Convexity 

Convexity 

Applying the duration and convexity ideas is crucial when assessing bonds. A bond’s or bond portfolio’s approximate price change can be predicted quite well using duration. However, duration loses accuracy in projecting price movements for assets with embedded options and bigger yield changes. Duration and convexity can be coupled to approximate the price for a given change in yield more closely. 

The convexity of a bond portfolio can significantly impact the portfolio’s overall return. For example, a portfolio with positive convexity will typically outperform a portfolio with negative convexity when interest rates rise. This is because the YTM curve of a portfolio with positive convexity will become steeper as interest rates rise, which means that the portfolio’s overall return will increase faster than a portfolio with negative convexity. 

Overall, the convexity of a bond portfolio is an important consideration for investors when choosing which bonds to include in their portfolio. 

Convexity 

 

What is convexity? 

Convexity is a metric for the degree of the curve between the price of bonds and their yields. Thus, convexity is a metric for the arc of the bond price–interest rate connection. It displays how quickly a bond’s duration alters in response to changes in interest rates. 

 Convexity shows how the term of a bond changes when the interest rate changes. If a bond’s duration increases along with yields, this is called negative convexity. If a bond’s tenure lengthens while its yield drops, it is said to have positive convexity. 

Understanding convexity 

Convexity and duration are two calculated metrics that, unfortunately for bond investors, are difficult to get. Although you could theoretically calculate it on your own in Excel, and professional fund managers use sources like Bloomberg to seek this information, your best bet is to find a broker. This is because it isn’t worth the effort to learn the formula, alter it, and use it in Excel regularly. If your broker doesn’t have a bond calculator, his fixed-income offerings may be inadequate. 

On a portfolio level, convexity is also incredibly helpful. When managing a bond portfolio, you can utilize duration and convexity to choose where to allocate existing bond positions and new purchases based on the portfolio’s duration and convexity.  

Apply the same interest-rate forecast criterion when considering the overall impact of a new position and its allocation. Using position sizes and diversity to reduce risk, you can still buy bonds you like, even if their duration or convexity is at odds with your predicted interest rate. 

Convexity and duration 

Investors can learn how interest rate changes will impact a bond’s price using duration and convexity measures. The course of a bond can help investors comprehend the implications for a bond’s price should interest rates change by indicating how a bond’s price responds to changes in interest rates. A bond’s convexity can be used to calculate the difference in duration for a specific change in yields. 

If rates are anticipated to rise, consider investing in bonds with shorter periods. These bonds will see less market volatility and less sensitivity to yield increases than bonds with longer periods. Higher-term bonds should be taken into consideration if rates are predicted to fall. Higher-duration bonds stand to gain more than their lower-duration counterparts when rates fall, and bond prices rise. 

Positive and negative convexity 

If a bond’s duration increases while the yield decreases, this is referred to as positive convexity. An increase in price brought on by a decrease in rates will have a greater impact on a bond with positive convexity than a rise in price brought on by an increase in yields. 

Negative convexity happens when the tenure of a bond increases at the same time that the yield does. Bond prices will fall as the yield increases. When interest rates fall, bond prices rise, but a bond with negative convexity depreciates as rates fall. 

Example of convexity 

Consider XYZ Corporation, a bond issuer, as having two bonds on the market now: bond A and B. Each bond has a 100,000 USD face value and a 5% coupon rate. Bond B matures in 10 years as opposed to bond A’s 5-year maturity. Bond A has a period of 4 years, but bond B has a duration of 5.5 years using the concept of duration. This implies that the price of bond A will vary by 4% for every 1% change in interest rates, whereas the price of bond B will change by 5.5%. 

Let’s now assume that interest rates unexpectedly rise by 2%. Accordingly, the cost of bond A should go down by 8%, while the cost of bond B would go down by 11%. However, based solely on bond B’s term, the price movement will be less than anticipated using the idea of convexity. 

This is because bond B has a higher convexity. After all, it has a longer maturity. Bond B’s higher convexity protects against changes in interest rates, resulting in a less significant price movement than predicted based on tenure. 

Frequently Asked Questions

Convexity = [1 / (P *(1+Y)2)] * Σ [(CFt / (1 + Y)t ) * t * (1+t)] 

Where, 

CFt = Cash inflow in the t Period (coupon payment and principal at maturity) 

P = Bond Price 

Y = Periodic Yield to Maturity 

t = Number of Periods 

T = Time to Maturity

The convexity of a bond gauges how sensitive its duration is to variations in yield. A bond’s price change can’t be accurately measured by duration since it suggests that the change is linear when it has a sloped or “convex” shape. 

The bond convexity formula is computed by dividing the total of the bond’s discounted future cash inflow by the number of years it will be outstanding by the sum of the bond’s discounted future cash inflow. 

We include the convexity adjustment to our initial duration calculation to estimate the change in the bond’s price given a specific change in yield. The convexity (C) formula is C=1P∂2P∂y2. where y is the yield-to-maturity and P is the bond’s price. 

When we talk about the convexity of a bond portfolio, we refer to the degree of curvature in the portfolio’s yield-to-maturity (YTM) curve. A bond portfolio with positive convexity will have a positively curved YTM curve, while a bond portfolio with negative convexity will have a negatively curved YTM curve. 

The convexity of a bond portfolio is computed by dividing the total of the discounted future cash inflow of the bond and the corresponding number of years by the sum of the discounted future cash inflow. 

    Read the Latest Market Journal

    From $50 to $100: Unveiling the Impact of Inflation

    Published on Apr 12, 2024 32 

    In recent years, inflation has become a hot topic, evoking strong emotions as the cost...

    Japan’s Economic Resurgence: Unveiling the Tailwinds Behind Nikkei 225’s Record Leap

    Published on Apr 11, 2024 51 

    Source: eSignal, Intercontinental Exchange, Inc. In the heart of Japan’s economic landscape, the Nikkei 225...

    Weekly Updates 8/4/24 – 12/4/24

    Published on Apr 8, 2024 92 

      This weekly update is designed to help you stay informed and relate economic and...

    What Makes Forex Trading Attractive?

    Published on Apr 2, 2024 172 

    In a world where the click of a button can send goods across oceans and...

    Weekly Updates 1/4/24 – 5/4/24

    Published on Apr 1, 2024 93 

    This weekly update is designed to help you stay informed and relate economic and company...

    How to soar higher with Positive Carry!

    Published on Mar 28, 2024 124 

    As US Fed interest rates are predicted to rise 6 times this year, it’s best...

    Why 2024 Offers A Small Window of Opportunity and How to Position Yourself to Capture It

    Published on Mar 28, 2024 171 

    With the Federal Reserve (FED) finally indicating rate cuts in 2024, we witnessed a significant...

    Weekly Updates 25/3/24 – 29/3/24

    Published on Mar 25, 2024 75 

    This weekly update is designed to help you stay informed and relate economic and company...

    Contact us to Open an Account

    Need Assistance? Share your Details and we’ll get back to you

    IMPORTANT INFORMATION

    This material is provided by Phillip Capital Management (S) Ltd (“PCM”) for general information only and does not constitute a recommendation, an offer to sell, or a solicitation of any offer to invest in any of the exchange-traded fund (“ETF”) or the unit trust (“Products”) mentioned herein. It does not have any regard to your specific investment objectives, financial situation and any of your particular needs. You should read the Prospectus and the accompanying Product Highlights Sheet (“PHS”) for key features, key risks and other important information of the Products and obtain advice from a financial adviser (“FA“) pursuant to a separate engagement before making a commitment to invest in the Products. In the event that you choose not to obtain advice from a FA, you should assess whether the Products are suitable for you before proceeding to invest. A copy of the Prospectus and PHS are available from PCM, any of its Participating Dealers (“PDs“) for the ETF, or any of its authorised distributors for the unit trust managed by PCM.  

    An ETF is not like a typical unit trust as the units of the ETF (the “Units“) are to be listed and traded like any share on the Singapore Exchange Securities Trading Limited (“SGX-ST”). Listing on the SGX-ST does not guarantee a liquid market for the Units which may be traded at prices above or below its NAV or may be suspended or delisted. Investors may buy or sell the Units on SGX-ST when it is listed. Investors cannot create or redeem Units directly with PCM and have no rights to request PCM to redeem or purchase their Units. Creation and redemption of Units are through PDs if investors are clients of the PDs, who have no obligation to agree to create or redeem Units on behalf of any investor and may impose terms and conditions in connection with such creation or redemption orders. Please refer to the Prospectus of the ETF for more details.  

    Investments are subject to investment risks including the possible loss of the principal amount invested. The purchase of a unit in a fund is not the same as placing your money on deposit with a bank or deposit-taking company. There is no guarantee as to the amount of capital invested or return received. The value of the units and the income accruing to the units may fall or rise. Past performance is not necessarily indicative of the future or likely performance of the Products. There can be no assurance that investment objectives will be achieved.  

    Where applicable, fund(s) may invest in financial derivatives and/or participate in securities lending and repurchase transactions for the purpose of hedging and/or efficient portfolio management, subject to the relevant regulatory requirements. PCM reserves the discretion to determine if currency exposure should be hedged actively, passively or not at all, in the best interest of the Products.  

    The regular dividend distributions, out of either income and/or capital, are not guaranteed and subject to PCM’s discretion. Past payout yields and payments do not represent future payout yields and payments. Such dividend distributions will reduce the available capital for reinvestment and may result in an immediate decrease in the net asset value (“NAV”) of the Products. Please refer to <www.phillipfunds.com> for more information in relation to the dividend distributions.  

    The information provided herein may be obtained or compiled from public and/or third party sources that PCM has no reason to believe are unreliable. Any opinion or view herein is an expression of belief of the individual author or the indicated source (as applicable) only. PCM makes no representation or warranty that such information is accurate, complete, verified or should be relied upon as such. The information does not constitute, and should not be used as a substitute for tax, legal or investment advice.  

    The information herein are not for any person in any jurisdiction or country where such distribution or availability for use would contravene any applicable law or regulation or would subject PCM to any registration or licensing requirement in such jurisdiction or country. The Products is not offered to U.S. Persons. PhillipCapital Group of Companies, including PCM, their affiliates and/or their officers, directors and/or employees may own or have positions in the Products. Any member of the PhillipCapital Group of Companies may have acted upon or used the information, analyses and opinions herein before they have been published. 

    This advertisement has not been reviewed by the Monetary Authority of Singapore.  

     

    Phillip Capital Management (S) Ltd (Co. Reg. No. 199905233W)  
    250 North Bridge Road #06-00, Raffles City Tower ,Singapore 179101 
    Tel: (65) 6230 8133 Fax: (65) 65383066 www.phillipfunds.com