Futures to adjust asset allocation contract, allocated, allocation

Dapper425

This example is on page 369 of CFAI

"Q-Tech Advisors manages a portfolio consisting of $100 million, allocated 70 percent to stock at a beta of 1.05 and 30 percent to bonds at a modified duration of 5.5. As a tactical strategy, it would like to temporarily adjust the allocation to 60 percent stock and 40 percent bonds. Also, it would like to change the beta on the stock position from 1.05 to 1.00 and the modified duration from 5.5 to 5.0. It will use a stock index futures contract, which is priced at $280,000 and has a beta of 0.98, and a bond futures contract, which is priced at $125,000 and has an implied modified duration of 6.50. Find out; (1) # of futures contracts to buy/sell"

The answer is:

Sell 38.26 Equity Futures [(0-1.05)/0.98]*($10,000,000/$280,000)
Buy 67.69 Bond Futures [(5.5-0)/6.5]*($10,000,000/$125,000)

My question is; why are we using 5.5 and not 5.0 while calculating the number of bond futures to buy? Isn't target duration 5? If we use 5, the answer is 61.54. Please help.

aidebaobao

one step at a time mate.

First they remove beta, then add the duration to get to a 60/40 split with D=5.5 and beta=1.05, Then further down the page they remove the extra 0.05 beta and 0.5 duration on the 60m equity and 40m bonds respectively.