# The Rupee-Dollar Equation

•  BY CFOIndia
• In OPINIONS
•  Feb 28, 2015
•  3731
•  0

Through the use of a mathematical and a statistical model it is possible to predict the value of the Indian rupee against the US dollar up to 80 per cent accuracy. And the model can be refined further. In the following pages, I have analyzed data for the US dollar and Indian rupee over the last 33 years, from 1980 onwards with respect to seven factors. These include lending rates, inflation, growth rate, consumption of crude oil, current account deficit (CAD) as a percentage of Gross Domestic Product (GDP), per capita income (PCI) and foreign direct investment (FDI).

## Building the mathematical model

The mathematical model was built by calculating the differential percentage of each of these determinants which has bearing on the two countries’ exchange rate. Where the determinants were not available as percentages, for instance crude oil consumption, the figure to use was worked out as a difference in proportion. For instance, if the proportion of India’s consumption of crude relative to US consumption of crude did not change, the figure to use was zero per cent. Depending on whether there was a direct or inverse relationship with the exchange rate, a positive or negative sign is assigned to them.

[image_library_tag 45409af2-e211-4b54-983c-4829475f7913 200x821 alt=" uilding the mathematical model for longterm exchange rates" width="200" border="0" ]Building the mathematical model for long-term exchange rates A simple arithmetic addition of these led to the figure of total impact of all variables with respect to the rupee or the dollar. Again an appropriate sign was assigned. The multiplier was arrived at by simply deducting the total impact number from 100. When this multiplier was applied to the previous year’s exchange rate, we got the theoretical exchange rate for the relevant year.

When the theoretical exchange values so calculated from 1980 to 2013 were plotted against the actual exchange rate, it was an amazing to note that a clear trend of exchange rate movement was visible and there was near perfect correlation. To my mind, this mathematically confirmed the impact that the aforesaid seven variables have on exchange rate.

It interesting to note that the weightage of each factor may vary in the short-term and the long-term.

In short-term as well as the long-term, it seems the differential in interest rates has maximum weight.

In the long-term inflation ranks second in terms of weight whereas in the short-term growth ranks second most important factor influencing exchange rate. This indicates that growth has emerged in the short-term period, especially post-1991 when the forces of liberalisation, privatisation and globalisation were unleashed. This indicates a positive healthy sign for India.

In the short-term, inflation and current account deficit as a percentage of GDP follow next. Ranking of all other factors remains the same.

There are several other non quantifiable variables such as government confidence, political stability, acts of God etc. which cannot be quantified. Similarly, RBI intervention too cannot be predicted. The closed Indian economy from 1980 to 1991 does not offer much by way of a test of this model.

## Building the regression model

In 1991 the economy was liberalised significantly. It is only from 2000 onwards that market factors could determine the exchange rate more freely and the short-term trend became more relevant.

Hence, as a test of the mathematical model, a regression analysis was done on the data that existed from 2000 onwards to test the degree of dependency of the exchange rate on these changing variables. Regression is a statistical measure that attempts to determine strength of the relationship between one dependent variable and a series of other changing variables

The results were fabulous and very close to the actual exchange rates. A 90 per cent correlation and 82 per cent dependency of the exchange rate was observed. When the regression values were plotted against the actual values, the regression plot was seen to be closer than the mathematical model.

One of the benefits of regression is that we get a linear equation where we can calculate the exchange rate with a multiplier constant for each variable. Past data shows that the values that emerge for the rupee versus the US dollar from the mathematical model built on the differences between the seven factors, are closely aligned to the real-world exchange rate By plotting the values obtained from both the mathematical and regression models, it is clearly established that there is a substaintial correlation between these seven factors and the exchange rate values

## Forecasting

The analysis of past data confirmed that the exchange rate is dependent by more than 80 per cent on the differentials between the seven variables of the two countries. Using the mathematical and statistical models also allowed for an understanding to emerge that the combined model can be used on live data, perhaps with greater frequency of time period.

Making assumptions about these variables allows us to do scenario analysis. A representative section of the results obtained by the mathematical model and regression analysis are shown on the next page on the basis of some assumptions. For instance, here it is assumed that the interest rates in India will go down while the interest rates in the US will go up.

Again we got surprising dependency and correlation.Therefore, my short conclusions are as follows:

. It is clear that the exchange rate relative to the US dollar of a nation such as India is clearly affected by the seven factors identified by us. And the dependence can be as high as 82 per cent.

. Other factors such as political stability will always be a strong determinant, but these cannot be predicted.

. In 2015 rupee is going to depreciate basis our assumptions.

. From 2016 onwards, it will reverse the trend and start appreciating till 2018, if our assumptions hold true.

. Short-term parameters may lead to around five per cent variation based on regression values. (Standard deviation of five per cent on both sides should be considered for the forecasted values). By assuming certain trends to the seven factors, it is possible to come up with reasonable forecasts for the value of the rupee versus the US dollar in times to come

This forecast is based on assumptions. Hence, it is to be expected that if we change the assumptions, we will get different results.

We can also figure out how by changing one factor the exchange rate will be affected. This, I suppose, will provide a unique and perhaps different view to evaluate the forex movements.

Some disclosures: The forecasts provided in these pages are on the basis of assumptions made in the November-December, 2014 period.

Now, say India’s current account deficit becomes positive to say 6 per cent and interest rates go down to say, again 6 per cent in the next two years or say growth gallops to 9-10 per cent then the predictions I make can come true on the basis of the model described.

I would encourage the finance fraternity to test this model on the basis of their assumptions as well. Similarly, using assumptions for the regression equation too yields credible values for the rupee value

They could perhaps also adjust for the non-quantifiable factors such as government stability etc. by giving marks (say -5 to 5) and then assign the remaining weightage of roughly 20 per cent to these factors.

I am firmly of the view that by following this process, we can arrive at a reasonable prediction. Since we have tested this on multiple sets of data with both, mathematical and regression models, I am willing to say that the rupee will depreciate slightly in 2015 and from then onwards stabilise.

Subsequently, there may well be a reversal of trend towards appreciation as well, if all assumptions hold.

Since both the mathematical model and the statistical model are tested on actual past data, I suppose, I can safely conclude that both the models work.

I hope that this model will help us take decisions more objectively, logically and rationally. It is my hope that we can use them as forecasting tools.