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# Modified Duration

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Modified Duration by definition expresses the sensitivity of the price of a bond to a change in interest rate. Here is a presentation that will help you to understand the term 'Modified Duration' better.

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### Modified Duration

1. 1. MODIFIED DURATION
2. 2. MODIFIED DURATION Let’s understand Modified Duration with an example.
3. 3. MODIFIED DURATION Let’s say I am a stockist of winter clothes such as sweaters and mufflers. In anticipation of a good winter, I have stocked clothes in excess. My biggest concern is whether I will be able to sell all these before the onset of summer.
4. 4. MODIFIED DURATION Let’s say if the summer steps in earlier than expected, then what do I do? Naturally to clear the stock I will have to lower its price. Contrary, if for some reason the winter gets more severe and prolonged, then what could happen? In such a situation I will charge a premium for the goods that I have in stock and since I have a large supply, I would therefore make more money.
5. 5. MODIFIED DURATION Thus, the behavior of an external factor seems to be having a major impact on the prices I charge in the market. Now keep this in mind as I attempt to explain “modified duration” for debt products.
6. 6. MODIFIED DURATION CURRENT ACCOUNT DEFICIT Let us see the formula of the Current Account Balance (CAB) CAB = X - M + NI + NCT X = Exports of goods and services M = Imports of goods and services NI = Net income abroad  [Salaries paid or received, credit / debit of income from FII by definition Modified Duration& FDI etc. ] expresses NCT = Net current transfers sensitivity of Remittancesbond to a the [Workers' the price of a change in interest rate.(unilateral), Donations, Aids & The change in interest rate can be linked Grants, Ofﬁcial, Assistance and with the season change as explained in the Pensions etc] previous example.
7. 7. MODIFIED DURATION So if the modified duration of a debt fund is less, it is similar to having less stock so that even if the interest rates were to change, the impact on price would be less. On the other hand, if the modified duration is higher, it would be like having excess stock so that if interest rates were to change, the impact on prices would be large.
8. 8. MODIFIED DURATION So higher the modified duration, higher is the risk of price fluctuation and lower the modified duration, the lower would be the price fluctuation.
9. 9. MODIFIED DURATION CHANGE IN BOND PRICE = - MODIFIED DURATION X % CHANGE IN YIELD The negative sign in this equation indicates inverse relationship between change in yield and change in bond price.
10. 10. MODIFIED DURATION For example, if the modified duration of a bond is 5 and yield is expected to fall by 2% in a year, expected change in price of the bond (on account of change in yield) can be calculated as CHANGE IN BOND PRICE = - 5 X -2% = + 10%.
11. 11. MODIFIED DURATION Similarly, if the modified duration of a bond is 5 and yield is expected to rise by 2% in a year, expected change in price of the bond can be calculated as CHANGE IN BOND PRICE = - 5 X 2% = - 10%
12. 12. MODIFIED DURATION Some key points about modified duration: 1.  A “Bond” with a lower “modified duration” implies that the “returns” are more from accrual income than from capital gains. 2.  A “Bond” with a higher “modified duration” implies that the “returns” are more from capital gains than from accrual income. 3.  Maturity remaining the same a high coupon yielding bond would have a lower duration and hence be less sensitive to changes in external interest rates as compared to a low coupon yielding bond.
13. 13. MODIFIED DURATION CURRENT ACCOUNT DEFICIT Let us see the formula of the Current Account Balance (CAB) CAB = X - M + NI + NCT X = Exports of goods and services M = Imports of goods and services NI = Net income abroad  [Salaries paid or received, credit / debit of income from FII & FDI etc. ] NCT = Net current transfersHope you have understood [Workers' Remittances (unilateral), Donations, Aids & Ofﬁcial, Assistance and etc] the concept of Grants, Modified Duration. Pensions