Unformatted text preview: a cum interest bond, where there is 111/184 = 0.6 of a period until the next
coupon payment, t1 = 0.6, t2 = 1.6, t3 = 2.6 … Assuming coupon payments are semi-annual, the ending MacDur
must be divided by 2 to give the annualised MacDur. D URATION AND IMMUNISATION OF INTEREST RISKS
Investors may remove or immunize themselves from interest rate risks by holding a bond for a period that
equals to its duration.
Thus, if expected HPR = actual HPR despite a change in rates, then we can conclude that price and income risks have completely offset one another and
the investor is immunized from interest rate risks C ONDITIONS OF INTEREST RATE RISK IMMUNISATION
There are 3 conditions that must be met in order that interest rate risks are completely removed or HPR equals
to the initial yield: Yield Curve is flat at the time of investment – bonds with different times to maturity have the same
yield as that of the bond under study. This ensures that the expected return from the bond is the
same return as its initial YTM.
Only a small parallel shift in the yield curve is allowed – any unexpected change in rates applies to
the entire spectrum of maturities. This ensures that the unexpected rise or fall in coupon
reinvestment income offsets the unexpected fall or rise in selling price of the bond completely.
No further change to interest is allowed beyond the first coupon payment. This is because – if
coupon interests received at different times during the holding period will be reinvested at different
rates, this violates the 2nd condition. Besides, once interest rates changes after the purchase, duration
will change, whilst holding period will remain the same. The mismatch between the 2 implies that the
2 types of interest rate risk will no longer offset one another completely when a second change in
interest rate occurs. While the holding period decreases linearly with time, duration is affected by changing interest rates in a nonlinear manner. Thus to stay immunized from interest rate risks for...
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