Case 077Structured finance and securitisationCore
You buy mortgage-backed pass-through bonds at 102. How do their average life and yield change if borrowers prepay 10% a year against 25% a year?
1The situation
Garvita Housing Finance has pooled Rs 500 crore of fixed-rate home loans with ten years left to run and a weighted average coupon of 9.5%. The pool is sold to investors as pass-through bonds: every rupee of interest and principal borrowers pay, less a 0.5% servicing fee, flows straight to bondholders, so the bonds pay a 9.0% coupon on whatever principal is still outstanding.
A fund buys the bonds at 102, a premium, because 9.0% is above current market rates. Each year borrowers pay their scheduled instalment, and some also repay early. Work per Rs 100 of bonds, with payments once a year, under two speeds of early repayment: 10% a year and 25% a year of the balance left after the scheduled instalment.
2Your task
What are the weighted average life and the yield at each prepayment speed, and why does the buyer at 102 care which one happens?
Quick check
The fund paid 102. If borrowers prepay faster, what happens to its yield?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
At 10% a year the bonds have a weighted average life of 4.6 years and yield 8.42%; at 25% the life falls to 3.1 years and the yield to 8.20%. Every prepaid rupee comes back at 100 on bonds bought at 102, so faster prepayment gives the fund fewer years of 9% coupon to earn back its premium. A buyer at a discount gains from the same speed-up.
Step 1Why does the life of a mortgage bond depend on the borrowers?
A home loan lets the borrower repay early without much penalty, and many do: they sell the house, get a bonus, or refinance when rates fall. The pass-through bond hands every such repayment straight to the investor. The investor has effectively sold every borrower the right to repay at par whenever they like. So the bond has no fixed life. Analysts summarise it with weighted average lifeThe average time until each rupee of principal is repaid, weighting each year by the principal returned in it., the average number of years each rupee of principal stays out.
| Year | Balance at start, 10% | Principal paid, 10% | Balance at start, 25% | Principal paid, 25% |
|---|---|---|---|---|
| 1 | 100.0 | 15.8 | 100.0 | 29.8 |
| 2 | 84.2 | 14.1 | 70.2 | 21.5 |
| 3 | 70.1 | 12.6 | 48.7 | 15.4 |
| 4 | 57.5 | 11.3 | 33.3 | 11.0 |
| 5 | 46.2 | 10.1 | 22.3 | 7.8 |
| 6 | 36.1 | 9.0 | 14.5 | 5.4 |
| 7 | 27.1 | 8.0 | 9.1 | 3.7 |
| 8 | 19.1 | 7.1 | 5.3 | 2.5 |
| 9 | 12.0 | 6.3 | 2.8 | 1.7 |
| 10 | 5.6 | 5.6 | 1.1 | 1.1 |
| Weighted average life | 4.58 yrs | 3.07 yrs |
Step 2Why does a shorter life cut the yield for this buyer?
The fund paid 2 points over face for a coupon above market. It earns that premium back slowly, a little each year, through the extra coupon. Every rupee that is prepaid stops earning the extra coupon and returns at 100, so the unrecovered premium is lost. At 10% a year there are enough coupon years to absorb it: the yield is 8.42%. At 25% a year there are not: 8.20%. It is like paying a premium for a long lease on a shop and then being bought out early at the original deposit.
Step 3When does prepayment speed up, and why does that make it worse?
Borrowers refinance when rates fall, which is exactly when the fund would like to keep its 9% coupon. Prepayment speeds up when reinvestment rates are lowest, so the principal comes back at the worst time to reinvest it. That is negative convexityA bond whose price rises less when rates fall than it drops when rates rise, because falling rates trigger early repayment.: when rates fall the bond shortens and its price gains are capped near par; when rates rise prepayments slow and the bond lengthens just as prices fall. The limitation of this case is the fixed speeds; real models tie prepayment to the gap between the loan rate and the market rate. The desk view: a premium pass-through should be bought only at a yield that still works at the fast speed, here 8.20%, not the 8.42% the slow speed shows.
Where candidates lose it
The usual loss is saying faster prepayment is good news because the money comes back sooner. That is true only for a buyer below par. Above par, every early rupee realises a loss of premium, and the question hands you a price of 102 precisely to test this.
The second is quoting the stated maturity of ten years as the life of the bond. With prepayments the weighted average life is well under half that, and it is the number the price and the hedge are built on.
What the interviewer asks next
- At what price would the yield be the same at both prepayment speeds?
- How would you hedge the fund's exposure to a fall in rates?
- Why might a pool of loans to first-time buyers in small towns prepay more slowly than a pool of large urban loans?
- What does an interest-only strip from this pool do when prepayments speed up?
Company names and figures are illustrative.