Fixed Income Duration and Credit Spread Analysis

The total expected change in yield is the sum of the change in the risk-free rate and the change in the credit spread. The risk-free rate is expected to rise by 50 basis points (0.50%) and the credit spread by 100 basis points (1.00%), so the total yield change is +1.50% or +0.015 in decimal. Using duration and convexity, the percentage price change is approximately: -Modified Duration * Δy + 0.5 * Convexity * (Δy)^2. Here Δy = 0.015. So -5.5 * 0.015 = -0.0825. Convexity adjustment: 0.5 * 40 * (0.015)^2 = 20 * 0.000225 = 0.0045. Total = -0.0825 + 0.0045 = -0.0780 or -7.80%. The expected price change is a decrease of about 7.8%. The new price would be approximately $9.5 million * (1 - 0.078) = $8.759 million. This is an estimate; actual price change may differ due to the bond's specific cash flows. The manager should note that the credit spread widening is not a parallel shift; it affects the bond's yield directly. The duration used is modified duration, which assumes a parallel shift in the yield curve. The convexity adjustment is positive, meaning the price decline is less than duration alone would suggest. The manager should also consider that the credit spread change may not be instantaneous and may affect the bond's liquidity. The estimate is useful for hedging decisions.

To hedge the interest rate risk, the manager needs to offset the dollar duration of the bond with the dollar duration of the futures contracts. The bond's dollar duration is modified duration times the bond's price: 5.5 * $9.5 million = $52.25 million. However, the manager wants to hedge only the interest rate risk, not the credit spread risk. The expected change in the risk-free rate is 0.50%, while the total yield change is 1.50%. The duration contribution from the risk-free rate is 5.5 * 0.005 = 0.0275 or 2.75% price change. The dollar duration with respect to the risk-free rate is 5.5 * $9.5 million = $52.25 million per 1% change, but we need to hedge the exposure to the risk-free rate. Actually, the bond's sensitivity to the risk-free rate is the same as its sensitivity to its own yield if we assume the credit spread is constant. But here the credit spread is expected to change, so the manager wants to hedge only the risk-free component. The dollar duration for the risk-free rate is still 5.5 * $9.5 million = $52.25 million per 1% change in the risk-free rate. The futures contract's dollar duration per contract is duration * contract price. The contract size is $100,000, and we assume the futures price is par (or we need the futures price). The problem does not give the futures price, so we assume it is $100,000 per contract. Then dollar duration per contract = 6.5 * $100,000 = $650,000. The number of contracts = bond dollar duration / futures dollar duration = $52.25 million / $650,000 = 80.38, so approximately 80 contracts. However, this hedge assumes a parallel shift in the yield curve and that the futures price moves one-for-one with the risk-free rate. It also ignores convexity and basis risk. The hedge does not protect against credit spread widening, which is intended. The manager should also consider that the futures contract may not perfectly track the bond's risk-free rate due to differences in maturity and liquidity. The hedge ratio may need to be adjusted for the CTD bond's duration. The manager should monitor the hedge dynamically.