per US dollar. Inflation showed a relatively high mean at approximately 17.12% over the period with a minimum level of 8.39% and a maximum of 4%. It may be seen that all the variables showed a very volatile trend across the years. It may be concluded form the observation that Ghana’s macroeconomic history exhibited immense volatilities in both exchange rates and inflation



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TABLE 3.2a DESCRIPTIVE STATISTICS

FIGURE 3.2a GRAPHICAL DISTRIBUTION OF VARIABLES Prices Ghana Cedis

INFLATION

1.2

50

1.0 40

0.8

30

0.6 0.4

20

0.2

10

0.0 98

00

02

04

06

08

10

0

12

98

00

02

04

06

08

10

12

Exchange Rate 2.0

1.5

1.0

0.5

0.0 98



00

02

04

06

08

10

12

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3.3

Vector Auto Regressive Model

The vector auto regression (VAR) model is one of the most successful and flexible models for the analysis of multivariate time series. Vector auto regression (VARs) was introduced into empirical economics by C. Sims (1980). It is an extension and natural generalisation of the univariate autoregressive model to dynamic multivariate time series. The VAR model has proven to be very useful for describing the dynamic behaviour of economic and financial time series and for forecasting. It often provides better forecasts than those from univariate time series models. VAR models can be made conditional on potential future paths of specified variables and are often seen to provide a more flexible forecast. In addition to data forecasting and description, the VAR model may be used for structural inference and policy analysis. In a typical structural analysis, the imposition of certain assumptions about the causal structure of the data under investigation is very crucial in order to summarize the causal impacts of unexpected shocks or innovations on the variables in the model. These causal impacts are usually summarized with impulse response functions and forecast error variance decompositions. The basic n-lag vector autoregressive (VAR (n)) model has the form 𝑌" = 𝑐 + Π' 𝑌()' + Π* 𝑌()* + Π+ 𝑌()+ +· · · + Π- 𝑌()- + εt,

t = 1, . . . , T

where Πi are (n×n) coefficient matrices and εt is an (n×1) unobservable zero mean white noise vector process (serially uncorrelated or independent) with time invariant covariance matrix Σ.



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A generalised 3 lag multivariate vector auto regression model for the three variables in respect of monthly prices, exchange rates and inflation is as follows ' ' ' 𝛽'' 𝛽'* 𝛽'+ 𝑐' 𝑑𝑝𝑟𝑖𝑐𝑒")' 𝑑𝑝𝑟𝑖𝑐𝑒 ' ' ' 𝑐* + 𝛽*' 𝛽** 𝛽*+ 𝑑𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 = 𝑑𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛")' ' ' ' 𝑐 𝑑𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑑𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒")' + 𝛽+' 𝛽+* 𝛽++ + + + 𝛽'' 𝛽'* 𝛽'+ 𝜀'" 𝑑𝑝𝑟𝑖𝑐𝑒")* 𝑑𝑝𝑟𝑖𝑐𝑒")+ + + + 𝑑𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛")* + 𝛽*' 𝛽** 𝛽*+ 𝑑𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛")+ + 𝜀*" + + + 𝜀+" 𝑑𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒")* 𝑑𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒")+ 𝛽+' 𝛽+* 𝛽++

+

* 𝛽'' * 𝛽*' * 𝛽+'

* 𝛽'* * 𝛽** * 𝛽+*

* 𝛽'+ * 𝛽*+ * 𝛽++

Estimating a VAR involves choosing which variables to include in the system, and deciding on the number of lags. The results obtained are mostly dependent on both of these choices. The optimal lag length is usually determined by statistical selection criteria and the variable selection is mostly informed by economic theory. This in itself results in some inherent and potential shortfalls in the use of VAR for estimation or forecasting. This is because the estimation problem increases as the number of variables and lag lengths increases leading to unreliable forecasts and estimates.

3.3.1 Arguments for and against the VAR model The VAR model was adopted because most researchers found it appropriate in analysing and forecasting macroeconomic variables (A.B.M. Munibur Rahman and Md. Salah Uddin Rajib 2013). Sims (1982) on the basis of endogeneity had objected to the specification of the population regression functions. His assertion was based on the assumption of the GaussMarkov Theorem on exogeneity of covariates which resulted in inconsistencies in the estimation of OLS partial regression coefficients. Sims argued that it is not entirely possible to identify the variables as totally endogenous or exogenous and suggested the use of the Vector Auto regression (VAR) Models. This further propagates the earlier established point about the flexibility in the use of the VAR model as all variables are assumed to be endogenous and variables appear both on the right and left side of the regression equation



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with lags. It is important for all variables to prove stationary before appearing in the VAR model. Another important feature about the VAR module is its ability to capture more information about the data as it incorporates not just the variables alone but lags of the variables as well. This makes the model better at forecasting than other traditional structural models. Sims (1980) argues that large scale structural models perform badly in terms of their sample forecast accuracy. McNees (1986), seconds this argument by showing that forecasts of some variables (e.g. Real GDP and Unemployment rate in the US) are produced more accurately using VAR estimates. Despite the above intriguing arguments about the VAR model, it has some inherent drawbacks and flaws. The model is viewed as a-theoretical as it relies very little on theoretical information about relationships between variables in specifying the model. This makes it less amendable to theoretical analysis and consequently to policy conclusions. In effect VAR models could lead to spurious regressions and often difficult in interpreting coefficients in a VAR module. Furthermore the module is quite complex as it involves the estimation of so many parameters. This could lead to smaller degrees of freedom and larger standard errors and confidence intervals. (Brooks C. (2008)). Regardless of these inherent problems in the module, the module was adopted due its suitability in establishing causal relationships between various macro-economic variables.



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3.3.2

Stationarity and unit root test

The test for stationarity was conducted using the Augmented Dickey-Fuller with optimal lag length selected by Schwarz Information Criteria (SIC). The Schwarz Information Criterion, Akaike Information Criterion and the Hannan-Quinn Information Criterion all chose an optimal lag length of 1. However in order to get rid of any auto-correlation the study employed a lag length of 3. The chosen lag length was also adopted to save for more degrees of freedom. The result of Augmented Dickey-Fuller (ADF) test shows that variables are in the same order of integration, as null hypothesis of “unit root or I (0) is rejected at 1, 5 and 10 percent level for all three variables with constant but no trend. Each of the level series was tested for a unit root using the ADF test. The results indicate that the level series of mutual fund prices, exchange rates and inflation are non-stationary processes at all three significance levels. In the case of prices, the ADF statistic was 0.124953 which compares against the 1 per cent, 5 per cent and 10 percent critical values of -3.464827 -2.876595 and -2.574874 respectively. As this ADF test statistic is greater than all critical values, the ADF test-null hypothesis of a unit root is accepted. In the case of exchange rates the ADF test statistic was 0.082202 which compares against the 1, 5 and 10 percent critical values of -3.464827, -2.876595and 2.574874 respectively. The ADF test statistic is greater than all critical values hence the ADF test-null hypotheses of a unit root is accepted. For inflation rate the ADF statistic was -2.560579 which compares against the 1 per cent, 5 per cent and 10 percent critical values of -3.464827, -2.876595 and -2.574874 respectively. The null hypothesis of a unit root is again accepted at all the three respective significant levels. The tables in Appendix B show in detail the results for the ADF tests.



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3.3.3

First differences

Each of the first differenced series was tested for a unit root using the ADF test. The results indicate that the first differenced series of stock prices exchange rates and inflation are stationary processes at the 1, 5 and 10 percent ADF critical levels. In the case of prices, the ADF statistic was -8.863802 which compares against the 1, 5 and 10 percent critical values of -3.464827, -2.876595 and -2.574874 respectively. As this ADF test statistic is lower than the 1, 5 and 10 percent critical values, the ADF test null hypotheses of a unit root is rejected. In the case of the exchange rate series, the ADF statistic was -3.767415, which is also less than the critical values of -3.465202, 2.876759 and -2.574962 indicating rejection of a null hypothesis of unit root. The same may be said for inflation which recorded -6.853566 as ADF test statistic which compares to the 1 percent, 5 percent and 10 percent ADF critical levels of -3.566994, 2.877544 and -2.575381 respectively indicating rejection of the null hypothesis of units roots. When the ADF test was applied to the residual terms of the first difference regression equation, the test statistic was found to be -11.48968 which is also less than the ADF critical values, meaning that the residuals are also stationary. Results obtained from the test of stationarity are shown in Table 3.6a



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TABLE 3.6a RESULT OF AUGMENTED DICKEY-FULLER (ADF) TEST OF STATIONARITY

Note: 1) Null hypothesis of ADF test is "Series has a unit root" 2) ** means Null hypothesis is rejected at 1 percent level

3.3.4 Cointegration & serial correlation Cointegration between the variables is tested using the Johansen Test. In performing the Johansen cointegration test, I first implemented a VAR model with the objective to decide the optimal numbers of lags for the test. I then tested the VAR for serial correlation with optimal lag length for each model based on the Hannan Quinn criteria as well as the results from the LM test for serial correlation which I have conducted to ensure that our VAR model is free of serial correlation. The p-values indicate the null hypothesis be accepted of no serial correlation at 5% significance. The null hypothesis states there is no cointegration relationship between prices, exchange rates and inflation. The results from the Johansen methodology indicate that there was no co-integrating relationship between the price, exchange rate and inflation at 5% significance. At zero cointegration vectors, the trace statistic recorded was 27.80289 with a critical value of



29

29.79707. The p-value recorded was 0.0835. With a hypothesis of at most 1 cointegrating vector the trace statistic recorded 13.93043 and 15.49471 for critical values. The p-value at this point was seen to be 0.0849. Lastly, with at most 2 co- integrating equations, the race statistic was 2.705745 and a critical value of 3.841466 and a p value of 0.100. The result reaffirms the earlier assertion that there were no co-integrating equations at 5 percent significance level. Both the Trace Statistic and the Max-Eigen value Statistic support rejection of the null hypothesis of no cointegration at 5% significance level. Therefore, we include an error correction term to capture the short-run relationship between the exchange rates and stock prices when performing the causality test. Detailed results of cointegration test is shown in Appendix C

TABLE 3.7a RESULT OF JOHANSEN COINTEGRATION TEST

Note: a) The first column represents the number of cointegrating vectors b) Trace test indicates no cointegration at 5% level c) Max Eigen Statistics indicates cointegration at 5% level. d) P-values obtained from MacKinnon-Haug-Michelis et al (1999)



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3.3.5 Granger causality Most economists are interested in establishing the direction of causation between several economic variables. They seek to establish whether one variable can granger-cause another or vice versa or whether there exists mutual two way causation between the variables. One of such notable concepts of causation is the Granger Causation. Proposed by Clive Granger in 1969; this method of deriving causation has been widely used by several economists and in many studies. According to Granger, an event say ‘X’ is said to Granger-cause another say ‘Y’ if predictions from Y can be improved by incorporating information on the past occurrences of event X. Relating this analogy to the study, I sought to establish if there were any such causation running between the price of the mutual fund, exchange rates and inflation over the chosen period of study. The study sought to reveal whether there was a unidirectional, bi-directional or no causal relationship between the variables using the pair wise granger causality test. To elaborate further on this approach, the granger causality test sought to show whether for example exchange rates could granger cause prices of the fund by employing in an auto-regression of prices on its past values and the past values of exchange rates. If the past values of exchange rates are statistically significant then exchange rates is said to granger cause prices. This test carried out by first estimating the equation 𝑃" = 𝑐 + α' 𝑃")' + α* 𝑃")* + ⋯ . α- 𝑃")G + β' 𝑃")' + β* 𝑃")* + ⋯ β- 𝑃")G + εt In the above equation assume 𝑃 is the price of the fund and n is the lag length selection criteria which in our case were the Akaike information selection criterion and Schwarz selection criterion as determine by the optimal lag length test. We then estimate the equation without the exchange rate. Using the residuals from both regressions we test the null



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hypothesis that β1 =β2 =βn . This hypothesis postulates that exchange rates does not granger cause prices. In essence exchange rate does not provide much information in predicting the price of the fund. This test would be carried out using the F-statistic or the Chi-square test. The reverse of the test would be carried out to reveal the converse relationship by regressing exchange rates on prices. This would also be performed for all the other variables in the study. Though a very buoyant test for causation it has certain limitations. The test focuses mainly on lead lag relationships which may not correspond to usual notation of causal relationships. For instance it may be revealed that event X could granger-cause event Y even if in reality the true relationship is the other way round. Another major criticism is in respect of the fact that they are mostly based on linear forecasting. As such, if the true econometric model is non-linear the test could present spurious relationships leading to inaccurate forecasts. Lastly, the test assumes that the coefficients, parameters and covariance matrix of the model are constant. It is however significant and appropriate to the study as causal relationships are needed to be established in respect of the effect of changes in macroeconomic variables to the price of the fund.

3.3.6 Impulse responses Impulse response function (IRF) may be defined as the output when presented with a brief input shock known as an impulse. In general terms, an impulse response refers to the reaction of any dynamic system to some external shock or change. This was carried out to reveal the response of each endogenous variable to a one time shock in any of the variables. This can be evaluated by re-writing the vector auto-regressive model as a Moving Average (MA∞) representation. This may follow a process as follows;

yt =µ+εt+Ψ1εt-1 + Ψ2εt-2……



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As such, the matrix Ψs may be interpreted as ∂yt+s/∂ε′t. That is holding all other innovations at all dates constant, the impact of a one unit increase in the jth variable’s innovation at date t (εjt) for all values of the ith variable at time t+s(yit+s) is determined by the row I and column j element of Ψs. The identity ∂yt+s/∂ε′t may be referred to as the impulse response. These shocks and responses are often expressed in units of standard deviation rather than in raw values as it is rather convenient to do so. Thus it shows the number of standard deviations by which each endogenous variable changes when there is a one-time impulse or shock in an element of ε. (Fortune P. 1997) A major criticism to this method is due to the fact that most researchers are concerned that the shocks to the endogenous variables as the error vector may be correlated. Consequently, there is the possibility that a shock that affects one endogenous variable may possibly affect another. This problem can however be curbed through a sophisticated process of transforming the VAR in to a diagonal covariance matrix to which most researchers try to avoid. The study was mindful of this inherent problem but proceeded to adopt this method as it was deemed appropriate in understanding the impact of a onetime shock on each of the endogenous variables. Furthermore it was a good basis to ensure consistency and a good comparison across previous studies.



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4.0

ANALSYSIS OF RESULTS AND INTERPRETATION FINDINGS

4.1

Results from Vector Auto Regression Estimates (VAR)

The results from VAR model indicates that individual lags of prices were significant in explain price only at one lag length. Lags of exchange rates and inflation were not significant in explaining the variations in prices. Variations in exchange rates were also explained by its own lags at lag one, two and three with a significant p-value at 5% for all three lags. Lags of prices and inflation were all not significant at all levels in explaining the variations in exchange rates. In respect of inflation, the individual lags of inflation were only significant at one lag length but not in lag two and three. Lags of prices and exchange rates were however not significant in explaining the variations in the inflation. It was discovered that all the dependent variables were explained by their own lags at one lag length. This reaffirms the earlier assertions that lag length one is the optimal lag length as indicated by Akaike and the Schwarz selection criterion. In order to further better our tests on the coefficients of the regression estimates, the Wald coefficient test was carried out to ascertain whether the lags of the variables were jointly significant in explaining variations in the dependent variables. The results showed lags of prices were jointly significant in explaining variations of itself with a chi square value 12.46623 and a p-value of 0.0020 which is significant at 1%. The joint lags of exchange rates were not significant in explaining prices as the p-value recorded was 0.8184. A similar finding was the case for inflation which was also jointly insignificant reporting a p-value of 0.2463. The joint lags of prices had no influence in the variations of exchange rates as the pvalue recorded from the Wald test was insignificant at 0.6120. However joint lags of exchange rates were significant at 1% in explaining its own variations. The joint lags of

34

inflation were also insignificant with a p-value of 0.9092 in explaining the variations of exchange rates. Lastly the joint lags of inflation were significant in explaining its own variations with a record p-value of 0.0002. Joint lags of exchange rates were also seen to be significant in explaining variations of inflation at 5% significance level recording a p value of 0.0431. The joint lags of prices were however significant in explaining the changes in prices. All the intercepts in the respective VAR system equations were also both individually and jointly significant with a p-value 0.0163. Results from the VAR are shown in Appendix D. 4.2

Causality Analysis

This search uses maximum likelihood tests to determine the optimum lag length. The optimum length is the one in which the value of most information criteria are minimised. Lag length criteria tests were undertaken for lengths of between 1 and 8 for the sample period. Most of the selection criteria were minimised at 1 lag length for the level series. Appendix A shows the results of this maximum likelihood test. The lag order selection criteria were applied to the first difference data and it was found that but for the sequential modified LR statistic which was minimized at lag length 3 with a value of 17.69225, all the other information criteria were minimised at lag length 1, with a values of -10.6774, -10.46699 and 10.59214 for Akaike, Schwarz and Hannan- Quinn information criterion respectively. The study further employed the lag exclusion Wald test. It was found that lags 1 and 3 three were not rejected where the joint Chi-Square value reported were 172.6383 and 19.68429 respectively. Appendix A shows detailed results of maximum likelihood and lag exclusions tests.



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The pair wise Granger causality tests were then run on the first differenced series for lags one to three lags. At one lag length, unidirectional causality is found with causality running from exchange rate to inflation recording an F-statistic of 7.69337 and a probability level of 0.0061. Causality at this point is significant at both 1 and 5 percent level. Conversely, there seem to be no causality moving from inflation to exchange rates. The F-statistic for the test of causality running from inflation to exchange rate was at one lag was 0.01368 with a probability level of 0.5012. There was quite an astonishing finding in respect of no causal relationship between the price and exchange rates in both directions at lag one. The f-statistic recorded for causality moving from exchange rates to prices was 0.13204 with a probability level of 0.7167 where as causality from prices to exchange rates recorded 1.12530 and 0.2901 for both f-statistic and significance level respectively. In respect of inflation and price of the fund, there was an almost significant relationship of causality running from inflation to price but was only significant at 10 percent. There however seemed to be no causality running from prices to inflation with an f-statistic of 0.00488 and probability value of 0.9444. At two lags, there again seem to be consistent and evident unidirectional causality from exchange rates to inflation though at a lower rate than earlier reported in lag one with an fstatistic of 4.65477 and a probability level of 0.0107. Here, causality is again seen to run from exchange rate to inflation at significance level of 5 percent. Meanwhile, there was no causality moving from inflation to exchange rate two lags. Again, there was no causal relationship between prices and exchange rates in both directions at lag two. In the case of causality from inflation to prices, the relationship further deteriorated as the lags increased from one to two with no significant causality in both directions.



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Causality between exchange rates and inflation continued to be unidirectional for lag three with causality running from exchange rate to inflation but again at a much lower rate than recorded for both lags one and two. The recorded f-statistic was 3.09689 with a probability of 0.0282 which is significant 5% level. There was however no causality in the opposite direction moving from inflation to exchange rates. There was also no causal relationship between prices and exchange rates in both directions at lag 3. Causality between inflation and prices disappeared totally at lag 3 with no causality in both directions. Beyond three lags, the pair wise causality between all three variables disappears with no causal relationships running in both directions between the variables. It may be seen that at the optimal lag length, unidirectional causality is only seen between exchange rate and inflation with causality running from exchange rate to inflation. Another unidirectional relationship is seen between inflation and price with causality moving from inflation to prices but was only significant 10 percent. Appendix E shows the results for Granger Causality Test.

In order to test for the stability of the unrestricted VAR, the lag structure/ AR roots Test was also applied as the test for the VAR stability condition. The results reported the roots of the characteristic autoregressive polynomial. The condition for which the VAR may be regarded as stationary or stable is if all roots have a modulus less than one and lie within or inside a unit circle. The results shows that the unrestricted VAR satisfies the above condition as all the polynomial roots have a value of less than one and lies within a unit circle. This suggests that our unrestricted was stable and stationary. The importance was to avoid the violation of the condition which could lead to an unreliable forecast estimate and spurious results. The results of VAR stability condition test are shown in Appendix H.



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When the Johansen co-integration test was applied based on the assumption of an intercept and a linear deterministic trend in the data, it was found that the test null hypothesis of zero co-integration could be rejected. For the test of zero co-integrating relations, the Eigen value statistic was 19.20027 and the trace statistic was 33.29248. Both test statistics were each greater than the 5% and 1% critical values of 21.13162 and 29.79707 respectively.

In

contrast, the trace and maximum Eigen value statistics for the test of at least one cointegrating relation were both less than the 5 per cent and 1 per cent critical values. This is enough evidence to support the rejection of the null hypotheses of no co-integrating relationship between the level series data. It is therefore evident that even though the level series are integrated (i.e. contain one unit root or I (1)), a linear combination of these I (1) variables becomes I (0) when the variables are co-integrated. This gives an indication of the possibility that the level series of prices exchange rates and inflation rates share a long-run relationship in the Ghanaian mutual fund industry.

4.3

Analysis of Impulse Responses

The study recorded nine impulses from the estimated multivariate VAR model of three lags for all three variables. The results obtained from the analysis of impulses responses show there seem to be no significant response to changes in prices when there is a one standard deviation shock to exchange rates. The response portrayed a negative but insignificant response at three months period but flattened thereof. This is an indication that the price of the fund did not respond to significant changes exchange rates. When the shock was imposed on inflation, there was a negative impact on the price from period one until three but flattens beyond period three. It can also be said that the fund price reacted to inflation only up to three months into the future. The response of price to a shock on itself was seen to be decreasing over but does not reach negative.



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The response of inflation to a shock on price showed that inflation was decreasing and reaches its minimum at four months into the future but rises and continues to stay negative. A one standard deviation shock to inflation on itself leads to decrease in inflation but reaches zero at ten months in to future but does not approach negative. There seem to be somewhat positive impact on a shock on exchange rates to inflation. This reaches its maximum at month four but reduces gradually but continues to stay positive.

There was negative but insignificant impact to exchange rates when a one standard deviation shock was imposed on prices. This relationship was however steady for ten months into the future. There seemed to be no significant reaction to exchange rates when the shock was imposed inflation. They reaction stayed slightly flat above the zero line. A shock to exchange rate on itself saw a decreasing reaction with a sharp decline between month three and four. However the reaction continued to stay positive. Appendix F shows the impulse responses of the variables. 4.4

Variance Decomposition

The study found it important to incorporate variance decomposition in the interpretation of the VAR model once it had be fitted. This indicates the amount of information that each variable contributes to each other in the model. It seeks to elaborate how much of the forecast variance of each variable may be explained by an exogenous shock to other variables. Whereas impulse response traces the effects of a shock to an endogenous variable on the variables in the VAR model, variance decomposition decomposes variation in an endogenous variable into the component shocks to the endogenous variables in the VAR. The results from the variance decomposition showed that the variance of price due to exchange rates were both insignificant in the first month. However that of inflation saw a drastic increase from zero to 2.56878% in month three. He variance price due to inflation



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continues to increase but at a steady level up to month ten recording its highest at 2.632440%. This figure was still small as its means that inflation could only explain approximately 3% of overall changes in the price of the fund. Exchange rates however continued to show an insignificant contribution to the variance of price recording 0.277076% as it’s highest at period ten. The variance of price due to itself was the highest constituting 97.09048% in period ten. The variance of exchange rates due to itself was highly significant at all periods recording a high of 99.50525% in period one but incurred a steady but insignificant reduction across the months. The price of the fund contributed 0.327629 in month one with inflation recording a low of 0.167107%. The contribution of price increases to its highest of 2.471893% in month ten but again was quite small in explaining changes in exchanges rates. Inflation however continued to be insignificant even at period ten with a high of 0.513716%. Lastly, the variance of inflation due to itself was highest in period one contributing 99.56660 but saw a quite significant reduction across the periods. This reached its minimum of 89.12961% in month ten indicating an approximate reduction of about 10%. This was however due to the drastic increase in the contribution of both exchange rates and prices to the variance of inflation between periods three and ten recording its highest of 7.3302% and 3.540154% respectively. The variance inflation was quite significantly affected by exchange rates. In a nut shell, the results from the variance decomposition show that the price of the fund was not significantly influenced by variations in exchange rates but slightly affect by changes in inflation ten months into the future. There was however some interaction between the other two macro-economic variables in respect of inflation and exchange rates.



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Inflation seems to be influenced by changes in exchange rates in Ghana as quite a significant portion of changes in inflation was seen to be explained by changes in exchange rates. It is important to note that the study adopted the Cholesky ordering approach. The ordering of the variables did not significantly impact on the results of both impulse responses and variance decomposition though it was not obvious from literature on as to how the variables were to be ordered. Appendix G shows the results obtained for variance decomposition of all the variables.



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5.0 CONCLUSION 5.1 Summary of Findings This paper sought to investigate the interaction between prices a major mutual fund, exchange rates and inflation rates in Ghana. With an expanded analysis to interrogate the changes in these key economic variables, the search through the process of the Granger causality test, impulse response functions and variance decompositions established a possible short run and long run relationship. The motivation for this paper was to test the degree of interaction between fund price and movements in both exchange rates and inflation in Ghana for the period January 1997 to December 2012. This period is somewhat fascinating considering the immense growth in the mutual fund industry of the Ghana, while Cedi exchange rate depreciated significantly relative to the US dollar. It is important to note that the interaction between the Ghanaian currency market and the Stock market are not factually known to have caused movements in each other during this period as postulated by economic theory. In respect of the broad relationship between the variables, the level series regression results support the above observation of a short-term positive relationship between the price of the fund and inflation rate during the sample period. There however seemed to be no significant relationship between the exchange rates and the price of the fund. It is however important that these results be treated with caution and not accepted in absolute terms in light of the possibility spurious regressions estimates as hinted as a limitation in the methodology. When first differences are examined, evidence of a positive relationship between the price of the fund and inflation remains, although these results again need to be treated with caution in light of the low explanatory power of the first differences the regression.



42

It has also been established that there is evidence for co-integrating relationships between the subject variables, implying that the variables do not only appear to be related in the short-run of the sample period, but also longer-term expectations contributes some part in activity in mutual fund industry and the macro-economic environment in Ghana. The Granger causality test provides a deeper insight into the degree of association between the variables during the sample period. Literature on the study of the relationship was viewed from three perspectives. The first approach was the flow oriented model rooted from the efficient market hypothesis which postulates any factor that affects a firm’s cash flows should reflect in its stock prices. Examples of studies of the flow oriented models are seen in respect of Dornbuscher and Fisher (1980) Aggarwal (1981), Franck and Young (1972), and Ma and Kao (1990). Their results found exchange rates to drive stock prices. The second approach used was portfolio balance theory approach as elaborated by Eiteman et al (2004) and Branson et al (1977).They also revealed similar findings but in the case of the former the impact of exchange rates was mostly dependent on factors such as liquidity in the market and segmentation. Lastly, the literature looked at Cointegration and Causality studies examined thoroughly by Ajayi et al (1998), by Bahmani, Oskooee and Sohrabian (1992), Yu Qiao (1997). There seemed to be a mix of evidence of causality by Granger et al (2000) and Ramasamy and Yeung (2005) with causality running from exchange rates to stock prices and vice versa. The literature also purports to show that mutual fund flows may be attracted by investor’s ability to time foreign exchange rate markets. The results of the study provide evidence that past evidence of causality running from exchange rates to prices are not supported. The search found non-causal relationship between exchange rates and the price of the fund in both directions and was not significant at 5%



43

level. There was a unidirectional causality between exchange rate and inflation with causality running from exchange rates at both 1 and 5 percent level. In respect of causality between price and inflation, there was a unidirectional causality running from inflation to price. It must be noted that this relationship was only significant at 10%. The most statistically significant causality was that between exchange rates and inflation in our analysis of first difference. This finding is however inconsistent with both the flow oriented model and the portfolio based approach. 5.2 Policy Implications In respect to policy implications of this research there is an indication that prices of commodities may be the ‘shadow element’ between the prices of the fund and exchange rates. Most often than not high commodity prices often triggers both the stock market and the domestic currency considering the fact that the Ghanaian economy is commodity based. The result suggests that exchange rates movement in respect of the Cedi/US dollar do not influence the returns in the fund. This is a quite an astonishing finding considering the fact that Ghanaian economy is an export based economy and one would have expected a more flow oriented result in that the exchange rates movements should cause movement in stock prices. The results further contradicts the portfolio balance theory considering the fact Ghana’s economy has experienced immense domestic currency depreciation over the years making local firms more competitive and increasing exports. However, many local firms in Ghana rely mostly on imported products in their production and as a result could nullify the earlier argument leading to a negative relation. There is therefore no direct consensus between stock prices and exchange rates in Ghana. Consequently, both investors and fund managers need not time and track their portfolios in response to exchange rate volatilities. As a result investor psychology in relation to exchange



44

rate volatility does not play an important role in driving prices of stocks within Ghanaian mutual fund industry contrary to the findings of Alexakis et al. (2005) on the Greek market. It is important to state that this result is not conclusive enough considering the limitations of the study. The results also reaffirms the fact that Ghana’s historical exchange rates has seen very volatile trends leading to the immense depreciation of the cedi over the years and spike in inflation levels particularly during the financial turmoil.

5.3 Limitations of the Study A very key limitation of the study is the fact the search focused on only one large fund and may not fully reflect the overall situation within Ghana’s mutual fund industry. The availability of a more compact data on the fund such as a daily or weekly fund prices was also another inherent limitation in the study. Furthermore the fund is seen to be highly diversified in several African countries and as such a more accurate basis of causality would have been an analysis of exchange rates of the respective sector allocated countries. Future research would focus on segmenting sample periods into a more stable and volatile periods and then further accessing the impact of these macro-economic variables in different periods of economic activity. The study would also employ a more detail data such as a daily data with several currency exchange rates. A longer period data encapsulating other mutual funds would be appropriate to through more light on the interaction between the mutual fund prices and macro-economic variables.



45

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51

APPENDICIES APPENDIX A: VAR LAG ORDER SELECTION CRITERIA Endogenous variables: DPRICE DINFLATION DEXC Exogenous variables: C Date: 06/28/13 Time: 15:10 Sample: 1997M01 2012M12 Included observations: 183 Lag 0 1 2 4 5 6 7 8

LogL 884.2508 988.9862 991.3371 3 1000.695 1004.389 1010.221 1015.395 1023.307 1028.500

LR

FPE

AIC

SC

HQ

NA 204.8920 4.522139 17.69225* 6.863149 10.64483 9.273677 13.92106 8.967929

1.32e-08 4.63e-09* 4.98e-09 4.96e-09 5.26e-09 5.45e-09 5.68e-09 5.76e-09 6.01e-09

-9.631157 -10.67744* -10.60478 -10.60868 -10.55070 -10.51608 -10.47426 -10.46237 -10.42077

-9.578542 -10.46699* -10.23648 -10.08254 -9.866706 -9.674243 -9.474586 -9.304848 -9.105403

-9.609830 -10.59214* -10.45549 -10.39541 -10.27344 -10.17484 -10.06904 -9.993168 -9.887585

* indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion VAR Lag Exclusion Wald Tests Date: 08/04/13 Time: 17:41 Sample: 1997M01 2012M12 Included observations: 188 Chi-squared test statistics for lag exclusion: Numbers in [ ] are p-values DINFLATIO N DEXC

RPRICE

Joint

Lag 1

20.88690 123.8094 29.03003 [ 0.000111] [ 0.000000] [ 2.21e-06]

Lag 2

0.515735 8.108937 2.028468 10.95070 [ 0.915421] [ 0.043813] [ 0.566519] [ 0.279103]

Lag 3

3.039498 12.43246 3.941713 19.68429 [ 0.385575] [ 0.006039] [ 0.267827] [ 0.019964]

Df

3



3

3

172.6383 [ 0.000000]

9

52

APPENDIX B: STATIONARITY AND UNIT ROOTS (AUGMENTED DICKEY FULLER TEST) DEXC

DPRICE .16

.6

.12 .4 .08 .2 .04 .0

.00 -.04

-.2 98

00

02

04

06

08

10

98

12

00

02

04

06

08

10

12

DINFLATION .8

.4

.0

-.4

-.8 98

00

02

04

06

08

10

12

LEVEL SERIES UNIT ROOT TEST Null Hypothesis: PRICES__GHANA_CEDIS has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=14)

Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level

t-Statistic

Prob.*

0.124953 -3.464827 -2.876595 -2.574874

0.9669

*MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(PRICES__GHANA_CEDIS) Method: Least Squares Date: 07/23/13 Time: 21:51 Sample (adjusted): 1997M03 2012M12 Included observations: 190 after adjustments Variable



Coefficient Std. Error

t-Statistic

Prob.

53

PRICES__GHANA_CEDIS (-1) 0.000429 0.003430 D(PRICES__GHANA_CE DIS(-1)) 0.391176 0.067981 C 0.003152 0.001956 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.151728 0.142656 0.017137 0.054919 504.5483 16.72408 0.000000

0.124953

0.9007

5.754206 1.610987

0.0000 0.1089

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

0.005369 0.018508 -5.279456 -5.228187 -5.258688 2.099481

Null Hypothesis: INFLATION has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=14)

Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level

t-Statistic

Prob.*

-2.560579 -3.464827 -2.876595 -2.574874

0.1031

t-Statistic

Prob.

*MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(INFLATION) Method: Least Squares Date: 07/23/13 Time: 21:49 Sample (adjusted): 1997M03 2012M12 Included observations: 190 after adjustments Variable

Coefficient Std. Error

INFLATION(-1) -0.037095 0.014487 D(INFLATION(-1)) 0.430298 0.065559 C 0.569334 0.274262 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)



0.201347 0.192806 1.606091 482.3716 -358.1089 23.57219 0.000000

-2.560579 0.0112 6.563558 0.0000 2.075872 0.0393

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

-0.114737 1.787644 3.801147 3.852415 3.821915 2.105169

54

Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=14)

Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level

t-Statistic

Prob.*

0.082202 -3.464827 -2.876595 -2.574874

0.9636

*MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(EXCHANGE_RATE) Method: Least Squares Sample (adjusted): 1997M03 2012M12 Included observations: 190 after adjustments Variable

Coefficient Std. Error

EXCHANGE_RATE (-1) 0.000149 0.001818 D(EXCHANGE_RA TE(-1)) 0.723305 0.051329 C 0.002320 0.001824 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)



0.523312 0.518214 0.011176 0.023358 585.7679 102.6452 0.000000

t-Statistic

Prob.

0.082202

0.9346

14.09149 1.272171

0.0000 0.2049

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

0.008966 0.016102 -6.134399 -6.083130 -6.113631 2.122033

55

FIRST DIFFERNCE UNIT ROOT TEST Null Hypothesis: DPRICE has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=14)

Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level

t-Statistic

Prob.*

-8.863802 -3.464827 -2.876595 -2.574874

0.0000

Prob.

*MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RPRICE) Method: Least Squares Date: 06/28/13 Time: 15:32 Sample (adjusted): 1997M03 2012M12 Included observations: 190 after adjustments Variable

Coefficient Std. Error

t-Statistic

DPRICE(-1) C

-0.588152 0.066354 0.014551 0.003948

-8.863802 0.0000 3.685997 0.0003

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.294736 0.290985 0.049668 0.463778 301.8621 78.56699 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

0.000256 0.058986 -3.156443 -3.122264 -3.142597 2.017109

Null Hypothesis: DINFLATION has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=14)

Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level

t-Statistic

Prob.*

-6.853566 -3.466994 -2.877544 -2.575381

0.0000

*MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DINFLATION)



56

Method: Least Squares Date: 06/28/13 Time: 15:33 Sample (adjusted): 1998M02 2012M12 Included observations: 179 after adjustments



Variable

Coefficient Std. Error

t-Statistic

DINFLATION(-1) D(DINFLATION(1)) D(DINFLATION(2)) D(DINFLATION(3)) D(DINFLATION(4)) D(DINFLATION(5)) D(DINFLATION(6)) D(DINFLATION(7)) D(DINFLATION(8)) D(DINFLATION(9)) D(DINFLATION(10)) D(DINFLATION(11)) C

-0.943075 0.137604

-6.853566 0.0000

0.236900 0.133326

1.776840

0.0774

0.220695 0.129418

1.705291

0.0900

0.254656 0.125332

2.031846

0.0438

0.295478 0.120501

2.452079

0.0152

0.331328 0.116584

2.841961

0.0050

0.361762 0.110815

3.264540

0.0013

0.445777 0.104293

4.274290

0.0000

0.422226 0.097941

4.311021

0.0000

0.459325 0.088730

5.176673

0.0000

0.455128 0.077882

5.843799

0.0000

0.501132 0.066458 -0.005159 0.005928

7.540560 0.0000 -0.870233 0.3854

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.507382 0.471772 0.078474 1.022245 208.3119 14.24795 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

Prob.

-3.35E-05 0.107972 -2.182256 -1.950770 -2.088390 1.877527

57

Null Hypothesis: DEXC has a unit root Exogenous: Constant Lag Length: 2 (Automatic - based on SIC, maxlag=14)

Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level

t-Statistic

Prob.*

-3.767415 -3.465202 -2.876759 -2.574962

0.0039

*MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DEXC) Method: Least Squares Date: 06/28/13 Time: 15:34 Sample (adjusted): 1997M05 2012M12 Included observations: 188 after adjustments



Variable

Coefficient Std. Error

t-Statistic

Prob.

DEXC(-1) D(DEXC(-1)) D(DEXC(-2)) C

-0.203898 0.006696 -0.243747 0.002262

-3.767415 0.092283 -3.415196 1.803051

0.0002 0.9266 0.0008 0.0730

R-squared Adjusted R-squared S.E. of regression Sum squared resid. Log likelihood F-statistic Prob(F-statistic)

0.182864 0.169541 0.014503 0.038701 531.1439 13.72553 0.000000

0.054121 0.072563 0.071371 0.001254

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

-0.000178 0.015914 -5.607914 -5.539054 -5.580015 2.037879

58

APPENDIX C: RESULT OF JOHANSEN COINTEGRATION TEST Sample (adjusted): 1997M05 2012M12 Included observations: 188 after adjustments Trend assumption: Linear deterministic trend Series: DPRICE DINFLATIO DEXC Lags interval (in first differences): 1 to 3 Unrestricted Cointegration Rank Test (Trace) Hypothesized No. of CE(s) Eigenvalue

Trace Statistic

0.05 Critical Value Prob.**

None At most 1 At most 2

27.80289 13.93043 2.705745

29.79707 15.49471 3.841466

0.071133 0.057958 0.014289

0.0835 0.0849 0.1000

Trace test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized No. of CE(s) Eigenvalue

Max-Eigen Statistic

0.05 Critical Value Prob.**

None At most 1 At most 2

13.87245 11.22469 2.705745

21.13162 14.26460 3.841466

0.071133 0.057958 0.014289

0.3756 0.1433 0.1000

Max-eigenvalue test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted b'*S11*b=I): LPRICE 0.348128 1.316634 -1.763192



Cointegrating LINFLATIO N -2.367321 1.986555 -1.582403

Coefficients

(normalized

by

LEXC -0.782140 -0.621641 3.943781

59

Unrestricted Adjustment Coefficients (alpha): D(LPRICE) -0.007343 D(LINFLATI ON) 0.016794 D(LEXC) 0.001219 1 Equation(s):

-0.007461

0.003014

-0.005365 -0.002428

0.006229 -0.001073

CointegratingLog likelihood

1039.580

Normalized cointegrating coefficients (standard error in parentheses) LINFLATIO LPRICE N LEXC 1.000000 -6.800155 -2.246706 (2.18262) (1.46259) Adjustment coefficients (standard error in parentheses) D(LPRICE) -0.002556 (0.00125) D(LINFLATI ON) 0.005847 (0.00217) D(LEXC) 0.000424 (0.00037) 2 Equation(s):

CointegratingLog likelihood

1045.192

Normalized cointegrating coefficients (standard error in parentheses) LINFLATIO LPRICE N LEXC 1.000000 0.000000 -0.794384 (0.41496) 0.000000 1.000000 0.213572 (0.17236) Adjustment coefficients (standard error in parentheses) D(LPRICE) -0.012379 0.002562 (0.00485) (0.01100) D(LINFLATI ON) -0.001217 -0.050416 (0.00848) (0.01925) D(LEXC) -0.002773 -0.007708 (0.00143) (0.00325)



60

APPENDIX D: VECTOR AUTO REGRESSION ESTIMATES Vector Autoregression Estimates Date: 08/04/13 Time: 18:06 Sample (adjusted): 1997M05 2012M12 Included observations: 188 after adjustments Standard errors in ( ) & t-statistics in [ ]



DPRICE

DEXC

DINFLATION

DPRICE(-1)

0.395534 (0.07414) [ 5.33495]

-0.020551 (0.02178) [-0.94349]

0.078643 (0.12945) [ 0.60750]

DPRICE(-2)

-0.004206 (0.07966) [-0.05279]

0.017322 (0.02340) [ 0.74014]

-0.048322 (0.13909) [-0.34741]

DPRICE(-3)

0.101112 (0.07396) [ 1.36716]

-0.020160 (0.02173) [-0.92781]

-0.201088 (0.12914) [-1.55719]

DEXC(-1)

-0.006174 (0.24740) [-0.02496]

0.801570 (0.07268) [ 11.0280]

0.481749 (0.43197) [ 1.11523]

DEXC(-2)

-0.160639 (0.31305) [-0.51314]

-0.251538 (0.09197) [-2.73490]

0.203980 (0.54661) [ 0.37318]

DEXC(-3)

0.239681 (0.25040) [ 0.95720]

0.239036 (0.07357) [ 3.24925]

0.299596 (0.43721) [ 0.68524]

DINFLATION(-1)

-0.043449 (0.04273) [-1.01677]

-0.001847 (0.01255) [-0.14710]

0.319577 (0.07461) [ 4.28306]

DINFLATION(-2)

-0.058856 (0.04495) [-1.30929]

-0.004240 (0.01321) [-0.32105]

-0.038183 (0.07849) [-0.48647]

DINFLATION(-3)

0.037480 (0.04231) [ 0.88587]

0.008705 (0.01243) [ 0.70031]

0.028568 (0.07387) [ 0.38671]

C

0.010883 (0.00513) [ 2.12339]

0.002937 (0.00151) [ 1.95064]

-0.012546 (0.00895) [-1.40194]

61

R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent

0.204334 0.164103 0.442555 0.049862 5.079098 302.0929 -3.107372 -2.935220 0.024310 0.054538

0.589982 0.569251 0.038200 0.014649 28.45859 532.3673 -5.557099 -5.384948 0.012050 0.022321

Determinant resid covariance (dof adj.) Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion

4.01E-09 3.40E-09 1032.643 -10.66642 -10.14997



0.201956 0.161605 1.349232 0.087063 5.005039 197.3087 -1.992646 -1.820495 -0.006362 0.095084

62

APPENDIX E: GRANGER CAUSALITY TEST Pairwise Granger Causality Tests Date: 07/28/13 Time: 13:09 Sample: 1997M01 2012M12 Lags: 1 Null Hypothesis:

Obs

F-Statistic Prob.

DINFLATION does not Granger Cause DEXC 190 DEXC does not Granger Cause DINFLATION

0.01368 0.9070 7.69337 0.0061

RPRICE does not Granger Cause DEXC DEXC does not Granger Cause RPRICE

1.12530 0.2901 0.13204 0.7167

190

RPRICE does not Granger Cause DINFLATION 190 DINFLATION does not Granger Cause RPRICE

0.00488 0.9444 2.61026 0.1079

Pairwise Granger Causality Tests Sample: 1997M01 2012M12 Lags: 3 Null Hypothesis:

Obs

DINFLATION does not Granger Cause DEXC 188 DEXC does not Granger Cause DINFLATION

0.17390 0.9139 3.09689 0.0282

RPRICE does not Granger Cause DEXC DEXC does not Granger Cause RPRICE

0.60418 0.6131 0.24622 0.8639

188

RPRICE does not Granger Cause DINFLATION 188 DINFLATION does not Granger Cause RPRICE



F-Statistic Prob.

1.49642 0.2171 1.33630 0.2641

63

APPENDIX F: IMPULSE RESPONSE Response to Cholesky One S.D. Innovations ± 2 S.E. Response of RPRICE to RPRICE

Response of RPRICE to DINFLATION .06

.06

.04

.04

.04

.02

.02

.02

.00

.00

.00

-.02

-.02 1

2

3

4

5

6

7

8

9

10

-.02 1

Response of DINFLATION to RPRICE

2

3

4

5

6

7

8

9

10

1

Response of DINFLATION to DINFLATION .12

.12

.08

.08

.08

.04

.04

.04

.00

.00

.00

-.04 1

2

3

4

5

6

7

8

9

10

Response of DEXC to RPRICE

2

3

4

5

6

7

8

9

10

1

.015

.015

.015

.010

.010

.010

.005

.005

.005

.000

.000

.000

-.005 3

4

5

6

7

8

9

10

4

5

6

7

8

9

10

3

4

5

6

7

8

9

10

9

10

Response of DEXC to DEXC .020

2

2

Response of DEXC to DINFLATION .020

-.005

3

-.04 1

.020

1

2

Response of DINFLATION to DEXC

.12

-.04



Response of RPRICE to DEXC

.06

-.005 1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

64

APPENDIX G: VARIANCE DECOMPOSITION Variance Decomposition Percent RPRICE variance due to RPRICE

Percent RPRICE variance due to DINFLATION

Percent RPRICE variance due to DEXC

100

100

100

80

80

80

60

60

60

40

40

40

20

20

20

0

0 1

2

3

4

5

6

7

8

9

10

Percent DINFLATION variance due to RPRICE

0 1

2

3

4

5

6

7

8

9

10

1

Percent DINFLATION variance due to DINFLATION 100

100

80

80

80

60

60

60

40

40

40

20

20

20

0

0 2

3

4

5

6

7

8

9

10

2

3

4

5

6

7

8

9

10

1

Percent DEXC variance due to DINFLATION 100

100

80

80

80

60

60

60

40

40

40

20

20

20

0 1



2

3

4

5

6

7

8

9

10

5

6

7

8

9

10

2

3

4

5

6

7

8

9

10

Percent DEXC variance due to DEXC

100

0

4

0 1

Percent DEXC variance due to RPRICE

3

Percent DINFLATION variance due to DEXC

100

1

2

0 1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

65

APPENDIX H: VAR STABILITY CONDITION CHECK Roots of Characteristic Polynomial Endogenous variables: DPRICE DINFLATION Exogenous variables: C Lag specification: 1 3 Date: 07/28/13 Time: 14:28 Root

DEXC

Modulus

0.847804 0.679996 0.016513 - 0.533797i 0.016513 + 0.533797i -0.241412 - 0.347230i -0.241412 + 0.347230i 0.036998 - 0.398816i 0.036998 + 0.398816i 0.364683

0.847804 0.679996 0.534052 0.534052 0.422905 0.422905 0.400529 0.400529 0.364683

No root lies outside the unit circle. VAR satisfies the stability condition.

Inverse Roots of AR Characteristic Polynomial 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -1.5



-1.0

-0.5

0.0

0.5

1.0

1.5

66