A Few Years Ago When the French Franc (FF) Still

Essay

A few years ago when the French franc (FF) still existed, the MATIF futures exchange in Paris had a very active market for the French government bond contract. The underlying asset is a notional long-term government bond with a yield of 10%. The size of the contract is FF 500,000 of nominal value. Futures prices are quoted in percentage of the nominal value. On April 1, the French term structure of interest rate is flat. The bond futures price for delivery in June is equal to 106.21%. The three French government bonds that can be used for delivery have the following characteristics:
$$\begin{array} { c c c c } & \text { Market Prica } & \text { Duration } & \text { Convarsinn Factar } \\\hline \text { Band A } & 107.46 \% & 7.00 & 101.171 \% \\\text { Band B } & 105.57 \% & 7.90 & 98.1441 \% \\\text { Band C } & 106.32 \% & 8.80 & 99.3104 \%\end{array}$$ a. Is the futures price consistent with the spot bond prices? (Find the bond cheapest to deliver.)
b. Estimate the interest rate sensitivity (duration) of the futures price.
c. You are an insurance company with a portfolio of French government bonds. The portfolio has a nominal value of FF 100 million and a market value of FF 110 million. Its average duration is 3.5. You are worried that social unrest in France could lead to an increase in French interest rates. Rather than selling the bonds, you wish to temporarily hedge the French interest rate risk. How many futures contracts would you sell and why?
Note to the instructor: The section on optimal hedge ratios for bond portfolios has been removed from the 5th edition. We include a brief summary of the theoretical derivations
given at the end of the solution.