On Developing Constant Maturity Yield Curves for India
Money & Finance, Vol. 2, No. 6, July-September 2001
Posted: 27 Jun 2002
It is a widespread practice among central banks over the world to report the base interest rates of the economy in terms of constant maturity yield curves for default risk free government securities. The usual practice worldwide is to provide spot rates for finely defined "points" of time. For example, the constant maturity yield curve of the Federal Reserve Bank of the USA provides spot rates for exactly 3-month, 6-month, 1-year, 2-year, 3-year, 5-year, 7-year, 10-year, 20-year, and 30-year maturity levels. Central Banks of countries with mature debt markets also regularly report constant maturity yields for a large number of maturities. In India, the debt market being very thin and relatively less mature, so far there was no published information on constant maturity yields for the economy. During the last four years, in Money & Finance, we have regularly depicted the movements of interest rates in the Indian economy with the help of (monthly) yield curves, based on secondary market yields of central government securities covering the entire maturity spectrum of gilts. These yield curves provided information on government bond yields for chosen maturity "bands" (e.g., 1-2year, 2-3 year, 3-4 year, 4-5 year, 5-10- year and greater-than-10 years to maturity). This, however, meant that it was difficult to read the spot rates for a specific maturity level off the above mentioned yield curves. Also, the Reserve Bank of India does not publish maturity-wise yields for the Indian economy . In this paper, we have sought to fill this void, by refining our already existing yield curve to reflect constant maturity yields in place of yields for wide maturity bands.
The imperfections of the Indian bond market make it almost impossible to have sufficient price-yield data for securities spanning a wide range of maturity levels, for every trading month. However, the increase in the depth and width of the Indian bond market in the recent past provided us with an opportunity to develop yield curves for "finer" maturity levels (i.e., estimate 1-year and 2-year spot rates separately, for example, as opposed to estimating the average spot rate for 1-2 year maturity "band"), and this remains the primary endeavour of this paper.
In order to deal with the existing problem of low frequency of trades and the resulting paucity of data while estimating the constant maturity yields, instead of maturity points we specify maturity "windows". These windows are the narrowest possible ones, being chosen on considerations of precision as well as representation of a sizable number of trades throughout the month. Further, the old and new constant maturity curves are compared to verify whether estimation of the computationally more costly "new" estimates leads to a significant improvement. A comparison with our former yield curve in terms of the coefficient of variation to measure the extent of divergence between the two curves and the confidence interval to verify the improvement in precision, shows that the constant maturity yield curve is indeed an improvement over the previous yield curve.
In order to find out whether the constant maturity yield estimates correctly reflect the term structure of interest rates, another comparison is made with the already existing zero-coupon yield estimates (ZCYC) published by the National Stock Exchange . We have compared the two estimates to verify whether or not the CMYC and the ZCYC manifest significantly different term structures of interest rates.
We first compare the monthly average yields generated by our CM method, and NSE's NS method and the results imply that the difference between the two estimates of monthly yields are significant for most of the maturity levels considered by us. However, for the period under consideration, the correlation between the two alternative series of spot rates is high for all maturity levels suggesting, though weakly, that they represent similar interest rate movements over time, at all maturities. Hence we proceed to test for cointegration between the two series of spot rates (CM and ZC), for each maturity, to see whether they exhibit any co-movement, though they may represent different levels of yields . The results show that barring the spot rates for the 90-day maturity level, for all other maturities the two series are cointegrated, implying that there is no significant difference between the CMYC and ZCYC in so far as the depiction of the movements of the Indian term-structure of interest rates is concerned. The difference between the two alternative series of yields for the 90-day maturity level is also evident from an analysis of the coefficient of variation (cv) between the average monthly yields of the two alternative series of yields, for all maturity levels. This divergence concerning the yield for the 90-day maturity level is not surprising because the CM yield estimates are based on realized yields while ZC estimates are based on curve fitting techniques and for the lower end of the maturity spectrum the model error - the difference between the ZC yield estimate and the realized market yield - is significantly high.
From the above analysis it is evident that the CM yield curve and the ZC yield curve are not significantly different qualitatively, with the exception of the 90-day maturity level, even though the actual estimates of daily and monthly average yields estimated using the two alternative methodologies may differ significantly. It should be noted though that prima facie the CM yields of the zero-coupon money market instruments seem to be more reliable than the ZC/NS estimates of the short end yields. The CM estimates of money market yields track the short term rates and other money market reference rates like the call money rate (CMR) and RBI's repo rates much more closely compared to the ZC yields.
Thus, we conclude that given the nature of the secondary market for government debt, the constant maturity yield curve, in its new incarnation that has replaced wide maturity "bands" with maturity "windows", provides an adequate representation of short, medium and long term interest rates. Also, our results point to the inability of the zero-coupon yield estimates to reflect the short term realised yields, while the constant maturity yields seem more plausible at the short end of the yield curve.
Note: This is a description of the article and not the actual abstract.
Keywords: constant maturity yield, government securities, ytm, developing debt market, term structure, interest rates
JEL Classification: E43, G19, C12
Suggested Citation: Suggested Citation