Convexity Hedging and its Impact on US Swap Spreads

Convexity Hedging and its Impact on US Swap Spreads
John Wraith, The Royal Bank of Scotland, Financial Markets

Introduction
While there is a huge diversity of factors which impact on the level and direction of swap spreads in interest rate markets, some clearly have more importance than others. Over time, the dominant influences change with other developments in underlying market, and the key to anyone exposed to changes in swap spreads must therefore be to keep abreast of the nature of major influences on spreads at any given time.

In the US over the past few years, the behaviour of negative convexity hedgers has become more and more important in this regard. The correlation between yield moves and spread levels has become ever more closely entwined, and as shall now be demonstrated, this can be put at the door of the convexity hedgers.

Before examining this relationship more closely, it is necessary to have a clear understanding of negative convexity, the products it is attached to, and the reason its existence leads to activity in the interest rate swaps market.

Convexity
In simple terms, convexity is the property of an asset that describes the dynamic that for each successive basis point fall in yield, the price rises at an increasing rate. The reason for this is that as rates fall, so the duration of a normal bond increases due to the fact that future cash flows are being discounted off a lower rate. The higher the duration of a bond, the more sensitive its price is to a move in the yield. For holders of bonds, this is a highly desirable property as profits increase exponentially as yields fall, while the rate of accumulation of losses slows down as yields rise. This protects the holder to some extent against adverse market moves while enhancing his return during market rallies.

There is, however, an increasingly large part of the US bond market comprised of debt where the convexity effect is the opposite of that described above. The reason for this is that bonds issued by US Agencies incorporate a facility whereby the issuers can repay their debt in the event that the mortgage holders, to whom the proceeds of the debt issues are lent, prepay on their mortgages. As rates fall, so homeowners are prone to repay their existing mortgage and take out a new one at the lower rates now available (US homeowners are highly proactive in this regard).

As a result, falling yields on agency debt with inbuilt pre-payment options, has the effect of reducing duration, and thus creating negative convexity, whereby for each successive fall in yields the price rises more slowly, while for each successive basis point rise in yields, losses for bondholders accelerate. The correlation on this is very strong; the Bloomberg index for mid-maturity Fannie Mae debt measured a fall in duration from 4.7 years at the end of June 2001 to 2.5 years by early September; over this period the generic 10-year Treasury yield fell from 5.42% to 4.30%.

Implications of Negative Convexity for the Swaps Market
While bonds with negative convexity properties are priced more cheaply than straight debt (reflecting the cost of the prepayment option embedded in the paper), there is still a desire on the part of holders of these bonds to avoid the undesirable impact of sizeable rate moves. To benefit from a fall in yields to the same extent as holders of positively convex bonds, there is a need to seek increased exposure to the market each time rates fall. Similarly, to avoid accelerating losses, there is a need to limit that exposure to the market when rates rise.

The mechanisms available to agency bondholders to manage their negative convexity are varied, and in the past tended to involve activity in the Treasury market. By buying US Treasuries in times of falling yields, the profits generated were enhanced by money made on this long Treasury position; by reversing this and establishing a short position in rising yield environments, the accelerating losses incurred on their agency bond holdings were reduced. While this activity is clearly not an exact science due to the uncertainty of future market direction, there will be trading levels at which large volumes of such hedging activity are triggered.

However, for such hedges to be efficient, the relationship between the underlying position and the hedge needs to be close. This implies that Treasuries only remained an effective counterweight to negative convexity as long as they could be relied upon to exhibit very similar yield changes to agencies. This relationship has deteriorated significantly over the past 3.5 years .


The initial spread dislocation came with the financial crises of Autumn 1998 (LTCM, Russia) and continued through the budgetary surplus period at the end of the decade that led to a scarcity premium being priced into Treasuries. A further shock came in early 2000 with the Baker Bill questioning the implicit government-guaranteed status of agency debt. This led to a further spike wider in the spread, but at the same time aligned mortgage bonds more closely with the swaps market by effectively moving them from being a government debt-linked instrument to a corporate debt-linked one.

While this premium has receded since President Bush's more expansive programmes were introduced, there is still an unwillingness to use Treasuries as a hedge for mortgage bonds; with the volume of agency debt in the secondary market set to outstrip the supply of Treasuries in the next ten years or so, the liquidity to use them as the hedge instrument of choice for agency bondholders is likely to decrease in the future.

As this relationship deteriorated, so agency bondholders sought an alternative hedge for their products, and in doing so have turned increasingly to the interest rate swaps market. The derivative nature of the market means that there will be none of the supply / demand issues associated with physical bonds, while the fact that there is no initial outlay of principal amounts also removes the danger of adverse repo market moves damaging the efficiency of the hedge.

Figure 2 demonstrates how swaps have behaved far more efficiently as a hedge instrument for mortgage bond portfolio managers, and why as a result the proportion of negative convexity hedging transacted through the swaps market is thought to be 70% of the total - the sharp fall in rates that saw the 10-year swap rate fall from 6.20% to 5.50% between mid-December 2001 and mid-January 2002, was estimated to have resulted in $60bn of convexity hedging flow through the swaps market.

Conclusion
Having explored the reasons behind the switch in the hedge instrument of choice for agency debt investors, we can now examine the impact such major flows have on swap spreads. The answer to this is clear: the relationship between swap spreads and directional moves in rates has become highly correlated over the past three years. As falling rates cause convexity hedgers to receive fixed in the swaps market to a far greater degree than they buy Treasuries as an alternative, so spreads narrow in response. Conversely, in a rising rate environment, spreads are pushed wider as mortgage bond investors seek to limit the impact of their exposure to negative convexity by paying fixed via the swaps market.

With the supply of agency debt set to continue increasing at a rapid rate for the foreseeable future and the proportion of convexity hedging carried out in the swaps market - as opposed to the Treasury market - likely to also continue growing, this relationship should become even more highly correlated. There are many other forces at work influencing swap spreads and each has a varying impact on the overall level, but the sheer size of the flows stemming from convexity hedging look set to keep this as the major determinant of swap spreads for a long time to come.