1. INTRODUCTION Fixed income instruments (FII) can be categorized bytype of payments. A periodic interest payment is paid by many fixed incomeinstruments to the holder, and an amount due at maturity, the redemption value.Some instruments pay the principal amount together with the entire outstandingamount of interest on the instrument as a lump sum amount at maturity. Theseinstruments are known as ‘zero coupon’ instruments (Eg: Treasury Bills).
A zero coupon bond is defined as “a debtsecurity that does not pay back an interest (a coupon)”. But it is traded in astock exchange at a greater discount, generating profits at the maturity whenthe bond is redeemed for its full face value. Others are bonds that arestripped off their coupons by a financial institution and resold as a zerocoupon bond. The entire payment including the coupon at the time of maturity isoffered later.
The price of zero coupon bonds have a tendency to fluctuate morethan the prices of coupon bonds (Momoh,2018). Yield curve is obtained by plotting theinterest rates obtained from the securities against the time (monthly, daily orannually) for securities having different maturity dates. These plotted datahave been used in various studies to identify behavior of the securities and topredict the future behaviors. Various studies have been conducted toinvestigate the behavior of various types of treasury bonds and bills by usingthe yield curve.
The return on capitalinvested in fixed income earning securities is commonly called as yield. Theyield on any instrument has two distinct aspects, a regular income in the formof interest income (coupon payments) and changes in the market value and thefixed income gearing securities (Thomas et al.). Durbha, Datta Roy andPawaskar in their paper titled “Estimating the Zero Coupon Yield Curve” havepointed out factors the Maturity period, Coupon rate, Tax rate, Marketabilityand Risk factor, which make a yield differential among the fixed income bearingsecurities. Further they have pointed out that the government securities whichare considered as the safest securities to invest also carries hidden risks as Purchasingpower risk and Interest rate risks. According to the authorsthe behavior of inflation within the country arises due to the purchasing powerrisk and lead to changes in real rate of return. Interest rate risk is produceddue to the oscillations in prices of the securities.
In such a case theinvestors should regulate their portfolios accordingly. Numerouscontributions in finance have proved that imposing no-arbitrage constraints inempirical models of the yield curve improve their empirical features. Theadditional features time-varying parameters, time-varying variances ofstructural shocks, flexible pricing kernels, additional shocks and latentvariables have brought model implied yields and experimental yields closertogether (Graeve, et al). Both the short term interest rate and the term spreadhave an impressive record in predicting GDP growth (Estrella 2005, Ang et al.2006,). 1.
1. Motivation behind the Useof Zero Coupon Yield Curve for Valuation of Fixed Income Instruments Modeled as a series of cash flows due at dissimilarpoints of time in the future, the causal price of a fixed income instrument canbe calculated as the net present value of the stream of cash flows. Each cashflow has to be discounted using the interest rate for the related term tomaturity. The appropriate spot rates to be used for this purpose are providedby the Zero Coupon Yield Curve(Thomas, et.al.
). The equationused is given below.C = couponR = redemption amountm = time to maturity 1.2.
The uses of estimating a term structure Once an estimate of the term structure based ondefault-free government securities is obtained, it can be used to price allfixed income instruments after adding an appropriate credit spread. It can beused to value government securities that do not trade on a given day, or toprovide default-free valuations for corporate bonds. Estimates of the Zero Coupon Yield Curveat regular intervals over a period of time provides us with a time-series ofthe interest rate structure in the economy, which can be used to analyze theextent of impact of monetary policy. This also forms an input for VaR systemsfor fixed income systems and portfolios. 1.3. The Yield Curve Predict Output andInflation The inflation and the real economic activity were empiricallypredicted by the slope of the yield curve. There is no standard theory for thisrelationship.
The model in this paper suggests that the relationships are notstructural but are instead influenced by the monetary policy regime. Even though theoretical foundation for the statisticalproof with regard to both output and inflation is limited, there are studiesdone separately. In the case of inflation, the results have been attributed toa simple model based on the Fisher equation. In the case of real activity, themenu of explanations has been broader and typically more heuristic. Estrellaand Hardouvelis (1991) and Dotsey (1998) attribute at least some of the predictivepower to the effects of countercyclical monetary policy.