Macaulay Duration
SEBI’s new norms on re-categorization of mutual funds have provided guidelines to fund houses to classify their debt mutual funds into categories based on their Macaulay Duration. So, what is this Macaulay Duration and how important is it?
Macaulay Duration is a concept developed by Frederick Macaulay in 1938. It measures the bond’s sensitivity to interest rate changes. Technically, it is the weighted average number of years the investor must hold a bond until the present value of the bond’s cash flows equals the amount paid for the bond. Following is the formula to calculate Macaulay Duration:
Macaulay Duration = PV1 ×T1+ PV2 ×T2+ PVn ×Tn PV PV PV
Where, PV1, PV2 and PVn refer to present value of cash flows that occur T1, T2 and Tn Years in future and PV is the price of the bond (the sum of present value of all the bond cash flows at time 0)
Example:
Bond A: Rs. 1,000 face value coupon bond with four-and-half years till maturity.
Bond B: 5-year Rs.1,000 face value bond paying 5% annual coupon yielding 5.2%.
Duration of Bond A is 4.5 years, that is the maturity period of the zero-coupon bond.
Duration of Bond B is calculated by finding out the present value of each of the annual coupons and maturity value. Annual coupon is Rs. 50 (5% of the Rs. 1,000) and the maturity value is Rs. 1,000. The present values of each coupon and its proportion to the total present value of the bond are as follows:
| Coupon No. | 1 | 2 | 3 | 4 | 5 | Total |
| Years till Coupon Payment | 1 | 2 | 3 | 4 | 5 | |
| Coupon Amount | 50.00 | 50.00 | 50.00 | 50.00 | 50.00 | |
| Maturity Value | - | - | - | - | 1,000.00 | |
| Total Cash Flow | 50.00 | 50.00 | 50.00 | 50.00 | 1050.00 | |
| Present Value @ 5.2% | ₹ 47.53 | ₹ 45.18 | ₹ 42.95 | ₹ 40.82 | ₹ 814.91 | ₹ 991.39 |
| PV/Price | 4.79% | 4.56% | 4.33% | 4.12% | 82.20% | |
Duration of Bond B equals the years till each cash flow weighted based on percentage calculations above:
MD = 4.79% × 1 + 4.56% × 2 + 4.33% × 3 + 4.12% × 4 + 82.20% × 5 = 4.5
Since Bond B has a slightly higher duration, it has higher interest rate risk.