Fixed income instruments (FII)

can be categorized by type of payments. A periodic interest payment is paid by

many fixed income instruments to the holder, and an amount due at maturity, the

redemption value. Some instruments pay the principal amount together with the

entire outstanding amount of interest on the instrument as a lump sum amount at

maturity. These instruments are known as ‘zero coupon’ instruments (E.g.:

Treasury Bills).

A zero coupon bond is

defined as “a debt security that does not pay back an interest (a coupon)”. But

it is traded in a stock exchange at a greater discount, generating profits at

the maturity when the bond is redeemed for its full face value. Others are

bonds that are stripped off their coupons by a financial institution and resold

as a zero coupon bond. The entire payment including the coupon at the time of

maturity is offered later. The price of zero coupon bonds have a tendency to fluctuate

more than the prices of coupon bonds (Momoh,

2018).

Yield curve is obtained

by 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 of

the securities and to predict the future behaviors. Various studies have been

conducted to investigate the behavior of various types of treasury bonds and

bills by using the yield curve.

The

return on capital invested in fixed income earning securities is commonly

called as yield. The yield on any instrument has two distinct aspects, a

regular income in the form of interest income (coupon payments) and changes in

the market value and the fixed income gearing securities (Thomas et al.).

Durbha,

Datta Roy and Pawaskar in their paper titled “Estimating the Zero Coupon Yield

Curve” have pointed out factors the Maturity period, Coupon rate, Tax rate,

Marketability and Risk factor, which make a yield differential among the fixed

income bearing securities. Further they have pointed out that the government

securities which are considered as the safest securities to invest also carries

hidden risks as Purchasing power risk and Interest rate risks.

According

to the authors the behavior of inflation within the country arises due to the

purchasing power risk and lead to changes in real rate of return. Interest rate

risk is produced due to the oscillations in prices of the securities. In such a

case the investors should regulate their portfolios accordingly.

Numerous

contributions in finance have proved that imposing no-arbitrage constraints in

empirical models of the yield curve improve their empirical features. The

additional features time-varying parameters, time-varying variances of

structural shocks, flexible pricing kernels, additional shocks and latent variables

have brought model implied yields and experimental yields closer together

(Graeve, et al). Both the short term interest rate and the term spread have an

impressive record in predicting GDP growth (Estrella 2005, Ang et al. 2006,).

Motivation behind the Use of Zero Coupon Yield Curve for Valuation of

Fixed Income Instruments

Modeled as a series of cash

flows due at dissimilar points of time in the future, the causal price of a

fixed income instrument can be calculated as the net present value of the

stream of cash flows. Each cash flow has to be discounted using the interest

rate for the related term to maturity. The appropriate spot rates to be used

for this purpose are provided by the

Zero Coupon Yield Curve (Thomas, et.al.). The equation used is given below.

C = coupon

R = redemption amount

m = time to maturity

The uses of

estimating a term structure

Once an estimate of the term

structure based on default-free government securities is obtained, it can be

used to price all fixed income instruments after adding an appropriate credit

spread. It can be used to value government securities that do not trade on a

given day, or to provide default-free valuations for corporate bonds. Estimates

of the Zero Coupon Yield Curve

at regular intervals over a period of time provides us with a time-series of

the interest rate structure in the economy, which can be used to analyze the

extent of impact of monetary policy. This also forms an input for VaR systems

for fixed income systems and portfolios.

The Yield

Curve Predict Output and Inflation

Estrella explains how the

inflation and the real economic activity were empirically predicted by the

slope of the yield curve. There is no standard theory for this relationship.

The model in this paper suggests that the relationships are not structural but

are instead influenced by the monetary policy regime.

Even though theoretical

foundation for the statistical proof with regard to both output and inflation

is limited, there are studies done separately. In the case of inflation, the

results have been attributed to a simple model based on the Fisher equation. In

the case of real activity, the menu of explanations has been broader and

typically more heuristic. Estrella and Hardouvelis (1991) and Dotsey (1998)

attribute at least some of the predictive power to the effects of

countercyclical monetary policy.

The monetary policy has a lot

to do with the predictive power, particularly for output. If monetary policy is

essentially reactive to deviations of inflation from target and of output from

potential. The predictive relationships for output and inflation depend

primarily on the magnitudes of the response parameters. If the monetary

authority optimizes methodically to achieve certain goals regarding inflation

and output variability. The predictive power of the yield curve is more

directly dependent on the structure of the macroeconomy.

Expressions that relate the

yield curve slope to expectations of future output and inflation are required.

Such predictive equations account first for the predictive power of the yield

curve, and then for any remaining information that may be required to obtain an

optimal prediction. The influence of the parameters of the policy rule on the prognostic

power of the yield curve.

To summarize, the model

suggests that the yield curve is in general a useful predictor of both output

and inflation. This result is robust in that it holds quite generally, unless

the policy reactions to both inflation and output approach infinity. Nevertheless,

the precise weight of the yield curve in the predictive relationships is a

function of the parameters of the monetary policy rule.

Price

discovery in the U.S Treasury Market: The Impact of Orderflow and Liquidity of

the Yield Curve

According to Brandt, Economist

are very keen in understanding the reasons for the fluctuations in the yield

curve. One factor for the changes in the yield is the collection of

heterogeneous private information at the process of trading in the treasury

market which is the mechanism is called as price discovery.

When considered a set of

treasury market participants where each participant have their own way how the

yield curve related to the economic fundamentals and about the existing

condition of the economy based on the public information available. Some

private institutes may have limited information. With the incomplete and

heterogeneous information available and the judgments made based on them the

participants are allowed to trade treasury securities.

The aim of this study is

to further investigate the role played by the price discovery in the U.S

Treasury Market. It has measured the response of yields to orderflow imbalance

(limit exceeded buying or selling pressure) on days without main macroeconomic

announcements.

The results obtained from the study has

strongly supported the hypothesis which state that the price discovery plays a

key role in the U.S Treasury Market. The study has confirmed that the overflow

imbalances results for 26% of the day today variations of the yields on days

without key macroeconomic changes in the market.

This study related to

vast number of currents studies available on overflow in the U.S treasury

Market. To analyze the relationships among the yields, overflows and liquidity

the study has arranged a structural plan on the analysis which is complex

enough to capture the variations in the data and possible enough to handle it.

The study has followed previously completed studies and have selected a two

dimensional partition of the data. First dimension is the remaining time to

maturity of the security which the study has divided into six categories.

a) 1

day to 6 months

b) 6

– 12 months

c) 12

months to two years

d) 2

– 5 years

e) 5

– 10 years

f) 10

– 30 years

The second dimension

selected by the study was seasonedness of a security, which give the

information on how the security has been auctioned very recently. Further

referring to previous studies the study has separated the bonds into on-the-run

and off-the-run for their analysis.

To better understand the

multivariate structure of the data across tome-to-maturity categories in a a

selected seasonedness category, the study has performed standard factor

decomposition. The study has used principal components analysis to gain the

orthogonal 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. The

study 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 first

order VAR as the base line model to study the daily dynamics of the yields. Due

to the changes done in the first order VAR model they have used the authors

have called the model as a restricted VAR model where the slope coefficient Br

satisfied by Br x L = Bu and the Bu denotes the

coefficient of the full VAR model. The authors have lagged the yields on a

constant and the lagged common factors (level, slope and curvature) Ft-1

= L x Yt-1 where L denotes the factor loadings. The authors have

concluded that the baseline model they have fitted is successful in capturing

the yield levels, but effectively removes all day today changes.

Finally the hypothesis of

this study was in the absence of material public information flow, orderflow

imbalances account for a substantial portion of the day today fluctuations of

the yield curve and that the role of orderflow depends on the liquidity in the

Treasury Market.

Their hypothesis is

strongly accepted by the results obtained from the empirical study. They study

shows that unconditionally 21% of the day today fluctuations in the yields on

days without major macroeconomic changes are caused by orderflow imbalances.

Further the study emphasis that the daily yield changes are permanent. Finally

the authors have emphasized 3 important factors to be considered when modeling

U.S Treasury Securities.

1.

Price discovery does occur in the treasury

market

2.

Price discovery process is focused within

the on the run market segment.

3.

Low liquidity magnify the price discovery

process

The Yield Curve as a

Predictor of U.S. Recessions

According

to Estrella et.al. the steepness

of the yield curve has to be an excellent indicator of a possible future

recession. Current monetary policy has a significant influence on the yield

curve spread. A rise in the short rate tends to flatten the yield curve as well

as to slow real growth in the near term. This relationship, however, is only

one part of the explanation for the yield curve’s usefulness as a forecasting

tool.

Although

the 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 much

attention. Finance theory suggests that “stock prices are determined by

expectations about future dividend streams, which in turn are related to the future

state of the economy”.