RDP 9609: Australian Financial Market Volatility: An Exploration of Cross-Country and Cross-Market Linkages 2. Bond, Share and Foreign Exchange Markets: Descriptive Statistics and Correlations

This section examines the volatility in bond, share and foreign exchange markets in Australia, the United States, Japan, Germany and the United Kingdom over the period from May 1987 to February 1996. It also takes a preliminary look at the international linkages between markets using simple correlations.

All of the analysis is based on moving samples of daily price data to capture time variations in volatility measures and relationships through time. Rolling correlations across markets are calculated using a 250-day moving window of observations.^[1]

Volatility is measured using an exponentially weighted rolling standard deviation of daily percentage changes in the market level observed over the preceding 60 working days.^[2] For share markets, the daily percentage change is calculated from the closing value of the relevant share price index. For the foreign exchange market, we use the daily percentage change in the rates quoted at 15.00 New York (Eastern) Time by Bankers Trust. In bond markets, however, volatility is calculated for daily basis point changes in 10-year benchmark bond yields.^[3] This preliminary analysis focuses on questions of whether financial markets have experienced any major changes in volatility or in the degree of cross-country linkage, within the period studied.

2.1 Bond Markets

2.1.1 Volatility

Historical volatilities for bond markets in the five countries are plotted in Figure 1. Summary statistics are presented in Table 1.

It is apparent from Figure 1 that bond volatility, both in the Australian and foreign markets, has two key attributes. First, the volatility is not constant, but fluctuates substantially over time. Second, it exhibits clustering, that is, there exist periods of heightened turbulence, often followed by longer periods of subdued or moderate volatility.

Several other facts emerge from the international comparisons.

• Australian bond-market volatility appears high in comparison to other countries. Over the period February 1987 to February 1996, Australia had the highest average level of bond volatility. It clearly exceeded the levels recorded for the US, Japan and the UK, and was more than double that which is experienced by the German bond market over the period. This may be related to higher average levels of bond yields in Australia compared to the other countries, in turn related to historically higher and more variable inflation in the 1970s and 1980s.
• Bond market volatility displays greater variability in Australia than in other countries. As Table 1 indicates, Australian bond-market volatility exhibits the largest fluctuations around its mean or average level for the period.
• A slight rising trend in volatility can be discerned over the period for the Australian bond market, although this result may be dominated by the 1994 episode. Time trends fitted to the volatility profiles of each market reveal that Australia is the only country that records a significant positive trend. Volatility profiles for the US, Japan and UK markets were found to contain significant, but negative, time trends.^[4]
• The magnitude and persistence of volatility triggered by the 1994 bond market collapse was higher in Australia than in other countries, with the next strongest reaction in the UK. It may be significant that these are the two countries in the sample with relatively poor inflation records, which may have contributed to higher perceived inflation risks and more volatile expectations of inflation.

2.1.2 Correlations and market linkages

Rolling correlations between the volatilities in Australia and other countries are shown in Figure 2. In three of the four cases, these correlations have increased over time.^[5] This suggests growing interdependence between bond markets during the 1990s, at least with respect to volatility. The growth in correlation is most striking in the Australia-US relationship, with the pick-up in correlation most evident from 1992.

Even more pronounced in the Australia-US relationship is the correlation between changes in daily bond yields. Figure 3 contains the rolling 250-day correlation of basis point changes between the Australian and other bond markets. While the correlations between basis point changes are understandably generally lower than those for volatilities, the trends evident in Figure 2 (rolling correlation of volatilities) are broadly similar to those contained in Figure 3 (rolling correlations of basis point changes). The most dramatic correlation profile in Figure 3 relates to the Australia-US pairing. Between late 1988 and late 1993 the correlation between basis point changes in Australian and US bond yields displays remarkable stability, fluctuating between around 0.15 and 0.25. It subsequently undergoes a rapid and substantial increase, rising from 0.15 to 0.55. The correlation remains at 0.55 for the rest of the sample, again displaying very little variation.

2.2 Share Market

2.2.1 Volatility

Table 2 presents summary statistics on share-market volatility and Figures 4a and 4b plot the volatility series for each market.^[6] As with bonds, volatility displays persistence and is not constant over time. Share-market volatility could be characterised as generally steady but punctuated by brief volatile episodes: some countries experienced more of such episodes than others.

A number of points may be made about share-market volatility.

• With the exception of Japan, volatility was more subdued in the second half of the sample period. While the level of background volatility seemed unaffected, there were fewer surges in volatility in the latter years.
• This observation is confirmed by simple regressions which reveal that every country except Japan had a negative time trend in its volatility. This result remains unchanged when the regressions are re-run starting at July 1988 to exclude the effects of the 1987 stock-market crash. Japan had a positive time trend in each set of regressions.
• The 1987 surge in volatility following the October stock-market crash dominates the series. In Australia and the US the reaction was much stronger than in other markets. The peak of the surge was over ten times the sample average volatility for these countries: this compares with over seven times in the UK, 4.8 in Japan and 4.5 in Germany. The extremity of the 1987 episode manifests itself in the large difference between the two tension coefficient values for each of the markets, but especially for Australia.
• The mini stock-market crash in 1989 occasioned another notable surge in volatility in several countries. In Australia and the US it is the only outstanding peak of volatility apart from 1987, and in Germany it is the highest episode of volatility, exceeding even 1987. In Japan and the UK, however, it barely registers, prompting only very slight increases in volatility.
• Japan and Germany had the most turbulent markets. Their average volatility was distinctly higher than the other countries. This is in contrast to the bond market, where they had the lowest volatility. In Japan, the end of the asset boom triggered large falls in the Nikkei during the 1990s, causing high volatility. Similarly the German stock market suffered large falls, and hence high volatility, during 1990 and 1991.

On the basis of the foregoing, it is possible to divide the countries into two groups. The first group, comprising Australia, the US and the UK, is characterised by relatively low and stable volatility (average around 0.8 per cent), a small number of surges and very high volatility during the 1987 episode. The second group, Japan and Germany, features higher average volatility (1 per cent or more) but a more subdued volatility response to the 1987 stock-market crash.

2.2.2 Correlations and market linkages

Rolling correlations of share-market volatility are shown in Figure 5. The correlations, while initially very high, (reflecting the 1987 stock-market crash), decline over the sample period.^[7] The falling correlations suggest that the Australian share market became less sensitive to other markets' volatility over the sample period.

Rolling correlations of daily percentage changes in Australian and foreign share price indices are shown in Figure 6. The main observation that can be made from the charts in Figure 6 is that for the Australian share market, its relationship with daily movements in the US share price is consistently stronger than it is with the other equity markets. The Australia-US correlation is not only consistently higher over the entire sample period, but also displays considerably less variation, than the other pairings.

2.3 Foreign Exchange Market^[8]

2.3.1 Volatility

Table 3 contains summary statistics of volatility in the foreign exchange market and Figure 7 plots the volatility series. From inspection of Figure 7, it appears that volatility does not show a consistent trend across the various exchange rates. It does appear that the USD/AUD had a negative trend and the JPY/USD a positive one. Simple regressions partially confirm these impressions. The volatility of the USD/AUD and the GBP/USD exchange rates have negative time trends, while the TWI has a positive trend. The yen and German mark do not have significant trends. For the USD/AUD from 1991 onwards, volatility was lower with fewer and less dramatic spikes. The GBP/USD experienced some high volatility in the early 1990s, culminating in September 1992 with the ERM crisis. Thereafter, it fell to its lowest volatility of the period. As might be expected, the TWI had more consistent volatility than the USD/AUD. While it had fewer large spikes of volatility in the second half, it also experienced higher troughs, giving it a positive trend.

The foreign exchange markets had low levels of volatility in terms of percentage changes compared to share markets.^[9] The TWI, as a composite exchange rate, may be expected to have lower average volatility, but the USD/AUD was also distinctly more subdued than the other bilateral rates. The DEM/USD had the highest average volatility, but there is little difference between the average volatilities of the German mark, yen and pound sterling exchange rates.

The TWI had the least variation in its volatility. Of more interest is the high variation about the mean of the yen and pound sterling volatilities. The comparatively low variability of the AUD and TWI volatilities is not, however, reflected in the exchange rates' tension coefficients. This is because while the AUD and TWI had fewer surges of volatility, the size of their surges were just as great as those of the other exchange rates. When combined with their lower troughs, this gives the AUD and the TWI the highest tension coefficients.

Unsurprisingly, the GBP/USD and DEM/USD exchange rates have quite similar volatility profiles, indicating closely aligned currencies. The JPY/USD shares several episodes of high volatility with these two currencies (early 1988, mid 1989 and early 1995) which the USD/AUD did not experience. This, combined with the low average volatility of the USD/AUD, suggests that the Australian dollar may be connected relatively closely to the US dollar.

Footnotes

The rolling correlations are calculated using a 250-day moving window. The time-zone differences between the various markets present a problem for data synchronisation. As the Australian day t occurs before day t in the other markets, the data from other markets are lagged one day when calculating the correlations. For example, the Australia-US correlations are between Australia day t and US day t−1. Given the minimal time difference between Australia and Japan, Japanese data are not lagged. Hence the Australia-Japan correlations are between Australia day t and Japan day t. [1]

In calculating the standard deviation, which is used as a measure of volatility, the observations are exponentially weighted, placing relatively more weight on recent observations. The weight allocated to each observation is w_j = (1 − λ)λ^j where λ = 0.89125. All of the data were obtained from Datastream. [2]

Observations are mid-points between closing-time bid and offer prices. Basis point changes are simply the daily change in yields: Basis Point Change_t = Yield_t − Yield_t−1. The usual definition of basis point changes produces values exactly one hundred times larger than those generated here, but, as this makes no difference to the results, the term basis point changes is adopted for convenience. [3]

Germany had a positive, but not statistically significant, trend. One question is whether the negative trends were secular trends, or essentially a result of the 1987 volatility surge. The regressions were re-run with the sample starting in 1988 to avoid the effects of the 1987 surge. In the second set of regressions, Germany joins Australia in having a significant positive trend, and the UK ceases to have a significant trend. The US and Japan retain their negative trends. [4]

Japan was the exception: in the 1990s its correlation with Australia was constant. [5]

Figure 4a plots the volatility profiles over the entire sample period, whereas Figure 4b covers the period 1988–1996, thereby excluding the very large movements associated with the 1987 stock-market crash. [6]

Again Japan is the exception, with its correlation with Australia, after falling in the late 1980s, showing no trend in the 1990s. [7]

The exchange rates considered here are: USD per AUD, JPY per USD; DEM per USD; and GBP per USD. With the exception of the USD/AUD, each exchange rate is expressed as the foreign currency price of one US dollar: the USD/AUD is the US dollar price of one Australian dollar. The observations are the rates quoted at 15.00 New York (Eastern) Time by Bankers Trust. As such, the time zone differences problem does not apply to exchange rates and there is no need to lag observations from some markets when calculating correlations. [8]

From Table 1 it would seem that the bond market had easily the lowest volatility. However, volatility in Table 1 is calculated using daily basis point changes. If daily percentage changes are used, bond-market volatility is approximately equal to that of the share market. [9]