**Bond valuation and Changes in interest rate**

The value of the bond declines as the market interest rate increases, bond values decline with rising fund interest rates because the bond cash flows are discounted at higher interest rates.

**Bond Maturity and Interest rate Risk**The value of a bond depends upon the market interest rate. As interest rate changes, the value of a bond also varies. There is an inverse relationship between the value of a bond and the interest rate. The bond value would decline when the interest rate rises and vice verse. Interest rates have the tendency of rising or falling in practice. Thus investors of bonds are exposed to the interest rate risk, which is the risk arising from the fluctuating interest rates.

**Bond Duration and Interest Rate Sensitivity**

That bond prices are sensitive to changes in the interest rates, and they are inversely related to the interest rates. The intensity of the price sensitivity depends on a bond’s maturity and the coupon rate of interest. The longer maturity of a bond, the higher will be its sensitivity to the interest rate changes. Similarly, the prices of a bond with low coupon rate will be more sensitive to the interest rate changes.

A bond’s maturity and coupon rate provide a general idea of its price sensitivity to interest rate changes. However, the bond’s price sensitivity can be more accurately estimated by its duration. A bond’s duration is measured as the weighted average of times to each cash flow. Duration calculation gives importance to the timing of cash flows, the weight is determined as the present value of cash flow to the bond value. Hence two bonds with similar maturity but different coupon rates and cash flow patterns will have different durations.

The volatility or the interest rate sensitivity of a bond is given by its duration and YTM. A bond’s volatility, referred to as its modified duration,

**Volatility of bond = Duration / (1+ YTM)**

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