A pension plan is obligated to make disbursements of $2.7 million, $3.7 million, and $2.7 million at the end of each of the next three years, respectively. The annual interest rate is 10%. If the plan wants to fully fund and immunize its position, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan?

The computation of duration is as follows:

Interest rate (YTM) is 10%.

(1)	(2)	(3)	(4)	(5)
Time until Payment (Years)	Payment (in millions of dollars)	Payment Discounted at 10%	Weight	Column (1) Column (4)
1	2.7	2.4545	0.3255	0.3255
2	3.7	3.0579	0.4055	0.8110
3	2.7	2.0285	0.2690	0.8070
	Column sum:	7.5409	1.0000	1.9435

Duration = 1.9435 years

The duration of the perpetuity is: (1 +y)/y= 1.10/0.10 = 11.00 years

Letwbe the weight of the zero-coupon bond. Then we findwby solving:

(w 1) + [(1 w) 11.00] = 1.9435w= 0.9056