Duration of zero coupon = 5
Duration of perpetuity = (1 + y) / y = (1 + 2%) / 2% = 51
a) Assume you invest y% in zero coupon and 1-y% in perpetuity such that the portfolio duration is 22
=> 5 * y + 51 * (1 - y) = 22
=> y = 63.04% invest in zero coupon and
1 - y = 39.96% in perpetuity
b) Next year duration of zero coupon = 4 and duration of perpetuity = 51
=> 4 y + 51 (1 - y) = 21
=> y = 63.83%
and 1 - y = 36.17%
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