Strips, real return bonds and mortgage-backed securities

No coupon at all: the strip

A dealer can take a GoC bond apart and sell each coupon and the principal (the residual) as separate strip bonds — zero-coupon claims to one payment on one date. A strip pays nothing until maturity, so its price is a single discount:

$$P=\frac{\text{Par}}{(1+r{)}^n}$$

keeping the semi-annual convention so it compares with coupon bonds. An 8-year $1,000 strip when yields are 4.4 %: =-PV(0.044/2,8*2,0,1000) = 705.97. The pmt slot is 0 — that is the whole difference from Lesson 9.1. Reprice at 5 %: =-PV(0.025,16,0,1000) = 673.62 — a 4.6 % fall for 60 bp, the largest for any 8-year bond, because all the cash is at the end and none can be reinvested at the new rate. A strip has the highest interest-rate risk of any bond of its term. In a taxable account the annual accretion of the discount is generally taxed as it accrues even though no cash arrives, which is why strips are usually held in registered plans.

A principal that grows: the real return bond

A real return bond (RRB) pays a fixed real coupon rate on a principal that is indexed to the CPI. The index ratio is CPI now over CPI at issue (with a lag); the coupon rate never changes, but the payment grows with the principal, and at maturity the indexed principal is repaid. Prairie Grid's pension fund holds a 4 % RRB whose index ratio has reached 1.25 — the price level is a quarter higher than at issue. Indexed principal: 1,000 × 1.25 = 1,250. Semi-annual coupon: =0.04*1000*1.25/2 = 25.00, against 20.00 at issue. At an index ratio of 1.32: 26.40. The holder earns the 4 % real rate whatever inflation does — the Fisher relation (Lesson 8.2) paid directly. The Government of Canada has discontinued new RRB issuance; outstanding issues still trade and still index.

A claim on a pool of mortgages

A mortgage-backed security (MBS) is a claim on the cash flows of a pool of residential mortgages. Because each mortgage is an amortising loan (Lesson 7.7), the pool pays interest and principal every month, and the security's cash flows are shaped like an annuity, not a bullet — the principal comes back through the term, not at the end, and comes back faster when homeowners prepay. In Canada, NHA MBS are pools of CMHC-insured mortgages, and Canada Mortgage Bonds (CMBs) are bullet bonds issued by Canada Housing Trust and guaranteed by CMHC, backed by NHA MBS — the trust converts the annuity-shaped pool into the bond-shaped payment investors prefer. The Government of Canada now buys and holds a share of each CMB issue.

Three shapes

A coupon bond pays level interest then par. A strip pays one lump at the end — deepest discount, highest rate risk. An MBS pays interest and principal all the way through — an annuity. Draw the three cash-flow lines and every question in this lesson is answered by the picture.