Understanding the Value of Convexity

In banking, the word “structure” is used all the time.  For example, management will ask a loan officer, “what is the structure of that loan deal?”  In other words, what is the term, amortization, and rate (fixed or floating).  Or at ALCO, the committee will discuss pricing on deposits and the terms the bank should be offering.  Should the team extend liabilities or work on strategies to shorten them?  The same type of discussions happens for the bond portfolio.  At the end of the day, you discuss structure ultimately to maximize current earnings and over the long term, maximize shareholder value.

However, focusing on the highest current yield may not be what actually maximized shareholder value.  While this is true throughout the balance sheet, let’s take a closer look using bonds to help understand this.  Below are three different bonds with different structures.  The first one is a deeply discounted 30-year MBS with a 1.50 percent coupon, call this Bond #1.  The second bond is a slightly discounted 30-year MBS with a 4.50 percent coupon, call this Bond #2.  The last bond is a 10-year treasury bond, call this Bond #3.  All of these bonds have very close average life and duration metrics in the base case.

Bond #1 has a 5.00 percent yield in the base case and extends less than a year if rates were to rise 300 basis points.  However, if rates fall 300 basis points, Bond #1 decreases by about 1.5 years in duration.  However, where the maximized shareholder value comes in to play is looking at the total return profile in these scenarios.  In the down 300 scenario, the total return is nearly 30 percent, whereas to total return in the up 300 scenario is only a negative 15 percent.

Bond #2 has a slightly higher yield in the base case of 5.13 percent and extends over 2 years in the up 300 basis point scenario.  When rates fall 300 basis points, the duration decreases 7 years.  Looking further at the total return profile, Bond #2 gains only 11.76 percent in the down 300 scenario and loses over 14 percent in the rising scenario.

Bond #3 is yielding 4.50 percent and the duration remains unchanged in both the rising and falling rate scenarios.  However, when looking at the total return profile, Bond #3 has a total return of 27.6 percent in the falling 300 scenario and a negative 15 percent in the up 300 scenario.

What we see in these three bonds is that they all have very similar total return profiles in the rising 300 scenario, but Bond #1 and Bond #3 significantly outperform in the falling scenarios.  These bonds are said to have positive convexity.  However, Bond #1 provides 50 basis points more of current yield than Bond #3 and gives up very little to Bond #2.  Bond #2 has negative convexity where the upside doesn’t outweigh the downside in the changing rate environment.

When looking at structure in this way, we can see the metrics that will help our overall balance sheet over the long-term.  Additionally, when looking at your MVE, or EVE, calculations in your interest rate risk reports, understanding the structure of the asset or liability in this way will help you manage your long-term balance sheet position for changing rate environments.  Also, this is key in understanding how you can adjust your overall balance sheet to get your risk profile within policy parameters. 

The next time you look at your Market Value of Equity position, think about how the decision of the structure you agree to on the next loan, next bond, or next deposit impacts the possible range of outcomes.  Or, if nothing else, make sure your bond representative is giving you this information so that your balance sheet isn’t working against you.

Bond #1

Bond #2

Bond #3