Summary
It is generally agreed by economists and finance specialists that the 21st century is Africa’s century. Growth in the continent now averages 6% over the last five years. It is believed that for Africa’s development to be sustainable, the largest economies in the four main regional blocs (that is Egypt, Kenya, Nigeria and South Africa) have to be stable economically. The stability of a currency is one attribute of a stable economy. A lot, therefore, can be said about the stability of a country by examining the stability of its currency. Factors contributing to the strength of a country's currency might include the long-term stability of the currency’s purchasing power, the policy posture of the issuing central bank and the associated country's fiscal and political condition and outlook. Conversely, a weak currency indicates a currency which is expected to fluctuate erratically or depreciate against other currencies. Such weakness (softness) is typically the result of political or fiscal instability within the associated country.
A Chinese investor plans to invest $1million in the currencies of the four countries (Egypt, Kenya, Nigeria and South Africa). Using the historical monthly bid rates of the four countries, advise her on the choice of her investment using the US dollar as a base currency.
Introduction
In this paper, we analyze the data on the exchange rates between the U.S. dollar and currencies of four African countries. According to our data sample, we consider the period from February of 2000 to February of 2013, i.e. data for 13 years. Addresses the four currency - U.S. Dollar to Egyptian Pound, to South African Rand, to Nigerian Naira and to Kenyan Shilling.
We will start with a brief description of research tools for data analysis, and then proceed to the descriptive statistics. Based on theoretical data, we have developed a mathematical model to predict each of the exchange rates, and then make a conclusion about the most useful model for use. This work requires knowledge of the theory of probability and mathematical statistics - namely, the construction of regression and data analysis.
Analysis and interpretation of the results
First of all we start with the descriptive statistics.
The purpose of the descriptive statistics is the processing of empirical data, their classification, visual representation in the form of graphs and tables, and their quantification by means of basic statistics.
Unlike the inductive statistics descriptive statistics do not make conclusions about the population based on the results of research of particular cases. Inductive same statistics across suggests that the properties and patterns identified in the study of objects of the sample are also inherent to a population.
Descriptive statistics using three main methods of data aggregation:
- Tabular presentation
- Diagram
- Calculation of statistical indicators
In this work we are using both Minitab and Excel to show that we can work in both these programs.
Now we put our data in Minitab and looking for a descriptive statistics:
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
USD/EGP 157 0 5,3799 0,0621 0,7776 3,4251 5,3053 5,6290 5,9338
USD/ZAR 157 0 7,676 0,101 1,261 5,713 6,825 7,464 8,111
USD/NGN 157 0 131,31 1,31 16,41 100,46 116,71 128,33 148,32
USD/KES 157 0 76,226 0,492 6,167 60,218 72,966 76,663 78,720
Variable Maximum
USD/EGP 6,6830
USD/ZAR 11,585
USD/NGN 160,80
USD/KES 100,042
As we can see from the results, we have 157 measurements of our exchange rates, i.e. the sample size is 157.
- USD/EGP
The average value of exchange rate between USD and EGP during the considered 13 years is 5.3799. The standard deviation is not very big, relatively to the mean, 0.7776. During these 13 years, the exchange rate changes from a minimum value 3.4251 to a maximum 6.6830
- USD/ZAR
The average value of exchange rate between USD and ZAR during the considered 13 years is 7.676. The standard deviation is quite bigger, relatively to the mean, 1.261. During these 13 years, the exchange rate changes from a minimum value 5.713 to a maximum 11.585
- USD/NGN
The average value of exchange rate between USD and NGN during the considered 13 years is 131.31. The standard deviation is not big, relatively to the mean, 16.41. During these 13 years, the exchange rate changes from a minimum value 100.46 to a maximum 160.80
- USD/KES
The average value of exchange rate between USD and KES during the considered 13 years is 76.226. The standard deviation is not big, relatively to the mean, 6.167. During these 13 years, the exchange rate changes from a minimum value 60.218 to a maximum 100.042
Now it is important to determine exactly which points in time exchange rates were close to their maximum and minimum values. To do this, we construct a graph for each exchange rate by month:
For the last several years, the exchange rate between USD and EGP shows a growth; its values in the last months are close to maximum.
The maximum values of the exchange rate between USD and ZAR were observed in 2001-2003 and 2008-2010 years. Now these values are quite lower.
The exchange rate of USD and NGN is slightly growing during the last 4.5 years. The maximum values are close to the end of the observed period.
The exchange rate of USD and KES is also growing in the last time, the maximum value was in 2011, but the indicators of last several months are also high.
The next step of our research is to construct a mathematical model for each type of the relations (USD/EPG, USD/ZAR, USD/NGN and USD/KES) and to determine, which type of a model is better. After that we will generate a forecast to see, which investment is the best.
We are starting with a dot-plot for each currency. Using the MS Excel tools, we add a trend line on each graph.
The coefficient of determination (R-squared) - is the proportion of variance in the dependent variable explained by the model under consideration depending, that is, the explanatory variables. More precisely - it is one minus the proportion of unexplained variance (variance of the random error model, or conditional on factors variance in the dependent variable) in the variance in the dependent variable. It is regarded as a universal measure of a random variable due to many other. In the particular case of the linear dependence R-squared is the square of the so-called multiple correlation coefficient between the dependent variable and the explanatory variables. In particular, a linear regression model steam determination factor equal to the square of the correlation coefficient between the conventional y and x.
Thus, the best model for our forecast appeared to be polynomial with 2th degree.
For USD/EGP the regression is:
y = -0,0002x2 + 0,017x + 5,542 With R² = 0,6498
For USD/ZAR
y = 0,0002x2 - 0,0279x + 8,3113
R² = 0,0814
For USD/NGN
y = 0,0011x2 - 0,4841x + 160,07R² = 0,7242
And for USD/KES:
y = 0,0021x2 - 0,3506x + 86,821R² = 0,4131
The coefficient of determination is ranging from 0 to 1. The closer the coefficient is to 1, the stronger is the relationship. In assessing the regression models is that the model is interpreted as data. For the acceptable models assumed that the coefficient of determination must be at least not less than 50% (in this case, the multiple correlation coefficient greater than 70% in absolute value). Models with a coefficient of determination greater than 80% can be considered quite good (correlation coefficient greater than 90%). The coefficient of determination of 1 means the functional relationship between the variables.
We see, that our R-squared in 2nd model is very close to 0. This means, that this model generates a very bad forecast. We must point out, that this exchange rate is very dynamic, and also the variance is quite large. Hence, this currency is very risky to invest.
Now let’s generate a forecast. Assume, the Chinese investor wants to invest in the last date of our data sample, and retrieve his funds after 1 year.
The exchange rates on 28.02.2013 are following:
Hence, with $1,000,000 he will obtain the following amount of four currencies:
Now let’s predict the exchange rates on 28.02.2014
We generate our forecast from 1st value in 02.2013 to 157th value in 02.2000, hence, the approximation of 02.2014 is x= - 12. We have to substitute this value in each formula
We have the following results:
For EGP:
Y(-12)=5.3092
For ZAR:
Y(-12)=8.6749
For NGN:
Y(-12)=166.038
For KES:
Y(-12)=91.3306
Hence, the future values of our investment in dollars are:
Conclusion
As we may see from our research, the largest amount of money the investor will receive if he will invest in Egyptian Pounds. Indeed, the high value of R-square coefficient shows us, that the model is quite significant; also, the trend line fits good to our dot-plot.
Of course, this forecast can be considered valid only under the condition that all the factors affecting the changes in exchange rates will continue to affect the same degree. It is also necessary to exclude the possibility of unforeseen circumstances the stock markets.
