A wealthy investor holds $$300,000$ worth of U$.$S$.$ Treasury bonds. These bonds are currently being quoted at $105\%$ of par. The investor is concerned, however, that rates are headed up over the next six months, and he would like to do something to protect this bond portfolio. His broker advises him to set up a hedge using T$-$bond futures contracts. Assume these contracts are now trading at $111-24.$

a$.$ Briefly describe how the investor would set up this hedge. Would he go long or short? How many contracts would he need?

b$.$ It's now six months later, and rates have indeed gone up$.$ The investor's Treasury bonds are now being quoted at $94\mathrm{.}5\%$ of par, and the T$-$bond futures contracts used in the hedge are now trading at $96-24.$ Show what has happened to the value of the bond portfolio and the profit $($or loss$)$ made on the futures hedge.

c$.$ Was this a successful hedge? Explain.