/risk-magazine/technical-paper/1497788/modelling-south-african-swap-spreads

01 Oct 2007, Risk magazine

In welcome contrast to the domestic corporate bond and (non-vanilla) derivatives market, the South African swap market - like its offshore counterparts - is highly liquid. Although the exponential growth in swap trading volumes of the 1994-2002 period slipped slightly from 2002 to 2005,1 according to the South African Reserve Bank, domestic swap turnover in nominal terms amounted to R2.5 billion in 2006, up from R1.9 billion in 2005. To July 2007, nominal swap turnover stands at R2.05 billion. With burgeoning hedge fund and private equity deals, the swap market is set to remain at the forefront of interest rate derivative activity.

So, when swap spreads (the difference between the swap rate and the government yield of the same maturity) are at decade highs, market participants want to know why, how and where they are going from here. Since the domestic swap market is so liquid, and historical data is relatively easy to come by, quantitative models can be called upon to offer some insight. Quantitative models have certainly been popularised by bank-driven articles, particularly as the underlying supply-demand imbalances of the late 1990s and early 2000s in the US and UK markets dissipated.2,3

Figure 1 shows historical 10-year swap spreads (that is, the difference between the 10-year swap rate and the 10-year government bond yield) for the US, UK, eurozone, Australia and South Africa, from 2000 to the present. Theoretically, swap spreads should reflect the risk premium of lending to a bank. However, as banks enjoy high credit ratings, wide spreads have often been the result of low government yields; the lack of supply of government paper, and high demand for it, have led to inflated swap spreads beyond what a 'fair' credit premium should reflect. This point has been argued for the US and UK swap markets and certainly holds for South Africa, particularly for longer maturities (of 10 years or more, where government supply has been scarce).2,3

Supply-demand imbalances aside, current swap spreads in the US, UK, eurozone and Australia are stretched, as are our own. As of mid-September, the US 10-year spread was 0.2 standard deviations above its seven-year mean and 2.0 standard deviations above its three-year mean. Similar patterns emerge for the UK and eurozone. Furthermore, the Australian 10-year spread was 2.4 standard deviations above its seven-year mean and 3.5 standard deviations above its three-year mean; and the South African spread was 2.6 standard deviations above its seven-year mean and 1.9 standard deviations above its three-year mean. From the start of the year, 10-year spreads in the US, UK and eurozone had increased by about 20 basis points (bp), and South African and Australian spreads by about 30bp. Hence, despite the general stabilisation of swap spreads across developed markets in recent times, swap spreads widened considerably by the third quarter of 2007, more so than the global credit crunch alone could account for.

The traditional drivers identified as significant, from a statistical perspective, in driving swap spreads2,3 are sufficiently intuitive and generic to be adopted as global drivers rather than idiosyncratic or country-specific, provided the underlying markets (swap and government bonds) are in supply-demand equilibrium and liquid. We have already mentioned one driver (credit premia). Other drivers that have proved significant relate to interest rate expectations and yield curve dynamics.

Before plunging into the drivers, we take a short statistical detour.

Stationary spreads

The purpose of this and a previous Standard Bank statistical (regression) analysis4 on the drivers of swap spreads is twofold: to determine the drivers of the long-term characteristics of the 10-year swap spread and to try ascertain, in a general sense, whether current wide spreads should be exploited as trading opportunities. Central to both goals is the concept of mean reversion or, more technically, 'stationarity'.

Broadly, stationary swap spreads have stable distributions. Hence, within the context of statistical stationarity, it is justifiable to assume that spreads revert to a longer-term mean, particularly when they are several standard deviations away from that mean. It would, however, be glib to set an upper bound for widening spreads arbitrarily at, say, three standard deviations. Nevertheless, stationarity is a crucial starting point for analysing how far spreads should (statistically) go. The US, UK, eurozone and Australian swap spreads are mean-reverting at high levels of statistical confidence, using both three- and seven-year samples. However, South African 10-year swap spreads are strictly stationary only for the seven-year sample illustrated in figure 1. Over three years, the swap spreads test trend stationary only, meaning that the spreads deviate around an upward trend in a stable fashion. The bottom line is that mean reversion over a shorter period is trickier to deal with for South African spreads as they exhibit a statistically viable upward trend. Furthermore, the seven-year (stationary) spread sample spans periods over which economic fundamental trends (the rand and inflation, to name two) have shifted considerably, and is therefore beset with other statistical bugbears.

Economic drivers of swap spreads

Macro-economic drivers of swap spreads hinge around when market participants pay the fixed rate of a swap (as opposed to receiving the fixed rate). Hence, the interest rate environment plays a part, and this manifests as a yield curve shape play and/or interest rate expectations.

First of all, interest rate expectations and swap spreads should be positively correlated. In other words, when interest rates are expected to increase, swap spreads should widen as liability hedgers fix exposures by paying fixed in swaps. Conversely, when interest rates are expected to ease, speculators and borrowers alike generally receive fixed and pay (the declining) floating rates, thus tightening spreads. Hence, from a statistical perspective, the regression co-efficient for interest rate expectations in regression modelling swap spreads should be positive.

Interest rate expectations prove statistically significant in explaining domestic 10-year swap spreads. As a proxy for expectations, the difference between the 6x9 and 2x5 forward rate agreements (FRAs) can be used. The 2x5 reflects market expectation for short-term (three-month) rates in two months' time, and the 6x9 expectations in six months' time.

Insofar as the current interest rate environment is reflected in the shape of the curve, a steeper curve generally encourages long-end swap receiving activity and short-end paying activity and hence concomitant swap spread tightening. On the other hand, a flat swap curve offers a natural incentive (in the absence of directional interest rate expectations) to pay fixed in the longer term, and therefore leads to wider spreads, all other things being equal.

A reasonable proxy for curve steepness is the 10-year/two-year swap spread. Given the inverse relationship between steepness and spreads (tighter spreads with steeper curves), the co-efficient of steepness in a correctly specified regression should be negative. Yield curve steepness also proves statistically significant in explaining the domestic 10-year swap spread.

It has been argued that interest rate expectations should play a more dominant role in driving swap spreads during times of trending interest rates (that is, during clear easing or hiking repo-rate cycles).2 This is quite intuitive. But, it is difficult to know - before the fact - when rate cycles will commence or come to an end. Furthermore, finding an objective proxy to reflect whether a point in time is or was (according to the market at the time) in a trending interest rate period is harrowing: after the fact is easy, but before the fact measures can be inconsistent (now we see the cycle, now we don't).

We found that including a variable that forces the impact of the rate expectations driver to be greater during a trending repo cycle created ambiguity in our model. This ambiguity occurred when perfect hindsight in rate expectations was assumed as well as when FRAs were used to proxy where the market believed short-term interest rates were headed. Although intuitively appealing, such a variable could introduce noise into forecasts. We believe that this occurs because there have been too few clearly demarcated rate-trending rate periods over the last seven years in South Africa.

Finally, determining a statistically significant domestic proxy for credit premia that is appropriately correlated to swap spreads (a higher credit premium implies higher swap levels and hence wider spreads) and has a sufficiently long history (at least three years' worth of data) proved difficult. The domestic credit market is beleaguered by illiquidity and price inconsistencies and, although international credit indexes are well-developed and available, a domestic measure is preferable as international credit events have not always filtered through with comparable demagnitude to the local swap market. In the end, the most practical measure that was statistically significant turned out to be the weighted (by nominal size) average spreads of local bank issues (corporate bonds).

All in all, our model accounts for about 85% of the long-run variability of historic 10-year swap spreads. Preliminary analysis shows that a short-run correction that incorporates some memory of recent spreads superimposed on the long-run model will have better forecasting power. For now though, our long-run model shows that the fair value of the 10-year spread should be around 65bp, or about 20bp tighter than current levels. Based on our model, therefore, we expect the 10-year spread to be biased towards tightening somewhat, but remaining well above three- and seven-year mean levels for a while yet.

1. Flint, Henry, "SA's softening interest rate-swap and bond turnover", Market Insight, Standard Bank Global Markets Research, 28 February 2005.

2. Wraith, John, "The dynamics of swap spreads: key drivers and the medium term outlook", Derivatives and Risk Management Handbook 2003/04, Royal Bank of Scotland, 2003.

3. Cortes, Fabio, "Understanding and modelling swap spreads", Bank of England Quarterly Bulletin, Winter 2003.

4. de Wet, Theuns, "A marked increase in risk aversion", Fixed Income Pulse,Standard Bank Global Markets Research, 13 March 2006.

Nicolette Roussos Head: Quantitative Strategy, Global Markets Research T. +27 11 378 7217. E. [email protected], www.standardbank.co.za.

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