Modified Duration

What Is Modified Duration?

Modified duration is a formula that communicates the quantifiable change in the value of a security in response to a change in interest rates. Modified duration follows the concept that interest rates and bond prices move in inverse bearings. This formula is utilized to determine the effect that a 100-premise point (1%) change in interest rates will have on the price of a bond.

Formula and Calculation of Modified Duration

$\begin&\text=\frac{\text}{1+\overset{\text}}\&\textbf\&\text=\text\&\qquad\text\&\text=\text\&n=\text\end$
Modified duration is an extension of the Macaulay duration, which permits investors to measure the sensitivity of a bond to changes in interest rates. Macaulay duration computes the weighted average time before a bondholder gets the bond's cash flows. To ascertain modified duration, the Macaulay duration must initially be calculated. The formula for the Macaulay duration is:
$\begin&\text=\frac{\sum^n_(\text\times \text)\times \text}{\text}\&\textbf\&\text\times \text=\textt\&\text=\text\&n=\text\end$
Here, (PV) * (CF) is the present value of a coupon at period t, and T is equivalent to an opportunity to each cash flow in years. This calculation is performed and added for the number of periods to maturity.

Everything that Modified Duration Can Say to You

Modified duration measures the average cash-weighted term to maturity of a bond. It is a vital number for portfolio managers, financial advisors, and clients to consider while choosing investments on the grounds that — any remaining risk factors equivalent — bonds with higher durations have greater price volatility than bonds with lower durations. There are many types of duration, and all parts of a bond, for example, its price, coupon, maturity date, and interest rates, are utilized to compute duration.

Here are a principles of duration to keep as a top priority. In the first place, as maturity increases, duration increases and the bond turns out to be more unpredictable. Second, as a bond's coupon increases, its duration diminishes and the bond turns out to be less unpredictable. Third, as interest rates increase, duration diminishes, and the bond's sensitivity to additional interest rate increases goes down.

Illustration of How to Use Modified Duration

Expect a $1,000 bond has a three-year maturity, pays a 10% coupon, and that interest rates are 5%. This bond, following the fundamental bond pricing formula would have a market price of:
$\begin &\text = \frac{ $100 }{ 1.05 } + \frac{ $100 }{ 1.05 ^ 2 } + \frac{ $1,100 }{ 1.05 ^ 3 } \ &\phantom{\text } = $95.24 + $90.70 + $950.22\ &\phantom{\text } = $1,136.16 \ \end$
Then, utilizing the Macaulay duration formula, the duration is calculated as:
$\begin\text&=\bigg($95.24\times\frac{1}{$1,136.16}\bigg)\&\quad+\bigg($90.70\times\frac{2}{$1,136.16}\bigg)\&\quad+\bigg($950.22\times\frac{3}{$1,136.16}\bigg)\&=2.753\end$
This outcome shows that it requires 2.753 years to recover the true cost of the bond. With this number, working out the modified duration is currently conceivable.

To find the modified duration, an investor should simply accept the Macaulay duration and gap it by 1 + (respect maturity/number of coupon periods each year). In this model that calculation would be 2.753/(1.05/1), or 2.62%. This means that for each 1% movement in interest rates, the bond in this model would contrarily move in price by 2.62%.

Features

• Modified duration is an extension of the Macaulay duration, and to ascertain modified duration, the Macaulay duration must initially be calculated.
• As a bond's maturity increases, duration increases, and as a bond's coupon and interest rate increases, its duration diminishes.
• Macaulay duration computes the weighted average time before a bondholder gets the bond's cash flows.
• Modified duration measures the change in the value of a bond in response to a change in 100-premise point (1%) change in interest rates.