Question

When bond price change measured by duration is not effective and why?

Answer 1

When bond price change measured by duration is not effective and why?

Duration of a bond is a measure often used to assess the risk involved with the bond instrument. It is the effective duration in years or maturity time, in which the bond price is repaid by the internal cash flows. The greater the duration, the more is the sensitivity to interest rate changes, which in turn means higher risk with the instrument. This measure is very useful in comparing the interest rate risks of various securities.

Duration is many times understood as the % change in the price of the bond for a unit percent change in yield to maturity. The duration can be approximated using the following formula:

Duration of bond = (Bond Price when interest rate increases – Bond Price when interest rate decreases) / (2 x Initial Bond Price x Change in interest rate)

Duration of bond can be visualized as a seesaw with a fulcrum whose position when changed balances the payments’ present values and the bond’s principal payment.

Factors that Affect Duration

The duration of a bond changes as the coupon payments keep getting made. If we visualize a seesaw with the length of plank equal to the maturity period, fulcrum placed at the duration of bond and money bags representing repayment cash flows placed on the plank all through the length to the maturity time, then every coupon payment is take off the plank as they get paid, causing the fulcrum (duration) to move forward at future point in time (representing the new duration of bond).

The duration value keeps on changing throughout the bond period. However, the value of duration in years, keep decreasing with the progress towards the maturity date. It also increases momentarily on the date of coupon payment. The duration value keeps varying in this fashion till it eventually becomes zero and merges with the maturity of the bond.

Other factors that affect the bond duration are the bond’s yield and coupon rate. Bonds that have high coupon rates, which in turn means high yields, usually have smaller durations than the vice versa case. A higher coupon rate or yield means that the bondholder is receiving the invested money at a faster rate, which is indicated by lower durations and hence, lower perceived risks.

Modified Duration

This is a modified version of Macaulay duration and takes into account the interest rate changes. Changes in interest rates affect duration as the yield gets affected each time the interest rate varies.

In regular bonds, the interest rates and bond price move in opposite directions. An approximate unit percent change in yield shares an inverse relationship with modified duration. This type of duration is very well suited for the purpose of gauging a particular bond’s volatility.

The formula for modified duration is as follows:

Modified duration = Macaulay Duration / (1 + (yield to maturity / no. of coupon periods per year))

Effective Duration

In above formula, cash flows are considered to be constant. However, in case of bonds with redemption features and embedded bond options, cash flows also change as the rate of interest changes. For such bonds, the duration calculation has to take into account this variability. Effective duration does just that. It uses binomial trees to estimate the option adjusted spread. These calculations can get a bit complex.

When bonds are issued, they are usually sold at their par value, which is also referred to as their face value. For most corporate bond issues, this par value is $1,000, while some of the government bonds can have a par value of $10,000. This is the principal amount of a bond and it is returned to the investors when the bond matures. However, during the term of a bond, market forces make the value of the bond change. At any time, the bond could be selling at a value higher than its par, lower than its par or at its par value.

Why Do Bond Prices Change

The main reason behind this change in bond value is change in interest rates. Interest rates in the economy are dynamic and they are constantly adjusted by the Federal Reserve in response to changing economic situation. When the economy is not doing well, the Fed can lower interest rates to encourage lending and to give a boost to economic activity.

But when there are serious inflationary expectations in the economy, the Fed can lower interest rates to cool things down. Such decisions can have a significant impact on the bond market, and prices of bonds always respond to changes in interest rates.

• Inverse Relationship with Interest Rates: Bond prices have an inverse relationship with interest rates. When interest rates in the economy go up (all other things being equal), bond prices go down, and vice versa. It is easy to understand why this happens.

  Let’s say you have invested in a plain vanilla bond at a par value of $1,000 and a coupon rate of 5%. When interest rates in the economy go up, future bond issues will have to pay a higher coupon rate, let’s say 6%. In such a scenario, an investor will be willing to buy your bond from you only if you sell it at a value lower than its par such that the buyer is compensated for the lower interest payments.

  The opposite of this happens when interest rates go down. Now future bonds will be issued at a lower interest rate and buyers will be willing to pay you more as your bond offers higher interest earnings. This will increase the price of the bond in the market.

• Impact of Creditworthiness: Another reason that can have a huge effect on bond prices is a change in the creditworthiness of the issuer. For example, if a company is facing financial difficulties that can adversely impact its ability to repay its obligations, credit rating agencies can decide to lower its credit rating.

  When that happens, markets will react by lowering the prices of bonds issued by the company as there is now a much greater risk of default associated with those bonds. The same thing can happen to countries and it is not uncommon to see the prices of bonds issued by a national government change drastically in response to bad economic data.

It should be noted that the bond market does not always wait for a credit rating agency to lower the rating of the issuer before lowering the price of its bonds. Large market participants are well aware of the risks that an issuer faces and expectations of default are always factored in bond prices.