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, the investor needs to know the bond’s modified duration. To calculate the bond’s modified duration, first, the investor needs to figure out one more thing: 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. The investor must determine the cash flowCash FlowCash Flow is the amount of cash or cash equivalent generated & consumed by a Company over a given period. It proves to be a prerequisite for analyzing the business’s strength, profitability, & scope for betterment. read more timing to calculate the Macaulay Duration.

Modified Duration Formula

So, the formula for the modified duration is simple.

Modified Duration = Macaulay Duration / (1+YTM/n)

Where,

Macaulay Duration= The duration calculates the weighted averageWeighted AverageIn Excel, we calculate Weighted Average by assigning weights to each data set. It is generally used to compute robust observations in statistics or portfolios and is calculated as (w1x1+w2x2+….+wnxn)/(w1+w2+..wn), where w is the weight allocated to the x value and the sumproduct function is used.read more time before receiving the bond’s cash flows. Therefore, modified duration is ordered to be calculated first. Then, the investor needs to compute the Macaulay duration of the bondBondBonds refer to the debt instruments issued by governments or corporations to acquire investors’ funds for a certain period.read more.

YTM = Yield to maturityYield To MaturityThe yield to maturity refers to the expected returns an investor anticipates after keeping the bond intact till the maturity date. In other words, a bond’s returns are scheduled after making all the payments on time throughout the life of a bond. Unlike current yield, which measures the present value of the bond, the yield to maturity measures the value of the bond at the end of the term of a bond.read more 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.read more 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.

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 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.read more as the bond priceBond PriceThe 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 volatility is directly related to the bond prices. The greater the bond’s duration, the greater the price volatility.The duration of any investment instrument can help manage better investment needs for the future as the investor can effectively plan the future course of its investment in time.It is also a measure of the risk of the bond to the change and the yield in the bond’s price.The fund’s average duration is also important because it tells how sensitive it will be to market interest rates.Interest Rates.Interest rate derivatives are the financial instruments that track the fluctuations of the underlying interest rates. These underlying interest-bearing assets can be a single interest rate or a bunch of different interest rates.read more

Disadvantages

  • Modified duration calculation is complex because of the Macaulay Duration CalculationCalculation 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.read more. The user or the investor also needs the inputs of yield and tenure to analyze the modified duration.Getting accurate and prevailing inputs in the market is hard to achieve as the price fluctuates every minute, making the calculation incorrect and obsolete.Duration is also not a complete measure of the risk in the bondRisk In The BondBond risks are the potential risks in corporate holdings and government bonds that could jeopardies your planned and earned returns. Inflation, interest rate, reinvestment, market, and default risk are all types of bond risks.read more price and the bond duration. The investor must not solely rely on the duration measure to produce accurate risk measures.Macaulay duration computes the weighted average time of the bond, which is not always a good measure of the risk in the bond.

Conclusion

Modified and Macaulay durations, although limited, are indeed a beneficial concept, especially for the Portfolio ManagersThe Portfolio ManagersA portfolio manager is a financial market expert who strategically designs investment portfolios.read more to measure the volatility of the bond and the risk associated with it. Hence, it can be helpful when the manager builds a portfolio of bonds and manages the risk associated with them.

This article has been a guide to Modified Duration and its definition. Here, we also provide the modified duration formula, calculation, and examples. Also, we have discussed its types along with its advantages and disadvantages. You can learn more about Excel modeling from the following articles: –

  • Macaulay Duration FormulaWhat is Duration?Current Yield of a BondOperating Lease Meaning