Analysis of foreign exchange rates using descriptive statistics

Introduction

No country is self sufficient; every country is depended on the other country for some goods and services. The aim of having the foreign exchange market is to promote international trade and investment. The foreign exchange market does not have any clearing house or central exchange house and it is one of the largest financial markets in the world. London exchange is one of the largest amongst the global foreign exchange markets. Foreign exchange is the market that never sleeps; it works round the clock with different buyers and sellers from different countries except for weekends. With the increase in trading volume, it signifies growth in international trade and investments. For the past several years, the global market has changed drastically and strategies play an important role in minimizing the risk and maximizing the portfolio returns. The foreign exchange market is very volatile and they determine the relative values of different currencies. The British Pound Sterling was used for settling trade differences between countries and is a major reserve currency like USD which is retained by government. British Pound still remains as a major international currency owing to large size of British economy and highly sophisticated financial sector. Pound Sterling is the third most popular reserve currency in the world after USD and Euro. This indicates that the foreign central banks are buying and storing large amount of pounds as a reserve capital so as to avoid any fluctuation of their own currency. The main objective of this paper is to study, analyse and compare the behaviour of four different currencies (namely US Dollar, Euro, Indian Rupee and Chinese RMB) against Pound Sterling using descriptive statistics for investor’s information. Before going further, let’s look at some of the background of these currencies for a better understanding.

Backgrounds

United States Dollar is commonly referred as ‘American dollar’ and is denoted by USD or by the symbol ‘$’. The history of dollar revolves around many countries in different continents and it was first issued in 1519. The American currency was officially known as the colonial script in earlier days and it was equivalent to goods and services in the economy. The US Dollar is intensively traded worldwide and it accounts for 87% global transaction. Dollar is globally accepted because of its role in investment currency in capital market, reserve currency in Central Banks and transaction currency in international commodity markets.

EURO

The Euro was launched on 1st January 1999 as an electronic currency in accordance with Maastricht Treaty. It became a legal tender on 1st January 2002; however, the entry of Euro marks the exit of 12 other national currencies in Germany, France, Italy, Spain, Portugal, Belgium, Luxembourg, Austria, Netherlands, Finland, Greece and Ireland respectively. The interest rates are determined by the European Central Banks which is based in Frankfurt. The benefit of introducing Euro was to remove currency risk for those companies operating across different countries. This has helped the companies to reduce large amount of transaction cost which in turn gave them a higher profit.

Chinese Renminbi

The official currency of People’s Republic of China is Renminbi (which mean people’s currency in Chinese). The official ISO 4217 abbreviation of China’s currency is CNY and it is also abbreviated as RMB. In 1949, the first RMB was issued before the takeover of Mainland China by the Communists. A dual currency system was established when the Chinese economy opened up in 1978, RMB could be used domestically only and for foreigners, they had to a foreign exchange certificates. The unrealistic level at which exchange rates were nailed upon led to a speculation in currency transactions. People’s Republic of China worked to make RMB more convertible. The dual currency system came to an end and exchange rate was brought to realistic level through the use of swap centres. The valuation of RMB has drawn a great deal of attention and pressure on developed nations for revaluation.

Indian Rupee

Indian Rupee (INR) was available in different form in different parts of India. It was only after independence (1947), the INR was made into single currency for Republic of India. With recent boom in the Indian economy and trade and rise in economic growth has made Indian Rupee stronger. On 15 July 2010, the new symbol for Rupee was implementing and its main aim was to mark the growing importance in World’s economy. India is one of the fastest growing economies along with China and during the global crisis, India economic growth never slowed down which reflects the strength of the economy. In India, the currency fluctuation is controlled by the Reserves Bank of India.

Methodology

For the analysis of behaviour of different currencies in the global market:

Five days moving average data of four years has been collected (i.e. from 01 June, 2005 to 31 May, 2009; source – DataStream).The purpose of using moving average data is that it tends to smoothen the price which then gives the trend or an indicator whether the price is going up or down.

Compare and contrast the behaviour of all four currencies during the year 2005 to 2009

Comparison of individual year’s data is made.

The parameters used for measuring the behaviour of the currencies are

Mean

Mode

Standard Deviation and

Variance

Calculation

Mean : commonly referred as average and the formulae use for calculating the mean is

∑ Exchange rates

No of elements

Mode: is the value of exchange rate which appears most often in the given data.

Standard Deviation:

Variance : is the square of standard deviation i.e. (SN)2

Table 1

Descriptive statistics

USD

RMB

EURO

INR

MEAN

1.8358

13.8462

1.3767

80.5642

MIN

1.3669

9.34685

1.0408

67.3335

MAX

2.0947

15.5665

1.5252

88.9596

MODE

1.7715

15.3862

1.4674

N/A

SD

0.1788

1.7426

0.1321

4.5069

VAR

0.032

3.0367

0.0175

20.3125

Notes: 1.SD stands for standard deviation, 2. VAR is the variance 3.Figures rounded up to four decimals place. 4. MIN-means minimum or the lowest exchange rate, 5. MAX-means maximum or the highest exchange rate.

Table 1 represents the summary statistic of the currency exchange rate for all four years that is from 1st June 2005 to 31st May 2009. From the above table, we can see that the average exchange rates for each individual currency against the British Pound are USD 1.8358, RMB 13.8462, Euro 1.3767 and INR 80.5642 respectively. This means that the exchange rate for the last four years stood near at about this exchange rate. The percentage change could be positive or negative but the change is very minute. But for an investor’s perspective, a slight fluctuation in the currency rate can have a huge impact on their returns.

Let us take an example of importer from United States who wish to import goods from the United Kingdom and the estimated expenses approximately about 500,000 Pound a year and the rate of exchange for USD at that point of time is 1.8358 which mean the importer has to pay 917,900 USD equivalent (1.8358*500,000) a year. Now if the pound rate goes up to 1.8360, it means the importer has to pay more in terms of USD i.e. 918,000 (1.8360*500,000) which is a loss. So to mitigate such kind of a loss, the importer can enter into a forward contract where the price will be fixed at one rate even though it may go up in the future, so when it is time for the importer to make the payment he can benefit from such uncertainties and losses.

Foreign exchange market is the most volatile market; any news that flashes in the economy causes fluctuation in the exchange rate. Therefore, it is very important to understand the risks associated with each currency, we all know that higher risk will give higher returns. Return is the primary motivating factor that drives investments. Risk is generally denoted by the symbol (σ), in other words it is standard deviation. If, we look carefully at table 1, the risk of Indian currency is the highest amongst all which is not a good indication for an economy. The lowest exchange rate for the period 01/06/2005 to 31/05/2009 against Pound Sterling stood at 1.3669 USD, 9.34685 RMB, 1.0408 Euro and 67.3335 Indian Rupee respectively. Similarly, the highest exchange rate during that period was 2.0947 US Dollar, 15.5665 RMB, 1.5252 Euro and 88.9596 Indian Rupee against Pound Sterling. Further, from table, mode indicates the value of the currencies which appears most often was USD1.7715, RMB 15.3862 and Euro 1.4674 respectively. This means that the currency rate is likely going to be repeated again in future.

Graph showing the movement of currencies in the global market from mid 2005 to mid 2009.

Source: Thompson Reuters DataStream

From the given graph, we can see the trend in which the currencies are moving. However, one common thing among all four currencies is the declining trend. Let’s start with Chinese RMB, the exchange rate as on 03 June 2005 was 15.0333 and it went down further until mid 2006 and then starting rising again in 2007 and it remained stable for the entire year 2007 then again started dropping in the early 2008 till beginning of 2009 and have started to rise again. The fluctuation was mainly because of the Asian financial crisis which slowly spread across the country. Euro seems to be running parallel with Chinese RMB as indicated by the graph. The Indian Rupee were the most disturbing currency as there was a huge fluctuation compared with the other currencies. On 23 January 2009, the Indian Currency fell as low as INR 67.3335 which is the lowest till date. On the other hand the US Dollar seems to be doing pretty well in the beginning and it started to fall drastically in 2008. We will further analyse all four currencies individually using different statistics and graphs.

Table 2

Descriptive Statistic (1st June 2005 to 31st May 2006)

USD

RMB

EURO

INR

MEAN

1.7752

14.3666

1.4642

78.8929

MIN

1.7138

13.8530

1.4334

75.6592

MAX

1.8903

15.1339

1.5070

85.2101

MODE

1.7715

#N/A

1.4674

#N/A

SD

0.0419

0.3757

0.0156

2.1642

VAR

0.0018

0.1411

0.0002

4.6836

From the year 2005 to 2006, we can see the average exchange rate for USD, RMB, Euro and Indian Rupee was 1.7752, 14.3666, 1.4642 and 78.8929 respectively. The minimum exchange rate for USD for the period was 1.7138 and the maximum was 1.8903 and similarly we can take the minimum and maximum exchange rate for the other currencies as well from the given table 2. In this period, USD and Euro have the same exchange rate which got repeated at 1.7715 and 1.4674 respectively. Further, if we look at the standard deviation for each currency, the Indian currency is the highest then followed by Chinese RMB. This is one of major reason why there is so much variation in the Indian Currency presented in the graph below as compared to US dollar and Euro.

Graph showing four different currencies movement during the year 2005-2006

The data shows that the Indian currency depreciated in early July -August 2005 and then appreciated, this was mainly because the growth in export. The depreciation of Indian currency was neutralised by the growth of export in the economy. The Chinese currency depreciated because of the Asian financial crisis that took place in Thailand which spread across the border of other countries. This has rapidly led to sharp fall in stock market and depreciation in local currency. Tse and Yip (2006) did a research to find out whether the Asian financial crisis led to changes in correlation of interest rates between the western countries and the eastern countries, the result showed that during the financial crisis there was a correlation breakdown of interest rates but it restored after the financial crisis. Fluctuation in currency also reflects the way the governments are spending. If there is a deficit in the economy, this will automatically force the currency to depreciation and as a result the economy becomes weaker. In this graph, Euro is the only currency which has reached its peak of 1.5070 against Pound and there was a drastic fall the very next moment. There was a decline of currency rate in early July 2005 because the central bank was trying to maintain interest rate and exchange rates simultaneously which resulted in increase of money supply and the ultimate outcome was depreciation of the currency. However, Euro currency remained below 1.50 for the entire year and it never rose above that figure. All three other currencies namely INR, USD and RMB had a wave movement which went up and down during the year but it moved higher up than it originally started. This indicates that the British economy is not at a very good situation and that is why the price of an exchange rate against the other currency is increasing leading to limited export and import. Whether this is going to be the same in the long run, we will find out in the next set of data.

Table 3

Descriptive Statistics (1st June 2006 to 31st May 2007)

USD

RMB

EURO

RMB

MEAN

1.9210

15.0719

1.4783

85.6754

MIN

1.8193

14.5548

1.4434

80.3442

MAX

2.0035

15.5208

1.5252

88.9596

MODE

#N/A

#N/A

1.4661

#N/A

SD

0.0506

0.2265

0.0174

1.9041

VAR

0.0026

0.0513

0.0003

3.6256

This table show that the average mean is relatively higher than the previous set of data (i.e. 2005 -2006) so is the minimum and the maximum exchange rate for the year 2006 to 2007. Further, we observe from the table that the risk on Indian Currency has gone down from 2.1642 to 1.9041 which means the government has taken some action on improving the policy and strategy of reducing the risk, whereas for the other countries the risk has increased slightly.

Graph showing indicating currencies movement during the year 2006-2007

Now let us look at the graphs which present an interesting movement. The Chinese RMB seems to be very stable; the variation is not that huge but it is showing an upward trend. Similarly, Euro also shows an upward trend but surprisingly the Indian Rupee is showing a downward trend and the US Dollar is showing a steep rising trend. One of the possible reasons was the housing bubbles crisis which started in 2005 but it became apparent only in early 2007. This has resulted in financial crisis which further led to recession n the US economy. These crises have an impact on other economies and it is still continuing to spread across to other countries. It not only affect the banks but the people in the entire economy as they lose their jobs and the consumer have to cut down on their expenses, so production become less and the importers reduced their goods that they used to import, all these made the market even more worse as a result the exchange rate goes down. Here, the rise in currency rate against Pound Sterling means that the economy is not doing well.

Table 4

Descriptive Statistics (1st June 2007 to 31st May 2008)

USD

RMB

EURO

INR

MEAN

2.0049

14.7152

1.3837

80.6087

MIN

1.94625

13.6078

1.2463

76.7981

MAX

2.0947

15.5665

1.4872

84.6349

MODE

1.9463

15.3862

#N/A

#N/A

SD

0.0353

0.6358

0.0822

1.8101

VAR

0.0012

0.4042

0.0068

3.2763

In comparison to the previous set of data, the average exchange rate of US Dollar has gone up from 1.9210 (2006-2007) to 2.0049 (2007-2008) whereas the rest of the currencies has gone down. The highest exchange rate for USD is 2.0947 followed by RMB which stood at 15.5665, Euro and Indian Rupee has gone down owing to improved economy and the value of their are appreciating.

The below graph reflects the currency movement for the period 2007 to 2008, RMB shows a steep slope with a negative trend then followed by Euro but it started to rise again in mid 2007. In this period, the US and Indian economy seems to be shaky, this is because of the subprime mortgage crisis that has resulted in the huge variation of the currencies exchange rate. The Indian economy is the most affected as the exchange rate soar to INR 84.6349 against Sterling making things difficult.

Graph indicating the currency movement for the year 2007-2008

Table 5

Descriptive Statistics (1st June 2008 to 31st May 2009)

USD

RMB

EURO

INR

MEAN

1.6390

11.2145

1.1805

77.0790

MIN

1.3669

9.3469

1.0408

67.3335

MAX

1.9965

13.6664

1.2855

85.7894

MODE

#N/A

#N/A

#N/A

#N/A

SD

0.2108

1.4580

0.0782

5.4150

VAR

0.0445

2.1256

0.0061

29.3227

From the last set data taken, the average currency rate for USD has dropped down from 2.0049 to 1.6390 against Sterling, so is the other three currencies as well. Compared to the previous year data, there has been huge change in the exchange rates. Let’s take a look at the Indian currency rate; the lowest value from the previous data was INR 76.7981and now it’s INR 67.3335. The highest value of exchange rate for India was INR 85.7894 whereas for the previous year it was INR 84.6349. In this we observe that the standard deviation is the highest amongst all four sets of data which indicates that the Indian currency has a very high risk associated in the currency and the investors should be aware of it before trading.

Graph indicating the currency movement for the year 2007-2008

No doubt that the graph for all four currencies is showing a negative downward sloping trend but from an importers perspective, if the rates are low they can import more goods by paying less otherwise they will incur a huge loss if they start importing goods when the prices are high. Risk can be mitigated by entering into a forward contact. So from the diagram, we can say that if the currency rates are low which mean it is favourable for the importer or businessmen. But from investor’s perspective, they will always invest in the market which gives high return, so for them if the price is high, they gain profit. From all four sets of data, the highest exchange rate for an Indian Rupee was INR 88.9596 in August 2006 and it has the highest risk among all four currencies. However, from the given data, it has been observed that risk increases as currency rate decreased and when currency rate increases the risk decreases. Euro currencies are less risky and are more stable. China also carries high percentage of risk as and when the price of RMB falls. Therefore, it is very important for investors to understand the market before investing. There are also several other measures which can used for measuring the risk and the returns, however, in this paper we have used only descriptive statistics to analyse the basic data collected from DataStream.

Conclusion

History repeats itself; whatever happens in the present is related to the past. The future price movement is all based on the past prices and the individual’s reaction in the market. Regulation also plays an important role in controlling the exchange rates. Sometimes, when the government does not control the interests’ rate or exchange rate, it results in excess supply of money and this can cause the value of the money to depreciate. Economic and financial crisis also causes the money to depreciate. So if the economy is sound then currency will be strong. In this paper, we have used the data collected to see that how each currency behave over a period of time using the statistical tools. What we infer from the given data is that all four currencies are moving in a downward trend which means that if I as an US investor will not invest in the UK market if the prices are high since the purpose of investment is have greater returns.