Econometric Forecasting of Short term Interest Rates in India
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![Financial Econometric<br />Forecasting the Short term yield & finding its dependence on the Macro factors 2011Submitted To :Dr. Kakali KanjilalProfessorIMT GhaziabadIMT Ghaziabad<br />Institute Of Management Technology, Ghaziabad<br />Project Report <br />Financial Econometrics<br />Under the guidance of Dr.Kakali Kanjilal, Professor<br /> IMT - Ghaziabad<br />Submitted By:<br />Sumit Chugh (10DCP-042)<br />Vatan Lunia (10DCP-046)<br />Akash Jauhari (10DCP-056)<br />Alok Mishra (10DCP-057)<br />Ankit Bhardwaj (10DCP-060)<br />Raghav Agarwal (10DCP-087) <br />Table of Contents TOC quot;
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1. Abstract PAGEREF _Toc303550173 32. Introduction: Short term T-bill yields in India PAGEREF _Toc303550174 42.1 Fluctuations in Security yields PAGEREF _Toc303550175 53. Data PAGEREF _Toc303550176 54. Methodology PAGEREF _Toc303550177 65. Linear regression Models PAGEREF _Toc303550178 65.1 Short term yield dependent on Macro Factors PAGEREF _Toc303550179 75.2 Short term yield dependent on growth variables PAGEREF _Toc303550180 85.3 Short term yield dependent on Macro factors-with Differencing PAGEREF _Toc303550181 115.4 Reverse Model – M3 on interest rates -with Differencing PAGEREF _Toc303550182 135.5 Reverse Model: WPI Growth dependent on Short term yield & Repo rate PAGEREF _Toc303550183 156. ARIMA Models…………………………………………………………………………………………………………………….…16 6.1 ARIMA for Log-Short term yield data………………………………………………………………………………...16 6.2 ARIMA output for Log-short term yield - with trend differencing…………………………….…………17 6.3 ARIMA output for Log-short term yield - with seasonal differencing…………………………………..186.4 Forecasting ARIMA for Log- Short term Yield PAGEREF _Toc303550184 207. Key findings and Conclusion PAGEREF _Toc303550185 21<br />1. Abstract<br />Key words: Short term yields, Linear Regression, ARIMA modeling<br />Interest rate is a key economic indicator for a country. It affects bank lending rates, foreign investments, exchange rates and stock returns. In a fast growing economy like India, appropriate interest rates are even more important as they are a vital balance between money supply, inflation and growth. However Indian 91 day T-bill yields have been quite volatile in past few years, stretching from a high of 9.1% in August 2008 to a low of about 3.2% in May 2009.<br />We attempt to understand the dependence of Short Term Yields on Macro factors and create a model to forecast yield, focusing on the 91-day T bill, based on Linear Multiple Regression and ARIMA modeling. We also intend to understand and study the reverse relationship i.e. any dependence of Macro factors like money supply and Inflation on the interest rates. Possible explanatory variables are – Repo rate, WPI, IIP, Money supply, Stock Indices, Global Oil prices, Exchange rate for rupee. Such a forecasting model can be decisive for banks and corporates in planning their operations as well as capital structure.<br />2. Introduction: Short term T-bill yields in India<br />Treasury Bills, which are money market instruments, are short term debt instruments issued by the Government of India and are presently issued in three tenors viz. 91 day, 182 day and 364 day. Treasury Bills are zero coupon securities and pay no coupon. They are issued at a discount and redeemed at the face value at maturity. For example, a 91 day Treasury Bill of Rs.100/- (face value) may be issued at a discount of say, Rs.1.80, that is Rs.98.20 and redeemed at the face value of Rs.100/-. The return to the investors is, therefore, the difference between the maturity value or face value (i.e., Rs.100) and the issue. Currently, the notified amount for issuance of 91 day and 182 day Treasury Bills is Rs.500 crore each whereas the notified amount for issuance of 364 day Bill is higher at Rs.1000 crore.<br />2.1 Fluctuations in Security yields<br />The price of a Government security, like other financial instruments, keeps fluctuating in the secondary market. The price is determined by demand and supply of the securities. Specifically, the prices of Government securities are influenced by the level and changes in interest rates in the economy and other macro-economic factors, such as, expected rate of inflation, liquidity in the market etc. Developments in other markets like money, foreign exchange, credit and capital markets also affect the price of the government securities. Further, developments in international bond markets, specifically the US Treasuries affect prices of Government securities in India. Policy actions by RBI (e.g. announcements regarding changes in policy interest rates like Repo Rate, Cash Reserve Ratio, Open Market Operations etc.) can also affect the prices of government securities.<br />Source: CMIE database.<br />,[object Object]](https://image.slidesharecdn.com/feprojectreport-110912035538-phpapp02/85/econometric-forecasting-of-short-term-interest-rates-in-india-1-320.jpg)
![Standard deviation of about 1.42 units considering data for Jan 2001 to Jun 2011.3. Data <br />,[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Econometric Forecasting of Short term Interest Rates in India
- 3. Short term yield: 91 day T-bill yield
- 4. WPI (Wholesale Price Index): Inflation
- 5. Money Supply (M-3, RBI data)
- 6. IIP (Index for Industrial Production)
- 7. Exchange Rate (Rs per $, average)
- 8. Repo rate (issued by RBI)
- 9. Oil Prices (WTI rate in $ per barrel)
- 10. Import & Exports for India (in million $)
- 11. Sensex (proxy for stock markets in India)
- 12. The period of data is from January 2001 to June 2011. Frequency of data taken is monthly average.
- 14. First we attempt to find the dependence of Short term yield on Macro factors like WPI, M-3 and Exchange rate etc. We used SAS for getting various outputs.
- 15. Based on the principles and issues of linear regression like autocorrelation, multi-co linearity, hetroscedasticity etc, we tried to improve our model at every step. Techniques like differencing, taking growth figures, log data were used.
- 16. Linear Regression: Reverse Model
- 17. We also tried to find any dependence of short term yield and Repo rate on Money supply and Inflation. Again linear regression though SAS was used.
- 18. ARIMA Modeling:
- 19. We tried to find out best estimated model based on Univariate ARIMA modeling. Based on the model we tried to forecast short term interest rates for next 20 months. Also to check our model we applied ex-post test on available data.
- 21. There is no hetroscedasticity, as P.0.79 and thus we accept the null hypothesis is absence of hetroscedasticity.
- 22. To improve the above model we go for –
- 23. Consider growth of variables WPI,IIP and Sensex
- 25. However, 5 of the 7 variables have become insignificant.
- 27. 1. The model is suffers from positive autocorrelation as the d value is very close to 0.
- 28. 2. Also there seems to be hetroscedasticity as we are rejecting hypothesis of absence of hetroscedasticity.
- 29. 3. To improve the model, we go for differencing.
- 30. Dependent Variable: Money Supply (M-3)
- 32. Both the independent variables are found to be insignificant.
- 34. There is a definite pattern in ACF, which shows presence of non stationary data.
- 35. Hence we apply trend differencing.
- 38. Also using Dickey Fuller test, we can say that data is now stationary.
- 39. Hence we can use this for forecasting. We will try to estimate the model through the ACF & PACF outputs.
- 40. ACF is declining exponentially and there is a spike in Non seasonal part of PACF above the X-axis. This indicates an AR – 1 component.
- 41. Also around 12, we find a spike in PACF on the seasonal part, which indicates a SAR – 1 component.
- 42. A MA-1 component as there is a spike in PACF on negative X-axis.
- 44. Hence we conclude that we do not find a substantial dependence of short term yields on Macro factors, for the given time period data.
- 45. This re-confirms the point that interest rates in India are highly regulated and are controlled by RBI and the Ministry of Finance.
- 46. Even the attempt to find the reverse dependence, i.e. of Macro factors like Money Supply and WPI on yields & repo rates, did not find any evidence of a strong relationship.
- 47. Applying Univariate ARIMA model to Short term yield, we found that there is some seasonality in the time series data, but no trend. The model was estimated to be (1,0,1)*(1,1,0).
- 48. Forecasted value show that short term yield to fluctuate between 8.15% and 9.5% for next twenty months, starting from July 2011.