# Relationship between convexity and duration calendar

### Duration & Convexity Calculation Example Remember, a bond or a portfolio with a duration of five years will go down in price by of an individual bond is easy enough to calculate with a bond calculator. Duration and convexity result from the inverse relationship between bond prices and yields. The lower the bond price, the higher the yield and vice versa. Duration & Convexity: The Price/Yield Relationship. Investors who own fixed income securities should be aware of the relationship between interest rates and a.

Yield Duration and convexity result from the inverse relationship between bond prices and yields.

## Estimating price changes with duration and convexity

The lower the bond price, the higher the yield and vice versa. Yield is the rate at which your money will grow. However bonds change hands at various prices. Duration While the price and yield of all bonds are inversely correlated, the precise relationship varies greatly among bonds. Duration measures the price sensitivity of a bond to changes in yield. The higher the duration, the more sensitive the bond's price is to interest rate variations.

If, for example, a bond has a duration of two, the price will move twice as much as yield. As the expiration date approaches, duration declines. Also, the duration of the bond when it's yielding 12 percent vs. Convexity measures the sensitivity of duration to changes in yield.

If the duration of a bond and yield increase together, it has positive convexity; if they move in opposite directions, the bond has negative convexity. The reverse where interest rate goes down causing an increase in bond price is also true.

The risk of the decrease in the price of a bond due to an increase in the interest rate is known as the Interest Rate Risk. One of the factors affecting the Interest Rate Risk is the maturity of a bond. With a longer time frame, the bond is more likely to subject to change in price due to a interest rate change. A higher coupon rate allows the price of the bond to be recovered in a shorter time frame and thus expose an investor to less Interest Rate Risk.

Reinvestment Rate Risk We might think that since a decrease in interest rates lead to an increase in Bond Price, it will not in anyway adversely affect a bond's investor.

### Estimating price changes with duration and convexity | AnalystForum

However, a decrease in interest rate will lead to a decrease in future income of the bond investor. For example, the coupon amount received by an investor can only be reinvested in lower yielding bonds. This risk of a decrease in income due to a decrease in interest rates is known as the Reinvestment Rate Risk. It combines the maturity of a bond and the coupon rate and can be thought of as how long it takes for the price of a bond to be recovered.

Macaulay Duration Macaulay Duration can be calculated as follows: If the number of years to maturity is 10 then t is 1 to Bond Market Price - The present value of all cash flows of the bond. Modified Duration One of the interesting side effects of Macaulay Duration is that it can be adjusted to approximate the interest rate sensitivity of a bond. This is the approximation of the percentage change in the price of the bond to the percentage change in yield. The basic assumptions are that the bond is not tied to any Options and changes in yields are small. Modified Duration is calculated as follows: In fact, the price and change in interest rate change relationship is not exactly linear. The relationship is actually curvilinear.

The diagram below shows the approximation using Modified Duration as a straight line and the actual price-interest rate change relationship as a curve.

## Duration & Convexity: The Price/Yield Relationship

It is important to note that the degree of the "curvature" of the curve is known as the convexity. How to use the Bond Convexity Bond Convexity is defined formally as the degree to which the duration changes when the yield to maturity changes. It can be used to account for the inaccuracies of the Modified Duration approximation.

On top of that, if we assume two bonds will provide the same duration and yield then the bond with the greater convexity will be less affected by interest rate change. This can be easily visualized from the diagram above where the greater the "curvature", the lesser the price drop when interest rate increase.

Convexity of Bond

Bond Duration and Convexity Spreadsheet The "Bond Duration" worksheet allows you to calculate the Duration of a bond quickly and easily. Input Values Coupon Payment Frequency pf - This field indicates whether the coupon is paid annually or semi-annually. The coupon rate is typically stated in an annual percentage.