Cash Flow Matching

Study guides: Exam FM-2, Exam ILA-101

Cash flow matching (also called dedication) is a portfolio strategy in which asset cash flows are structured to exactly equal liability cash flows at every future date, eliminating both Price Risk and Reinvestment Risk entirely.

• Unlike Redington Immunization, which only protects against small parallel rate shifts and needs periodic rebalancing, a matched portfolio requires no rebalancing once constructed — each liability is funded directly by a matching asset cash flow.
• It is more conservative, and typically more expensive, than immunization: it removes reinvestment risk at the cost of reduced flexibility.
• Construction proceeds backwards from the last liability date — fund the final liability first, then the second-to-last, and so on.
• A coupon bond bought for a later liability also pays coupons on the earlier dates, so those coupons reduce the amount still to be funded at each earlier date.

Cash Flow Matching a Two-Period Liability A company has liabilities of $5{,}000 due at time 1 and $10{,}000 due at time 2. Zero-coupon bonds are available at all maturities. Show how to construct a cash flow matched portfolio.

Answer Step 1 — Fund the time-2 liability: Buy a 2-year zero-coupon bond with face value $10{,}000. At time 2 it pays exactly $10{,}000. ✓

Step 2 — Fund the time-1 liability: Buy a 1-year zero-coupon bond with face value $5{,}000. At time 1 it pays exactly $5{,}000. ✓

The portfolio cost is \dfrac{10{,}000}{(1+s_2)^2} + \dfrac{5{,}000}{1+s_1}, where s_1, s_2 are the current spot rates. Once purchased, no rebalancing is needed and the liabilities are fully funded regardless of future interest rate movements.

Matching with a Coupon Bond A pension fund must pay 1{,}000 at time 1 and 2{,}000 at time 2. It can buy a 1-year zero-coupon bond and a 2-year bond with 5% annual coupons. Find the face amount of each bond that exactly matches the liabilities.

Answer Time 2 first: the 2-year bond pays its face F plus a coupon of 0.05F at time 2, so

\begin{align*}
1.05F &= 2{,}000 \\
F &= 1{,}904.76
\end{align*}

Then time 1: that bond also pays a coupon of 0.05(1{,}904.76) = 95.24 at time 1, so the zero-coupon bond only has to supply the rest: 1{,}000 - 95.24 = 904.76 Buy a 2-year bond with face 1{,}904.76 and a 1-year zero-coupon bond with face 904.76; the asset cash flows are exactly 1{,}000 at time 1 and 2{,}000 at time 2.