( Note 100-13 = 100 13/ 32 )

Assume a 6-month hedging horizon and a portfolio calue of $30 million. Further assume that the 6-month Treasury bond (T-bond) contract is quoted at 100-13, with a contract size of $100,000. The duration of the portfolio is 8, and the duration of the futures contract is 12. Provide the # of contracts to completely hedge and the direction (long, short).