There are many firms with exposure to long bond yields.
Pension funds are known to have long bond exposure, with liabilities typically stretching out longer than 50 years and assets, which are invested in both fixed income and equities. Insurance companies certainly have exposure as their liabilities also extend longer than 50 years, although these firms tend to be more vigilant about matching assets and liabilities. Infrastructure firms and investors may have exposure, depending on the structure of the debt relative to expected project revenue. Any firm with exposure to long bond yields must be aware that the value of this exposure can change significantly in a low-yield environment.
As yields have dropped in the current environment, it’s common to hear both investment advisors and experts claim that yields do not have much further to drop and that significant inflation is around the corner.
First, let’s assume that rates will not fall below zero, since in that situation investors would prefer to hide their money in mattresses rather than purchase bonds that guarantee a loss of principal. Based on this assumption, we can understand how investment experts can claim that rates can’t drop much further, as they can’t fall more than the current yield of approximately 3.50%. But, on the other hand, yields can climb much more than this amount in an inflationary environment.
In fact, in the early 1980’s bond yields sometimes fluctuated by 150 basis points in one month! Therefore, for these pundits, the upside of being correct and yields increasing is far greater than the potential downside of yields falling further from their already low levels. For firms with exposure to long yields, however, the situation is not identical.
Defining and understanding convexity
A firm, such as a pension fund, must understand convexity and how it impacts exposure to long yields. Convexity is defined as the sensitivity of the duration of a bond to changes in interest rates. Duration is defined as the sensitivity of the asset price to changes in interest rates.
For a portfolio of assets, high convexity is considered a good thing, since sensitivity increases as markets rally creating more profit while the opposite is true when markets sell off. Pension fund liabilities are considered convex, which means the fund as a whole has negative convexity from its liability cash flows. Unless the fund’s assets have equivalent positive convexity, the fund as a whole, will have negative convexity.
Further interest rate changes will impact the asset price based on the new duration values.
For example, we may consider a 30-year bond with a coupon of 6% and a yield of 6% (and hence priced at par). The duration for such a bond is approximately 13.84 and the convexity is 0.03. What this means is that for a one-basis-point decline in yields, the bond price increases by 13.84 cents and the duration increases to 13.87. While this change may seem small, let us reconsider with yields at 3.00% for a bond with a current coupon of 3%. At these lower yields, the duration has increased to 19.69 and the convexity is now 0.05. This means that the price of the bond is more sensitive to changes in yield and the sensitivity of the bond will also vary to a greater degree with yield moves.
Don’t underestimate the importance of convexity.
For firms that have unhedged exposure to rates for long-maturity bonds, a recognition that basis point sensitivity has increased is crucial.
Based on our calculations above, a $1 billion pension fund with characteristics similar to our bond has a liability value change per basis point of close to $2 million at current yields. If this pension fund has the bulk of its assets invested in equities, then there’s a serious mismatch between assets and liabilities. And even if yields eventually move higher, is the fund able to withstand an actuarial valuation if yields drop by 50 basis points first? Convexity is an important and little understood concept, which investors at all firms should consider as part of their risk management program.