27.1 Duration (also known as Macaulay Duration) of a bond is a measure of the time taken to recover the initial investment in present value terms. In simplest form, duration refers to the payback period of a bond to break even, i.e., the time taken for a bond to repay its own purchase price. Duration is expressed in number of years. A step by step approach for working out duration is given in the Box IV below.

More formally, duration refers to:

1. The weighted average term (time from now to payment) of a bond's cash flows or of any series of linked cash flows.

2. The higher the coupon rate of a bond, the shorter the duration (if the term of the bond is kept constant).

3. Duration is always less than or equal to the overall life (to maturity) of the bond.

4. Only a zero coupon bond (a bond with no coupons) will have duration equal to its maturity.

What is Modified Duration?

27.2 Modified duration (MD) is a modified version of Macaulay Duration. It refers to the change in value of the security to one per cent change in interest rates (Yield). The formula is

Illustration

In the above example given in Box IV, MD = 1.86/(1+0.09/2) = 1.78

Duration is useful primarily as a measure of the sensitivity of a bond's market price to interest rate (i.e., yield) movements. It is approximately equal to the percentage change in price for one percent change in yield. For example the duration is the approximate percentage by which the value of the bond will fall for a 1% per annum increase in market interest rate. So, a 15-year bond with a duration of 7 years would fall approximately 7% in value if the interest rate increased by 1% per annum. In other words, duration is the elasticity of the bond's price with respect to interest rates. This ignores convexity explained in para 24.7

What is PV 01?

27.3 PV01 describes the actual change in price of a bond if the yield changes by one basis point (equal to one hundredth of a percentage point). It is the present value impact of 1 basis point (0.01%) (1%=100 bps) movement in interest rate. It is often used as a price alternative to duration (a time measure). Higher the PV01, the higher would be the volatility (sensitivity of price to change in yield).

Illustration

From the modified duration (given in the illustration under 27.2), we know that the security value will change by 1.78% for a change of 100 basis point (1%) change in the yield. In value terms that is equal to 1.78*(101.79/100) = ₹ 1.81.

Hence the PV01 = 1.81/100 = ₹0.018, which is 1.8 paise. Thus, if the yield of a bond with a Modified Duration of 1.78 years moves from say 9% to 9.05% (5 basis points), the price of the bond moves from ₹101.79 to ₹101.70 (reduction of 9 paise, i.e., 5x1.8 paise).

What is Convexity?

27.4 Calculation of change in price for change in yields based on duration works only for small changes in yields. This is because the relationship between bond price and yield is not strictly linear. Over large variations in yields, the relationship is curvilinear i.e., the reduction in option free bond price is less than the change calculated based only on duration for yield increase, and increase in option free bond price will be more than the change calculated based only on duration for yield decrease. This is measured by a concept called convexity, which is the change in duration of a bond due to change in the yield of the bond.

Reserve Bank of India has deregulated interest rates to be charged to borrowers by NBFCs. The rate of interest to be charged by the company is governed by the terms and conditions of the loan agreement entered into between the borrower and the NBFCs. However, the NBFCs have to be transparent and the rate of interest and manner of arriving at the rate of interest to different categories of borrowers should be disclosed to the borrower or customer in the application form and communicated explicitly in the sanction letter and on their websites, Key Facts Statement, etc., to enable the borrower to take an informed decision.