A Bond is a debt instrument issued by
governments, corporations and other
entities in order to finance projects or
In essence, a bond is a loan
that investors make to the bonds issuer.
Immunization is a set of rules that is being
used for the purpose of minimizing the
impact of a change in interest rate of a
Bond immunization is an investment
strategy used to minimize the interest rate
of bond investments by adjusting the
portfolio duration to match the investors
investment time horizon.
Immunization is a technique that makes
the bond portfolio holder to be relatively
stream of cash flows.
The bond interest rate risk from the
changes in the market interest rate.
The market rate effect the coupon rate and
the price of the bond . Immunization locks
in a fixed rate of return during the amount
of time an investor plans to keep the bond
without cashing it in.
In general, the longer the term to maturity,
the greater the sensitivity to interest rate
Example: Suppose the zero coupon yield
curve is flat at 12%. Bond A pays $1762.34
in five years. Bond B pays $3105.85 in ten
years, and both are currently priced at
• Bond A: P = $1000 = $1762.34/(1.12)5
• Bond B: P = $1000 = $3105.84/(1.12)10
Now suppose the interest rate increases by
• Bond A: P = $1762.34/(1.13)5 = $956.53
• Bond B: P = $3105.84/(1.13)10 = $914.94
The longer maturity bond has the greater drop in
price because the payment is discounted a
greater number of times.
A portfolio is Immunized when its duration
equals the investors time horizon.
Maintaining an Immunized portfolio means
rebalancing the portfolios average duration
every time interest rates change, so that
the average duration continuous to equal
the investors time horizon.
• Default and call risk ignored
• Multiple nonparallel shifts in a nonhorizontal
• Costly rebalancing ignored
• Choosing from a wide range of candidate bond
portfolios is not very easy
Here coupon rate risk and the price risk can be
made to offset each other.
Whenever there is an increase in the market
interest rate ,the prices of the bonds fall. At the
same time the newly issued bonds offer higher
The coupon can be re-invested issued bonds offer
higher int rate & losses that occur due to the fall in
the price of bond can be offset &the portfolio is
said to be immunized.
Example : If an investor has invested
equal amount of money in 3 bonds namely
A,B&C with duration of 2,3,4 years
respectively , than the bond portfolio
= 2.77 or 3 years
Every time market interest rates change
the duration of every bond changes.
During tends to diminish more slowly than
calendar time for coupon-paying bonds
when interest rates do not change.