RDP 9010: Volatility of the Australian Dollar Exchange Rate 2. Measuring Volatility

There are two commonly used measures of exchange rate volatility: the average of absolute exchange rate movements and the standard deviation of percentage changes.^[1] As its name suggests, the former is simply an arithmetic average of the absolute value of percentage movements in an exchange rate, while the latter measures the dispersion of exchange rate movements.

Despite their obvious computational differences, the average absolute change and the standard deviation measures are similar in that every movement in the exchange rate over a period of time is assumed to contribute to volatility. A different approach is one that reflects deviations from an expected or trend forecast of future exchange rates. This approach recognises that much of the concern with volatility lies with an increased likelihood of error in exchange rate forecasts and its consequences for the efficiency of foreign exchange markets. Hence, it has been asserted that if some part of a currency's fluctuation is predicted, a more appropriate measure of volatility is one which measures the dispersion of “unpredicted fluctuations”^[2], that is, changes in the extent to which observed movements in the exchange rate deviate from movements in the equilibrium or expected exchange rate.

In principle, the best approach to identifying any unpredicted fluctuation in the exchange rate is to compare actual changes in the market rate with movements in an equilibrium rate determined on the basis of economic fundamentals. However, this approach suffers from several major problems associated with the estimation of a fundamental equilibrium path for the exchange rate; not the least is that there is little academic agreement on what the fundamentals are and on their exact relationship with the exchange rate. Furthermore, estimates of fundamental equilibrium exchange rates have proven to be highly model-specific.^[3]

In response to these problems, some studies have employed simple time-series models to identify a long run average or an expected time path in a currency's exchange value. For example, in a previous attempt to measure the dispersion of unpredicted fluctuations in the Australian dollar, Mathews and Valentine (1986) employed five different time-series models to estimate an average time path for the local currency between 1984 and 1986. In general, they found that the volatility of the Australian dollar was not very different from that of a number of other currencies.

However, this is a questionable approach to estimating predicted movements in the exchange rate. There is now substantial empirical evidence that time-series of nominal exchange rates exhibit non-stationarity, a condition in which the mean and variance of the series are not constant, but time-dependent.^[4] In most cases the time-series models used to estimate average time paths for the exchange rate – including many of those employed by Mathews and Valentine – implicitly require that the underlying series be stationary for the estimates to be statistically reliable. Consequently, measures of the dispersion of unpredicted fluctuations in the exchange rate based on these models may be misleading.

In view of the statistical problems involved in estimating a long-run average path for nominal exchange rates, this paper does not explicitly attempt to measure the dispersion of unpredicted fluctuations in the Australian dollar. Instead, the two commonly-used measures of volatility – the average of absolute exchange rate movements and the standard deviation of percentage changes – are employed.^[5]

While both measures provide an indication of exchange rate volatility, they are inappropriate for making isolated comparisons of volatility. Any assertion that a currency is “excessively” volatile obviously implies reference to some benchmark of volatility. Two are used here. First, Australian dollar volatility is compared with that of other currencies. Secondly, it is compared with the volatility of other asset prices. This reference to other asset prices acknowledges that exchange rates are like any other auction price, incorporating expectations of future events and moving rapidly in response to new information.

Footnotes

See, for example, Frenkel and Mussa (1980), Frenkel and Goldstein (1989), and MacDonald (1988). [1]

See Trevor and Donald (1986). [2]

For a discussion of fundamental equilibrium exchange rates see Williamson (1985), and Barrell and Wren-Lewis (1989). For an example of the empirical problems involved see West (1987). [3]

See, for example, Meese (1990), Meese and Singleton (1982), and Wasserfallen and Kyburz (1985). Recent empirical tests by Smith and Gruen (1989) accept the hypothesis that the Australian dollar exchange rate since the float exhibits non-stationarity. [4]

An alternative measure of exchange rate volatility used by Edey and Elliott (1989) involves identifying so-called “implied volatility” from the market price of currency options contracts. While this approach has some appeal, the lack of a long series of suitable price information on currency options in Australia makes it of limited use in this study. [5]