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Understanding Modified Duration
Let me explain modified duration to you directly: it tells you how much the price of a bond is likely to change when interest rates go up or down by 1%.
You need to know that modified duration builds on the idea that interest rates and bond prices move in opposite directions. This formula shows the impact of a 100-basis-point (that's 1%) change in interest rates on a bond's price.
Key Takeaways on Modified Duration
Modified duration measures how a bond's value shifts in response to a 1% change in interest rates. It's an extension of Macaulay duration, so you have to calculate that first. Macaulay duration figures out the weighted average time before you, as a bondholder, get the bond's cash flows. Remember, as a bond's maturity gets longer, its duration increases, but as the coupon or interest rate rises, duration decreases.
The Formula for Modified Duration
Here's the formula you use to calculate modified duration: Modified Duration = Macaulay Duration / (1 + YTM / n), where Macaulay Duration is the weighted average term to maturity of the cash flows from a bond, YTM is the yield to maturity, and n is the number of coupon periods per year.
Modified duration extends Macaulay duration, letting you measure how sensitive a bond is to interest rate changes. Macaulay duration itself calculates the weighted average time until you receive the bond's cash flows. You must compute Macaulay duration first. The formula for Macaulay duration is: Macaulay Duration = [sum from t=1 to n of (PV * CF) * t] / Market Price of Bond, where PV * CF is the present value of the coupon at period t, t is the time to each cash flow in years, and n is the number of coupon periods per year. You perform this calculation and sum it up for all periods to maturity.
What Modified Duration Reveals
Modified duration gives you the average cash-weighted term to maturity of a bond. It's a crucial figure for portfolio managers, financial advisors, and clients like you when picking investments, because—assuming other risks are equal—bonds with higher durations fluctuate more in price than those with lower durations.
There are various types of duration, and they all factor in elements of a bond like its price, coupon, maturity date, and interest rates. Keep these principles in mind: first, as maturity increases, duration goes up and the bond gets more volatile; second, as the coupon increases, duration drops and volatility decreases; third, as interest rates rise, duration decreases, reducing the bond's sensitivity to further rate hikes.
Example of Using Modified Duration
Let's walk through an example. Suppose you have a $1,000 bond with a three-year maturity, a 10% coupon, and interest rates at 5%. Using the basic bond pricing formula, the market price comes out to $1,136.16, calculated as the present values of the coupons and principal discounted at 5%.
Now, for Macaulay duration: it's (95.24 * 1 / 1,136.16) + (90.70 * 2 / 1,136.16) + (950.22 * 3 / 1,136.16) = 2.753. This means it takes 2.753 years to recoup the bond's true cost.
To get modified duration, divide that by 1 + (yield-to-maturity / number of coupon periods per year): 2.753 / (1.05 / 1) = 2.62%. So, for every 1% change in interest rates, the bond's price moves inversely by 2.62%.
Why Modified Duration Matters
Modified duration is key because it offers you critical insights into bond valuation. When interest rates shift, it approximates how much the bond's price will change, serving as a risk management tool—for instance, showing you how much the price drops if rates rise by a certain amount.
Difference Between Duration and Modified Duration
Duration, often meaning Macaulay duration, focuses on the weighted average time to receive a bond's cash flows, while modified duration specifically measures the bond's price sensitivity to interest rate changes.
Do Zero-Coupon Bonds Pay Interest?
No, zero-coupon bonds don't pay interest. They trade at a discount below face value and are redeemed at face value, with your return being the difference between the two.
The Bottom Line
Bond prices and interest rates move inversely, and modified duration helps you understand this by measuring price sensitivity to rate changes. This allows you to make informed investment choices and manage risk effectively.
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