Finance Case Study Paper on Fisher’s and t – test equation

Fisher’s and t-test equation

Summary

The report analyses the relationship between Fisher’s equation and the t-test. It will use data from two countries to try to prove the relationship. The report will use two countries, United State data, and the United Kingdom data as examples. The analysis will be done using various methods as the formulas hold in accordance with Fisher’s equation and t-test. The report will then try to analyze the outcome of the results as it analyzes whether Fisher’s equation holds (Hawawini, 2011, 39). The outcomes of the results will be used to draw conclusions about the interest rates of the countries used in the report. After the conclusion in accordance with the reporting requirement, this will be used to show whether Fisher’s equation holds.

        Aim: The aim of this report is to try to prove Fisher’s equation. It intends to look into Fisher’s equation if it holds according to international nominal rates in relation to inflation. The report intends to try to do an analysis of the outcome of the data used as examples (Monro Barbara, 2005, 105). It aims at analyzing the data by applying fisher’s equation and t-test in relation to other methodologies related such as mean and standard deviation.

        Objectives: The objectives of the report are to analyze the example data by use of Fisher’s equation. The report also tries to prove Fisher’s equation of the international. Another objective is to determine which country will have the highest interest rate if the international fisher’s equation holds. To determine the t-test of the data recorded. Another is to give the conclusion of the county with a higher interest rate in relation to the country with the low-interest rate and to determine the GPB buying rate in terms of the interest rate.

        Data: The data bellow has 60 periods of the exchange rate of the US and the United Kingdom as per day. The data are the records of the respective countries as shown on daily basis excluding Saturday and Sunday

Jul.Day YYYY/MM/DD Wdy GBP/USD   
2456295 2013/01/02 Wed 0.61523
2456296 2013/01/03 Thu 0.61918
2456297 2013/01/04 Fri 0.62360
2456300 2013/01/07 Mon 0.62192
2456301 2013/01/08 Tue 0.62349
2456302 2013/01/09 Wed 0.62396
2456303 2013/01/10 Thu 0.62020
2456304 2013/01/11 Fri 0.62002
2456307 2013/01/14 Mon 0.62204
2456308 2013/01/15 Tue 0.62158
2456309 2013/01/16 Wed 0.62468
2456310 2013/01/17 Thu 0.62539
2456311 2013/01/18 Fri 0.62992
2456314 2013/01/21 Mon 0.63199
2456315 2013/01/22 Tue 0.63049
2456316 2013/01/23 Wed 0.63103
2456317 2013/01/24 Thu 0.63339
2456318 2013/01/25 Fri 0.63296
2456321 2013/01/28 Mon 0.63756
2456322 2013/01/29 Tue 0.63495
2456323 2013/01/30 Wed 0.63324
2456324 2013/01/31 Thu 0.63073
2456325 2013/02/01 Fri 0.63519
2456328 2013/02/04 Mon 0.63548
2456329 2013/02/05 Tue 0.63894
2456330 2013/02/06 Wed 0.63883
2456331 2013/02/07 Thu 0.63650
2456332 2013/02/08 Fri 0.63242
2456335 2013/02/11 Mon 0.63828
2456336 2013/02/12 Tue 0.63887
2456337 2013/02/13 Wed 0.64338
2456338 2013/02/14 Thu 0.64509
2456339 2013/02/15 Fri 0.64444
2456343 2013/02/19 Tue 0.64805
2456344 2013/02/20 Wed 0.65361
2456345 2013/02/21 Thu 0.65524
2456346 2013/02/22 Fri 0.65551
2456349 2013/02/25 Mon 0.66179
2456350 2013/02/26 Tue 0.66118
2456351 2013/02/27 Wed 0.66078
2456352 2013/02/28 Thu 0.65832
2456353 2013/03/01 Fri 0.66527
2456356 2013/03/04 Mon 0.66302
2456357 2013/03/05 Tue 0.66242
2456358 2013/03/06 Wed 0.66508
2456359 2013/03/07 Thu 0.66529
2456360 2013/03/08 Fri 0.66999
2456363 2013/03/11 Mon 0.67129
2456364 2013/03/12 Tue 0.67182
2456365 2013/03/13 Wed 0.67004
2456366 2013/03/14 Thu 0.66440
2456367 2013/03/15 Fri 0.66077
2456370 2013/03/18 Mon 0.66189
2456371 2013/03/19 Tue 0.66147
2456372 2013/03/20 Wed 0.66083
2456373 2013/03/21 Thu 0.65880
2456374 2013/03/22 Fri 0.65625
2456377 2013/03/25 Mon 0.65859
2456378 2013/03/26 Tue 0.65983
2456379 2013/03/27 Wed 0.66181
Jul.Day YYYY/MM/DD Wdy USD/GBP
2456295 2013/01/02 Wed 1.6254
2456296 2013/01/03 Thu 1.6150
2456297 2013/01/04 Fri 1.6036
2456300 2013/01/07 Mon 1.6079
2456301 2013/01/08 Tue 1.6039
2456302 2013/01/09 Wed 1.6027
2456303 2013/01/10 Thu 1.6124
2456304 2013/01/11 Fri 1.6128
2456307 2013/01/14 Mon 1.6076
2456308 2013/01/15 Tue 1.6088
2456309 2013/01/16 Wed 1.6008
2456310 2013/01/17 Thu 1.5990
2456311 2013/01/18 Fri 1.5875
2456314 2013/01/21 Mon 1.5823
2456315 2013/01/22 Tue 1.5861
2456316 2013/01/23 Wed 1.5847
2456317 2013/01/24 Thu 1.5788
2456318 2013/01/25 Fri 1.5799
2456321 2013/01/28 Mon 1.5685
2456322 2013/01/29 Tue 1.5749
2456323 2013/01/30 Wed 1.5792
2456324 2013/01/31 Thu 1.5855
2456325 2013/02/01 Fri 1.5743
2456328 2013/02/04 Mon 1.5736
2456329 2013/02/05 Tue 1.5651
2456330 2013/02/06 Wed 1.5654
2456331 2013/02/07 Thu 1.5711
2456332 2013/02/08 Fri 1.5812
2456335 2013/02/11 Mon 1.5667
2456336 2013/02/12 Tue 1.5653
2456337 2013/02/13 Wed 1.5543
2456338 2013/02/14 Thu 1.5502
2456339 2013/02/15 Fri 1.5517
2456343 2013/02/19 Tue 1.5431
2456344 2013/02/20 Wed 1.5300
2456345 2013/02/21 Thu 1.5262
2456346 2013/02/22 Fri 1.5255
2456349 2013/02/25 Mon 1.5111
2456350 2013/02/26 Tue 1.5125
2456351 2013/02/27 Wed 1.5134
2456352 2013/02/28 Thu 1.5190
2456353 2013/03/01 Fri 1.5032
2456356 2013/03/04 Mon 1.5083
2456357 2013/03/05 Tue 1.5096
2456358 2013/03/06 Wed 1.5036
2456359 2013/03/07 Thu 1.5031
2456360 2013/03/08 Fri 1.4926
2456363 2013/03/11 Mon 1.4897
2456364 2013/03/12 Tue 1.4885
2456365 2013/03/13 Wed 1.4925
2456366 2013/03/14 Thu 1.5051
2456367 2013/03/15 Fri 1.5134
2456370 2013/03/18 Mon 1.5108
2456371 2013/03/19 Tue 1.5118
2456372 2013/03/20 Wed 1.5132
2456373 2013/03/21 Thu 1.5179
2456374 2013/03/22 Fri 1.5238
2456377 2013/03/25 Mon 1.5184
2456378 2013/03/26 Tue 1.5155
2456379 2013/03/27 Wed 1.5110

 

        Methodology: Methodology is the method or methods that apply in computing the data (Hawawini, 2011, 39). This is actually to give meaning to the data that has been collected and arranged in a particular manner. This report will apply several methodologies to analyze the data by at the end to use t – test and finally international Fisher’s equation. The analysis will involve the calculation of mean, variance, standard deviation, which enables arriving at the t – test. The analysis of the data is as follows:

Taking the data to be unpaired and running the t – test, the results are as follows (Hawawini, 2011, 39)

t-test (Z)

Z =

 

t= -159.
sdev= 0.313E-01
degrees of freedom =118

The probability of this result, assuming the null hypothesis, is less than .0001

Group A: Number of items (n) = 60

0.615 0.619 0.620 0.620 0.622 0.622 0.622 0.623 0.624 0.624 0.625 0.625 0.630 0.630 0.631 0.631 0.632 0.632 0.633 0.633 0.633 0.635 0.635 0.635 0.636 0.638 0.638 0.639 0.639 0.639 0.643 0.644 0.645 0.648 0.654 0.655 0.656 0.656 0.658 0.659 0.659 0.660 0.661 0.661 0.661 0.661 0.661 0.662 0.662 0.662 0.662 0.663 0.664 0.665 0.665 0.665 0.670 0.670 0.671 0.672

Mean () = summation of data/data size = 38.67831/60 = 0.645

Mean () = 0.645
95% confidence interval for Mean: 0.6366 thru 0.6526

Variance of the data = 0.000287

Standard Deviation = √variance

Standard Deviation = 1.694E-02
High = 0.672                 Low = 0.615
Median = 0.641
Average Absolute Deviation from Median = 1.524E-02

Group B: Number of items (n) = 60
1.49 1.49 1.49 1.49 1.50 1.50 1.50 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.52 1.52 1.52 1.52 1.52 1.53 1.53 1.53 1.54 1.55 1.55 1.55 1.57 1.57 1.57 1.57 1.57 1.57 1.57 1.57 1.57 1.58 1.58 1.58 1.58 1.58 1.58 1.59 1.59 1.59 1.60 1.60 1.60 1.60 1.60 1.61 1.61 1.61 1.61 1.61 1.61 1.63

Mean () = summation of data/data size = 93.139 /60 =1.55

Mean = 1.55

This mean is on the assumption that the used data sampled randomly and independently.
95% confidence interval for Mean: 1.544 thru 1.560, as calculated

Variance = 0.001666, as calculated

Standard Deviation = √variance
Standard Deviation = 4.082E-02, as calculated
High = 1.63                   Low = 1.49
Median = 1.56
Average Absolute Deviation from Median = 3.668E-02

International Fisher’s Equation

 

E(e) = (i$ – ic)/(1 + ic) = i$ – ic

 

Rearranging this equation gives

E(e) = (1 + i$)/(1 + ic) – 1 = i$ – ic

E(e) –  the expected rate of change in the exchange rate

i$ – nominal interest rate

ic – real interest rate

 

Spot exchange between United States and United Kingdom is 1.55 USD/GPB, as calculated

US interest rate as per now = 4, as calculated

U.K interest rate as per now = 6%, as calculated

From the given data we can estimate the expected spot change rate in 12 months from now according to International Fisher’s effect (Wang Peijie, 2009, 321)

From the equation: E(e) = (1 + i$)/(1 + ic)  =   (1 + 4%)/(1 + 6%) = 0.981

1.55* 0.981 = 1.521

Rearranging the equation and performing the calculations

E(e) = (4% – 6%)/(1 + 6%) = -0.017632

E(e) = ((1 + 4%)/(1 + 6%)) – 1 = -0.01762

From the two calculations, the percentage is -1.7632%. (Wang Peijie, 2009, 276)

       Analysis:  From the methodologies, calculations of means are on the assumption that the used data are sampled randomly and independently. This assumption gives the confident interval for the mean of 95% by many sampled data. The calculations are done on the unpaired groups of data. The difference in their means is then taken into account on how far apart are the differences. The confident interval is 95% as in the methodology, which shows that the assumptions are true, and gives how far the means of the data are.

From the international Fisher’s equation, the expected percentage rate of change is a depreciation of 1.7632% as it gives a negative result from the calculation. That is, the expected rate of change yields the same values of -1.7632% (Wang Peijie, 2009, 213). This depreciation is for the GBP of the country with higher interest rate as compared to the other country (Wang Peijie, 2009, 213). It shows that the cost of purchasing $ per 1GBP is now only 1.521 rather than 1.55 as it was calculated before. This shows that the value of the currency of the country that has higher interest rate will depreciate. This shows that International fisher’s equation holds (Wang Peijie, 2009, 418).

Conclusion

From the analysis, it is true that International Fisher’s equation holds. This shows that the country with the high interest rate will actually have the depreciation. The report has proved this from the analysis of the ample data. These results may change if there are some changes within the data. The methodologies hold as long the there are consistent in how the data occurs. These changes may be because of the factors that come with immediate changes may be in economy. This leads to immediate change in the interest rate, which will affect the entire calculation. Otherwise, the prediction of the calculations as shown holds for any data collected. The analysis of the data using statistical methods gives the way to enable arriving at the right conclusion over the particular data.

Therefore, from the calculations, the GBP of the country has been seen to go higher depending on the interest rate. The higher interest rate therefore needs to be controlled to prevent the country from form having inflation. Inflation in this case, will mean that the county’s economy is down.

 

 

Works Cited

Hawawini, Gabriel A, and Claude Viallet. Finance for Executives: Managing for Value   

            Creation. Mason, Ohio: South-Western Cengage Learning, 2011. Print.

Munro, Barbara H. Statistical Methods for Health Care Research. Philadelphia: Lippincott

Williams & Wilkins, 2005. Print.

Wang, Peijie. The Economics of Foreign Exchange and Global Finance. Berlin: Springer-

Verlag, 2009. Internet resource.

 

Appendices

Unpaired data:  data, which are not corresponding in accordance to collection

 Period:  the number of times the data occurs

Data:   raw facts that has not been analyzed to give the information

Methodology:  the method applied to analyze the data

Depreciation:  the decrease of something downwards not as it is expected

Equation:  an expression that is used to analyze certain problem mathematically

Hypothesis:  answers of the objectives of what is intended to be achieved

Null hypothesis:  hypothesis, which is not positive