Reinvestment risk:

An  interest rate risk is the fluctuation in bond prices that may come about due to the variations in interest rates over time. A rise in interest rates will lower the market price of the bond whereas a fall in interest rates will push the prices up. Interest rate risk is also called market risk, since there is a risk regarding the price of bonds. It is measured by the percentage change in the value of the bond in response to a given change in interest rates. It depends on the maturity period of the bond and the coupon interest rate associated with it. It can be shown from the general formula for the current price of a bond that:

- the longer the maturity period, the greater the sensitivity of bond prices tochanges in interest rates;

- the larger the coupon payment, the lesser the sensitivity of bond prices to changes in the interest rates

We know that bond prices and yields are inversely related. As interest rates fluctuate, there occur capital losses and gains for bondholders. The reason can be explained with the following illustration. Suppose the market demands a 5.5 per cent yield on a 10-year bond. If the coupon rate is also 5.5 per cent, the bond will trade at par. But what if the market demands a yield of 6 per cent on a 10-year bond? There will be no demand for the 5.5 per cent 10-year bond. So, the price of the 5.5 per cent coupon 10-year bond will decline in value such that it yields 6 per cent. Those who hold bonds, therefore, run the risk of interest rate increase. This risk is called the interest rate risk. Now, interest rate risk is dependent on the maturity of the bond; longer the bond maturity, higher the interest rate risk. So, the 5.5 per cent 10-year bond will decline more to yield 6 per cent compared with a 5.5 per cent five-year bond. When you buy a bond, you receive interest every year and the redemption price on maturity. The bond price is, hence, a function of the present value of these cash flows. When the market demands higher yield, we have to use a  higher discount factor to calculate the present value of cash flows. In the case of a 10-year bond, we have to use the higher discount factor for 10 years. For a five-year bond, a higher discount factor has to be used only for five years. But higher discount  factor means lower price. That is why longer maturity bonds are more sensitive to increase in interest rates. 

The price of a bond as we have seen depends mainly on three things: its coupon rate, its maturity, and the prevailing rate of interest. Hence over time, the price of a bond can change due to any of the following reasons: a change in the level of interest rate in the economy; a change in the price of a bond selling at a price other than par as it moves towards maturity without any change in the required yield; also, though we are not much concerned with it in the present unit, a change in the perceived credit quality of the issuer. The following relations exist between bond prices, interest and yields:

(1) There is an inverse relation between relationship bond prices and yields. (2) An increase in yield causes a proportionately smaller price change than a decrease in yield of the same magnitude. (3) Prices of long-term bonds are more sensitive to interest rate changes than prices of short-term bonds. (4) As maturity increases, interest rate increases, but at a decreasing rate. (5) Prices of low-coupon bonds are more sensitive to interest rate changes than prices of high-coupon bonds. (6) Bond
prices are more sensitive to yield changes when the bond is initially selling at a lower yield.
Another significant risk that may arise is what is called reinvestment risk.