Duration and convexity are tools that people use to measure all the daily investments. Duration and convexity study the risk you can have when making fixed investments. While the duration measures the changes in the interest rate of the bonds, the convexity makes a relation between the prices and the yield of the bonds.
People can use these elements, for example, for coupon bonds. Through the duration, you, as an investor, will be able to measure the sensitivity of the price of a bond and its interest rate. With a quota bonus, you will have to make several payments; that’s why fixed-income investors must establish an expiration date to have a statistic.
Some keys are important for you to understand how coupon bonds work:
- Through coupon bonds, investors can use metrics to study changes in price and interest rates.
- Experts use Gap management so banks can match assets and liabilities. Also, you can control the movements of the interest rate.
Frederick Robertson Macaulay is an economist who, in 1938, spoke about the duration of the bond. In his speech, he pointed out that the duration should be calculated as a weighted average from the beginning until the coupon expires. For this, the economist made a formula to make an exact calculation.
It is important to understand how duration is managed
Fixed income portfolios are managed throughout the duration, and there are a few reasons to implement this measure:
- This statistic allows you to see the most effective maturity in a portfolio.
- You can avoid interest rate risks in portfolios.
- You can estimate the interest rate in a portfolio.
To minimize the risk in profitability, control should be carried out on the portfolios because all fixed-income assets are exposed to variations in their price. When this happens, a loss of value can occur, and it is what should be avoided. To control this type of risk that may occur in fixed income or the portfolio, the duration will always be used.
Duration will be the tool to measure the duration of the bond through analysis of repayments and the price of the fixed income value. You should know that the higher the
Convexity is also important
Duration is not the only tool that plays an important role in measuring coupon bonds. You must take into account convexity to know the risks that a bond may have, and thus know how to choose the best options. The internal rate of return is related to convexity.
The price of the bond and its profitability are taken in a mathematically convex curve. This means that the tangent curve indifferently at the point where it is located is below the curve.
Through convexity, experts can measure the variation in the duration of the bond when the change in profitability occurs. In this way, the approximate duration and variations in bond prices can be improved. With convexity, you will be able to analyze more clearly the entire portfolio process.
Many portfolios usually combine assets where are those that have less duration and those of longer duration. The purpose of these is to achieve high connections to be able to easily identify portfolios that are sensitive to declines in different interest rates.
Although this tool is complex, managers must find ways to provide better returns on portfolios and investment funds.
You must understand what a bond is
A bond is a set of cash flows in which a debtor makes a payment to a creditor. People also know these cash flows as coupons, and it is normal for the value of each flow to be paid.
In the financial market, you will find several types of bonds among which are:
- Corporate bonds issued by companies.
- Corporate bonds issued by the government.
- Carbon credits.
Each of these bonuses works differently, but you can’t fail to mention the classic bonus. These bonds are coupons and the main payment until maturity. People can applied duration and convexity to study any bond and to fixed income.
Here are some abbreviations to better understand the concepts related to bonds:
- P: Price of the bond.
- n: Number of coupons.
- VN: face or face value of the bond.
- Ct: Coupon paid in the period.
- A: Market rate to maturity.
It is important that if you are interested in bonds, study and know necessary information on the duration and convexity. With these two tools, you can know the variations in the values of the bond portfolios, and you can be alert to the risks that may occur in the interest rate.
On a curve, experts measure changes with points in interest rates, each being one-hundredth of that percentage point. For banking institutions, changes in the value of sensitive assets and liabilities are relevant. And here duration plays its role in measuring any risk that may occur.
When the duration of the liabilities is less than the duration of the assets, this can be a trigger for the bank.
Both tools are vital
The increase in the duration of the security will depend on the variations that occur in the coupon rate and the discount of the coupons. The longer the maturity is, the more the modified duration will be. Now, the lower the interest coupon, the greater the duration and profitability.
This would happen to take into account the duration, now see what happens with convexity. The increase in convexity will occur when there is an increase in duration. When a bond is segregated, it will always have greater convexity. Segregated bonds can sometimes be the best as they get portfolios with a longer duration.
To make it clearer to you, convexity provides a more accurate measurement when it comes to knowing changes in prices and profitability. While on the other side is the duration of the bond, where it reaches between price and profitability is constant.
But on many occasions, the reality may be different from what is expected. For this reason, experts use these two tools through graphics. Graphically, this type of procedure will be easier to understand, and a clearer representation can be seen and then analyzed.