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The duration of Groton's portfolio is7.33.mv is $450million And the duration of Treasury future contract is 6.5，priced at $110,425。Conversion factor is 0.9117. yield beta is 1.12.
Now he wants to adjust the duration to 6.83. Here is the solution:（6.83-7.33）/6.5*0.9177*450,000,000/110,425.
Why dont we mutiply the yield beta 1.12? I dont think it's useless. Without the yield beta in the hedge, wont we face the basis risk?
