Case 096Rates and hedgingHard

A lender makes three-year fixed-rate loans funded with one-year borrowings. Rates rise 150 basis points. What happens to net interest income, what is the duration gap, and how would you change the funding?

The situation

Lavanyam Finance, a non-bank lender to small businesses, has Rs 5,000 crore of three-year fixed-rate loans yielding 12%. The book is laddered: a third matures each year and is re-lent. It funds itself with Rs 4,300 crore of one-year borrowings costing 8%, and Rs 700 crore of equity.

Market rates rise 150 basis points across all maturities. For simplicity, assume both the borrowings and the maturing third of the loan book roll over on the first day of each year at the new rates, and interest is paid annually.

Your task

What happens to net interest income next year and after, what is the duration gap and the hit to economic value, and what funding would you recommend?

Quick check

Next year, does the rate rise help or hurt Lavanyam's net interest income?

Worked solution

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

30-second answerThe answer to give first

Net interest income falls about Rs 39.5 crore next year, 15% of Rs 256 crore, because borrowings reprice three times faster than loans. The squeeze eases to Rs 14.5 crore in year two and turns positive in year three. The duration gap is about 0.87 years, so the rise costs about Rs 65 crore of economic value, 9% of equity. Fund the book in a ladder matching the loans, at a cost of about Rs 15 crore a year.

Step 1Why does a rate rise hurt a lender that lends long and borrows short?

Because the two sides reprice at different speeds. Every rupee of one-year borrowing reprices within the year, but only a third of the three-year loan book does. A family that locked its rental income for three years but pays a floating-rate home loan feels the same thing: the loan payment rises this year, the rent only when the lease ends. In the first year 4,300 crore of liabilities reprice against Rs 1,667 crore of assets, a repricing gapAssets that reprice in a period minus liabilities that reprice in the same period. A negative gap means income falls when rates rise. of minus Rs 2,633 crore.

All Rs 4,300 crore of Lavanyam's borrowings reprice within a year while only Rs 1,667 crore of loans do, a first-year gap of minus Rs 2,633 crore, and the loans that make up the difference reprice only in years two and three.

Step 2What happens to net interest income, year by year?

Today it earns Rs 600 crore on loans and pays Rs 344 crore on borrowings, net interest income of Rs 256 crore. Next year borrowings cost Rs 64.5 crore more and the re-lent third earns Rs 25 crore more, so income falls Rs 39.5 crore, to Rs 216.5 crore. In year two two thirds of the loans have repriced, and the hit shrinks to Rs 14.5 crore. By year three all Rs 5,000 crore earns the higher rate against Rs 4,300 crore paying it, and income is Rs 10.5 crore higher, because Rs 700 crore of loans are funded by equity that costs no interest.

After a 150 basis point rise Lavanyam's net interest income falls Rs 39.5 crore in year one and Rs 14.5 crore in year two, then rises Rs 10.5 crore in year three once every loan has repriced, so the damage is front-loaded.

Step 3What is the duration gap, and what does it say about value?

Income is one lens; the value of the balance sheet is the other. The three loan tranches have modified durations of about 0.89, 1.69 and 2.40 years, averaging 1.66; the one-year borrowings about 0.93. The duration gap is 1.66 minus 0.86 times 0.93, about 0.87 years, so a 150 basis point rise cuts the economic value of equity by about Rs 65 crore, 9.3% of Lavanyam's Rs 700 crore.

The relationship

\Delta EVE \approx -\Big(D_A - \tfrac{L}{A} D_L\Big) \times A \times \Delta y = -(1.66 - 0.86 \times 0.93) \times 5{,}000 \times 0.015 \approx -65

D_A, D_L	modified duration of loans and of borrowings, years
L/A	borrowings over loans, 4,300 / 5,000 = 0.86
0.015	the 150 basis point rise

What it says in wordsA rise of 1.5 points takes about Rs 65 crore off the present value of what Lavanyam owns net of what it owes.

Step 4What funding would you recommend?

Match the funding to the ladder. Keep about Rs 1,667 crore at one year, raise Rs 1,300 crore at two years and Rs 1,333 crore at three years, so each year's repricing on both sides is roughly equal. Longer money costs more: at an assumed 8.4% for two years and 8.7% for three, the term premium is about Rs 14.5 crore a year. In return, a 150 basis point rise now costs about -0.0 crore of income in year one instead of -39.5, and the duration gap falls to about 0.21 years, cutting the value hit to about Rs 16 crore. Pay-fixed interest rate swaps on the one-year borrowings do the same job without refinancing, if the lender can use them.

State the limitation. Assuming everything rolls on the first day overstates year-one damage; with repricing spread through the year it would be roughly half. And a lender to small businesses faces a second risk the gap does not show: if rates rise sharply, some borrowers struggle to pay, so credit losses and rate losses tend to arrive together.

Where candidates lose it

The common slip is saying higher rates help a lender because new loans earn more. That is true only for the part of the book that reprices. With all the borrowings repricing and a third of the loans, the first effect is a squeeze.

The second is stopping at income. The interviewer asked for the duration gap too, because it captures the damage to value in one number even after the income effect has passed.

What the interviewer asks next

What if rates fell 150 basis points instead?
How would floating-rate loans change the gap?
Why might a lender deliberately keep some mismatch?
How much would a pay-fixed swap on Rs 2,600 crore cost to put on, and what would it save?

Company names and figures are illustrative.