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Estimation of
the European
Equity Model

European Bond
and Currency Markets
in Anticipation of
Monetary Union


Volatile Markets
BARRA Models

Part One:
The Case for
the Market Neutral

BARRA announces new
managing director of
research

The BARRA Brainteaser
for Winter 1999

Solution for the Fall 1998
Brainteaser

European Bond and Currency Markets in Anticipation of Monetary Union

by Lisa R. Goldberg and Anton Honikman

Portions of this article appeared in the December 1998 issue of Euro Magazine

Introduction

When European Monetary Union took effect on January 1, 1999, eleven currencies collapsed into one and a common monetary policy for eleven countries came under the authority of a single central bank. Europe now has a reserve currency that competes with the U.S. dollar. As a result, business and financial transactions across European borders will become increasingly fluid, and markets will behave in new ways that are difficult to predict.

Developing EMU-compatible investment tools presented a unique challenge. Some required features were known in advance - for example, new settlement and accrual rules and dual currency reporting capabilities could be incorporated into existing models ahead of time. Modification of valuation and risk models was a trickier problem and there was no "right way" to handle it. Would EMU sovereign bond markets collapse into a single homogenous market? How could Euro volatility forecasts be generated early in January with no data history? How should models be modified to handle markets exiting and entering EMU?

This article answers these questions by examining the ways in which bond and currency markets anticipated monetary union. The information revealed by this examination was used by BARRA to design EMU-compatible fixed income valuation and risk models that should perform well no matter what the Euro brings.

Term Structures

At the core of any fixed income valuation model is a term structure of interest rates. This is the curve that comprises lending rates for terms of different length. There are different term structures for different markets such as French sovereign bonds, Japanese AA bonds, or GNMA 30-year mortgages. Market, however, is at best a loosely defined term. Candidate attributes used to characterize a market include its currency of denomination, credit level, liquidity, the nature of the issuing entity and other factors.

Should one continue to differentiate between EMU markets based on country of issue? Fluctuating exchange rates have historically enabled the term structures of EMU markets, as defined by their principal currency, to move with relative independence. FIGURE 1 shows a time series of French and Italian 5-year sovereign spreads over Germany. These spreads were quite large, especially for Italy, until November 1997. In the past year, however, these markets have become more uniform. Will they eventually collapse into a single market?

Figure 1: Spreads of 5-Year Sovereign Spot Rates

FIIGURES 2a and 2b show implied forward swap curves beginning with the inception of the Euro on January 1, 1999. Curves of this type formed the basis of the now defunct J. P. Morgan implied probability calculator which was used to forecast the likelihood of markets joining the EMU. The curve in figure 2a is derived from the July 1, 1997 while the curve in figure 2b is as of July 1, 1998. The convergence is dramatic. The forward curves in figure 2b practically coincide. This is encouraging, since the existence of a single EMU central bank implies that there will be a single swap curve for all EMU markets once the Euro is launched.

Figure 2a Forward Swap Curves for EMU Markets: January 1, 1999 as seen from July 1, 1997

Figure 2b Forward Swap Curves for EMU Markets: January 1, 1999 as seen from July 1, 1998

A similar analysis made for sovereign markets shows a similar but less dramatic trend. The results are displayed in FIGURES 3a and 3b.

Figure 3a: Forward Sovereign Curves for EMU Markets: January 1, 1999 as seen from July 1, 1997

Figure 3b: Forward Sovereign Curves for EMU Markets: January 1, 1999 as seen from July 1, 1998

While sovereign term structures have converged, spreads as high as 75 basis points remain. The existence of these spreads indicates the market’s perception of the credit-worthiness of the issuing sovereign. While liquidity and supply do affect bond prices, credit quality is the overriding means by which market participants differentiate between sovereign issuers within EMU.

What are the model implications? Credit-worthiness characterizes markets in EMU. Global models therefore need to account for the credit spreads between legacy markets. A single sovereign EMU term structure will not give sufficiently accurate model values since the differences between legacy markets are significant. More evidence for this conclusion is given below.

BARRA’s EMU Term Structure

What is the right benchmark against which to measure sovereign term structures in EMU markets? The most obvious candidates are the German sovereign term structure and the EMU swap curve. While both candidates have been adopted by analysts and market commentators, neither is perfect. Germany is the dominant EMU market in the sense that it has the largest GDP, the least credit risk, and the greatest supply. The Germany term structure, however, does not reflect "average" EMU behavior. The second choice, the EMU swap curve, is more appealing since it belongs to all EMU markets. However, the swap curve prices debt issued by commercial financial institutions, not sovereigns. Part of the spread between the EMU swap curve and an EMU sovereign curve results from the fact that a bank is more likely to default than a government. The swap curve does not provide a basis for comparing markets which have sovereign credit qualities.

An ideal approach is to estimate an EMU sovereign term structure from a pool of sovereign bonds belonging to EMU markets. A convenient pool is provided by the leading European sovereign indices: the J. P. Morgan EMU Bond Index and the Salomon Smith Barney EMU Government Bond Index (EGBI).

figure 4 displays BARRA’s Benchmark EMU term structure, estimated from the J. P. Morgan EMU Bond Index comprising bonds from all the EMU markets except Luxembourg.¹

Figure 4: Sovereign Term Structures for EMU Markets and Euro: July 1, 1998

FIGURE 5 displays the GDP weights used in the estimation procedure.2 Although we use the broader spectrum of EMU member markets in the estimation universe, GDP weights dictate that the combination of France, Germany and Italy will dominate the outcome.

Figure 5: GDP Weights

FIGURE 6 shows a less cluttered picture of the EMU term structure plotted with the three dominant markets: Germany, France and Italy.

Figure 6: Sovereign Term Structure for Dominant EMU Markets and Euro: July 1, 1998

Despite contributing over 18% of the estimation weight, Italy trades at a significant positive spread over the EMU baseline. The market is clearly pricing Italian sovereign debt differently from that of other markets in the currency union. There is a premium for perceived extra credit risk and potential departure from EMU.

FIGURE 7 gives a more detailed look at these spreads. It provides a cross-sectional view of member markets forward spreads relative to the EMU term structure at the 5- and 10-year vertices.

Figure 7: Implied 5- and 10-Year Forward Spreads for EMU Markets: January 1, 1999 as seen from July 1, 1998

France and Germany are clearly perceived as having the greatest credit-worthiness, Italy and Portugal the least.

The EMU sovereign term structure is a natural choice of benchmark. It elucidates the differences between the member markets. But how accurately does it value bonds? FIGURE 8 shows a table of root mean square pricing errors for the universes used to estimate EMU and legacy term structures.

Figure 8: Root Mean Square Pricing Errors, Term Structure Estimation: July 1, 1998

When valued off the EMU term structure, the typical pricing error for the universe of EMU sovereign bonds is 80 basis points. The analogous pricing error, if legacy market term structures are used, is roughly nine basis points. Hence, a typical EMU bond will have a much larger pricing error relative to the EMU term structure than to a legacy term structure. This further supports the conclusion that legacy sovereign term structures should continue after the introduction of the Euro. They do a much better job of pricing debt issued by their own sovereign entity.

Term Structure Movements

The dominant source of risk for sovereign and investment grade corporate bonds in a single market is change in term structure.³ Moreover, the dominant component of term structure change is a shift in level of rates.

FIGURE 9A looks at EMU market shift volatilities at July 1, 1997 and July 1, 1998. In all cases, volatility decreased by roughly 10-15%. figure 9b displays volatility forecasts for EMU markets as of July 1, 1998 as a function of half-life.⁴ Data were weighted exponentially with half-lives of 6, 12 and 24 months. As one would expect, volatility decreases with half-life uniformly across EMU members. As we give greater importance to more recent data, market stability through July end has a greater effect on the volatility estimates, dragging them downwards.

Figure 9a: Shift Volatility of EMU Markets

Figure 9b: Shift Volatilities of EMU Markets: of EMU Markets: July 1, 1998

FIGURES 10a and 10b display correlations between EMU market term structure shifts. figure 10a shows correlations by date, while figure 10b shows correlations as of July 1, 1998 as a function of half-life. These results are intuitive. Correlations tend to increase as monetary union approaches and as halflife shortens.

Figure 10a: Shift Correlations Between Pairs of EMU Markets

Figure 10b: Shift Correlations Between Pairs of EMU Markets: July 1, 1998

On the other hand, these markets are still imperfectly correlated. The July 1, 1998 shift correlation between Germany and Italy estimated with a halflife of 6 months is .55. The analogous estimates for Germany and Italy shift volatilities differ by more than 25 basis points. Separate risk factors for legacy markets still carry important, non-redundant information.

Currencies

Risk management systems will require Euro risk forecasts after the first trading date of monetary union, January 4, 1999. Since there is no history for the Euro, a proxy history is required to generate these forecasts. Natural candidates for the proxy are the Deutschmark or a weighted basket of EMU markets.

In the absence of Euro data, it is hard to imagine a test that would identify the best scheme. It turns out, however, that such a test is unnecessary since EMU currencies are already behaving as a single currency. FIGURE 11 shows a time series of daily returns for EMU currencies from a U.S. dollar perspective for the months of August and September. The data points are virtually on top of one another despite market turbulence throughout this period.

Figure 11: Daily Currency Returns in European Markets

FIGURE 12 displays monthly volatility forecasts for EMU currencies for January through September 1998. At the end of September, all EMU currency volatilities were approximately 9.4%. From August end to September end, volatility increased significantly. The only outlier is the Irish Punt which had a September end volatility forecast of 9.9%. figure 13 shows the correlation of the Deutschmark with other EMU currencies. By August end, all currencies other than the Irish Punt were perfectly correlated with the Deutschmark. The latest Deutschmark-Punt correlation is .92.

Figure 12: Volatilities of European Currencies

Figure 13; Correlations of EMU Currencies with the Deutschmark

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Is the U.K. an Island?

Our attention now turns to the most intriguing of the "Outs"⁵ - the United Kingdom. Among Outs, the UK has by far the largest economy. It has deep-rooted trade links with all EMU members and presided over the European Union while most of the EMU convergence took place.⁶ Since the economies and policies of the UK and EMU markets are so closely linked, one would expect their bond markets and currencies to exhibit similar behavior. This section superimposes an analysis of the UK onto analyzes already performed for EMU members. This puts some of our previous results in context.

Recall that market volatility⁷ decreased as a function of a reduction in half-life. In FIGURE 14 we observe that while the market volatility in the UK has also decreased, it does so at a more constant rate than in EMU markets.

Figure 14: Shift Volatilities of EMU Markets and the UK: July 1, 1998

Contrary to initial expectations, the UK market exhibits lower correlation with EMU members as one weights recent data more heavily. figure 15 shows shift correlation between the UK and EMU members as a function of half-life. In every case the use of a 6-month half-life significantly decreases the correlation.

Figure 15: Shift Correlations Between EMU Markets and UK: July 1, 1998

Interestingly, the correlation with France (0.31) and Germany (0.38) are low, and are even lower than the correlations of the U.S. with those markets: France (0.41) and Germany (.54).

FIGURE 16 shows how the volatilities of EMU currencies are virtually identical to one another while Sterling volatility is about 100bps lower. Similarly, the Sterling-Deutschmark correlation diminished during 1998. Earlier in 1998, Sterling exhibited a profile similar to the Irish Punt - both had a correlation coefficient of just under .7 with Deutschmark. As of September end, the Punt-Deutschmark correlation was .92 while the Sterling-Deutschmark was less than 0.6. By contrast, all EMU currencies with the exception of Punt were perfectly correlated with Deutschmark. This information is displayed in FIGURE 17.

Figure 16: Volatilities of European Markets

Figure 17: Correlations of EMU Currencies and Sterling with Deutschmark

Further disparities between the UK and the EMU markets are found in their term structures of interest rates. Forward curves beginning January 1, 1998 implied by July 1, 1998 term structures are shown in FIGURE 18. The EMU markets have upwardly sloping curves, and offer similar yields to maturity. The UK has an inverted yield curve whose rates bear no resemblance to those of the EMU.

Figure 18: Forward Sovereign Curves for EMU Markets and UK: January 1, 1999 as seen from July 1, 1997

The behavior of the bond and currency markets of the United Kingdom in this context attests to the homogeneity of EMU members. Despite economic and geographic ties with the European continent, the United Kingdom is most definitely an island.

Conclusion

Severe turmoil has prevailed in world markets since we started this study. The crash of the ruble at the end of August and the subsequent Asian and Brazilian currency crises have had serious repercussions in more developed markets. These events and the ensuing market volatility have raised the specter of default in the minds of investors, who are sacrificing expected return in favor of lower risk and flocking to the most conservative securities. As a result, spreads of all kinds have widened.

How much has worldwide volatility shaken up the EMU? Implied sovereign forward 5-year EMU spreads widened significantly between July 1, 1998 and October 16, 1998. Several of these spreads are depicted in figure 19.

Figure 19: Sovereign 5-Year Forward Spreads of European Markets Over EMU: January 1, 1999

By contrast, swap spreads have remained tight. figure 20 displays forward swap curves for January 1, 1999 implied by October 16, 1998. It is instructive to compare FIGURE 20 and FIGURE 2b. With the exception of Ireland, long end swap spreads were as tight on October 16 as they were on July 1. Short end spreads have narrowed significantly. This is reassuring insofar as monetary union mandates a single swap curve for all EMU markets beginning in January.

Figure 20: Implied Forward Swap Curves: January 1, 1999 as seen from October 16, 1999

FIGURE 17 depicts a dramatic increase in EMU currency volatility for the month of September during which forecasts rose by roughly 150 basis points. Nevertheless, the EMU currencies continued to behave in unison. Excluding the Punt, the largest September end volatility spread was between the Belgian Franc and the Deutschmark at 21 basis points and the lowest September end correlation was between the Lira and the Deutschmark at .982. Furthermore, correlations between pairs of EMU currencies remained perfect in the face of high volatility.

Clearly, currency and swap markets have converged. But the evidence given above confirms the hypothesis that perceptions of creditworthiness differentiate between markets in EMU. Good models need to support this distinction. N

¹ There are many ways to estimate a term structure of interest rates. The curve displayed in this document uses the same estimation procedure as in all BARRA fixed income models. We solve for rates that minimize relative pricing error. In this example, the Gross Domestic Products of the sovereign issuers weight bonds in the estimation universe.

² As remarked in "Weight Problem" on page 80 of the November 6, 1998 Economist, bond indexes suffer from the "perverse logic" of heavily weighting countries with large debt, even though these countries may be "borrowing their way into trouble." GDP weighting ensures that BARRA’s EMU term structure is dominated by the strongest markets rather than those markets with the largest debt.

³ Typically, a term structure is specified by rates at a set of key maturities or vertices, together with an interpolating rule to determine rates between vertices. The term structure specification suggests a risk model specification, which is a key rate model whose factors are changes in key interest rates. Empirical studies show that a key rate model forecasts risk effectively within a single market.

Nevertheless, a collection of key rate models is not the ideal design for a global model. Accurate valuation requires a term structure to have roughly 10 vertices. Even without considering credit or currency risk, a global model covering 20 markets with 10 interest rate factors per market results 200 risk factors. A history of at least 200 data points is needed in order to estimate the model parameters in a meaningful fashion. If the model has a monthly horizon, data from 17 years before the analysis date must be incorporated into the model. On the other hand, economic models benefit only from recent data. Old data tend to corrupt rather than improve economic forecasts. Fortunately, many of the key rate factors are redundant. Changes in interest rates within a single market are highly correlated, and a shift in interest rates accounts for more than 75% of term structure volatility in most developed markets. This fact enables us to compare market moves by looking at their shift volatilities and correlations.

⁴ For many economic time series, statistical parameters such as mean and standard deviation change over time. In these cases, parameter estimates should count recent information more heavily than old information. A simple, effective way to accomplish this is with an exponential weighting scheme. The scheme depends on a weight l between 0 and 1. The ith oldest data point is multiplied by a constant times li. The constant is chosen so that the resulting estimates are unbiased. The most intuitive way to understand a weighting scheme is in terms of its half-life, -log 2/ log l. The data point x(j - hl) counts roughly half as much as x(j).

⁵ The term "Outs" commonly refers to countries that are eligible for inclusion in EMU by virtue of the fact that they are members of the European Union, but have either not satisfied the inclusion criteria or have voluntarily excluded themselves.

⁶The United Kingdom held the presidency of the European Union from January 1, through June 30, 1998.

⁷ As expressed by shift volatity.