When creating a synthetic position using futures, we calculated the number of contracts to buy/sell, we rounded it up and we found the effective initial amount invested.

When altering asset allocation, let’s assume a portfolio of $100M and that we wanted to add 10% to stocks and reduce bonds by 10%. We found the number of futures to long, we rounded it up, we then found the number of bonds futures to short for an amount equal to $10M.

**My question is** : after rounding the number of futures, the effective value of stock futures to go long is no more $10M, it is higher/lower (depending on the rounding direction). Why didn’t we short an amount equal to that value (i.e $9.8M) in bonds instead of shorting the whole $10M?