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Relatively simple question, but came upon it in class and have not been able to come up with an answer:

The two-year bond yield is equal to 4% while the 10-year one is equal to 10%. You want to put on a yield curve flattening trade such that for every 1% flattening you will make a $1000 profit. You can trade 2-year and 10-year 0-coupon bonds at t = 0. For each bond specify, how much you are trading in PV terms and whether you are long or short. (Note: a 1% flattening implies that ∆y10 = ∆y2 - 1%.

My understanding is that since we expect the increase on the 2-year yield to outweigh that of the 10-year yield, we should go long 10-yr while shorting 2-yr. The initial investment would have a net value of 0, since we would fund our investment in the 10-year bond by borrowing at the 2-year rate. But how would we determine the amount allocated to each bond?

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    $\begingroup$ Hint: What is the price sensitivity of each of the bonds to a change in yield. $\endgroup$ – AlRacoon Jun 17 at 16:36
  • $\begingroup$ Another suggestion: Suppose you are long USD 10,000 of the 10 year and short the same amount of the 2 year. In response to a 1% flattening, how much profit do you make? If the answer is not equal to the desired USD 1000 adjust the initially assumed size of the position up or down as required. $\endgroup$ – Alex C Jun 17 at 16:42
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This is not a duration neutral trade then if you're assuming equal proceeds in on each leg. In that case, why do you need to know how much to allocate to each bond? If you short $100 million on one leg, then you use that to buy the long leg

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