Why investors should not overlook the effects of Convexity
A trip down convexity lane
Introduction
A relatively calm period of low rates was ended by high inflation and central banks hiking interest rates to combat this. The quickly rising interest rates in 2022 and 2023 means that Convexity or the effect of Convexity is back in play. Not only for an investor seeking to outperform a benchmark, but also for pension funds or insurance companies seeking to hedge the interest rate risk of its liabilities. Their liabilities can run well into the next century, while their main hedging instrument (IRS) has a maximum maturity of 50 years. This means that they are short convexity even if they are fully hedged on paper. This highlights the need to look at the effects of Convexity.
Summary
• After a relatively calm period of low rates, volatility is back and so is Convexity!
• Convexity is a valuable feature and its effects become clear during periods of high volatility.
• There are several ways of setting up a Convexity trade, where a 30s50s curve is arguably the most pure trade in linear space.
• Convexity is not free of charge, there is a certain ‘give up’ cost associated with it.
• In the end being long or short Convexity should be an active decision!
In this paper we examine and explain the effects of Convexity. We start by dissecting the price-yield relationship and why there is need for a Convexity adjustment in it. We show the effects of Convexity for bonds and IRS and introduce a third-order effect called: “Speed”. Next we apply the established theoretical framework of Convexity in the real world and set up a Convexity trade. Finally we discuss the costs and risks associated with this trade and run a historical analysis on it.
