Altered Duration's Definition, Equation, Illustrations
Unfamiliar phrase for numerous investors when it comes to finance is modified duration, but its fundamental concept might not be. The assessment of financial instruments' values, particularly bonds, varies with shifts in interest rates. Modified duration offers investors a method to quantify this alteration.
Let's delve deeper into the essence of modified duration, how to compute it, and provide an illustration of its application. Additionally, we'll explain why modified duration is significant for investors.
Definition and Essence
What is modified duration, exactly?
Certain financial securities' prices increase when interest rates decrease and decline as rates increase. But by how much? Modified duration is a mathematical formula that quantifies the influence of interest rate fluctuations on a security's valuation change.
Modified duration is primarily used with bonds. However, the formula is applicable to other financial instruments sensitive to interest rate modifications, such as mortgage-backed securities and preferred stocks.
Computation
How to calculate modified duration's formula
The formula for calculating modified duration is:
Modified Duration = Macaulay Duration / (1 + YTM/n)
Where:
Macaulay Duration = the average number of years to maturity of cash flows, weighted
YTM = Yield to maturity (the investment's total return)
1
n = number of coupon periods per year
The concept of Macaulay Duration is associated with economist and mathematician Frederick Macaulay, who introduced the notion of bond duration in the 1930s. Calculating the Macaulay Duration is the most challenging aspect of determining the modified duration for an asset.
Coupon payment = $50 ($1,000 X 5%)
The Macaulay Duration formula is as follows:
Macaulay Duration = ∑ti (PVi/V)
$50 / (1 + 7%) = $46.73
Where:
i = index for time flows
$46.73 X 1 = $46.73
n = number of coupon periods per year
ti = time period until the ith payment is received
PVi = present value of the time-weighted cash flow
V = present value of all cash flows
2
Illustration
Modified duration demonstration
Coupon payment = $50
Consider a bond with a face value of $1,000 that matures in three years. This bond offers an annual coupon rate (yield through maturity) of 5%. Suppose the current interest rate is 7%.
To calculate the modified duration for this bond, first, we need to establish the Macaulay duration. The table below shows how this number can be computed:
$50 / (1 + 7%)2 = $43.67
| Time Period (t) | Cash Flow | PV of Cash Flow | PV of Time-Weighted Cash Flow || --- | --- | --- | --- || 1 | Coupon payment = $50 ($1,000 X 5%) | $50 / (1 + 7%) = $46.73 | $46.73 X 1 = $46.73 || 2 | Coupon payment = $50 | $50 / (1 + 7%)2 = $43.67 | $43.67 X 2 = $87.34 || 3 | Coupon + face value = $50 + $1,000 = $1,050 | $1,050 / (1 + 7%)3 = $857.11 | $857.11 X 3 = $2,571.33 || Sum | $947.51 | $2,705.40 |
We then divide the present value of the time-weighted cash flow by the present value of all cash flows to determine the Macaulay duration:
$43.67 X 2 = $87.34
Macaulay Duration = $2,705.40 / $947.51 = 2.86 years
Now, we can calculate the modified duration:
Modified Duration = 2.86 years / (1 + 7% / 1) = 2.67
What does this modified duration indicate? If interest rates rise by 1%, the price of the hypothetical three-year bond will decrease by 2.67%. Conversely, if interest rates fall by 1%, the bond's price will increase by 2.67%.
3
Significance
Why is modified duration essential?
Coupon + face value = $50 + $1,000 = $1,050
Modified duration is crucial for individual bond investors as it helps them evaluate the impact of interest rate changes on their investments. For instance, when interest rates increase, bond prices decrease, and the opposite occurs when rates decrease. Investors can calculate the modified duration for the bonds they own to decide whether to hold or sell, based on the interest rate shifts.
Insurance companies and pension funds can use modified duration to manage their interest rate-related risks, as well. These organizations often maintain bond investments in their fixed-income portfolios with prices that can fluctuate based on interest rate modifications.
$1,050 / (1 +7%)3 = $857.11
Additional Investing Topics
**### Different Types of Stocks to Invest In: What Are They?
$857.11 X 3 = $2,571.33
Stocks present various dimensions and kinds. We explore in detail.### Taxes on Investments: Understanding the Basics
You might query about taxes associated with different investment portfolio income. We provide answers.### What Is a Good Return on Investment?
You invest to earn a return. So, what constitutes a good ROI?### When to Sell Stocks — for Profit or Loss
When is it appropriate to abandon your stock position? Consider these factors.**## A more convenient method
Sum
Making modified duration more user-friendly
The concept underlying modified duration is simple, but the calculation of the measure might not be as straightforward as you'd like. The positive aspect is that available tools simplify the calculation of modified duration.
$947.51
For instance, Excel workbooks incorporate an MDURATION function that computes the Macaulay duration. Equivalently, Google Sheets houses a comparable feature. Following the calculation of the Macaulay duration, the computation of the adjusted duration becomes fairly straightforward.
You can also discover numerous online tools that can aid you in computing both Macaulay and modified durations. Numerous websites provide these online tools for free usage.
$2,705.40
In essence, you don't need to feel intimidated by the intricacy of the modified duration. A wealth of resources exists to simplify the computations necessary for estimating how interest rate fluctuations could impact your investments.
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Investors can use modified duration to assess the impact of interest rate changes on their bond investments, as the price of bonds tends to decrease when interest rates increase and vice versa. This calculation is especially important for organizations like insurance companies and pension funds that maintain bond portfolios, as they need to manage their interest rate-related risks.
Modified duration can also be used with other financial instruments, such as mortgage-backed securities and preferred stocks, that are sensitive to interest rate modifications. The MDURATION function in Excel or Google Sheets, or various online tools, can make the calculation of modified duration more convenient and user-friendly for investors.
