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 (Eg: 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,
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.
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.
1.1. 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
1.2. 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.
1.3. The Yield Curve Predict Output and
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.