In: Accounting
A company must pay a liability of $1,000 in 2 years. Zero coupon bonds with term of 1 year and 4 years are available for investment. The effective rate of interest is 7.5%.
(b) Show empirically that immunization has been achieved even for large changes in the interest rate. Take as an example a decrease in the interest rate to 0% and an increase to 100%.
Solution:
A)
To immunize against interest rate fluctuation risk, company has to invest in bond or bond portfolio, so that duration of bond or bond portfolio is equal to the investment horizon i.e. 2 years in this case.
A zero coupon bond always has a duration equal to its maturity.
Hence the duration of one year term zero coupon bond would be 1 year and the duration of four year term zero coupon bond would be 4 years.
But the company investment horizon is 2 years. So, we have to invest in 1 year and 4 year term zero coupon bonds in such a proportion that the total duration of the bond portfolio would be 2 years.
Let us assume that to maintain portfolio duration of 2 years, the proportion of total fund to be invested in one year term bond be p and in four year term bond be 1-p.
So, we can write the following:
(p*1)+[(1-p)*4]=2
Therefore p=0.67
It means, to maintain the portfolio duration of 2 years, 67% sould be invested in 1 year term bond and 33% sould be invested in 4 year term bond.
Total amount to be invested= $1,000/1.075*1/1.075= $865
Investment to be made in 1 year term bond = $865*67%= $579.55
Investment to be made in 4 year term bond = $865*33%= $285.45
It means to immunize the company should buy $579.55 of 1 year term bond and $285.45 of 4 year yerm bond.