## What is Modified Duration?

Modified Duration tells the investor how much the price of the bond will change, given the change in its yield. As the bond world is more complex than the stock world, it is important for the investor to know the modified duration of the bond. To simply calculate the modified duration of the bond first, the investor needs to calculate one more thing, which is the Macauley duration. In order to calculate the Macauley duration, the investor needs to figure out what is the timing of the cash flow

### Modified Duration Formula

So the formula for Modified Duration is simply.

Where,

**Macauley Duration =**The duration calculates the weighted average time before the bond would receive the bond’s cash flows. Modified duration is ordered to be calculated first. The investor needs to compute the Macauley duration of the bond.**YTM**= Yield to maturity is simply the total return that the investor would earn in a bond when the bond is held until maturity**N**= number of coupon periods per year

### Calculation of Modified Duration with Examples

#### Example #1

A 2-year annual payment of $5,000 bond has a Macaulay Duration of 1.87 years. The YTM of the bond is 6.5%. Calculate the modified duration of the bond.

#### Example #2

A 2-year annual payment of $2,000 bond has a Macaulay Duration of 2 years. The YTM of the bond is 5%. Calculate the modified duration of the bond.

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#### Example #3

A 4-year annual payment of $12,000 bond has a Macaulay Duration of 5.87 years. The YTM of the bond is 4.5%. Calculate the modified duration of the bond.

#### Example #4

A 5-year annual payment of $11,000 bond has a Macaulay Duration of 1.5 years. The YTM of the bond is 7%. Calculate the modified duration of the bond.

### Advantages

- The main advantage is that the investor needs to know the duration of the bond as the bond price volatility is directly related to the bond prices. The greater the duration of the bond, the greater is the price volatility
- Duration of any investment instrument can help in the management of better investment needs for the future as the investor can effectively plan the future course of its investment in the duration
- It is also a measure of the risk of the bond to the change and the yield in the price of the bond
- The average duration of the fund is also important because it tells you how sensitive the fund will be to changes in market interest rates

### Disadvantages

- Modified duration calculation is complex in nature because of the calculation of the Macaulay Duration, and then the user or the investor also needs the inputs of yield and tenure of the calculation of the modified duration
- Getting inputs which are accurate and are prevailing in the market is hard to achieve as the price fluctuations and the market prices change every minute, which makes the calculation incorrect and obsolete
- Duration is also not a complete measure of the risk containing in the bond price and the bond duration. The investor cannot sole relay on the duration measure to produce accurate risk measures
- Macaulay duration computes the weighted average duration of the bond, which is not every time a good measure of the risk in the bond

### Conclusion

Modified and Macaulay although having limitations is indeed a very helpful concept, especially for the portfolio managers to measure the volatility of the bond and the risk associated with it, hence it can serve as a very useful tool when the manager is building a portfolio of bonds and managing the risk associated with it.

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