Modified Duration

What is Modified Duration?

Modified Duration tells the investor how much the price of the bondPrice Of The BondThe bond pricing formula calculates the present value of the probable future cash flows, which include coupon payments and the par value, which is the redemption amount at maturity. The yield to maturity (YTM) refers to the rate of interest used to discount future cash flows.read more 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 durationMacauley DurationMacaulay Duration is the amount of time it takes for an investor to recover his invested money in a bond through coupons and principal repayment. This is the weighted average of the period the investor should stay invested in the security in order for the present value of the cash flows from the investment to be equal to the amount paid for the bond.read more. 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.

Modified Duration = Maculay Duration / (1+YTM/n)
Modified-Duration

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For eg:
Source: Modified Duration (wallstreetmojo.com)

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For eg:
Source: Modified Duration (wallstreetmojo.com)

Where,

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.

Modified Duration Example 1

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.

Example 2

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 3

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.

Example 4

Advantages

Disadvantages

Conclusion

Modified and Macaulay although having limitations is indeed a very helpful concept, especially for the portfolio managersThe Portfolio ManagersA Portfolio Manager is an executive responsible for making investment decisions & handle investment portfolios for fulfilling the client’s investment-related objectives. Also, he/she works towards maximizing the benefits & minimizing the potential risks for clients. read more 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.

Recommended Articles

This has been a guide to What has Modified Duration and its Definition. Here we provide you the formula for modified duration along with its calculation and practical examples. Here we also discuss its types along with Advantages and Disadvantages. You can learn more about excel modeling from the following articles –

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