How do you calculate duration of a bond portfolio?

Asked By: Pathe Schumann | Last Updated: 30th April, 2020
Category: business and finance interest rates
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The formula is complicated, but what it boils down to is: Duration = Present value of a bond's cash flows, weighted by length of time to receipt and divided by the bond's current market value. As an example, let's calculate the duration of a three-year, $1,000 Company XYZ bond with a semiannual 10% coupon.

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Hereof, how do you calculate duration of a bond?

The formula for the duration is a measure of a bond's sensitivity to changes in interest rate and 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.

Also, what is the formula for duration? The formula is complicated, but what it boils down to is: Duration = Present value of a bond's cash flows, weighted by length of time to receipt and divided by the bond's current market value. As an example, let's calculate the duration of a three-year, $1,000 Company XYZ bond with a semiannual 10% coupon.

In respect to this, what is duration on a bond?

Duration is an approximate measure of a bond's price sensitivity to changes in interest rates. If a bond has a duration of 6 years, for example, its price will rise about 6% if its yield drops by a percentage point (100 basis points), and its price will fall by about 6% if its yield rises by that amount.

Why is Bond duration important?

Duration is important to bond investors because it acts as a guide for how sensitive a bond (or bond portfolio) is to changes in interest rates. Specifically, when yields rise, a bond's price will fall by an amount approximately equal to the change in the yield, multiplied by the duration of the bond.

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What is the formula for modified duration?

The formula for the modified duration is the value of the Macaulay duration divided by 1, plus the yield to maturity, divided by the number of coupon periods per year. The modified duration determines the changes in a bond's duration and price for each percentage change in the yield to maturity.

What is a good modified duration?

Modified Duration. Modified duration is a measure of a bond price sensitivity to changes in its yield to maturity. It is calculated by dividing the Macaulay's duration of the bond by a factor of (1 + y/m) where y is the annual yield to maturity and m is the total number of coupon payments per period.

What affects bond duration?

Certain factors can affect a bond's duration, including: Time to maturity. The longer the maturity, the higher the duration, and the greater the interest rate risk. A bond that matures faster – say, in one year – would repay its true cost faster than a bond that matures in 10 years.

What is the difference between bond maturity and duration?

Duration and maturity are key concepts that apply to bond investments. Effective duration and average maturity apply if you have a portfolio consisting of several bonds. While maturity refers to when a bond expires, or matures, duration is a measure of the bond's price sensitivity to changes in interest rates.

What is the duration of a zero coupon bond?


Zero coupon bond can be of any duration , can be from one year to 10 years. It is ordinarily from 3 to 5 years.

What does Macaulay duration measure?

The Macaulay duration is the weighted average term to maturity of the cash flows from a bond. The weight of each cash flow is determined by dividing the present value of the cash flow by the price. Macaulay duration is frequently used by portfolio managers who use an immunization strategy.

What is key rate duration?

Key rate duration measures how the value of a security or portfolio changes at a specific maturity point along the entirety of the yield curve. When keeping other maturities constant, the key rate duration can be used to measure the sensitivity in a security's price to a 1% change in yield for a specific maturity.

How do you calculate the duration of a floating bond?

Duration of a floating rate bond. It is known that the price pt of a floating rate bond can be calculated discounting (L+k) the sum of the next coupon payment k and the face value L at the relevant risk-free rate.

Can Modified duration be negative?


1 Answer. The price-yield relationship is negatively correlated; when prices go down, the implied yield goes up. The minus sign allows the modified duration to be positive for a normal bond.

How do you find the duration of a zero coupon bond?

The Macaulay duration is complicated and has a number of variations, but the primary version is calculated by adding up the coupon payment per period, multiplied by the time to maturity, divided by 1, plus the yield per period raised to the time to maturity.

How does duration change with yield?

Duration is affected by the bond's coupon rate, yield to maturity, and the amount of time to maturity. Duration is inversely related to the bond's yield to maturity (YTM). Duration can increase or decrease given an increase in the time to maturity (but it usually increases).

How do you calculate the price of a bond?

The basic steps required to determine the issue price are:
  1. Determine the interest paid by the bond. For example, if a bond pays a 5% interest rate once a year on a face amount of $1,000, the interest payment is $50.
  2. Find the present value of the bond.
  3. Calculate present value of interest payments.
  4. Calculate bond price.

What determines convexity of a bond?

Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest rate, i.e. how the duration of a bond changes as the interest rate changes. Specifically, one assumes that the interest rate is constant across the life of the bond and that changes in interest rates occur evenly.

Why do higher coupon bonds have lower duration?


The lower a bond's coupon, the longer its duration, because proportionately less payment is received before final maturity. The higher a bond's coupon, the shorter its duration, because proportionately more payment is received before final maturity.

How do you calculate the value of a bond?

To calculate the value of a bond, add the present value of the interest payments plus the present value of the principal you receive at maturity. To calculate the present value of your interest payments, you calculate the value of a series of equal payments each over time.

What is the relationship between bond price and yield?

Coupon rate—The higher a bond's coupon rate, or interest payment, the higher its yield. That's because each year the bond will pay a higher percentage of its face value as interest. Price—The higher a bond's price, the lower its yield. That's because an investor buying the bond has to pay more for the same return.