A 18 year bond at YTM 6%, coupon rate of 9.215% face value of $1000, that was $1350.95. Called price $1120, called at 5 years at 12% premium over par for a realized yield of 3.675%? If you bought one of these bonds today, what would be your  interest rate risk?

**Interest rate risk** refers to the potential for a bond's price to fluctuate due to changes in prevailing interest rates. When interest rates rise, bond prices typically fall, and vice versa. The degree to which a bond's price is affected by interest rate changes is influenced by several factors, including the bond's duration, coupon rate, and yield to maturity (YTM).

### Key Concepts:
1. **Duration**: Duration is a measure of a bond's sensitivity to changes in interest rates. The longer the duration, the more sensitive the bond is to interest rate changes. Since the bond has 18 years to maturity, its duration will be longer than that of a bond with a shorter time to maturity, meaning it has higher interest rate risk.

2. **Coupon Rate**: Bonds with higher coupon rates are generally less sensitive to interest rate changes than bonds with lower coupon rates. Since this bond has a relatively high coupon rate of 9.215%, it is less sensitive to interest rate changes compared to a bond with a lower coupon rate. However, because the bond is currently priced significantly above its face value (at $1,350.95), its sensitivity to interest rate changes (measured by its modified duration) may still be high.

3. **Yield to Maturity (YTM)**: The bond has a YTM of 6%, which is lower than the coupon rate. This implies that the bond is trading at a premium (i.e., the bond price is higher than its face value). Premium bonds tend to have higher interest rate risk because their price will drop more significantly if interest rates rise.

### Interest Rate Risk Assessment for This Bond:
Given the details:

1. **Long Maturity**: An 18-year maturity means that the bond is relatively long-term, which inherently increases its interest rate risk. Long-term bonds are more sensitive to interest rate changes because their cash flows extend further into the future.

2. **Premium Price**: The bond is currently priced at $1,350.95, well above its face value of $1,000. Premium bonds typically experience greater price volatility when interest rates change, particularly because the higher coupon payments are worth less in a rising interest rate environment.

3. **Callable Feature**: The bond is callable at $1,120 after 5 years. If interest rates fall, the issuer is likely to call the bond, which caps the upside potential for bondholders. However, if interest rates rise, the bond’s price could fall significantly since it might not be called.

### **Quantifying Interest Rate Risk (Duration & Convexity):**
- **Modified Duration**: This would give us an estimate of the percentage change in the bond's price for a 1% change in interest rates. Although we haven't calculated the exact modified duration here, it would be fairly high due to the long maturity and the premium price.

- **Convexity**: This measures the curvature of the price-yield relationship. Higher convexity indicates that the bond's price is more sensitive to interest rate changes.

### Conclusion:
If you buy this bond today, **your interest rate risk is relatively high** due to its long duration and the fact that it's trading at a premium. The bond's price will be sensitive to interest rate increases, and since it is callable, the bond might be called if interest rates decrease, limiting your upside. 

This risk assessment suggests that you should be cautious if you expect interest rates to rise, as the bond's price could decrease significantly.

### Do you want more details or have any questions? Here are some related questions:

1. How can you calculate the modified duration for this bond?
2. What impact does convexity have on the interest rate risk of a bond?
3. How does the callable feature affect your overall interest rate risk?
4. What strategies can be used to hedge against interest rate risk?
5. How does interest rate risk differ between premium and discount bonds?

**Tip:** Consider diversifying your bond portfolio with bonds of varying maturities and durations to reduce overall interest rate risk.

Explore the interest rate risk assessment of an 18-year bond with a yield to maturity (YTM) of 6%, a coupon rate of 9.215%, and a callable feature at a premium. Learn about bond valuation, modified duration, and the impact of callable bonds on interest rate risk.

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