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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
    Commented Jun 17, 2019 at 16:36
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    $\begingroup$ If you make zero net investment you will end up with similar notional (there will be a price differences) on both bonds. Because each has different sensitivity to rates, the investment value will not (even approximately) move constantly for a change in rates. What you want is to have opposite BPV on both bonds: value of 2y bond x duration x 1bps = - value of 10y bond x duration x 1 bps. Solving the for the notional of one given the other will result in different notional and different from zero net investment $\endgroup$
    – David Duarte
    Commented Dec 5, 2020 at 9:12

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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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