Mock Exam Q.37 and 38

The portfolio has 27.5 billion Yen in Bonds and 27.5 billion Yen in Stocks. (50-50 allocation). The allocation is to be changed to 60% stocks (33 billion yen) and 40% bonds (22 billion yen).

The stocks have a beta of 1.15 and the bonds have a duration of 4.75. The stock futures have a beta of 1.05 and a price of Yen 1,525,000. The bond futures have a duration of 6.90 and a pice of Yen 4,830,000. Assume the cash position has duration of 0.25.

Determine the number of contracts to be bought and sold.

The solution says that bond contract # = (0.25-4.75)/6.90 *5,500,000,000/4,830,000 = -743 which makes sense.

However, for stock futures, the solution is contracts # = (1.15-0)/1.05*5,500,000,000/1,525,000 = 3,950.

My question: why is the cash duration in stock futures “0” but for bond futures “0.25”? Should it not be “0.25” for both?

Wait, I think I got it (to answer my own quesion):

The duration of synthetic cash is 0.25 but its beta is 0.