# Bond duration and interest rate sensitivity

by We have discussed that bond prices are sensitive to changes the interest rate, 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 the interest rate changes. Similarly, the price 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 duration. A bond’ s duration is measured as the weighted average of time to each cash flow( interest payment or repayment of principal).

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 similarly maturity but different coupon rates and cash flow patterns will have different duration.

Let us consider two bonds with five year maturity. The percent rate bond of rs.1000 face value has a current market value of rs.954.74 and YTM of 10 percent, and the 11.5 rate bond of rs.1000 face value has a current market value of rs.1044.57 and a yield to maturity of 10.6 percent . The duration of the bond is calculated as the weighted average of times to the proportion of the present value of cash flows.

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, is given as follows:

Volatility of bond=$\frac{Duratiin}{(1+YTM)}$

THE TERM STRUCTURE OF INTEREST RATES

So far in our discussion, we did not explicitly mention whether there were one single interest rate or several rates. In fact, there are several interest rates in practice. Both companies and the Government of India offer bonds with different maturities and risk features. Debt in a particular risk class will have its own interest rate.

Yield curve shows the relationship between the yields to maturity of bonds and their maturities. It is also called the term structure of interest rates. The upward sloping yield curve implies that the long-term yields are higher than the short-term yields. This is the normal shape of the yield curve l, which is generally verified by historical evidence. However, many economics in high – inflation periods have witnessed the short term yields being higher than the long-term yields being higher than the long-term yields. The inverted yields curves result when the short-term rates are higher than the long-term rates.

Following theory for yield curve structure.

1) Expectation theory- The expectation theory supports the upward slopping yield curve since investor always expect the short-term rates to increase in the future. This implies that the long-term rates will be higher than the short-term rates will be higher than the short-term rates.

But in the present value terms, the return from investing in a long-term security will equal to the return from investing in a series of a short-term security.

A significant implication of the expectation theory is that given their investment horizon, investor will earn the same average expected returns on all maturity combination .Hence a firm will not be able to lower its interest cost in the long run by the maturity structure of its debt.

2) The liquidity premium theory-  The liquidity or risk premium theory provides an explanation for the expectation of the investors. We have explained earlier that the prices of the long-term bonds are more sensitive than the prices of the short-term bonds to the changes in the market rates of interest. Hence investor prefer short-term bonds to the long-term bonds.

The investor will be compensated for risk by offering higher returns on long-term bonds.This extra return, which is called liquidity premium, gives the yield curve its upward bias.

3) The segmented market theory- The segmented markets theory assumes that the debt market is divided into several segment based on the maturity of debt. In each segment , the yield of debt depends on the demand and supply.Investors’ preferences of each segment arise because they want to match the maturities of assets and liabilities to reduce the susceptibility to interest rate changes.

The segmented markets theory approach assumes investors do not shift from one maturity to another in their borrowing lending activities and therefore, the shift in yields are caused changes in the demand and supply for bonds of different maturities.