This article does not cite any sources. Duration is a linear measure or 1st derivative bond convexity how the price of a bond changes in response to interest rate changes. As interest rates change, the price is not likely to change linearly, but instead it would change over some curved function of interest rates.
Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest rate, i. Specifically, one assumes that the interest rate is constant across the life of the bond and that changes in interest rates occur evenly. In actual markets the assumption of constant interest rates and even changes is not correct, and more complex models are needed to actually price bonds. However, these simplifying assumptions allow one to quickly and easily calculate factors which describe the sensitivity of the bond prices to interest rate changes.
For two bonds with same par value, same coupon and same maturity, convexity may differ depending on at what point on the price yield curve they are located. Though both bonds have same p-y combination bond A may be located on a more elastic segment of the p-y curve compared to bond B. This means if yield increases further, price of bond A may fall drastically while price of bond B won’t change, i. This means bond B has better rating than bond A. Given the relation between convexity and duration above, conventional bond convexities must always be positive. The positivity of convexity can also be proven analytically for basic interest rate securities. If the combined convexity and duration of a trading book is high, so is the risk.
Frank Fabozzi, The Handbook of Fixed Income Securities, 7th ed. The basics of duration and convexity”. Duration, Convexity, and Other Bond Risk Measures. The standard reference for conventions applicable to US securities. This article needs additional citations for verification.
A government bond or sovereign bond is a bond issued by a national government, generally with a promise to pay periodic interest payments and to repay the face value on the maturity date. The terms on which a government can sell bonds depend on how creditworthy the market considers it to be. International credit rating agencies will provide ratings for the bonds, but market participants will make up their own minds about this. The first general government bonds were issued in the Netherlands in 1517. Because the Netherlands did not exist at that time, the bonds issued by the city of Amsterdam are considered their predecessor which later merged into Netherlands government bonds. The first ever bond issued by a national government was issued by the Bank of England in 1694 to raise money to fund a war against France. It was in the form of a tontine.