Case 038Structured finance and securitisationCore

Pass-through certificates on a home loan pool were priced for slow prepayment, and borrowers are prepaying much faster. Show how the weighted average life shortens and what that does to an investor who paid a premium.

The situation

Kerawal Home Loans Trust issued pass-through certificates on a Rs 1,000 crore pool of 15-year level-payment home loans at 9%. Every month, the borrowers' interest and principal, scheduled and prepaid, pass straight to certificate holders. For simplicity, the certificates also pay 9%, with servicing costs ignored.

The certificates were priced assuming borrowers prepay 8% of the outstanding balance a year. Home loan rates then fall, borrowers refinance and move their loans to other lenders, and prepayment runs at 20% a year. An investor bought certificates at 102, a 2% premium over par.

Your task

What is the weighted average life at 8% and at 20% prepayment, and what happens to the premium investor's yield?

Quick check

At 20% prepayment, what happens to the investor who paid 102?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The weighted average life falls from about 6.1 years to 3.6 years, and the premium buyer's yield drops from 8.53% to 8.29%. Prepaid principal comes back at par, so the 2 point premium is spread over fewer years of coupons. Worse, the cash returns just when rates have fallen and can only be reinvested at lower yields. That timing is prepayment risk.

Step 1What is weighted average life, and why does prepayment move it?

Weighted average life (WAL) is the average time until each rupee of principal is repaid, weighted by how much comes back when. With no prepayment the pool's WAL would be about 9.2 years; at 8% a year it is 6.1; at 20% it is 3.6. Each month a conditional prepayment rateThe share of the outstanding loan balance that borrowers repay early in a year, beyond their scheduled instalments; converted to a monthly rate for the cash flow model. of 20% a year removes about 1.8% of the balance on top of the scheduled instalment, so the balance collapses much faster than planned.

The relationship
SMM=1−(1−CPR)1/12WAL=∑tt Pt12∑tPt\text{SMM} = 1 - (1 - \text{CPR})^{1/12} \qquad \text{WAL} = \frac{\sum_t t\,P_t}{12\sum_t P_t}
\text{CPR}yearly prepayment rate, 8% priced and 20% actual
\text{SMM}the same rate as a monthly share of the balance
P_tprincipal repaid in month t, scheduled plus prepaid
What it says in wordsConvert the yearly prepayment rate to a monthly one, run the pool month by month, and average the months in which principal comes back.
Faster prepayment cuts the average life from 6.1 to 3.6 years2505007501,00003691215Years since issueBalance outstanding, Rs croreWAL 6.1 yrs at 8%WAL 3.6 yrs at 20%no prepayment
At the priced 8% prepayment rate the pool's balance runs down with a weighted average life of 6.1 years; at 20% it falls far faster, leaving 456 rather than 694 after three years, and the average life shortens to 3.6 years.
Step 2Why does the premium buyer lose?

Pay Rs 102 for a certificate and every rupee of principal is repaid at Rs 100. The investor recovers the extra 2 only through years of 9% coupons. Shorten those years and the premium is not earned back: the yield falls from 8.53% at the priced speed to 8.29% at the actual speed. A buyer at 98 sees the opposite: the discount is collected sooner, and the yield rises from 9.48% to 9.73%. So prepayment risk has a direction, and whether it hurts depends on the price paid.

Fast prepayment hurts whoever paid above par, and helps whoever paid belowPaid 102, prepay 8%8.53%Paid 102, prepay 20%8.29%Paid 98, prepay 8%9.48%Paid 98, prepay 20%9.73%bars start at 7.0%
Bought at 102 the certificates yield 8.53% at 8% prepayment and 8.29% at 20%, while bought at 98 they yield 9.48% and 9.73%, so faster prepayment hurts the premium buyer and helps the discount buyer.
Step 3Why is the timing worse than the arithmetic suggests?

Borrowers prepay most when rates fall, because refinancing is cheaper. That is exactly when the investor would like to keep a 9% asset. The cash comes back when it can only be reinvested at lower rates, and slows to a trickle when rates rise and the investor would like it back. The certificate behaves like a bond with a call option sold to the borrowers. A rating agency or treasury analyst therefore runs the cash flows at several prepayment speeds and reports the yield and WAL under each, rather than one priced case.

One caveat on the model: a constant 20% is itself a simplification. Real prepayment rises with the gap between the loan rate and new rates, falls as the pool ages and the most rate-sensitive borrowers have already left, and varies with seasonal bonuses. The direction of the answer holds; the exact figures depend on the assumed path.

Where candidates lose it

Candidates often say faster prepayment is good because the investor gets cash back sooner and there is less credit risk. For a premium buyer it is bad, because every early rupee is repaid at par against a price above par.

The second miss is quoting the coupon as the return. The 9% coupon is fixed; the yield depends on the price paid and on how long the principal stays out, which is precisely what prepayment changes.

What the interviewer asks next

  • What prepayment speed would make the 102 buyer earn exactly 8.75%?
  • How could the deal be tranched so one class of investors bears most of the prepayment risk?
  • Why might prepayment in an Indian home loan pool rise even without a fall in rates?

Company names and figures are illustrative.