Q: when using short term contracts (#1 on p302), does basis risk exist assuming that the expiration of the final contract coincides with the underlying? If so, why?
The short-term contracts bear basis risk, since the maturity of the first contract is not equal to the hedge period.
Let’s assume the hedge horizon is six months and the maturity of short term contract is 3 months. The first contract matures in 3 months and then it is rolled over to a new 3-month contract. But the new futures price could be different from the original futures price(matured in 6th month). So the 6-month contract has 0 basis risk, but the 3-month contract bear the basis risk.
In other words, the short term contract hedge the currency for only a short term, the rest of the hedge period is still exposed to the currency risk.
I would say yes. Short term contract needs to be rolled over at expiry. New contract will depend on the how the int rates have evolved during the period.