Case 083Model risk and validationCore

A bank values Rs 600 crore of illiquid corporate bonds off a proxy curve that independent price verification finds 35 basis points too tight. With duration 4, what is the valuation gap and how big a reserve do you hold?

The situation

Lorvani Bank holds Rs 600 crore of corporate bonds from mid-sized issuers that rarely trade. The desk marks them off a proxy curve built from more liquid bonds of similar rating. The book's average duration is 4.

The product control team runs its monthly independent price verification and collects quotes from three dealers. Against the proxy, the dealers' yields are 25, 35 and 45 basis points wider, 35 on average. The desk argues the quotes are indicative and that it would never sell at those levels.

Your task

What is the valuation gap in rupees, how big should the adjustment and reserve be, and what happens to the proxy model?

Quick check

Roughly how much are the bonds overvalued?

Worked solution

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

30-second answerThe answer to give first

The proxy overstates the book by about Rs 8.4 crore, and a prudent total is about Rs 10.8 crore. Duration 4 times 35 basis points is a 1.4% price gap on Rs 600 crore. Book the Rs 8.4 crore as a fair value adjustment now, because three independent quotes agree on direction, and hold a further Rs 2.4 crore reserve for the spread between quotes. Then fix the proxy: it is missing an illiquidity premium.

Step 1How do you turn 35 basis points into rupees?

Duration converts a yield error into a price error. If a house valuer uses prices from the smart apartment block next door to value a flat on a noisy corner, every estimate is a little too high, and the error is larger for a bigger flat. A 35 basis point error at duration 4 is a 1.4% price error, and 1.4% of Rs 600 crore is Rs 8.4 crore of value on the books that a buyer would not pay. Small in basis points, large in rupees, because the book is big and illiquid.

The relationship

\Delta V \approx -D \times \Delta y \times V = -4 \times 0.0035 \times 600 = -8.4 \text{ crore}

D	duration of the book, 4
\Delta y	yield gap between the proxy and the dealer quotes, 35 bp
V	book value on the proxy curve, Rs 600 crore

What it says in wordsA 35 basis point higher yield at duration 4 means the bonds are worth about Rs 8.4 crore less than the proxy says.

The dealer-implied curve sits 35 basis points above the proxy curve Lorvani uses to value its illiquid bonds, which at a duration of 4 overstates the Rs 600 crore book by Rs 8.4 crore.

Step 2Is Rs 8.4 crore an adjustment or a reserve, and is it enough?

Split it into what you know and what you do not. Three independent dealers all put yields wider than the proxy, so the direction is not in doubt. The Rs 8.4 crore at the average quote is a correction to fair value and should hit profit and loss now, not sit in a reserve the desk can argue about later. The quotes then range from 25 to 45 basis points. Holding a valuation reserveAn amount set aside against a book value because the fair value itself is uncertain, sized from the spread of plausible prices. out to the widest quote, another 10 basis points, adds Rs 2.4 crore, for a total of Rs 10.8 crore.

Piece	Basis points	Rs crore	Treatment
Average dealer quote against proxy	35	8.4	Fair value adjustment, booked now
Widest quote beyond the average	10	2.4	Valuation uncertainty reserve
Total hit to reported value	45	10.8	Reviewed monthly with each price check

Of the Rs 10.8 crore total, Rs 8.4 crore corrects the proxy to the average dealer level and Rs 2.4 crore reserves for the 10 basis point spread to the widest quote.

Step 3What do you say to the desk, and to the model owner?

The desk's argument, that it would never sell at those levels, is the argument fair value rules exist to overrule: the value is what the market would pay today, not what the holder hopes to get later. A proxy built from liquid bonds will be too tight on illiquid ones every month, so the lasting fix is a model change: add an illiquidity spread, calibrated to dealer quotes and recent trades, and set an escalation threshold, say any gap over 10 basis points or Rs 1 crore. Record the finding, the owner and the date in the model inventory so validation can check it was closed.

Where candidates lose it

The common slip is to leave the whole gap as a reserve, which lets the desk keep reporting the proxy value and release the reserve quietly when it chooses. Where independent evidence agrees on direction, the value itself is wrong and should be corrected.

The second is forgetting duration and treating 35 basis points as 0.35% of value, Rs 2.1 crore, which understates the problem fourfold.

What the interviewer asks next

Only one dealer will quote, at 60 basis points wider. How do you size the reserve now?
The desk sells Rs 50 crore of the bonds at 30 basis points wide. What does that tell you?
Why might an auditor treat these bonds as level 3 in the fair value hierarchy?

Company names and figures are illustrative.