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.:
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,
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.
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.).
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.
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.
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.
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.
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
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.
day to 6 months
– 12 months
months to two years
– 5 years
– 10 years
– 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
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.
Price discovery does occur in the treasury
Price discovery process is focused within
the on the run market segment.
Low liquidity magnify the price discovery
The Yield Curve as a
Predictor of U.S. Recessions
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
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”.