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. 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.. 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.
- 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 bondBondA bond is financial instrument that denotes the debt owed by the issuer to the bondholder. Issuer is liable to pay the coupon (an interest) on the same. These are also negotiable and the interest can be paid monthly, quarterly, half-yearly or even annually whichever is agreed mutually..
- YTM = Yield to maturity is simply the total returnTotal ReturnThe term “Total Return” refers to the sum of the difference between the opening and closing value of all the assets over a particular period of time and the returns thereon. To put it simply, the changes in opening and closing values of assets plus the number of returns earned thereof is the Total Return of the entity over a period of time. 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
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.
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.
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.
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.
- The main advantage is that the investor needs to know the duration of the bondDuration Of The BondThe duration formula measures a bond’s sensitivity to changes in the interest rate. It is calculated by dividing the sum product of discounted future cash inflow of the bond and a corresponding number of years by a sum of the discounted future cash inflow. 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
- Modified duration calculation is complex in nature because of the calculation of the Macaulay DurationCalculation Of The Macaulay 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., 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
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. 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.
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 –