Fixed income instruments (FII)can be categorized by type of payments. A periodic interest payment is paid bymany fixed income instruments to the holder, and an amount due at maturity, theredemption value. Some instruments pay the principal amount together with theentire outstanding amount of interest on the instrument as a lump sum amount atmaturity. These instruments are known as ‘zero coupon’ instruments (E.
g.:Treasury Bills). A zero coupon bond isdefined as “a debt security that does not pay back an interest (a coupon)”. Butit is traded in a stock exchange at a greater discount, generating profits atthe maturity when the bond is redeemed for its full face value.
Others arebonds that are stripped off their coupons by a financial institution and resoldas a zero coupon bond. The entire payment including the coupon at the time ofmaturity is offered later. The price of zero coupon bonds have a tendency to fluctuatemore than the prices of coupon bonds (Momoh,2018). Yield curve is obtainedby plotting the interest rates obtained from the securities against the time(monthly, daily or annually) for securities having different maturity dates.These plotted data have been used in various studies to identify behavior ofthe securities and to predict the future behaviors. Various studies have beenconducted to investigate the behavior of various types of treasury bonds andbills by using the yield curve. Thereturn on capital invested in fixed income earning securities is commonlycalled as yield.
The yield on any instrument has two distinct aspects, aregular income in the form of interest income (coupon payments) and changes inthe market value and the fixed income gearing securities (Thomas et al.). Durbha,Datta Roy and Pawaskar in their paper titled “Estimating the Zero Coupon YieldCurve” have pointed out factors the Maturity period, Coupon rate, Tax rate,Marketability and Risk factor, which make a yield differential among the fixedincome bearing securities. Further they have pointed out that the governmentsecurities which are considered as the safest securities to invest also carrieshidden risks as Purchasing power risk and Interest rate risks.Accordingto the authors the behavior of inflation within the country arises due to thepurchasing power risk and lead to changes in real rate of return.
Interest raterisk is produced due to the oscillations in prices of the securities. In such acase the investors 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 latent variableshave brought model implied yields and experimental yields closer together(Graeve, et al). Both the short term interest rate and the term spread have animpressive record in predicting GDP growth (Estrella 2005, Ang et al. 2006,). Motivation behind the Use of Zero Coupon Yield Curve for Valuation ofFixed Income Instruments Modeled as a series of cashflows due at dissimilar points of time in the future, the causal price of afixed income instrument can be calculated as the net present value of thestream of cash flows.
Each cash flow has to be discounted using the interestrate for the related term to maturity. The appropriate spot rates to be usedfor this purpose are provided by theZero Coupon Yield Curve (Thomas, et.al.). The equation used is given below.C = couponR = redemption amountm = time to maturity The uses ofestimating a term structure Once an estimate of the termstructure based on default-free government securities is obtained, it can beused to price all fixed income instruments after adding an appropriate creditspread. It can be used to value government securities that do not trade on agiven day, or to provide default-free valuations for corporate bonds.
Estimatesof 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. The YieldCurve Predict Output and Inflation Estrella explains how theinflation and the real economic activity were empirically predicted by theslope of the yield curve. There is no standard theory for this relationship.The model in this paper suggests that the relationships are not structural butare instead influenced by the monetary policy regime. Even though theoreticalfoundation for the statistical proof with regard to both output and inflationis limited, there are studies done separately. In the case of inflation, theresults have been attributed to a simple model based on the Fisher equation. Inthe case of real activity, the menu of explanations has been broader andtypically more heuristic.
Estrella and Hardouvelis (1991) and Dotsey (1998)attribute at least some of the predictive power to the effects ofcountercyclical monetary policy. The monetary policy has a lotto do with the predictive power, particularly for output. If monetary policy isessentially reactive to deviations of inflation from target and of output frompotential. The predictive relationships for output and inflation dependprimarily on the magnitudes of the response parameters. If the monetaryauthority optimizes methodically to achieve certain goals regarding inflationand output variability. The predictive power of the yield curve is moredirectly dependent on the structure of the macroeconomy. Expressions that relate theyield curve slope to expectations of future output and inflation are required.
Such predictive equations account first for the predictive power of the yieldcurve, and then for any remaining information that may be required to obtain anoptimal prediction. The influence of the parameters of the policy rule on the prognosticpower of the yield curve. To summarize, the modelsuggests that the yield curve is in general a useful predictor of both outputand inflation. This result is robust in that it holds quite generally, unlessthe policy reactions to both inflation and output approach infinity. Nevertheless,the precise weight of the yield curve in the predictive relationships is afunction of the parameters of the monetary policy rule.
Pricediscovery in the U.S Treasury Market: The Impact of Orderflow and Liquidity ofthe Yield Curve According to Brandt, Economistare very keen in understanding the reasons for the fluctuations in the yieldcurve. One factor for the changes in the yield is the collection ofheterogeneous private information at the process of trading in the treasurymarket which is the mechanism is called as price discovery. When considered a set oftreasury market participants where each participant have their own way how theyield curve related to the economic fundamentals and about the existingcondition of the economy based on the public information available. Someprivate institutes may have limited information. With the incomplete andheterogeneous information available and the judgments made based on them theparticipants are allowed to trade treasury securities. The aim of this study isto further investigate the role played by the price discovery in the U.
STreasury Market. It has measured the response of yields to orderflow imbalance(limit exceeded buying or selling pressure) on days without main macroeconomicannouncements.The results obtained from the study hasstrongly supported the hypothesis which state that the price discovery plays akey role in the U.S Treasury Market. The study has confirmed that the overflowimbalances results for 26% of the day today variations of the yields on dayswithout key macroeconomic changes in the market. This study related tovast number of currents studies available on overflow in the U.S treasuryMarket.
To analyze the relationships among the yields, overflows and liquiditythe study has arranged a structural plan on the analysis which is complexenough to capture the variations in the data and possible enough to handle it.The study has followed previously completed studies and have selected a twodimensional partition of the data. First dimension is the remaining time tomaturity of the security which the study has divided into six categories.a) 1day to 6 monthsb) 6– 12 monthsc) 12months to two yearsd) 2– 5 yearse) 5– 10 yearsf) 10– 30 yearsThe second dimensionselected by the study was seasonedness of a security, which give theinformation on how the security has been auctioned very recently. Furtherreferring to previous studies the study has separated the bonds into on-the-runand off-the-run for their analysis. To better understand themultivariate structure of the data across tome-to-maturity categories in a aselected seasonedness category, the study has performed standard factordecomposition. The study has used principal components analysis to gain theorthogonal factor F(t) from the covariance matrix of the vector X(t), thus X(t)= A + B x F(t). The A and B are matrices of constants and factor loadings.
Thestudy has allowed the X(t) to be the (6×1) vector of yields, net orderflow,bid-ask spreads, or quoted depth within a given seasonedness category. The study has used firstorder VAR as the base line model to study the daily dynamics of the yields. Dueto the changes done in the first order VAR model they have used the authorshave called the model as a restricted VAR model where the slope coefficient Brsatisfied by Br x L = Bu and the Bu denotes thecoefficient of the full VAR model. The authors have lagged the yields on aconstant and the lagged common factors (level, slope and curvature) Ft-1= L x Yt-1 where L denotes the factor loadings.
The authors haveconcluded that the baseline model they have fitted is successful in capturingthe yield levels, but effectively removes all day today changes. Finally the hypothesis ofthis study was in the absence of material public information flow, orderflowimbalances account for a substantial portion of the day today fluctuations ofthe yield curve and that the role of orderflow depends on the liquidity in theTreasury Market. Their hypothesis isstrongly accepted by the results obtained from the empirical study. They studyshows that unconditionally 21% of the day today fluctuations in the yields ondays without major macroeconomic changes are caused by orderflow imbalances.Further the study emphasis that the daily yield changes are permanent.
Finallythe authors have emphasized 3 important factors to be considered when modelingU.S Treasury Securities. 1. Price discovery does occur in the treasurymarket 2. Price discovery process is focused withinthe on the run market segment.3.
Low liquidity magnify the price discoveryprocessThe Yield Curve as aPredictor of U.S. Recessions Accordingto Estrella et.al. the steepnessof the yield curve has to be an excellent indicator of a possible futurerecession. Current monetary policy has a significant influence on the yieldcurve spread. A rise in the short rate tends to flatten the yield curve as wellas to slow real growth in the near term.
This relationship, however, is onlyone part of the explanation for the yield curve’s usefulness as a forecastingtool. Althoughthe yield curve has clear benefits as a predictor of future economic events,several other variables have been widely used to forecast the path of the economy. Among financial variables, stock prices have received muchattention. Finance theory suggests that “stock prices are determined byexpectations about future dividend streams, which in turn are related to the futurestate of the economy”.