Case 069Indian debt market executionCore

A housing finance company raises Rs 500 crore on the electronic bidding platform. From a list of bids, find the cut-off yield and allotments under uniform-yield and multiple-yield allotment, and the cost difference.

The situation

Aruvela Housing Finance issues Rs 500 crore of three-year bonds through an electronic bidding platform. Investors bid a yield and an amount. At the close the book shows: Rs 80 crore at 7.60%, Rs 120 crore at 7.62%, Rs 150 crore at 7.65%, Rs 100 crore at 7.68%, Rs 150 crore at 7.70% and Rs 100 crore at 7.75%, Rs 700 crore in all.

Aruvela must choose, before bidding opens, between uniform-yield allotment, where every successful bidder gets the cut-off yield, and multiple-yield allotment, where each successful bidder gets the yield it bid. Assume no green-shoe option and that bids are otherwise identical.

Your task

What is the cut-off yield, who gets what, and how much a year does the allotment method change Aruvela's cost?

Quick check

Filling Rs 500 crore from the lowest yield up, where does the cut-off fall?

Worked solution

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

30-second answerThe answer to give first

The cut-off is 7.70%: bids up to 7.68% are filled in full, Rs 50 crore of the Rs 150 crore at 7.70% is filled, and the 7.75% bid misses. Uniform-yield allotment pays everyone 7.70%, Rs 38.50 crore a year. Multiple-yield pays each bidder its own yield, averaging 7.646%, about Rs 27 lakh a year less. The saving is on paper: bidders who know the method bid differently.

Step 1How is the cut-off found?

Think of hiring for 500 seats on a bus and taking the cheapest quotes first: you accept the lowest fares until the bus is full, and the fare of the last seat filled is the cut-off. An issuer fills its size from the lowest yield upwards, and the yield at which the size is reached is the cut-off yieldThe highest yield accepted in the auction; every bid below it is filled and every bid above it is rejected.. Cumulatively the bids reach Rs 80, 200, 350 and 450 crore at 7.68%. The next Rs 150 crore at 7.70% takes the book past Rs 500 crore, so 7.70% is the cut-off and only Rs 50 crore of that level is filled.

Stacking Aruvela's bids from the lowest yield, the Rs 500 crore line falls inside the Rs 150 crore bid at 7.70%, which becomes the cut-off; uniform-yield allotment costs Rs 38.50 crore a year and multiple-yield about Rs 27 lakh a year less.

Bid yield	Bid, Rs crore	Allotted	Uniform: yearly cost at 7.70%	Multiple: yearly cost at own yield
7.60%	80	80	6.160	6.080
7.62%	120	120	9.240	9.144
7.65%	150	150	11.550	11.475
7.68%	100	100	7.700	7.680
7.70%	150	50	3.850	3.850
7.75%	100	0
Total	700	500	38.500	38.229

Rs crore a year. Uniform-yield allotment costs Rs 38.500 crore a year; multiple-yield costs Rs 38.229 crore, an average of 7.646%, a saving of about Rs 27 lakh a year, or about Rs 81 lakh over three years.

Step 2Who is filled at 7.70%, and does the saving really exist?

The Rs 150 crore at 7.70% competes for Rs 50 crore. Whether the bids at the cut-off are filled by time of bid or in proportion is set by the platform's operating rules, which change from time to time, so confirm the current rules before telling investors how they will be treated. On the saving: under multiple-yield allotment, a bidder who expects the cut-off near 7.70% has no reason to bid 7.60% and be paid 7.60%; it will shade its bid up toward the expected cut-off. The Rs 27 lakh is what this book would save, not what a book built under multiple-yield rules would save, because bidders read the rules too.

The view for Aruvela: multiple-yield can save a little when demand is deep and bidders are uncertain, but it can also discourage aggressive bids and thin the book, and a thin book raises the cut-off. Uniform-yield is simpler, rewards investors who bid tight and tends to give a cleaner secondary market because everyone holds the same yield. For a frequent issuer that cares about repeat demand, uniform-yield is the usual choice; the cost of the choice here is about Rs 27 lakh a year on paper.

Where candidates lose it

The usual mechanical error is stopping at 7.68%, where cumulative bids are Rs 450 crore, and calling it the cut-off. The book is not full until the 7.70% level.

The judgement error is treating the multiple-yield saving as certain. Bidders change behaviour when the allotment rule changes, so the saving on this book overstates the saving on a real one.

What the interviewer asks next

With a Rs 200 crore green-shoe option, what would the cut-off and cost be?
How would you advise an investor to bid under multiple-yield allotment?
Why might an issuer set a yield cap before bidding opens, and what happens if the cut-off would exceed it?

Company names and figures are illustrative.