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What is Immunisation of Bond?


Immunization of bond: It is a strategy used by the bond portfolio manager to reduce the interest risk which affects the bond price through ups and down in interest rate. There is an inverse relationship between interest rate and bond price. It means when interest rate fall then there is a rise in the price of a bond and vice versa.  So, to minimize the changes in interest rate during an investment period immunization is used. The changes in interest rate will affect the investors’ future obligations. The process of immunization is done by reinvesting the coupon amount in new bond which offers high interest rate due to which the price of a old bond price is decreases and reinvesting the coupon amount in a bond will offset the losses in bond price due to rise in interest rate. Immunization helps to ascertain the investment quantity in a security will provide the definite cash flows to meet the future obligations in time.

Formula:
Immunization = X1*d1 + X2*d2 = X1, X2
Where,
D1 = duration of 1st bond or security
D2 = duration of 2nd bond or security
X2 = Weight of 2nd security
X1,X2 = liabilities duration

Example: Find out the bond portfolio duration which consist 3 bonds A, B and C in which each bond have Rs. 10, 000 face values and bears 9%, 8.9% and 10% coupon rate respectively. The duration of bond A is 2.7 years, bond B is 3 yrs and bond C is 3.5 yrs. The investor invested in 3:2:1 ratio in 3 bonds respectively. The duration of a liabilities is 3 yrs.
Solution:
Portfolio duration = X1*d1 + X2*d2 = X1, X2
= 2/6*2 + 3/6*3 + 1/6*3.5 = 2
= 4.5 yrs

Example: Mr. Sharma has purchased 2 bonds whose face value is Rs. 10, 000 each and market value of bond P is Rs. 1,102 and bond Q is Rs. 990. The yield rate is 6% p.a. of each bond. Mr. Sharma needs Rs.2 0,000 after 3 years. Find out how much amount is invested in these 2 bonds of a bond if the duration is 2 and 5 years respectively.
Solution: X1*d1 + X2*d2 = X1, X2
X1*2+ (1 - X1)*5 = 3
2X1 + 5 – 5X1 = 3
-3X1 = -2
X1 = 0.666 or 67%
X2 = 0.333 or 33%
Total amount invested in 2 bonds are: 20, 000/ (1.06) 3 = Rs. 16, 792.61
Amount invested in Bond P: 16, 792.61*0.666 = Rs. 11, 183.87
Amount invested in bond Q: 16, 792.61*0.333 = Rs. 5, 591.93

Example: Mr. Chopra is working in a software company and he wants to invest his savings in a security for 5 years to get Rs. 2, 00, 000 for his child higher education. There are 2 bonds are available bond A and bond B and there durations are 3yrs, 7 yrs respectively. The market value of bond A is Rs. 700. The yield rate is 7% annually. The maturity value of bond A and B is Rs. 900 and Rs. 1,060 respectively.  The yield rate of bond B is 7%. The market value of bond is Rs. 880. Find out how much quantity is purchased by Mr. Chopra to fulfil his future obligations.
Solution: X1*d1 + X2*d2 = X1, X2
X1*3 + (1- X1)*7= 5
3X1 + 7 – 7X1 = 5
X1 = 0.5
X2 = 0.5
Total amount invested in 2 bonds are: 2, 00, 000/ (1.07) 5 = Rs. 1, 42, 857.14
Amount invested in Bond A:  1, 42,857.14*0.5 = Rs. 71, 428.57
Amount invested in bond B:  1, 42,857.14*0.5 = Rs. 71, 428.57
Number of bond A purchased = 71, 428.57/ 700 = 102.04
Number of bond B purchased = 71, 428.57/ 880 = 81.16

                                                                              




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