PARAMETRIC MEASURE OF EXCHANGE RATE VOLATILITY IN KENYA
By
Kimaru K Job
A Research Proposal Submitted in partial fulfillment of the requirements for the Degree of Bachelor of Science in Mathematics and Computer Science of Taita Taveta University College
2016
DECLARATION
This proposal is my original work and has not been presented for a degree in any other university.
Signature: …………………………………Date………………………….
Declaration by Supervisors
This research proposal has been submitted for examination with our approval as supervisors
• Mr. Noah Cheruiyot, Mathematics and Informatics Department
Signature………………………………………Date…………………………….
• Dr. Ngesa , Mathematics and Informatics Department
Signature……………………………………….……Date……………………………………
ACKNOWLEDGEMENT
First, I would like to thank God for the far He has brought me, the journey has not been easy.
My sincerest gratitude to my Supervisor Mr. Noah Mutai for her guidance and availability throughout this process. I am indebted for your dedication.
Many thanks to DR.Ngesa for his very important input and suggestions, Mr.mutotya for his invaluable input at the inception of this project and my course mates for their insight and advice.
Lastly, I would like to sincerely thank my mother, Margaret Biwott for constantly cheering me on and being my best fan and critics. Without your support, encouragement and prayers, it would not have been possible.
LIST OF ABBREVIATIONS
GARCH-Generalized autoregressive conditional heteroscedacity
EGARCH- Exponential Generalized autoregressive conditional heteroscedacity
KES- Kenyan shilling
USD-united states dollar
CKB- central bank of Kenya
FOREX- foreign exchange
Abstract
Real exchange rate has proven to be an important factor in economy of a country therefore its volatility information is of importance to investors, policy makers, government and also other researchers. Exchange rates volatility has increase uncertainty in both industrial and agricultural sector in Kenya.
This paper seeks to use a parametric measure to discover the trend and characteristic of exchange rate volatility in Kenya .The study will use EGARCH model to determine the presence of exchange rate volatility.
Its uses forex data over the period June 2007 to Jan 2016 to measure the volatility and analyze the exchanges rates changes over the specified period.
A set of parametric test will be used to test the mean and standard deviations of exchange rates.
In addition to the analysis, graphical representation of exchange rates will be done.
Key words: exchange rates, volatility, standard deviation
Chapter one
• Introduction
This chapter entails the history and the nature of the Kenya exchange rate system. It also indicates the root of the problem being studied, its scope and the extent to which previous studies have successfully investigated the problem, noting, in particular, where gaps exist that my study attempt to address.
1.1 Background of the Study
Over many years, Kenyan shilling have enjoyed appreciable value against US dollar, this factor has created opportunities for rapid economic growth and stability after a successful movement from a fixed exchange rate to a crawling per regime in the early 1980s and finally to exchange rate system in 1990s. But with introduction of new economic policies and program, the country began to suffer unstable exchange rate that caused a high degree of uncertainty in the Kenya business environment. Domestic investors faces a lot risk as no one could predict the performance of the foreign exchange market. This situation also has an effect on importation and exportation level of the country. Kenya as a developing country striving to develop its agricultural and industrial base needs to improve its foreign exchange market to enable domestic investors export agricultural produce and import relevant Machineries, equipment’s and raw materials for the industrial consumption without uncertainties in the system. The increasing volatility of exchange rates after the fall of the Bretton Woods agreements has been a constant source of concern for both investors, policymakers and academician and we can recall how developed countries tried hard in the 1980s to limit US dollar volatility (one thinks of the Plaza and Louvre’s agreements, respectively in 1985 and 1987), and some European countries took a more radical and wiser decision by giving up their national currency for the euro in the year 1999.However, more recent studies shows that these results could be due both to an aggregation bias (Broda and Romalis 2010) and an excessive focus on developed countries with highly developed exchange rate systems, since much more enough negative effects of the exchange-rate volatility on trade (Grier and Smallwood 2007) and growth (Aghion et al. 2009) are found for developing countries. Surprisingly, macroeconomic evidence of the effect of exchange-rate volatility on economy for instance, trade, and more generally on growth, has been quite unclear, pointing to minimal or insignificant effects. In that context, it seems quite disturbing to see a number of countries, specifically the developing ones, adopting more or less fixed exchange-rate systems, especially when one remembers the painful collapses of south-east Asian fixed pegs at the turn of the century.
The existence of well-developed financial markets should allow agents to deal appropriately on exchange-rate risk, thus eliminating its negative effects on major economic sectors as a case of foreing trading. In that sense, mitigation of exchange-rate risk is unlikely to be the main sources of the growth-enhancing effect of financial development found in the literature.
Economic fundamentals such as the inflation rate, interest rate and the balance of payments, which have been more volatile in the 1980s and early 1990s, by themselves, are sources of exchange rate volatility (Oz Turk, 2006). The NEWS impacts suggested by Tibesigw and Kaberuka (2014) could also be added onto the list of the factors that bring about volatilities. In the exchange rates of any economy the volatilities in the macroeconomic variables have attracted most researchers to not only study the phenomenon but also suggest some remedies to this problem. This paper aims at using a different approach to the measure of volatility in exchange rate, which is parametric in nature and then analyses the trend which the exchange rate follow in responds to both negative and positive trends.
1.1.1 The concept of heteroskedasticity
In statistics, a sequences of random variables is heteroskedastic, if the random variables have different variances. The term means “differing variance” and come from Greek “hetero”(different) and “ skedasis” (dispersion).when the standard deviations of a variable, monitored over a specific amount of time are non-constant. Heteroskedaticity often arise in two forms. Conditional and unconditional.
Conditional heteroskedasticity identifies non constant when the future periods of high and low volatility can be identified.
1.1.2 Volatility of exchange rate definition
Volatility refers to the spread of all unlikely outcomes of an uncertain variable (Abdalla, 2011).
Exchange rate volatility is defined as the risk associated with the unexpected movement in the exchange rate(Oz Turk, 2006).
1.1.3 Evolution of the Foreign Exchange Markets in Kenya
The KES/USD exchange rate changed from fixed to crawling to floating eras between the year 1969 and 2009. Between 1966 and 1992, Kenya operated a fixed exchange regime and the country had to frequently devalue its currency to reduce the negative effects that real exchange rate volatility had on its economy (Munyoki et al., 2012)
The floating exchange rate system was adopted in 1993; however, there is no available evidence that success has been achieved in realizing the objective for which the foreign exchange market was liberalized (Munyoki et al., 2012)
1.1.4 Parametric measures
The parametric measure of exchange rate volatility on the other hand estimates volatility in exchange rate using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (E-GARCH) model in this study. This is distinct from some past studies that employed the pure GARCH model to estimate exchange rate volatility. Literatures have given a number of advantages of the E-GARCH model over other methods of measuring volatility. For instance, first, E-GARCH automatically tests for ARCH effects in the series. Secondly, the model expresses explicitly the log of the conditional variance which implies that the leverage effect is exponential rather than quadratic, and that forecasts of the conditional variance are guaranteed to be nonnegative. The presence of leverage effect can be tested by the hypothesis that the impact is asymmetric
1.2 Statement of the Problem
The Kenya shilling has registered mixed performances against the USD. The fluctuations ranged between 35 in 1994 when the Kenya shilling was strongest and 106 in 2016 when it was at its weakest. This has been a great hindrance to international transactions especially exportation of Agricultural products in Kenya. Several authors have therefore written on the extent to which the volatility in exchange rate has affected some basic macroeconomics factors which normally determine the directions of the working of the economy. Different approaches and methods of measuring exchange rate volatility have been used by different researchers over time leading to divergent results thus no consesus arrived at. This because there are no general ways of measuring volatility according to existing theories. Different statistical measures of exchange rate volatility have been proposed in the literature. However, two measures of volatility have widely been used in the literature which are the standard deviation method and a volatility measure generated from a generalized autoregressive conditional heteroscedasticity (GARCH) process. The standard deviation method has been criticized for simply assuming that the empirical distribution of the exchange rate is gaussian and for ignoring the difference between predictable and unpredictable elements in the exchange rates process (Musonda, 2000; Hook and Boon, 2000).The GARCH method has two problems associated with it. Firstly, the non-negativity conditions of the variance may be violated by the estimated model. Secondly, the models cannot account for leverage effects, although they can account for volatility clustering and leptokurtosis(fat tails) in the series. Different economists use different models to measure exchange rate volatility (Orkhan, 2010). Orkhan (2010) however gives the list of various means of measuring volatility in the exchange rate and their users including the results.
The purpose of this paper therefore aims at using a different approach to the measure of volatility in exchange rate, which is parametric in nature and then analyses the trend which the exchange rate volatility has followed Kenyan exchange rate system.
1.3 Justification
Whether the research findings relate to the volatility in the annual and daily exchange rates in CBK, the relevance is of interest to both long term investing and speculations as the information derived from the findings can help organization, policy makers, analysts alike, investors or individuals to gain in depth understanding of dynamics of exchange rates in Kenya capital markets. Thus the need to investigate the financial market trends a case of exchange rates volatility.
1.4 Objectives of the Study
1.4.1 General Objectives
The overall objective of this study is to empirically establish how Kenya exchange rate changes of the specified period of study changes by modelling the volatility of KESH/USD using EGARCH model.
1.4.2 Specific Objective
1. To show the characteristics and the trend in which Kenya exchange rate follows.
2. To build a volatility model that show the volatility of KES/USD exchange rate.
1.6 Hypothesis
The research will want to test volatility of the exchanges rate in Kenya
: Exchange rates in Kenya are highly volatile
1.7 Significance of Study
This study is conducted to discover the trend and pattern that exchange rate volatility follows in Kenya. Given the fact that exchange rates across world’s major currency have ceased to assume a fixed rate, it is necessary to conduct a research on the extent to which exchange rate has been volatile in Kenya so that the country’s policy makers at all capacities can be informed and awared of the dangers attached to volatility in exchange rate and suggest possible way-out
Chapter two
Literature review
2.0 Introduction
This chapter will elicit text of scholarly paper, which include the current knowledge including substantive findings, as well as theoretical and methodological contributions to this study done by other researchers.
2.1 Previous Literature
Over the last three decades thats it is from 1980s to date, Researchers including Engle (1982), Bollerslev (1986) have done alot in a number of time series models and improved the ARCH model to generate a more generalized ARCH model.
Tibesigwa and Kaberuka (2014) however, stated that though these models have been used in developed countries there is less applicability in the analysis of developing countries(third world countries) like Kenya.In one of the noticeable empirical studies done by Vergil (2002) where he did a study on the impact of real exchange rate volatility on the export flows of Turkey to the United States and its three major trading Partners in the European Union for the period between 1990 and 2000 found that the standard deviation of the percentage change in the exchange rate can be used to measure the exchange rate volatility.
Additionally, many authors (Christie, 1982; and Nelson, 1991) have cited out the evidence of asymmetric effects, suggesting the leverage effect relys on the direction of price changes.
In response to the weakness of symmetric assumption, Nelson (1991) brought out exponential GARCH (EGARCH) models with a conditional variance formulation that successfully captured asymmetric response in the conditional variance. EGARCH models have been demonstrated to be superior compare to other competing asymmetric conditional variance in many studies (Alexander (2009).
Another research done Alberg et al. (2006) to forecast performance of GARCH, EGARCH, GJR and APARCH models and found that the EGARCH model, which used a skewed Student-t distribution, produced significant results than any other model.
Latifa et al. (2013) come up with a research to model heteroscedasticity in foreign exchange for US, UK, Euro and Japanese Yen data based GARCH models. Monthly averages for the various currency exchange rates were collected for the period from January 2001 to December 2010, a total of 120 observations per foreign currency. The period was chosen because of the two major events that the country went through that is Election period followed by the post-election violence in 2007/2008. Their major objective was to study how these election factor affected the performance of the said currencies.Maana et al. (2010) applied the GARCH process in the estimation of volatility of the foreign exchange market in Kenya using daily exchange rates data from January 1993 to December 2006. Currencies used
were USD, sterling pound, Euro and Japanese Yen. Data used was obtained from the CBK archives .In is study of volatility in exchange rates, logarithm rates returns were used.Using the descriptive statistics for exchange rate returns, he found that skewness coefficients were greater than zero implying that the exchange returns distributions are not gaussian.
Chipili (2006) states that, in spite of the importance of exchange rate volatility in macroeconomics he found that studies on kwacha exchangee rate volatility has not been explored in delevoping countries, Zambia to be exact. The research was conducted over a longer sample period, 1964-2006 using relatively higher frequency data at monthly intervals. He employs both symmetric and asymmetric GARCH models.
Abdalla (2011) used daily observations from 19 Arab countries and considered the GARCH technique in modelling exchange rates. Observations in the period 1st January 2000 to 19th November 2011, a total of 4341, were used. The LM test was used to test for heteroscedasticity. GARCH model was then used to investigate the volatility clustering and persistence. EGARCH was used to capture leverage effects as GARCH models are poor in capturing these effects.
Sandoval (2006) studied the daily exchange rate data, from year 2000 to 2004, of seven Asian and developing Latin American countries, by employing the ARMA, GARCH, EGARCH and GJR- GARCH models for modeling the exchange rates . He founded out that, in the developing countries the absence of statistical significance between asymmetric and symmetric models was conditional to the application of in-sample and out-of-sample tests jointly.
Also, in an attempt to adopt a parametric measure of exchange rate volatility in Nigeria, Isitua and Neville (2006) investigated the effect of exchange rate volatility on trade flows in Nigeria. Their study employed the generalized autoregressive conditional heteroskedasticity (GARCH) technique to measure exchange rate volatility.
Furthermore the GARCH model has also been applied in research done by Danson et al. (2012) that analyzed the impact of real exchange rate volatility on economic growth in Kenya. Results depicted that exchange rate was very volatile for the entire period under study .These results imply the presence of the volatility periods in the most macroeconomic variables of the East African countries and therefore gives confidence in the a applicability of the GARCH model in capturing the volatility of these variables in the regional economies,he never captured the assymetric effect.
The idea of the exhibition of the volatility periods in economic variables is also stressed by Oz Turk (2006) who in his paper confirms the existence of the volatility in trade brought about by shifts in the volatility of exchange rates who further suggests some critics of GARCH model .
In conclusion, a critical look at the findings of these various authors reveals that the degree of exchange rate volatility differs from one study to the other. This, of course, might be the reason why the findings of these studies on the effect of exchange rate volatility on a particular macroeconomic phenomenon, such as trade are not uniform given the fact that several researchers have ignored the degree of volatility in exchange rate among world Currencies. This paper adopts a more rigorous parametric measures of exchange rate volatility in Kenya using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (E-GARCH) modelling technique which addresses the defects identified with GARCH model .
Chapter three
Methodology
• Introduction
This chapter entails the methods to be used in order to gain perspective of the research study. The aims, research design, data collection and data analysis are discussed.
• THE GARCH MODEL
The standard GARCH model allows the conditional variance to be dependent upon previous own lags. The basic structure of the symmetric normal GARCH model is GARCH (1, 1) given by Chris Brooks (2008)
,
Where denote the conditional variances.
The GARCH model above cannot account for leverage effect, does not allow for any feedback between the conditional Variance and mean and violates the non-negativity conditions.
For these reason I opted to model the problem using asymmetric GARCH model called EGARCH.
• EGARCH MODEL
The exponential generalized autoregressive conditional heteroskedasticity model (EGARCH) is one of the many forms of GARCH model by nelson (1991).We shall use EGARCH which has added benefit because it is expressed in terms of the log of conditional variance so that even if the parameters are negative, the conditional variance will always be positive thus we do not therefore have to artificially impose non-negativity constraints
Let be an identically and indeed sequence such that and
Then the conventional EGARCH model becomes
Where , the conditional variance are coefficients. May be a standard normal variable or a generalized error distribution. The sign and the magnitude of is allowed by the formulation of enabling it to have separate effect on the volatility.
Furthermore parameter represent a magnitude effect or the symmetric effect of the model. Measures the persistence in conditional volatility. The parameter measures the leverage effect. This parameter is important as it allows the EGARCH model to test for Asymmetrics.If then the model is symmetric when is greater than zero the positive shocks (good news) generate less volatility than negative shocks (bad news). When it implies that good news is more destabilizing than bad news. The EGARCH model used got a distinctive feature, i.e., conditional variance was modeled to capture the leverage effect of volatility.
The parameter measures the asymmetry or the leverage effect, the parameter of
importance so that the EGARCH model allows for testing of asymmetries.If , then the model is symmetric. When , then positive shocks (good news) generate less volatility than negative shocks (bad news).
Student t-distribution
The EGARCH model takes an assumption of student t distribution with mean 0 and variance 1 with k degree of freedoms and it is written as
The parameter can be explained as the degree of leptokurtosis
The interpretation by Su and Fleisher (1999) is that large values of are associated with
the absence of leptokurtosis whereas small values are associated with some degree of leptokurtosis.
If approaches 0 the Student t-distribution approaches to a standard normal distribution, but when
the t-distribution has fatter tails that the corresponding normal distribution.
3.1.0 Parametric Measures
We previously mentioned that the most common measure of dispersion is the standard deviation. This it’s estimated as
Where is is the mean defined by =
SKEWNESS
Most set of data have either positive or negative skew rather than following the balanced normal distribution(which has a skewedness of zero).By knowing which way data is skwed,one can better estimate whether a given data point will be more or less than the mean.
for univariate data
Where the means is the standard deviation and N is the data points
Coefficient of variation = standard deviation/Expected rate
DATA COLLECTION TECHNIQUES
The research will use data of June 2007 and January 2016.The data will be collected from the central bank of Kenya website.
DATA ANALYSIS
After collection of the data, analysis will be done with use of statistical package for social sciences (SPSS) and R software to come up with empirical results.
References
• Abba, G. (2009). Impact of foreign exchange volatility on import: A case of Nigeria foreign exchange Market. Proceedings of the 7th International Conference on Innovation and Management.
• Bah, I., & Amusa, H. (2003). Real Exchange Rate Volatility and Foreign Trade: Evidence from South African Exports to the United States.
• The African Finance Journal 5, 2:1-20 Isitua, K., & Neville N. I. (2006). Exchange Rate Volatility and Nigeria-USA Trade Flows:
• Oloba, O. M. 2012. The Effect of Exchange Rate Volatility on Trade Flows in Nigeria.
• Master of Science Thesis, Obafemi Awolowo University, Ile-Ife (Unpublished) Vergil H. (2002). Exchange Rate Volatility in Turkey.
• Journal of Economic and Social Research Engle, Robert F. (1982). "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom.
• St. Pierre, Eileen F. (1998). "Estimating EGARCH-M Models: Science or Art". The Quarterly Review of Economics and Finance.
• Chang, S. (2012). Application of EGARCH model to estimate financial volatility of daily returns: The empirical case of china.
APPENDICE
WORKPLAN
2.0 GANTT CHART
Activity Duration(weeks)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Preliminary Work
Project Identification
Draft Proposal
Proposal Presentation
Proposal Defense
literature search
Data Analysis
Modeling of the solution
Drafting final report
Report publishing & submission
Final Presentation
Key
Activity
BUDGET ESTIMATE
ITEM DESCRIPTION COST(KSH)
Flash disk For backing up research files and documents 2GB 1500.00
Travel (field study) To gather the necessary information as pertains to the research proposal 4000.00
Binding and Photocopying Proposal papers 3000.00
Internet bundles For internet access to facilitate efficient project research 1500.00
TOTAL 10000.00