Foreign Exchange Rate Distribution And Forecasting: Analysis And Risk Assessment

Evaluation of the Distribution Method for USD/ AUD and Graphical Representation of its Return

The aim of this particular study is to portray the importance of forecasting that can be used by the investors in order to help them in making decisions regarding investment. Moreover, it has been noted that this specified study helps in the evaluation of various kinds of models regarding forecasting that might help the investors in increasing the total return from their overall amount of investment. In addition to these, it can also be said that the particular study also guides to understand the comparison between the return which is created from USD/ AUD along with the method of normal distribution. Additionally, the implementation of the process of evaluation helps the novice to understand the present trend in the USD/ AUD efficiently and effectively in order to depict the decision regarding investment that can be adopted by most of the customers for increasing their total return amount (Gomes et al. 2013). In addition to this, the novice has used the data of the year 2003 for creating an accurate and authentic outcome. This might be useful for the novice to understand the trend of return distribution of USD/ AUD.      

Evaluation of the Distribution Method for USD/ AUD and Graphical Representation of its Return:     

Figure 1: The Continuous Return of USD/ AUD that Generated from the Year 2003 till Today

(Source: Created by Author)

The above graph indicates that the entire spontaneous return that has been given by USD/ AUD from the data and information of the year 2003 till present day. In addition to this, after the analysis of the entire figures it can be said that the USD/ AUD has a special type of approach for distribution that is known as non-symmetric approach of distribution. According to Okawa and Van Wincoop (2012), the return of stock is primarily considered as non-symmetric. Moreover, this stock return can also be counted as the basic rule for supply and demand that is able to lose its friction for the determination of the stock prices. Therefore, it can be said that the return offered by the USD/ AUD does not tracks the system of normal distribution. On the contrary, Mundy and Menashy (2014) stated that some of the inexperienced investors still use the statistical method of distribution for the identification of the opportunities within the share market that primarily raises the entire risk from the term of investment.      

Providing Evidence for the Distribution Method of the USD/ AUD by using the Normal Thumb Rule of 68-95-99.7:

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Mean Value	-0.00849959
Value of Standard Deviation	0.84263895
Normal Rule of Thumb	From	To	Total Numbers of observations
At 68% of the rule	-0.8511385	0.834139353	2588
At 95% of the rule	-1.6937775	1.676778299	666
At 97.7% of the rule	-2.5364164	2.519417245	109
		Total	3363

Table 1: Illustrating the Return Distribution of USD/ AUD by Using the Normal Thumb Rule of 68-95-99.7

(Source: Created by Author)

The above provided table primarily guides the novice to depict and also to compare the distribution of the return that has been provided through USD/ AUD. In addition to this, the above particular table is also useful for portraying the several numbers of observations which lies underneath the distribution of normal thumb rule of 68-95-99.7. Moreover, it has been found that about 2632 observations are under the rule of 68 %, around 636 observations are under the rule of 95 % and only 97 observations are under the rule of 97.7 %. Nevertheless, the overall value that has been used by the particular thumb rule of normal distribution is found to be 3363. This specified value is relatively lesser than the total numbers of observations that have been used during the calculations i.e. 3406. In addition to these, this specified evidence is considered as sufficient for understanding the concept and method of normal distribution that is the method of normal distribution is not implemented to the distribution of return which is offered by USD/ AUD. Moreover, the particular thumb rule of normal distribution i.e. 68-95-99.7 normal thumb rule primarily distributes the information and data in the range, whether it has the characteristics of normal distribution or not. It has been found that as per Kalinowski (2012), the irregular distribution of return primarily helps the investors for using the growth model. This growth model helps in reducing the risk percentage from the total return. Opined to Tyson, Te Velde and Griffiths-Jones (2014), the return from the stock market is counted as predetermined than the entire trust of the investors that could be deduced and can also affect the capital market’s liquidity.     

Providing Evidence for the Distribution Method of the USD/ AUD by using the Normal Thumb Rule of 68-95-99.7

Analysis of the Graphical Differences between the Artificially Created and Actual Returns:

Figure 2: Portraying the Differences between Artificial and Continues Returns

(Source: Created by Author)

The above graph indicates the difference between the actual and continuous return that is offered by the USD/ AUD from the data and information from the year 2013 till the present day. Moreover, the spontaneous compound return primarily helps to give enormous calculations of the return which is developed from a specified stock. Additionally, Isard, Razin and Rose (2012) stated that the spontaneous method of return primarily uses the LN function that is used in the particular stocks that have high beta in order to evaluate the overall return and the risks that are created due to volatility. Nevertheless, the normal return provides value based on the probability. It has been found that the relatively smaller investors evaluate the change percentages in the prices of certain shares that use the method of calculating cumulative return. On the contrary, Chi?u, Eichengreen and Mehl (2014) stated that most of the investors use the calculation of return on the basis of its own awareness that raises the exposure to risk in their portfolio.

Portraying the Current Trend of USD/ AUD and Preparing Effective Strategies of Trading:

Figure 3: Portraying the Current Trend of USD/ AUD

(Source: Created by Author)

The above graph indicates the entire movement of price of USD/ AUD from the year 2003 till present day. These data and figures generally help to evaluate the entire strategies that might be used for making enormous investment for next 30 days. Opined to Dincer and Eichengreen (2012), the investors primarily use the historical prices for evaluating the entire trend of the stock market and also to make a decision regarding an enormous amount of investment. In addition to these, the mean has been found to be -0.008499593 and the Standard Deviation (SD) have been found to be 0.84263895. These values primarily help to depict that the trend of USD/ AUD is currently a downtrend.  

Use of Adequate Hypothesis for Testing the Investment Decisions for Next 30 Days:

Statistics of Regression
Multiple R	0.308344642
R Square	0.095076418
Adjusted R Square	0.062757719
Standard Error	0.011841204
Interpretations	30

ANOVA CALCULATIONS
	df	SS	MS	F	Significance F
Regression	1	0.000412487	0.000412	2.941839	0.097361
Residual	28	0.003925995	0.00014
Total	29	0.004338483
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1.3348033	0.002171362	614.7309	2.24E-59	1.330355	1.339251	1.330355	1.339251
X Variable 1	0.005799303	0.003381165	1.715179	0.097361	-0.00113	0.012725	-0.00113	0.012725

Table 2: Portraying the Calculation of Hypothesis for Analyzing the Trend of USD/ AUD

(Source: Created by Author)

This above table primarily helps in identifying the hypotheses calculation that is used for making sufficient decisions regarding investment. In addition to this, the entire hypotheses calculations primarily help to depict the initiation of the Sell Side traders that can be conducted by the investors. Moreover, the valuation of the entire hypotheses is conducted based on the previous 30 days in order to determine the opportunities in the short run period. This process is generally used by the investors. Additionally, the standard error has been found to be 0.011841204 that indicates the continuation of the downtrend in the USD/ AUD. Opined to Gray and Richard (2014), these hypotheses primarily help the investors in making several assumptions that might decrease the probability of risks from the investments.

Analysis of the Graphical Differences between the Artificially Created and Actual Returns

1. Prompting the Efficiency of FX Market through Random Walk Model and Autoregressive of Order 1 Model:      

The spontaneous return that is offered by the FX market can be evaluated efficiently from various types of return calculations and hypotheses. In addition to these, after the evaluation of the continuous return that developed from the data of the year 2003 to present days, it can be conducted that there are no important return provided to the investors. It has been found that the FX market does not have much fluctuation that might affect the return directly that is provided from various currencies. Moreover, with the help of ‘Random Walk Model’ and ‘Autoregressive of order 1 model’ the investors derive the movement of future price of USD/ AUD effectively. In addition to this, the “Autoregressive of order 1 model” primarily adds value and intercept that can be multiplied effectively with the closing price of the present day. As per Shim and Constas (2016), the methodology of forecasting primarily helps in identifying the future trends that might help to reduce the entire risk of the investment.

2.

Evaluation of Best Model that can be implemented for Forecasting the Future:

Evaluating Random Walk Model

Random Walk Model	MSE	RMSE	MAE
0.00042	0.020390349	0.0180
Period	A	F	Abs	SQ error	Error(A-F)
7/15/2016	1.311303	1.313400178	0.00209674	4.39633E-06	-0.0020967
7/18/2016	1.315789	1.312912562	0.00287691	8.27662E-06	0.00287691
7/19/2016	1.328198	1.312424945	0.01577269	0.000248778	0.01577269
7/20/2016	1.333156	1.311937329	0.02121825	0.000450214	0.02121825
7/21/2016	1.335648	1.311449713	0.02419874	0.000585579	0.02419874
7/22/2016	1.337614	1.310962097	0.0266516	0.000710308	0.0266516
7/25/2016	1.336005	1.310474481	0.02553086	0.000651825	0.02553086
7/26/2016	1.329257	1.309986864	0.01927008	0.000371336	0.01927008
7/27/2016	1.336541	1.309499248	0.02704178	0.000731258	0.02704178
7/28/2016	1.328904	1.309011632	0.01989202	0.000395693	0.01989202

Table 3: Portraying the Method of Forecast – Random Walk Model

(Source: Created by Author)

Evaluating Autoregressive of order 1 model

Autoregressive of order 1 model	RMSE	MAE	MSE
0.026483887	-0.0258	0.00070
Period	A	F	SQ error	Abs	Error(A-F)
7/15/2016	1.311303436	1.340891409	0.000875448	0.029587973	-0.029587973
7/18/2016	1.315789474	1.338253936	0.000504652	0.022464462	-0.022464462
7/19/2016	1.328197636	1.342832173	0.00021417	0.014634537	-0.014634537
7/20/2016	1.333155579	1.355495353	0.000499065	0.022339774	-0.022339774
7/21/2016	1.335648457	1.360555194	0.000620346	0.024906737	-0.024906737
7/22/2016	1.337613697	1.363099307	0.000649516	0.02548561	-0.02548561
7/25/2016	1.336005344	1.365104937	0.000846786	0.029099593	-0.029099593
7/26/2016	1.329256945	1.363463529	0.00117009	0.034206583	-0.034206583
7/27/2016	1.336541032	1.356576434	0.000401417	0.020035402	-0.020035402
7/28/2016	1.328903654	1.364010226	0.001232471	0.035106572	-0.035106572

       
Table 4: Portraying the Method of Forecast – Autoregressive of order 1 model

(Source: Created by Author)

Both of these above tables i.e. Table 3 and Table 4 primarily helps to depict the methods of forecast – ‘Random Walk Model’ and ‘Autoregressive of order 1 model’ respectively. These particular models can be used for forecasting the trends of the future regarding USD/ AUD. Moreover, the “Autoregressive of order 1 model” has a negative MAE, so this can affect the entire process of future forecasting regarding USD/ AUD. However, it can be said that the “Random walk model” is considered as the most accurate or appropriate model for forecasting the future as it has a positive effect and positive values regarding RMSE, MAE and MSE. In addition to these, during the period of calculating the variance between the actual prices and the forecasted prices, it has been noted that primarily the RWM has depicted the nearest prediction value that might be used for the generation of higher return from the investment. Opined to Cafaggi and Miller (2013), due to the spontaneous volatility, it has been found that the forecasted prices generally depict the entire trend that in turn raises the risk probability of the investors.

Risk Assessment and Implications for the Investment on Daily Basis

Particulars	Value ($)
Value of Portfolio	1000000
Average Return	-0.037383246
Standard Deviation	0.000405447
Level of Confidence	0.99
Calculations
Min Return with 99% probability	-0.038326457
Portfolio Value	961673.5430
Value at Risk	38326.4570
Percentage Risk	3.83%

Table 5: Evaluation of Investment Risk – The Parametric Method

(Source: Created by Author)

The above table represents the calculation of parametric method by help of which the total amount of risk from the investment has been calculated and it is represented as $38326.4570. This particular type of method primarily implies that its implementation will result into 3.83 % of risk in terms of investment of around 1 million USD. Therefore, it can be said that the volatility of the financial market might increase the entire risk implications for the subsequent 90 days. Moreover, Philippon and Reshef (2013) stated that during the economic crisis, the forecasted prices might lose its friction and can also enhance the probability of risk regarding the entire portfolio.

Figure 5: Evaluation of Investment Risk – Historical Method

(Source: Created by Author)

Moreover, the above graph implies that the particular method of historical simulation is very useful for analyzing the investment risk effectively. In addition to this, it has been found that the entire risk lies within the range of 0.08909734 to 0.091654614. This range effectively depicts that both the minimum and maximum return can be developed from the investment of an amount of 1 million USD. Additionally, it can also be said that the maximum risk lies within the range of -0.009408956 to 0.018153836 that might affect the entire investment risk of an amount of 1 million USD.

Conclusion

Therefore, it can be concluded that this particular study primarily helps in the process of evaluation of various kinds of investment strategies that can be used by the investors in order to make several decisions regarding investment. Moreover, it has been found that the Random Walk Model is considered as the accurate method for forecasting that might be used by the investors for making several decisions regarding investment. Additionally, it has been depicted that the entire risk evaluation could be organized through both historical and parametric simulation method. Finally, this study also depicts the present trend of USD/ AUD by using the hypothesis and harmonic method.   

References

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Okawa, Y. and Van Wincoop, E., 2012. Gravity in international finance.Journal of international Economics, 87(2), pp.205-215.

Mundy, K. and Menashy, F., 2014. Investing in private education for poverty alleviation: The case of the World Bank’s International Finance Corporation.International Journal of Educational Development, 35, pp.16-24.

Tyson, J., Te Velde, D. and Griffiths-Jones, S., 2014. Current and Future Trends In International Finance To Developing Countries. London: ODI.

Kalinowski, T., 2012. Regulating international finance and the diversity of capitalism. Socio-Economic Review, p.mws023.

Isard, P., Razin, A. and Rose, A.K. eds., 2012. International finance and financial crises: essays in honor of Robert P. Flood, Jr. Springer Science & Business Media.

Chi?u, L., Eichengreen, B. and Mehl, A., 2014. History, gravity and international finance. Journal of International Money and Finance, 46, pp.104-129.

Dincer, N.N. and Eichengreen, B., 2012. The architecture and governance of financial supervision: Sources and implications. International Finance, 15(3), pp.309-325.

Gray, H.P. and Richard, S.C. eds., 2014. International finance in the new world order. Elsevier.

Shim, J.K. and Constas, M., 2016. Encyclopedic dictionary of international finance and banking. CRC Press.

Cafaggi, F. and Miller, G.P., 2013. The governance and regulation of international finance. Edward Elgar Publishing.

Philippon, T. and Reshef, A., 2013. An international look at the growth of modern finance. The Journal of Economic Perspectives, 27(2), pp.73-96.