4.2.4 Zero rate
An nyear zero interest rate is the interest rate on an investment which
starts on todays date and last for nyears. In this time period no intermediate
payment is made. All the interest and principal payment is realized at the
end of nye
4.5
Hedging with Tbond futures
Fixed interest bearing securities have risks associated with the volatile
interest rate markets. Unfavourable interest rate change may lead to
potential capital loss to the investors. Interest rate futures have been devised
fixed and pay floating. These rates are quoted for the number of maturities
and number of different currencies. The following table 5.1 shown an
illustration of the quotes where payments are exchanged semiannually.
TABLE 5.1: BID AND OFFER RATES IN A SWA
price sensitivity w.r.t. interest rate changes. In other words, a high duration
bonds price is more sensitive to interest rate changes than the low duration
bond. It is also defined as the weighted average as the maturities of the
bonds coupon and the pri
3.9
Self assessment questions
1.
What do you understand by hedging? Explain the concept with
suitable illustrations.
2.
Discuss various concepts of hedging with suitable illustrations.
3.
Hedging prevents the investor from future price fluctuations? Do
yo
4.3.5 Euro Dollar Futures
Dollars deposited in foreign banks are known as Eurodollars. This
practice was started in Europe to gain higher yield available on other
instruments in US money market. The foreign banks offer attractive interest
on deposits beca
fixed rate at 68 basis points above (i.e. 5.95 + 0.68 = 6.63%) the Treasury
yield. Another example to understand the concept: Suppose a bank quotes a
US dollar floating to a fixed 6years swap rate as:
Treasury + 30 bp/Treasury + 60 bp vs. six months LIBO
to initiate trading in longterm interest rate futures with the introduction of
Tbonds by CBOT in 1977. Other countries like Japan, France and UK have
longterm interest future market with almost similar pricing mechanism and
same functioning.
4.3.1 TBo
TABLE 4.2: CALCULATION OF FORWARD RATES
Year (m)
Zero rate for an nyear Forward
rate
investment (% p.a.)
year (% p.a.)
1
10.0

2
10.5
11.0
3
10.8
11.4
4
11.0
11.6
5
11.1
11.5
for
nth
Thus a 10% p.a. rate for one year means that in return for an
investme
5.5
Rationale behind swapping
To avoid risk of fluctuation in forex, interest rates, stock indices
investors attitude etc. the swap market has merged now to explain that why
firms and people want to enter into swap agreement. The rationale can be
explaine
The deals of currency swaps are structured by a bank which also routes
the payments from one party to another. Currency swaps involve exchange of
assets and liabilities. The structure of a currency swap agreement can be
understood with the help of the fol
3.6.1 Monitoring of hedge
To monitor the hedge on a continuous basis the following information
should be looked for:
Cash/spot position: The hedger should have an idea of the current
position in cash/spot and the relevant changes in the same. The gains/lo
Theories determining term structure: There are two types of risks
associated with interest bearing securities. Interest risk arises due to
changing nature of macroeconomic variables such as inflation, money supply,
growth rates, government policy and ex
3
face value. E.g. bid price of 6 % of Dec. 06 Tnote is 100 and
8
4/32% of face value.
The US government has the option of calling the bonds away
from their owners before maturity and are called callable
Tbonds. E.g. 12% of Nov. 0913 T bonds are first
Suppose an FRA in which a financial institution agrees to earn an
interest rate of Rk for the period of time between T1 and T2 on a principal
amount of L.
Let RF is the forward LIBOR interest rate for the period between T1
and T2. R is the actual LIBOR in
to floating swap, one party pays one floating rate and the other pays another
floating. Forward swaps include exchange of interest rate payments that do
not begin until a predetermined future date in time. In a swaption, the
features of swaps and options
4.
If m = 3 or 9 months, then the CBOT estimates allowed interest
to be c/4 (half a semiannual coupon). Under these assumptions,
the price of the bond if YTM is 3% will be:
CF =
C /2 + C /2(PVIFA3%,2 y+1 ) + 1(PVIF8%,2 y+1 ) C
4
(1 + 0.03)0.5
if m = 9.
C
5.1
Introduction
In the recent past, there has been integration of financial markets
worldwide which have led to the emergence of some innovative financial
instruments. In a complex world of variety of financial transactions being
taken place every now a
B =
BD
.
1 + y/7
Dmod =
D
(1 + y)
B=BDmody
(4.7)
(4.8)
Hence the modified duration is the relative price change with respect to
change in yield.
In the above Table 4.1 the price of the bond is 94.213 and duration is
2.653. The view expressed in semi
Fabozzi et al., Foundations of Financial Markets and
Institutions, Pearson Education inc. Delhi, 2002.
Gupta, S.L., Financial Derivatives (Theory, Concepts and
Problems), Prentice Hall of India Ltd., New Delhi, 2005.
Hull, John C., Options, Futures and O
the hedge ratio, which denotes the number of futures contracts made by
comparing relative price sensitivities of futures and cash instruments. With
the help of duration period and regression method, this hedge ratio can be
calculated. Minimum hedge ratio
rs = a + brF.
(4.10)
where rs is historical changes in interest rate of the cash instrument
rF = Historical changes in the futures interest rates.
a, b = Regression coefficients
The hedger will be interested in seeking a relationship between yield
change
For infinitesimally change in yield curve ( y) the bonds price will be
changed as B shown by following equation.
B
= BD
y
or
B
B
= D y
(4.5)
(4.6)
Hence from relationship expressed by equation (4.6) it is clear that the
percentage change in bond price i
brokerage, fees, translation and management costs etc. For this purpose expost measure of effectiveness should be calculated with the help of deviation
or significant difference between the anticipated and expost hedged strategy.
3.7
Summary
Hedging is a
portfolio of Rs. 1,00000 is vulnerable contracts.
Future
price
is
to increase in longterm interest rate.
reflecting 6% p.a. interest rate.
August 8
August 8
1000
Long term interest rate rises to 71% Closes out by buying 4 futures bond
p.a. The value of b
in ABCL Ltd. Share price for every Rs. 20 change in SRKL Ltd.
Determine the amount of contract required to minimise risk.
3.10 References/suggested readings
Apte, Prakash, G., International Financial Management, 3rd
edition, Tata McGraw Hill Publishing Co
which the short (seller) intentions to deliver bonds. The first day is called
intention day or position day. On this day the short can notify the exchange
for his intention to deliver until 8.00 p.m. Central time on the position day to
declare an intentio
lower cost and can swap for a particular market. A low credit rated firm can
raise funds from floating rate credit market and enjoy comparative advantage
over highly rated company because it pay a smaller risk premium. The
differing interest rates in diff