The scenario we are presented within this workout is that a trader sees the one month sofa future strip trading with the following prices.

We then have a number of questions we need to answer.

The first thing we need to do is fill in the implied rate for each futures contract, and we can ignore convexity.

We know that the price of a futures contract is 100 minus R.

So to work out the implied rate, all we need to do is take 100 minus the price.

And I'm just gonna copy that formula down for all 12 contracts.

We are then asked if the current sofa fixing is 5.31%, what is the implied movement in sofa rates over the next 12 months? So the current sofa fixing is 5.31% implied sofa in 12 months.

We are going to take the implied rate from the 12th contract, which is 4.39%.

So the implied movement in sofa is the 4.39% minus the 5.31%.

So that is a decrease of 0.92% or 92 basis points.

Part C is if the trader thinks rates drop by less than the market expects over the next 12 months, what trade might they put on? And the answer is they should sell the 12th futures contract because the market is pricing in a larger decline than the trader anticipates in Part D, we are told to assume that the trader executed the trade.

We suggested in C in a size of 1000 contracts at the price quoted in the table 12 months later.

The arithmetic average sofa for the contract month was 4.5600000000000005%.

We're asked to calculate the traders p and l at the final settlement day, and remember that one month sofa futures have a contract size of $41.67 per basis point.

We also can ignore margins.

I've got some headings that are gonna help us along.

Starting with the price of the futures sold.

The traders sold the 12th futures contract and the price is 95.61.

Next, the settlement price, if the arithmetic average sofa for the contract month was 4.5600000000000005%, that is a price of 100 minus 4.56, which is 95.44.

So the profit in basis points is the difference between the selling price and the settlement price.

And I'm gonna multiply by 100 to put that into basis points.

So we have a profit of 17 basis points.

The position size is a thousand contracts.

The DVO one in dollars, which is the p and l for one basis.

Point move is 41.67.

So the total p and l is the 17 basis points times 1000 contracts times $41.67, which is a total profit of $708,390.

The final question is, if the trader thinks rates drop by the same amount as the market expects over 12 months, but the drop happens more quickly than is priced in, what trade or trades might they put on? The first thing they could do is take an outright long position.

They could take an outright long position in the middle, for example, by the sixth contract.

The choice of contract thereby will depend upon actual expectation of rates.

This strategy does leave them with an outright interest rate risk position if the whole curve moves.

In parallel, they could also put on a curve flattener to position for a flattening of the forward curve.

They could, for example, sell the first and buy the sixth contract.

The rationale here is that the difference in prices between one month and six month will increase as the forward curve will flatten.

If the same number of futures are traded in both the long and short position, this trade has no outright risk as Devi O one of the long and short position will offset each other.

Finally, the trader could put on a butterfly.

They would sell wings, for example, the first and 12th, and by body, for example, the sixth, the expectation would be that the middle of the curve, the body will move down in yield terms relative to the outer points, the wings.

This would be constructed as a one by two butterfly X contracts of body versus X over two contracts of both wings.

The total number of contracts long equals the total number of contracts short.

Hence no outright risk.