Case 082Structured products and client solutionsCore

A six-month range accrual on USD/INR pays 8% a year for each day the fix is between 82.00 and 85.00. Ninety of 125 fixing days fall inside. What is the coupon, and what is the client short?

The situation

Kolad Bank's structuring desk sold a corporate client a six-month range accrual note on Rs 50 crore. The note pays interest at 8% a year, accrued only for each business day on which the USD/INR reference fix lies between 82.00 and 85.00, inclusive. Days with the fix outside the band earn nothing. Principal is returned in full at maturity. The period has 125 fixing days, and a plain six-month deposit at the time paid 7% a year.

The rupee was steady for four months and then weakened past 85 in the last six weeks. Of the 125 fixings, 90 fell inside the band.

Your task

Compute the coupon the client receives, compare it with the plain deposit, and explain what the client sold to get the headline 8%.

Quick check

Before computing: the headline says 8%. For six months with 90 of 125 days inside, what does the client actually get?

Worked solution

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

30-second answerThe answer to give first

The coupon is 2.88% for the half year, Rs 1.44 crore on Rs 50 crore, below the Rs 1.75 crore a plain 7% deposit would have paid. The rate is 8% a year, so six months earns at most 4%, and only 90 of 125 days qualified: 4% times 0.72. The client earned the extra 1% of headline rate by selling the bank a strip of 125 daily digital options, each paying the bank one day of coupon whenever the fix leaves the band. A one-way rupee move knocked out 35 of them.

Step 1How is the coupon built, day by day?

Think of a daily-wage worker paid Rs 1,000 for each day the factory opens and nothing for each day it shuts. The headline wage is Rs 1,000 a day, but the month's income depends on how many days the gate was open. A range accrual pays its coupon one day at a time, and every day is a separate question: was the fix inside the band? Each qualifying day earns 8% divided by the days in the period, which on Rs 50 crore is about Rs 1.60 lakh. 90 days earn it and 35 days earn nothing.

The relationship

\text{Coupon} = 8\% \times \tfrac{1}{2} \times \frac{90}{125} = 2.88\% \quad\Rightarrow\quad \text{Rs }50\text{ crore} \times 2.88\% = \text{Rs }1.44\text{ crore}

8%	the annual accrual rate printed on the term sheet
1/2	the six-month period as a fraction of a year
90/125	the share of fixing days on which the fix was inside 82.00 to 85.00

What it says in wordsThe coupon is the annual rate, scaled to the period, scaled again by the fraction of days that stayed inside the band.

The fix stayed inside 82.00 to 85.00 for 90 of 125 days and left it for 35, almost all in the late rally above 85, so the note paid 8% times a half year times 90 over 125, which is 2.88% instead of the 4% maximum.

Step 2What did the client sell to get a headline above the deposit rate?

Nobody pays 8% in a 7% world for free. The client has sold the bank 125 tiny digital optionsOptions that pay a fixed amount if a condition is met on a date and nothing otherwise, here one day of coupon if the fix is outside the band., one per fixing day, each one knocking out that day's coupon if the fix is outside the band. The premium for those options is the extra 1% of headline rate and the appearance of a product that only pays. The exposure is not symmetric in the way a client expects: the band is 3 rupees wide, the rupee trends, and once the fix crosses 85 it tends to stay there, so the days are lost in a block, not scattered. That is what happened: four quiet months, then 35 lost days in six weeks.

Outcome	Days inside	Coupon, %	Rs crore on 50 crore
Every day inside	125	4.00	2.00
Plain deposit at 7%		3.50	1.75
This period	90	2.88	1.44
Break-even with the deposit	109	3.50	1.75
Half the days outside	63	2.02	1.01

The note beats the 7% deposit only if at least 109 of 125 days fix inside the band; this period's 90 days paid Rs 1.44 crore against Rs 1.75 crore for the deposit.

Step 3How would you explain the trade to the client, and what is the limit of the product?

Say the sentence the term sheet does not. You are being paid 1% a year above the deposit to bet that the rupee stays in a 3 rupee band for six months, and the bank has set the band using its own forecast of where the rate will drift. The note needs 109 of 125 days inside just to match the deposit, and a single trend can take out 30 days in a row. The product suits a treasurer with a strong view on stability and a tolerance for earning less, not one chasing yield. The limit of the structure is that the client's loss is capped at the coupon: principal is safe, which is why the sale is allowed, and also why the client underestimates how much coupon can vanish.

Where candidates lose it

The common loss is treating 8% as the return. It is an annual rate on a six-month note, paid only on qualifying days, so the realistic figure is 4% scaled by the share of days inside the band.

The second is seeing the coupon as a symmetric bet. Days are lost in blocks when the rate trends, not one at a time, which is why the client's downside arrives all at once.

What the interviewer asks next

How would you price the note at inception using the forward curve and the volatility of USD/INR?
The client asks for a wider band, 81 to 86. What happens to the headline coupon, and why?
How would the bank hedge its exposure to the daily fixings?
If the note had a two-year tenor, which direction of risk grows the most?

Company names and figures are illustrative.