FM for Actuaries

242 CHAPTER 7
i S t
t: 1 2 3 4 5
Year 3 5.40% 5.50% 5.60% 5.70% 5.80%
Scenario Year 2 5.30% 5.40% 5.50% 5.60% 5.70%
UP Year 1 5.20% 5.30% 5.40% 5.50% 5.60%
Year 0 5.10% 5.20% 5.30% 5.40% 5.50%
Current spot rate Year 0 5.00% 5.10% 5.20% 5.30% 5.40%
Year 0 4.90% 5.00% 5.10% 5.20% 5.30%
Scenario Year 1 4.80% 4.90% 5.00% 5.10% 5.20%
DOWN Year 2 4.70% 4.80% 4.90% 5.00% 5.10%
Year 3 4.60% 4.70% 4.80% 4.90% 5.00%
If the manager has an investment horizon of 3 years and we assume that all
coupons are invested at the prevailing one-year spot rate, what is her recommended
strategy under each scenario?
7.17 The following table gives the prices of zero-coupon and semiannual coupon
bonds:
Maturity Coupon rate r Price per
(years) (% per annum) 100 face value
0.5 0.0 98
1.0 0.0 95
1.5 4.0 96
2.0 6.0 97
Calculate the spot rates for maturities of 0.5, 1, 1.5 and 2 years using the
bootstrap method.
7.18 The following table gives the prices of some zero-coupon and annual-coupon
bonds:
Maturity Coupon rate r Price per
(years) (% per annum) 100 face value
1 0.0 98
2 0.0 95
3 4.0 96
4 6.0 97
Calculate the spot rates for maturities of 1, 2, 3 and 4 years using the bootstrap
method.