RDP 9301: The Response of Australian Stock, Foreign Exchange and Bond Markets to Foreign Asset Returns and Volatilities 3. Exchange Rate Volatilities and Correlations

The time-series and Schwert volatility measures for the Australian dollar/US Dollar, the US dollar/Canadian dollar, US dollar/German mark, US dollar/UK pound, and US dollar/Japanese yen exchange rates appear in Figures 9 through 13. As with the stock price indices, all data are end-of-month observations^[12].

The Schwert volatility measure for the Australian dollar/US dollar exchange rate appears to be centred on a value of two percent. Unlike the stock price index, there is no sharp break in the process. Rather, there is gradual decline in the value of the Australian dollar until the mid-1980s. Then there is a gradual appreciation, followed by a stable value at the end of the decade.

In Figure 10, the US dollar shows a steady appreciation against the Canadian dollar until the mid-1980s, followed by a steady and continuing depreciation. The volatility measure appears to be centred on a mean value of 0.75 percent.

The behaviour of the US dollar with respect to the German market appears in Figure 11. The same pattern of gradual appreciation followed by reversal takes place.

What is interesting is that the value of the US dollar peaks earlier against the German mark than against the Canadian dollar. The volatility measure is centred on a value between 2 and 3 percent. The pattern for the US dollar with respect to the UK pound in Figure 12 mirrors the pattern of the US dollar/German mark exchange rate in Figure 11, both in its rise and fall, and in its volatility index.

For the US dollar/Japanese yen exchange rate pattern, Figure 13 shows that there is no dramatic appreciation at the beginning of the sample period in the early 1980s. However, in the mid-1980s, a decline in the value of the US dollar against the Japanese yen, similar to the behaviour of the US dollar against the German mark, the UK pound, and the Australian dollar, takes place. By the end of the decade the US dollar appears to have levelled off at the stable, lower value. The Schwert volatility index for the US dollar/Japanese yen exchange rate also appears to be centred on a value slightly above 2 percent.

3.1. Contemporaneous Correlations

Table IV contains the contemporaneous correlations of the estimated volatilities. The volatility in the Australian index shows very little correlation with the foreign exchange rate volatilities. There is even a negative correlation with the US dollar/German mark volatility measure. However, small changes in the interval can cause sign changes in the correlation coefficients, so there is little significance in the signs of the estimates. With the exception of the European Monetary System (EMS) currencies, the foreign exchange correlations are lower than the stock market correlations reported in the previous section.

3.2. Tests of Granger Causality

The F-statistics and Wald statistics in Panels B and C of Table IV show a strong role for the US dollar/Canadian dollar exchange rate volatility index. It is exogenous to the volatility measures of the other exchange rate volatility measures. With significant but lesser importance, both the volatility measures of the US dollar/Japanese yen and US dollar/German mark outweigh, according to the Wald statistics, the own lagged effects for explaining the Australian dollar/US dollar exchange rate volatility.

3.3. Impulse Response Functions and Variance Decomposition

Three impulse-response functions for the Australian dollar/US dollar volatility index appear in Figure 14. I picture the response function for changes in the Australian dollar/US dollar volatility index, in the US dollar/Canadian dollar volatility index, and in the US dollar/Japanese yen volatility index.

Figure 14 shows that a unit shock to the Australian dollar/US dollar exchange rate volatility disappears rapidly. However, for a unit shock in the US dollar/Canadian dollar volatility index, the effect on the Australian dollar/US dollar volatility measure is more than 100 percent. While there is a fall in the succeeding period, there is no quick dampening, since the intermediate impulses are also high. By comparison, a unit shock in the US dollar/Japanese yen volatility index has rather small initial effects, which quickly dampen. The same is true for the other exchange-rate volatility measures.

The variance-decomposition analysis in Table V confirms the results of the impulse-response functions on the importance of the US dollar/Canadian dollar volatility measure. While shocks to the Australian dollar/US dollar volatility index explain most of its own variance at shorter horizons, at longer horizons shocks to the US dollar/Canadian dollar volatility index become considerably more important. At the longest horizons, the US dollar/Canadian dollar index explains 75% of the variance in the Australian dollar/US dollar measure.

3.4. Analysis of Time-Varying Exchange Rate Coefficients

As in Section 2.4, I examine whether or not the asset price in question became more closely correlated with corresponding asset prices when the volatility indices became larger in value. I thus examine the following equation with time-varying parameters:

where [Δe_US/Can,t Δe_US/DM,t Δe_US/UK,t Δe_US/Yen,t] is the matrix of logarithmic first differences of the Canadian (Can), German (DM), British (UK), and Japanese (Yen) exchange rates against the US dollar at time t, Δe_A/US,t is the first difference of the Australian exchange rate against the US dollar at time t, [β_t' δ_t'] are the time-varying coefficients of the contemporaneous foreign exchange rates and lagged own rate, and ε_t' is a random variable, with independent and identical distribution.

The time-path for two of the time-varying coefficients estimated by Kalman-filtering appear in Figure 15, the coefficient of the US dollar/UK pound exchange rate, and the coefficient of the lagged own exchange rate. Other coefficients showed even smaller variation from zero.

Figure 15 shows some jumps at the same time the stock-market crash occurred, as well as during the time the US dollar began its decline against the Australian and the UK, Canadian, German, and Japanese currencies.

Table VI contains the correlations of the two time-varying coefficients with the volatility measures of the exchange rates during the entire sample period. Narrower sample periods did not affect the correlation coefficients to any noticeable extent. Table VI shows that the correlations at most are slightly less than twenty percent. Volatility in the US dollar/Japanese yen exchange rate has the highest correlation with the coefficient linking the Australian dollar/US dollar rate with the US dollar/UK pound rate, although this correlation may not be significant.

Table VI: Correlations of Return Coefficients with Volatility Measures, 1981–1992

Volatility Index:	Coefficients
	β'US/UK,t	δt'
Aus/US	0.0080	0.2037
US/Can	0.0770	0.1387
US/DM	0.1356	0.0033
US/UK	0.1507	−0.1184
US/Yen	0.1837	−0.0293

Analysis of the Australian exchange market indicates that volatility of US dollar/Canadian dollar rate has the most significance for forecasting volatility in the Australian dollar/US dollar rate. This result is in contrast to the analysis of the stock market, which links Australian volatility with volatility in the UK stock market.

Footnote

In this section, the Canadian dollar/US dollar exchange rate replaces the Singapore exchange rate. Shocks to the Canadian dollar/US dollar rate are more likely to be correlated with shocks to the Australian dollar/US dollar rate, since the Australian and Canadian economies have a similar agricultural export base, and are subject to similar terms of trade shocks. [12]