TABLE OF CONTENTS Executive summary ………………………………………………………8 1. Project Profile …………………. …………………………………………9 2. Introduction……………………………………………………………… 10 3. Theoretical aspects………………………………………………………13 4. Review of the Literature …….. …………………………………….. ….. 16 5. Determinants of yield curve………………………………………….. …19 6. Analysis…………………………………………………………………. 31 7. Findings…………………………………………………………………. 37 8. Bibliography ……………………………………………………………. 38 9. Appendices ……………………………………………………………… 39 LIST OF FIGURES Figure 1: Time series of the yield of the treasury bills….. ………………. ………… 21 Figure 2: Time series of the Spread of the treasury bills…………………. …. ……….. 22 Figure 3: Time series of the yield of the treasury bills and WPI index…. ……………24 Figure 4: Relation between yield and GDP …………………………………. ……. …25 Figure 5: Relation between yield and SENSEX …………………………….. ………. 27 Figure 6: Relation between yield and PLR ………………………………….. ………. 27 Figure 7: Relation between yield and CALL RATE ………………………….. …….. 28 Figure 8: Relation between yield and GDP …………………………………….. ……29
Figure 9: Relation between yield and rupee per dollar …………………………………… 29 EXECUTIVE SUMMURY The purpose of this paper is to provide an overview of recent developments in Indian interest rate yield structure and to describe some of the major factors which have driven these developments. Short-term interest rates have emerged as the key indicators of the monetary policy stance all over the world. It is also recognized that stability in financial markets is critical for efficient price discovery and meaningful signaling.
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Since the interest rate and exchange rate are key prices reflecting the cost of money, it is particularly important for efficient functioning of the economy that they be market determined and easily observed. Central banks follow a variety of operating frameworks and procedures for signaling and implementing the monetary policy stance on a day-to-day basis, with a view to achieving the ultimate objectives ??? price stability and growth. In this paper, I have correlated different economic indicators with the rate of treasury bills.
I have taken the various indicators like T bill 91 days, 182 days, 384 days, real growth rate of GDP, Sensex, Net FIIs flows, call money, rate of rupee against dollar etc. Paper correlates the various economic indicators with the short term yield of the treasury yield. It identifies the effect of spurious error while applying the correlation and regression analysis. Paper finds that there is a presence of unit root in the time series, so simple regression is not a proper indicator for forecasting the interest rate.
It also proves that time series of Treasury bill is non stationary and finds the order of time series to make it stationary using Augmented Dicky Fuller test. 1. PROJECT PROFILE Project Name: Term Structure Of Interest Rate. Developed For:Asia Pacific Institute Of Management, New Delhi. Objective : To examine the usefulness of the slope of the yield curve as a predictor of domestic growth using a sample of the T bill of Indian economy. Prepared By:Manohar Jobanputra 2k72a21, PGDM (2007 – 09) Project Guide:Dr. Shrnivasan Shirur 2. Introduction
In the last two decades, international financial markets have integrated to an extent unprecedented in history. This process has profound implications for the transmission of shocks, both across financial asset prices and to the real economy. This year since January, US crisis have made a decreases a growth of both developed and developing countries. This paper investigates the extent to which the slope of the yield curve in Indian economy is related to the domestic factors and growth. Indian wholesale debt market plays a major role while deciding an interest rate.
The Indian bond market is a third largest in Asia. Some of the key reforms since 1992 include: ??? The auction system for trading of government securities ??? Primary dealer ship system in 1995 ??? The wholesale debt market has been set up to promote a transparency Over the time, the degree of monetization of deficits has fallen significantly, lowering the long term inflation expectation and increasing appetite for longer term paper. As in the developed debt market, the maturity profile of government debt has extended.
Further, norms and maturity profile of other money market instruments such has commercial paper and certificate of deposit has been modified to encouraged the participation. The RBI switched emphasis to setting a product limits on borrowing and lending in the CALL money market, encouraging migration towards the collateralized segment and developing derivative instrument for hedging market risk. The institutionalization of clearing corporation of India Ltd. as a central counter party has been undertaken. The upgrading of payment system technologies have also enabled market participants to improve their asset liability management.
In the Indian context, reforms in the monetary policy operating framework, which were initiated in the late 1980s crystallized into the Liquidity Adjustment Facility (LAF) in 2000 (Annex VI). Under the LAF, the Reserve Bank sets its policy rates, i. e. , repo and reverse repo rates and carries out repo/reverse repo operations, thereby providing a corridor for overnight money market rates After implementation of LAF in 2000, there is a better stability in a money market. Volatility in the market has been increased and it becomes more stable.
Figure shown below, indicates the steps taken by government as a monetary policy and their effect. In the Indian context, there are a few studies that have attempted to examine the determinants of interest rates. B B Bhattacharya, N R Bhanumurthy, Hrushikesh Mallick, have done a research on the possible indicators of the interest rate. They have forecasted the interest rate by using the single and multi variant models. They have said that the interest rates depend on both domestic and foreign factors by different short-term interest rates through the use of various time series models.
Following the literature, I have correlated different economic indicators with the rate of treasury bills. I have taken the various indicators like T bill 91 days, 182 days, 384 days, real growth rate of GDP, Sensex, Net FIIs flows, call money, rate of rupee against dollar etc. I have applied a simple regression and correlation between this variable and found that there is a evidence of spurious error while determining results. Due to the non stationary behavior of this time series, we can not forecast the interest rate by simple regression.
After that I have applied a augmented dicky fuller (ADF) to this time series and found that this time series is a non stationary. After applying unit root test, we can apply the cointegration model and also the different tnivariable and multivariable model of economic time series to forecast the interest. My report is limited upto unit root test only. DATA BASE: To study the interest rate, various indicators are considered, which are, T bill 91 days, 182 days, 384 days, real growth rate of GDP, Sensex, Net FIIs flows, call money, rate of rupee against dollar etc. hese data are collected from the handbook of statistic of RBI, yahoo finance. For correlation and regression annual data are taken from 1996 to 2007, while for ADF test monthly data for T bill ??? 91days and 364 days are taken from last 2003 to 2007. For yield spread, we consider the difference between domestic long-term yield and short-term yields. Methodology For investigating the behavior of interest rates in India, I have applied correlation and regression between different variables, and also applied augmented dicky fuller (ADF) to find out that there is a presence of unit root in this time series. . Theoretical aspects To find the time series is a stationary or not, Unit Root Test is used which is given below. Dickey-Fuller test In statistics, the Dickey-Fuller test tests whether a unit root is present in an autoregressive model. It is named after the statisticians D. A. Dickey and W. A. Fuller, who developed the test in the 1970s. A simple AR(1) model is yt = ? yt ? 1 + ut, where yt is the variable of interest, t is the time index, ? is a coefficient, and ut is the error term. A unit root is present if |? |??=??1. The model would be non-stationary in this case.
Naturally it would be even more non-stationary if |? |??? 1. The regression model can be written as ?yt = (? ? 1)yt ? 1 + ut = ? yt ? 1 + ut, where ? is the first difference operator. This model can be estimated and testing for a unit root is equivalent to testing ? =??0 (where ? =??? ???1). Since the test is done over the residual term rather than raw data, it is not possible to use standard t-distribution to as critical values. Therefore this statistic ? has a specific distribution simply known as the Dickey-Fuller table. There are three main versions of the test: 1. Test for a unit root: ?yt = ? t ? 1 + ut 2. Test for a unit root with drift: ?yt = a0 + ? yt ? 1 + ut 3. Test for a unit root with drift and deterministic time trend: ? yt = a0 + a1t + ? yt ? 1 + ut Each version of the test has its own critical value which depends on the size of the sample. In each case, the null hypothesis is that there is a unit root, ? =??0. The tests have low Statistical power in that they often cannot distinguish between true unit-root processes (? =??0), and near unit-root processes (? is close to zero). This is called the “near observation equivalence” problem. The intuition behind the test is as follows.
If the series y is (trend-)stationary, then it has a tendency to return to a constant (or deterministically trending) mean. Therefore large values will tend to be followed by smaller values (negative changes), and small values by larger values (positive changes). Accordingly, the level of the series will be a significant predictor of next period’s change, and will have a negative coefficient. If, on the other hand, the series is integrated, then positive changes and negative changes will occur with probabilities that do not depend on the current level of the series; in a random walk
There is also an extension called the augmented Dickey-Fuller test (ADF), which removes all the structural effects (autocorrelation) in the time series and then tests using the same procedure. Augmented Dickey-Fuller test In statistics and econometrics, an augmented Dickey-Fuller test (ADF) is a test for a unit root in a time series sample. It is an augmented version of the Dickey-Fuller test for a larger and more complicated set of time series models. The augmented Dickey-Fuller (ADF) statistic, used in the test, is a negative number.
The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence. The testing procedure for the ADF test is the same as for the Dickey-Fuller test but it is applied to the model [pic] where ? is a constant, ? the coefficient on a time trend and p the lag order of the autoregressive process. Imposing the contraints ? = 0 and ? = 0 corresponds to modelling a random walk and using the constraint ? = 0 corresponds to modelling a random walk with a drift.
By including lags of the order p the ADF formulation allows for higher-order autoregressive processes. This means that the lag length p has to be determined when applying the test. One possible approach is to test down from high orders and examine the t-values on coefficients. The unit root test is then carried out under the null hypothesis ? = 0 against the alternative hypothesis of ? ; 0. Once a value for the test statistic is computed it can be compared to the relevant critical value for the Dickey-Fuller Test.
If the test statistic is greater (in absolute value) than the critical value, then the null hypothesis of ? = 0 is rejected and no unit root is present. 4. A REVIEW OF THE LITERATURE Fisher Effect The relationship between interest rates and inflation, first put forward by Fisher (1930), postulates that the nominal interest rate in any period is equal to the sum of the real interest rate and the expected rate of inflation. This is termed the Fisher Effect. Fisher (1930) hypothesized that the nominal interest rate could be decomposed into two components, a real ate plus an expected inflation rate. He claimed a one-toone relationship between inflation and interest rates in a world of perfect foresight, with real interest rates being unrelated to the expected rate of inflation and determined entirely by the real factors in an economy, such as the productivity of capital and investor time preference. This is an important prediction of the Fisher Hypothesis for, if real interest rates are related to the expected rate of inflation, changes in the real rate will not lead to full adjustment in nominal rates in response to expected inflation.
A problem that arises when testing for the Fisher effect is the lack of any direct measure of inflationary expectations. For this reason, a proxy variable for inflationary expectations must be employed. Over the years, a number of approaches have been used to derive proxies for the expected rate of inflation. The majority of early studies on the Fisher effect used some form of distributed lag on past inflation rates to proxy for inflationary expectations. Models based upon this approach can be found in Cagan (1956), Meiselman (1962), Sargent (1969) and Gibson (1970).
With the theory of rational expectations pioneered by Muth (1961), and the theory of efficient markets advanced by Fama (1970), there developed an alternative approach to modeling expectations. Subsequent studies, therefore, saw the incorporation of rational expectations in the formation of expectations. This approach is adopted by Fama (1975), Lahiri and Lee (1979), and Levi and Makin (1979). With the incorporation of these theories in the Fisher hypothesis, methodological advances involved examining the time series properties of the variables in question.
See Mishkin (1992), Wallace and Warner (1993), MacDonald and Murphy (1989), Peng (1995). Fisher (1930) hypothesized that the nominal rate of interest was equal to the sum of both the real rate of interest and the expected rate of inflation. He claimed a one-toone relationship between the rate of interest and expected inflation, with the real rate being independent of the rate of inflation. Adaptive Expectations The work of Sargent (1969), Gibson (1970), Yohe and Karnosky (1969), Lahiri (1976) concentrated primarily on verifying Fisher’s results with respect to the existence of a distributed lag structure in expectations formation.
While adopting the basic distributed lag mechanism as that of Fisher in the formation of expectations, the specifications involving the lagged variables differed from the arithmetically declining weights as originally proposed by Fisher. Sargent (1969) and Gibson (1970) employed geometrically declining weights,2 while Yohe and Karnosky (1969) used the Almon lag technique 3 in order to avoid problems of multicollinearity. The studies of Sargent and Gibson, based on data from the pre-war period, confirmed Fisher’s findings of a significant distributed lag effect in expectations formation.
Gibson, moreover, observed that there appeared to be a cyclical factor in the formation of price expectations, suggestive of a higher-order weighting pattern for past price changes. An important implication that emerged from his study was that policy action designed to influence interest rates would eventually be felt on price expectations. From the 1960s, there was significant evidence of a shortening of the time lag in expectations formation, as suggested by the studies by Yohe and Karnosky (1969), Gibson (1972) and Lahiri (1976).
Yohe and Karnosky found an acceleration in the speed of expectations formation, with the price expectation effect much greater for the 1961???1969 period than the 1952???1960 period. Gibson (1972) similarly observed that there was almost a point-for-point adjustment in nominal interest rates to changes in inflation during the 1959???1970 period, with a time lag of about six months. The results revealed a shorter lag in the formation of expectations and greater impact of expectations on interest rates for the period after 1959, supporting the evidence of Yohe and Karnosky.
Lahiri, employing four approaches to estimate inflationary expectations???the weighted, adaptive, extrapolative, and Frenkel’s approach???found that expectations were forming more rapidly in the period after 1960, consistent with the findings of Yohe and Karnosky and Gibson. Gibson’s (1972) model, however, differs in its use of data. To overcome the problem of systematic forecasting errors produced by backward-looking models of expectations formation, Gibson employed survey data published by the Federal Reserve Bank of Philadelphia.
While the structural break observed in the 1960s was attributed by Yohe and Karnosky to a shift in the interest rates equation, Gibson suggested the possibility of a shift in the formation of the price expectations equation. Lahiri’s findings appeared to support that of Gibson. Therefore, a positive relation between interest rates and inflation with a significant shortening of the time lag in expectations formation from the 1960s onwards is evidenced by these studies. Moreover, the Fisher hypothesis took a different turn during this period in that it began to be integrated with the theories of rational expectations and efficient markets.
Rational Expectations and Efficient Markets The crux of the argument changed with the incorporation of the theories of rational expectations put forward by Muth (1961) and efficient markets developed by Fama (1970) in the Fisher hypothesis. While Fisher argued that past changes in the price level became embodied in the current rate of interest, Fama (1975) argued that future price changes were reflected in the current rate of interest. This was interpreted by him as evidence of an efficient market. Fama’s study, therefore, differed from the models discussed above in its analysis of inflationary expectations.
This approach rejected Fisher’s conclusions of a distributed lag structure in the formation of expectations. Instead, it assumed that rational forecasters would use all available information in forming price expectations. 5. Determinants of yield curve Yield curves are usually upward sloping asymptotically; the longer the maturity, the higher the yield, with diminishing marginal growth. There are two common explanations for this phenomenon. First, it may be that the market is anticipating a rise in the risk-free rate.
If investors hold off investing now, they may receive a better rate in the future. Therefore, under the arbitrage pricing theory, investors who are willing to lock their money in now need to be compensated for the anticipated rise in rates ??? thus the higher interest rate on long-term investments. However, interest rates can fall just as they can rise. Another explanation is that longer maturities entail greater risks for the investor (i. e. the lender). Risk premium should be paid, since with longer maturities, more catastrophic events might occur that impact the investment.
This explanation depends on the notion that the economy faces more uncertainties in the distant future than in the near term, and the risk of future adverse events (such as default and higher short-term interest rates) is higher than the chance of future positive events (such as lower short-term interest rates). This effect is referred to as the liquidity spread. If the market expects more volatility in the future, even if interest rates are anticipated to decline, the increase in the risk premium can influence the spread and cause an increasing yield.
The opposite situation ??? short-term interest rates higher than long-term ??? also can occur. The market’s anticipation of falling interest rates causes such incidents. Negative liquidity premiums can exist if long-term investors dominate the market, but the revailing view is that a positive liquidity premium dominates, so only the anticipation of falling interest rates will cause an inverted yield curve. Strongly inverted yield curves have historically preceded economic depressions. The yield curve may also be flat or hump-shaped, due to anticipated interest rates being steady or short-term volatility outweighing long-term volatility.
Yield curves move on a daily basis, reflecting the market’s reaction to news. A further “stylized fact” is that yield curves tend to move in parallel (i. e. , the yield curve shifts up and down as interest rate levels rise and fall). In contrast of a flat or negatively sloped yield curve, the movements in the spread have been driven by a fall in long bond rates rather than rises in short-term interest rates resulting from monetary tightening. As movements in Indian long-term bond yields are strongly correlated international factors, it may be difficult to isolate the relative contributions of omestic and international factors. In particular, it is possible that there may be a speculative element in global bond prices for some of this period. In this case, current long-term bond yields may not be an accurate reflection of market expectations about future real economic activity and bond prices would be expected to adjust downwards (that is, yields rise) as the speculative element moderates. [pic] Source: handbook of RBI Figure 1 (A to D): Time series of the yield of the treasury bills Figure shows the yield curve of the different treasury bills.
Here, A shows the yield curve of the 91 days Treasury bill, Figure B shows the yield curve of the 182 days Treasury bill, Figure C shows the yield curve of the 364 days Treasury bill, Figure D shows the yield curve of the combined Treasury bill. Here, data are taken from 5th January 2007 to 14th November 2008; graphs are showing that there are major fluctuations within this time period. Treasury bill of 364 days fluctuated from 9. 5% to 7%, which gives the gap of 2. 5%, gives the huge decline in the interest rate in previous 20 weeks. This sharp fluctuation shows the decline in the growth rate of Indian economy due to the global decline. pic] Source: handbook of RBI Figure 2 (A to D): Time series of the Spread of the treasury bills Figure shows the Spread between the different treasury bills. Here, A shows the Spread curve of the 91 days and 182 days Treasury bill, Figure B shows the Spread curve of the 182 days and 364 days Treasury bill, Figure C shows the Spread curve of the 364 days and 182 days Treasury bill, Figure D shows the yield curve of the combined Treasury bill. Here, data are taken from 5th January 2007 to 14th November 2008; graphs are showing that there are major fluctuations within this time period.
Spread of every Treasury bill gives the sharp decline in the interest rate in previous 20 weeks. Initial rise in the curve was due to decrease in the liquidity and increase in the demand due to the market slowdown, then after due to the government monetary rate cut and decreased demand has caused curve to move down. On the other hand, economic commentators have identified a range of longer term factors which suggest current low bond yields may be a rational reflection of longer term factors being taken into account by bond markets.
Such factors include a structural decline in inflation and inflation expectations, excess global savings placing pressure on bond yields and a change in the portfolio preferences of investors, represented by a shift away from equities and shorter maturity bonds to 10-year government bonds. The yield curve typically slopes upwards as bond investors require higher interest rates to hold bonds of longer maturities. This is known as the liquidity or term premium. However, bond yields may also provide information about financial market expectations of future real economic activity. pic] Source: handbook of RBI Figure 3: Time series of the yield of the treasury bills and WPI index Figure 3 shows the graph between treasury bills yield curve and whole sale price index data. This curve gives the relation between the price level and the interest rate. Fisher effect which shows the relation between inflation and interest rate can be seen in above curve. Expected inflation rate is almost going with the yield curve and coming on down side. this curve shows that there is a slowdown in the market and demand has been decreased.
Price of commodities is coming down and rate of interest is also following the same. As Fisher has suggested that nominal interest rate in any period is equal to the sum of the real interest rate and the expected rate of inflation. This is termed the Fisher Effect. Fisher hypothesized that the nominal interest rate could be decomposed into two components, a real rate plus an expected inflation rate. He claimed a one-to one relationship between inflation and interest rates in a world of perfect foresight,
Historically, there has been a correlation between the slope of the yield curve (measured by the spread) and expectations of future inflation and economic activity, with an upward-sloping (flat or inverted) yield curve interpreted as signaling stronger (weaker) real economic activity and inflation in the future. This correlation has been supported empirically, with various studies finding a significant relationship in Organization for Economic Co-operation and Development (OECD) countries between the yield spread and measures of future real economic activity such as real GDP, industrial production and consumption
Source: handbook of RBI Figure: 4, Relation between yield of T bill and GDP, A standard economic explanation for the relationship between the yield spread and future economic growth is that, when the economy is strong, there will be an expectation of higher average short-term interest rates in the future. Expectations of higher average short-term rates will lead to bond yields being higher than present short-term rates and thus to a higher yield spread. Conversely, when the economy is weak there will be an expectation of lower average short-term interest rates in the future, leading to a lower (and possibly negative) yield spread.
Domestic yield spread would be positively related to the domestic interest rates, because the short rates follow up the movements in long rates. Otherwise, it would distort the financial market. The growth rate of the economy would have a negative impact because an increase in income has implications for the expansion of money supply, adversely affecting the interest rates. The traditional interpretation of a narrowing spread preceding a decline in future real economic activity would suggest that financial markets are expecting weakness in the Indian economy.
However, such a view is at odds with the performance of the Indian economy, which has achieved solid real GDP growth and strong employment growth. The outlook is also positive, with solid real economic growth. In addition, the narrowing spread over the last few years has primarily been driven by a fall in long-term bond yields, rather than monetary tightening. Given the recent performance of the Indian economy and the positive outlook for 2008-09, the fall in the Indian yield spread may well be a rational response by bond market participants to improved economic conditions.
That is, the fall in long-term bond yields will have been driven, in part, by a structural decline in inflation and inflation expectations due to more credible monetary policy and more stable economic conditions. This would decrease the spread as long-term bond investors are willing to bear risk at a lower level of nominal return. This suggests that some flattening of the slope of the yield curve may well be consistent with a market view that the economy is expected to grow at, or around, its trend rate and is not facing significant inflationary pressures.
That said, portfolio preference considerations would continue to suggest, other factors unchanged, some upward slope to the yield curve. This is because higher interest rates are generally required for bond investors to hold bonds of longer maturities. This suggests that factors other than expectations about future conditions in the Indian economy have been influencing long-term bond yields. Source: handbook of RBI Figure: 5, Relation between yield of T bills and SENSEX, If we relate the economic barometer Sensex with the yield curve then they both are negatively correlated with each other.
As sensex would give a more return to the investors, they will move more towards the stock market and on the opposite time investors would prefer to stay in bond market. Source: handbook of RBI Figure: 6, Relation between yield of T bills and PLR, Government specifies the PLR to the commercial banks. This rate also follows the yield curve of the treasury market. Both are positively correlated with each other. As the rate of interest falls in the market, banks also decrease the lending rates to the market to supply the money in the market. And this will cause a increase in the rates in the future.
Source: handbook of RBI Figure: 7, Relation between yield of T bills and CALL RATE, Call money rates are directly related to the T bill rate of interest. It follows th same pattern as shown in the figure. Banks maintain their liquidity as per the RBI norms by managing the asset and liability on the call rate, this rate produce the volatility in the short term rate of interest. Source: handbook of RBI Figure: 8, Relation between yield of T bills and GDP, There are many literatures, which gives the relation of interest rate with both domestic and international indicators.
Although, the relation from this figure is not clear but usually when rate of interest in the Indian market is more then international market, FIIs invest in Indian market, but relation of FIIs relates negatively with both stock market and debt market. FIIs come in a debt market only when they find better prospects in the debt market or else they prefer to go to the stock market. Source: handbook of RBI Figure: 9, relation between yield of T bills and rupee per dollar, If depreciation in the exchange rate is expected in the future, it is likely to exert a negative impact on the domestic interest rate.
Given the fact that there is a depreciation of the domestic rupee against the US dollar, there will be more demand for the dollar. The greater demand for the dollar resulting in inflow of foreign currencies will lead to expansion of the money supply and a consequent fall in the domestic interest rates in the economy. It is also generally argued that when there will be a fall in the value of the domestic currency, there will be less demand for domestic bonds, leading to a fall in the price of bonds and a consequent rise in the interest rates. . Analysis Regression Analysis Regression Analysis: 91 days versus 182 days, 364 days The regression equation is 91 days = 1. 45 – 0. 338 182 days + 1. 05 364 days R-Sq = 84. 95% Regression Analysis: 91 days versus 182 days, 364 days, GDP, PLR, FII The regression equation is 91 days = 3. 41 + 0. 033 182 days + 0. 882 364 days + 0. 014 GDP – 0. 299 PLR + 0. 000003 FII R-Sq = 97. 4% Here, r-sq measures only the strength of a linear relationship between the variables. We can conclude that 182 days, 364 days, GDP, PLR, FII explains 97. % of the variation in the 91 days treasury bill. Correlation Matrix [pic] The correlation matrix presented in Table 1 shows that all the domestic interest rates are moreover correlated with each other, But although the correlation with the GDP is not clear from the given data. Rate of inflation and growth of GDP are positively correlated with each other. Interest rate should also define the more concrete relationship with this factor. Here, FIIs relationship is also unclear as interest rate goes up, there is a huge inflows of FIIs in the bond market.
While modeling through the time series analysis, for an appropriate time series analysis, one requires knowing the time series properties of all the variables under consideration. Application of Augmented Dickey-Fuller test, which gives the better understanding of the stationary or non stationary behavior of the interest rate. So, to check this behavior, we need to apply the ADF test to check whether the unit root is present in time series or not. I have applied a unit root test on two time series, which are T bill 91 days and T bill 364 days by using the monthly data from 2003 to 2006. result of this test is given below.
Test Results: Augmented Dickey-Fuller (ADF) test 1). Time series with no trend and no trend Null hypothesis H(0): z(t) is a unit root process: a = 0. Alternative hypothesis (H1): z(t) is a zero-mean stationary process: a < 0. Lag p =1 Variable to be tested: z(t) = T 91 H0: Unit root; H1: Zero mean stationarity ADF model for z(t)-z(t-1): OLS estimate t-value Asymptotic critical regions: z(t-1) 0. 0080 0. 7797 < -1. 93 (5%) < -1. 60 (10%) z(t-1)-z(t-2) -0. 3797 -3. 0383 Residual s. e. : 44. 38075E-002 : 58 Test result: H0 is not rejected at the 10% significance level 2). Time series with drift but no trend Lag p =1 Variable to be tested: z(t) = T 91 H0: Unit root; H1: Stationary around a constant ADF model for z(t)-z(t-1): OLS estimate t-value Asymptotic critical regions: z(t-1) -0. 0576 -1. 0044 < -2. 89 (5%) < -2. 58 (10%) z(t-1)-z(t-2) -0. 3462 -2. 7077 1 0. 3825 1. 1614 Residual s. e. : 44. 24318E-002 n: 58
Test result: H0 is not rejected at the 10% significance level 3). Time series with drift and trend z(t)-z(t-1) = a. z(t-1) + b(1). (z(t-1)-z(t-2)) + … + b(p). (z(t-p)-z(t-p-1)) + b(p+1) + b(p+2). t + u(t), Lag p =1 Variable to be tested: z(t) = T 91 H0: Unit root with drift; H1: Linear trend stationary ADF model for z(t)-z(t-1): OLS estimate t-value Asymptotic critical regions: z(t-1) -0. 4592 -3. 3831 < -3. 40 (5%) < -3. 13 (10%) z(t-1)-z(t-2) -0. 1545 -1. 1667 1 1. 8207 3. 639 t 0. 0264 3. 2142 Residual s. e. : 40. 90876E-002 n: 58 Test result: H0 is not rejected at the 5% significance level H0 is rejected in favor of H1 at the 10% significance level Above results of ADF test shows that time series with drift and coefficient gives the series as a stationary at 10% significant level. In above results, tau value can be found by dividing the value of coefficient (OLS estimate) by residual standard error. Here, we have to compare the tau value with the critical values given by Dicky ??? Fuller for different significance level.
Table 1: Unit root test (1) [pic] Here, Table 1 gives results of the ADF test which shows that with lag 1 and Unit root with coefficient and drift makes T 91 days time series stationary at 10% of significance level. FINDINGS From the qualitative and quantitative analysis, findings for the major factors affecting the interest rate are as below: From correlation matrix, we can say that T bill 91 days rates are correlated with T bill 180days, T bill 364 days, primary lending rate, call money rate. While, T bill 91 days rates are negatively correlated with FIIs and sensex.
Behavior of interest rate with GDP growth rate and currency rate is undetermined through the correlation. Graph of interest rate with treasury bills gives the perfect relation between them. By simply putting the different values in the regression equation, we can find out the future value of the treasury bills but it will not give the exact forecast due to the non stationary behavior of the Treasury bill or it may give the spurious error. Through analysis of unit root test, we can say that time series for the Treasury bill is a non stationary in behavior and simple regression would not give an exact result of the future rate.
Here, Table 1 gives results of the ADF test which shows that with lag 1 and Unit root with coefficient and drift makes T 91 days time series stationary at 10% of significance level. 8. BIBLIOGRAPHY BOOKS: ??? Basics of econometrics, By Gujarati, ??? Econometrics time series, chapter: Term structure of interest rate, by Kevin Peterson ??? Statistics for management, By Richard Levin and David Rubin Article: ??? Modeling Interest Rate Cycles in India, By B B Bhattacharya, N R Bhanumurthy, Hrushikesh Mallick, Development Planning Centre, Institute of Economic Growth, Delhi FIMMDA-NSE Debt Market (Basic) Module, NCFM test module WEBSITES: http://www. rbi. org. in/scripts/Statistics. aspx http://www. federalreserve. gov/releases/h15/data. htm http://finance. yahoo. com/q/hp? s=FEDBX&a=04&b=31&c=1996&d=10&e=26&f=2008&g=w http://www. rbi. org. in/Scripts/AnnualPublications. aspx? head=Handbook%20of%20Statistics%20on%20Indian%20Economy http://www. nseindia. com/ [pic] Table 1: Treasury Bills of 14 days, 91 days, 182 days, 364 days. [pic] [pic] [pic] Table 2: T bills, GDP rate, PLR, FII, Sensex, Call money, Dollar rates