Case 017Global macro tradesCore

Sethra Macro Fund expects the gap between 10-year and 2-year government yields to widen from 20 to 80 basis points. The 2-year has a DV01 of Rs 1.9 lakh and the 10-year Rs 7.5 lakh per Rs 100 crore of notional. How do you size a DV01-neutral steepener, and what do you make if you are right?

The situation

Government bond yields are 6.80% for the 2-year and 7.00% for the 10-year, a slope of only 20 basis points. Sethra Macro Fund's view is that the central bank will start cutting rates within a year while long-term inflation risk keeps 10-year yields up, so the slope will widen to about 80 basis points. It has no view on whether yields as a whole go up or down.

A 1 basis point change in yield moves the value of Rs 100 crore of 2-year bonds by about Rs 1.9 lakh, its DV01, and Rs 100 crore of 10-year bonds by about Rs 7.5 lakh. The fund wants Rs 100 crore of notional on the 10-year leg.

Your task

How much 2-year notional makes the trade neutral to parallel moves, what does it make if the slope reaches 80 basis points, and what does it lose if the curve flattens?

Quick check

Against Rs 100 crore of 10-year notional, how much 2-year notional makes the trade DV01-neutral?

Worked solution

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

30-second answerThe answer to give first

Hold about 3.95 times as much 2-year notional as 10-year: Rs 395 crore long the 2-year against Rs 100 crore short the 10-year, each leg carrying Rs 7.5 lakh per basis point. If the slope widens by 60 basis points, the trade makes 60 times Rs 7.5 lakh, Rs 4.5 crore, whichever end moves. A parallel shift makes nothing. If the curve flattens to zero, it loses Rs 1.5 crore.

Step 1Why can't the two legs have equal notionals?

A 10-year bond's price moves about four times as much as a 2-year bond's for the same change in yield, because its cash flows are further away. Think of a seesaw with a child at each end: to balance it, the lighter child sits further out. To be neutral to a parallel move, each leg must gain or lose the same rupees per basis point, so the 2-year notional has to be 7.5 over 1.9, about 3.95 times the 10-year. With Rs 100 crore of 10-year, that is Rs 394.7 crore of 2-year, each leg carrying DV01The change in value of a bond position, in rupees, for a one basis point change in its yield; the unit a rates desk uses to size and compare risk. of Rs 7.5 lakh.

The steepener holds Rs 394.7 crore of 2-year against Rs 100 crore of 10-year, 3.95 times the notional, so that each leg carries the same Rs 7.5 lakh of DV01 and a parallel move in yields leaves the book flat.

Step 2What does the trade make if the view is right?

The long 2-year gains when 2-year yields fall; the short 10-year gains when 10-year yields rise. Because both legs carry Rs 7.5 lakh per basis point, the trade earns Rs 7.5 lakh for every basis point the slope widens, so 60 basis points of steepening makes Rs 4.5 crore. It does not matter which end moves. If the central bank cuts and the 2-year falls to 6.20%, the long leg makes it; if inflation fears push the 10-year to 7.60%, the short leg does.

The relationship

N_2 = N_{10}\times\frac{DV01_{10}}{DV01_{2}} = 100 \times \frac{7.5}{1.9} = 394.7 \qquad P\&L = (80 - 20) \times 7.5\ \text{lakh} = 4.5\ \text{crore}

N_2, N_10	notionals of the 2-year and 10-year legs, Rs crore
DV01	rupee value change per basis point per Rs 100 crore of notional
80 - 20	the change in slope, basis points

What it says in wordsScale the 2-year leg up until its rupee risk per basis point equals the 10-year leg's, then the profit is the change in slope times that risk.

From a 2-year yield of 6.80% and a 10-year of 7.00%, the slope can reach 80 basis points through a bear steepener, the 10-year rising to 7.60%, or a bull steepener, the 2-year falling to 6.20%, and the DV01-neutral trade makes Rs 4.5 crore in either case.

Step 3What are the risks, and how would you manage them?

The obvious one is being wrong: if the curve flattens from 20 basis points to zero, the trade loses Rs 1.5 crore, so the payoff is about three times the loss to that stop. Three subtler ones. DV01 changes as yields move and time passes, so the ratio needs rebalancing. The trade also has carry: with a flat curve, the income on the long 2-year roughly offsets the cost of the short 10-year, which is one reason to put it on now rather than after the slope has widened. And the neutrality is to parallel moves only; a twist in the 5-year area, which neither leg holds, can still hurt a book of several positions. The judgement: a well-sized steepener with a clear stop, not a bet on the level of rates.

Where candidates lose it

The trap is sizing by notional: Rs 100 crore of each looks balanced but leaves the trade almost four times as exposed to the 10-year, so a parallel sell-off becomes the main driver of profit and loss, and the slope view barely matters.

The second is getting the direction of each leg wrong. A steepener profits when short yields fall relative to long yields, so you are long the 2-year and short the 10-year, not the other way round.

What the interviewer asks next

The fund also expects yields overall to fall. How would you tilt the trade to express that?
How does the trade's carry and roll-down change if the curve is already steep?
How would you put on the same view with interest rate swaps instead of bonds?

Company names and figures are illustrative.