Macaulay Duration is the weighted average maturity of the cash flow from the bond.
When Interest rate rise, the price of the bond falls, then the question arise, is that any matrix that we can use to evaluate a bond? See how sensitive it is going to be the price of that bond and given that there is a change in the interest rate.
So, we have a Macaulay duration which will perform that function.
Macaulay Duration is expressed in terms of years. So, we can compare the duration in years for different bonds.
In a bond for the higher number of years for its Macaulay duration it is going to be more sensitive to interest rate changes.
Let us understand the calculation,
Suppose
Face Value of the Bond is Rs.1000/-
Annual Coupon Rate is 6%
Current Market Rate of interest is 6.5%
Since we have a Face Value of Bond Rs.1000/- and the annual coupon rate is 6% means its going to pay Rs.60/- p.a. Here, we can use the market rate of interest of 6.5% to discount the cash flow.
We are going to move by each time the present value of the cash flow, the formula is.
Cash Flow / (1 + Current Market Rate of Interest) ^t
60 / (1+6.5%) ^1 = 56.34 for the first year.
Further, I am discounting the Present value of the cash flow for each year.
Finally, in the 5th year we have a cash flow of Rs.1060/- since we are getting the face value of the bond along with its interest.
In each case we take the time (t) & we multiply by the present value of the cash flow we get present value of time Weighted Cash Flow.
Now once we have Present Value of Cash Flow & Present Value of time Weighted Cash Flow we can sum up.
| Time Period
(t) |
Cash Flow | Present Value of Cash Flow | Formula | Present Value of time Weighted Cash Flow | Formula |
| 1 | 60 | 56.34 | 60/ (1+6.5%) ^1 | 56.34 | 56.34*1 |
| 2 | 60 | 52.90 | 60/ (1+6.5%) ^2 | 105.80 | 52.90*2 |
| 3 | 60 | 49.67 | 60/ (1+6.5%) ^3 | 149.01 | 49.67*3 |
| 4 | 60 | 46.64 | 60/ (1+6.5%) ^4 | 186.56 | 46.64*4 |
| 5 | 1060 | 773.67 | 1040/ (1+6.5%) ^5 | 3868.37 | 773.67*5 |
| Total | 979.22 | 4366.08 | |||
| Macaulay Duration | 4.46 |
4366.08 / 979.22 |
|||
This makes sense that the bond is trading at a discount since the current market rate of interest is higher than what bond pays.
Here, you see that the bond is trading at a discount (Rs.979.22) then its face value. To calculate Macaulay Duration, divide Present Value of time Weighted Cash Flow with Present Value of Cash Flow.
After discounting the cashflow the Macaulay Duration comes to 4.46 years.
Suppose we have another bond with Macaulay Duration of 7.85 years that means the bond is going to be exposed to more interest rate risk if interest rate changes. If the interest rates skyrocket that is going to affect the bond with the higher duration, more.
The volatility of the bonds price is going to be higher with respect to changes in the interest rates.
