Case 020Rates and hedgingHard

The syndicate desk is left with Rs 200 crore of unsold Pavanjit Steel seven-year bonds overnight and hedges with government bond futures. Overnight, government yields fall 10 basis points and Pavanjit's spread widens 15. What is the hedged P&L?

The situation

Your desk priced a new seven-year bond for Pavanjit Steel at par with an 8.5% annual coupon, and Rs 200 crore went unsold. Rather than carry the rate risk overnight, the desk shorts government bond futures sized so that their sensitivity to a one basis point move in government yields matches the bonds'. Treat the futures as moving exactly with government yields, and assume each contract gains or loses Rs 1,000 per basis point, an illustrative figure.

Overnight, a weak inflation print pulls government yields down 10 basis points. At the same time, news of a rival's plant closure makes investors nervous about steel, and Pavanjit's spread over government bonds widens 15 basis points.

Your task

Work out the P&L on the bonds, the futures and the hedged position, and explain what the hedge did and did not protect.

Quick check

Before any maths: is the desk better or worse off than if it had not hedged?

Worked solution

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

30-second answerThe answer to give first

The hedged position loses about Rs 1.54 crore, exactly the 15 basis point spread widening, against an unhedged loss of about Rs 0.51 crore. The bonds' yield rises a net 5 basis points, costing Rs 0.51 crore; the short futures lose Rs 1.02 crore as government yields fall 10. A rate hedge removes rate risk, good or bad, and leaves the spread risk of unsold bonds on the desk.

Step 1How much does the position move for each basis point?

Everything hangs off one number. A seven-year 8.5% bond at par has a modified durationThe percentage change in the price of a bond for a one percentage point change in its yield, used to measure rate sensitivity. of about 5.12. On Rs 200 crore that is a DV01The change in the value of a position, in rupees, for a one basis point change in yield. of about Rs 10.2 lakh: every basis point the bonds' yield rises costs the desk about Rs 10 lakh. The hedge is sized to match it: about 1,024 contracts at Rs 1,000 a basis point.

Step 2What happens to the bonds overnight?

A corporate bond's yield is the government yield plus a spread, and both moved. The government yield fell 10 and the spread widened 15, so the bonds' yield rose a net 5 basis points, a loss of about Rs 0.51 crore. These figures use the DV01, which ignores a convexity effect of under Rs 1 lakh here. Split it: the rate move alone would have made Rs 1.02 crore and the spread move alone lost Rs 1.54 crore.

Step 3And the hedge?

Think of travel insurance that pays you if flights are cancelled and charges you if they run on time: you have given up the good outcome as well as the bad one. The futures are short government bonds, so when government yields fall 10 basis points they lose about Rs 1.02 crore, precisely the rate gain on the bonds. Total: Rs -0.51 crore on the bonds and Rs -1.02 crore on the futures, about Rs -1.54 crore, which is the spread effect and nothing else.

The bonds gain Rs 1.02 crore from the 10 basis point rate fall and lose Rs 1.54 crore from the 15 basis point spread widening, a net Rs -0.51 crore; the short futures lose Rs 1.02 crore, so the hedged total of Rs -1.54 crore equals the spread effect alone.

The relationship

\text{P\&L}_{\text{hedged}} \approx -\text{DV01} \times \Delta s = -10.24\text{ lakh} \times 15 \approx -154\text{ lakh}

DV01	rupees lost per basis point rise in the bonds' yield
\Delta s	the change in Pavanjit's spread, in basis points

What it says in wordsOnce the rate risk is hedged, what is left is the spread move times the position's sensitivity.

Step 4Was the hedge a mistake?

No, and saying why is the point of the question. The hedge did its job: it removed rate risk in both directions, so the desk's result now depends only on Pavanjit's spread. Run the other nights. If rates had risen 10 with the spread flat, the unhedged desk would have lost about Rs 1.02 crore and the hedged desk nothing. With spreads widening 15 and rates flat, both lose the same. The desk traded an unknown rate outcome for a known zero, and kept the spread risk it was always going to carry.

Across three overnight scenarios the hedged position's P and L depends only on Pavanjit's spread: zero when only rates move, and about Rs 1.54 crore lost whenever the spread widens 15 basis points, whatever government yields do.

Two limits to name. The futures track a benchmark government bond, not exactly a seven-year one, so a change in the shape of the government curve leaves some residual risk. And the only hedge for the spread is selling the bonds, or buying credit protection where a market exists. The practical answer is to hedge the rates overnight and work hard to place the Rs 200 crore the next morning.

Where candidates lose it

The usual miss is netting the moves before thinking: the yield rose 5, so the loss is 5 basis points, hedged or not. That ignores that the futures lose on the rally, which is the whole point of the question.

The second is concluding the hedge was a mistake because it lost money tonight. A hedge is judged by the risk it removed, and here it did exactly what it was built to do.

What the interviewer asks next

How would you hedge the spread risk as well?
The futures reference a ten-year bond. What extra risk does that introduce?
The desk holds the bonds for a week. What would you watch each morning?

Company names and figures are illustrative.