RDP 8906: A Random Walk Around the $A: Expectations, Risk, Interest Rates and Consequences for External Imbalance VI. Discussion

Despite continuous repetition of the claim that the efficient markets hypothesis implies that exchange rates should move as random walks with no drift, the claim is false. In fact, the joint hypothesis that (i) market-participants are risk-neutral, (ii) transactions costs are small enough to be ignored^[29] and (iii) the market is efficient (or equivalently, market-participants form and use rational expectations) implies that the exchange rate must undergo a random walk around the forward rate.^[30] As we have seen, there is now very strong international evidence – supported by our analysis of the $US/$A market – that exchange rates do not do this. There are three possible interpretations of this evidence. Firstly, there could be a time-varying risk premium which investors demand to hold, say, $A nominal assets. Secondly, the market could be inefficient. Thirdly, there could be a ‘peso problem’. We examine each of these interpretations in turn. For convenience, we repeat the arbitrage conditions introduced at the beginning of the paper which should be satisfied by Australian interest rates:

A time-varying risk premium

Both our evidence, and the more extensive survey evidence of Thorpe et. al. (1988) suggest that there was a statistically significant gap between the forward discount and market expectations of depreciation – and hence a risk premium – from late 84 to late 85. Since then, the survey data leads us both to accept the null hypothesis of zero risk premium. Section III of our paper presents two a priori calculations of the average magnitude of the risk premium necessary to induce a US consumer-investor to hold a small part of her wealth in Australian nominal assets. Within the chosen framework the calculations are as realistic as we could make them, but in some respects they are pretty naive.^[31] Be that as it may, these theoretically-based estimates of the average risk premium are so small as to be negligible (compared, for example, with the average real interest differentials between Australia and the US derived in section IV). These calculations are consistent with the fairly well established inability of current models of time-varying risk premia to account for interest rate differences between countries with essentially no impediments to the movement of capital (e.g., Hodrick, 1987; Cumby, 1988).

An inefficient foreign exchange market

Consider the Dornbusch (1976) model of a small open economy with perfect capital mobility, rational market participants, sticky goods prices and no risk premia.^[32] In this model, an unanticipated increase in domestic nominal and real interest rates (i.e., a tightening of monetary policy in the small economy) leads to a market anticipation that in the long-run, domestic inflation will be lower than previously expected. As a direct consequence, in the long-run, the domestic nominal exchange rate will be higher than previously expected, while the long-run real exchange rate will be unchanged. Immediately the tightening is recognised by the market, the domestic exchange rate jumps up – overshooting its long-run nominal appreciation. This jump is necessary so that, during adjustment to the long-run, the exchange rate depreciates (in both real and nominal terms) at exactly the rate necessary to equate the return on domestic and world short-term nominal assets. If there are repeated shocks, they cause repeated jumps in the nominal exchange rate, but during periods in which there is no relevant new information, the return on short-term domestic nominal assets is the same as it is on foreign ones.

Unfortunately, the world does not seem to work like this model. Apparently unanticipated changes in domestic interest rates do not lead to jumps in the exchange rate (Goodhart, 1988). Tight domestic monetary policy does not lead to an adjustment path for the exchange rate like that described in the previous paragraph.^[33] It is an oft repeated claim – and it seems to be true – that the domestic real (and nominal) exchange rate of an open economy tends to be held up during periods when the domestic real interest rate is higher than the rest of the world.^[34] What is rarely remarked is that this claim strongly suggests that the foreign exchange market is inefficient. This follows because, provided risk premia are small (which, at least since late 85, all our evidence suggests they are), the expectation that the exchange rate will be held up combined with high domestic real interest rates should lead to a flood of foreign demands for domestic interest-bearing assets – setting off the adjustment process described in the previous paragraph. In the real world, instead of a flood, there is a trickle, which, on average, slowly appreciates the domestic currency.^[35] As a consequence, for an extended period (many months) there is the opportunity for substantial gain (with what seems an associated small risk) but this opportunity is seized by comparatively few.

These observations can be rationalized by the evidence of Froot and Frankel (1989) that survey expectations follow the forward rate. Because of covered interest parity, when domestic nominal interest rates are higher than world nominal interest rates, the forward rate predicts depreciation of the domestic currency (at a rate which, if it were realised, would equalise the yield from domestic and foreign assets). For market participants who use the forward rate as an ‘anchor’ for their expectations of the future spot rate,^[36] the gain from higher domestic nominal interest rates is completely offset by an expected depreciation. This may explain why there is no massive foreign demand for domestic nominal assets when domestic interest rates are high. But if that is so, what remains is the substantial puzzle that the actual behaviour of exchange rates does not alter market expectations.

A peso problem

In regions renowned for earthquakes, many people invest in earthquake insurance. Consider econometricians studying this behaviour during a time in which there have been no earthquakes. They may falsely conclude that the behaviour is irrational, because, over their sample, there has been no return from the investment. A similar difficulty exists in the foreign exchange market. In Mexico in the 1970's, the peso was permanently at a forward discount compared to the $US despite a fixed exchange rate between Mexico and the US which had been in place for years (Krasker, 1980). The market continually expected a devaluation of the peso, and while it did not occur a ‘peso problem’ was said to exist. This term has now become standard to describe this small-sample problem (Hodrick, 1987). A peso problem is often invoked in defence of the hypothesis of rational market expectations, but our comments in this sub-section also apply if the market's expectations are not rational.

We have some evidence that the $A does suffer from a peso problem. Firstly, our survey expectations data from Mar 85 (Nov 85) to Sept 87 imply that, over this period, market participants expected a real depreciation of the $A at an average rate of 2.4% p.a. (4% p.a.) while the actual rate appreciated. Secondly, since late 84 (late 85), Australian ex post short-term real interest rates have been at an average premium of 2.4% p.a. (2.8% p.a.) compared to the US.

By themselves, these observations do not constitute overwhelming evidence that the $A suffers from a peso problem. They could be explained by the argument presented at the end of the last sub-section.^[37] What makes a peso problem for Australia a distinct possibility are two further observations. Firstly, our skewness analysis demonstrates that, unlike all the other currencies we examined, over one week and four weeks the $A is subject to infrequent, unpredictable and large depreciations. So it seems reasonable that the market should have such events built into their expectations. Secondly, there is an obvious candidate for the cause of a peso problem – that in the longer run the real economy must adjust to put us on a sustainable net external debt/ GDP path – with a lower real (and nominal) exchange rate during the adjustment process. Examining what appear to have been the causes of the ten largest weekly depreciations of the $A since Jan 86 (Table 10), seven appear interpretable in terms of events in the Australian economy (all but the first, seventh and ninth falls in the Table). Of these seven, five (the second, third, sixth, eighth and tenth) appear related to the need for the real economy to adjust to put us on a sustainable net external debt/ GDP path. This evidence supports the view that if the $A suffers from a peso problem, its cause is a market perception of the need for a lower real exchange rate to put the economy on a sustainable net external debt/ GDP path.^[38]

We briefly deal with two questions suggested by this analysis. Firstly: if there is a widespread and long-held expectation that the real value of the $A will fall, why doesn't it? The answer is probably that high short-term real interest rates have held it above the level it would otherwise have been.^[39]

Secondly: if a peso problem exists, what will solve it? From the end of May to the end of July 86, the $A fell 15% against the $US and 19% against the TWI. The survey of market participants (Figure 2) for the ten Fridays immediately following this depreciation show that, on average, they expected a depreciation of the $A of 1.03% over the next four weeks; equivalent to depreciation at an annual rate of 12.6%. This number is again substantially higher than the depreciation predicted by the inflation differential, 7.2% p.a.^[40], but closer to the annualized depreciation predicted by the 1 month forward rate over these ten weeks (10.8% p.a.).^[41] This suggests that even a reasonably large depreciation may not be enough to influence expectations sufficiently to eliminate a peso problem. In principle, there should be a depreciation large enough to turn expectations around – but it is hard to know how large is sufficient. An alternative possibility is that the peso problem will not be eliminated until the real economy is clearly seen to be moving onto a sustainable path for net external debt/GDP.

Consequences for external imbalance

Finally, we comment on the relevance of these observations for the current debate on Australia's external imbalance. For an extended period since late 85, market participants have expected the real value of the $A to fall against the $US at roughly 4% p.a. This may explain why a substantial real interest premium on short-term $A denominated assets can persist without setting off an adjustment of the Dornbusch (1976) type. If the market perceives significant real depreciation is necessary to put Australia onto a sustainable debt path, these consequences follow. Firstly, while the monetary authorities keep short-term interest rates high, the Australian economy pays a real interest premium on the substantial proportion of short-term $A-denominated external debt. Secondly, when the monetary authorities reduce Australian short-term nominal interest rates, at some unpredictable time there may be a big fall in demand for Australian nominal assets and a large rapid depreciation. Presumably after a sufficiently large depreciation the market will cease to expect further real depreciation – but the depreciation required to change market expectations may be very large indeed. The hope is that such an abrupt exchange rate adjustment does not have serious adverse consequences for the wider economy.

Footnotes

This should be true for large enough transactions. Goodhart and Taylor (1987) provide detailed estimates of transactions costs in the London and Chicago futures markets. [29]

To be precise, the three conditions imply that the forward rate must be an unbiased predictor of the future spot rate or, equivalently, that s_{t + k} − f_t,k must be a martingale. [30]

Investors are assumed to be homogeneous with a constant relative risk-aversion and to do their intertemporal optimization one period at a time. [31]

This seminal model forms the basis of most modern open-economy macro-models including, in the Australian context, the Murphy (1988) model and the MSG2 (McKibbin and Elliott, 1989 and McKibbin and Sachs, 1989) model. [32]

In discussing the fact that the long-term real interest differential between the US and its trading partners increased by about 5 percentage points from 1980 to mid-1984, and the real appreciation of the $US from 1980 to 1985, Dornbusch and Frankel (1987) comment: [the overshooting model implies that] “the entire increase in … the value of the dollar should have occurred in one (or two or three) big jumps, for example when it was discovered that monetary policy was going to be tighter than previously expected, or fiscal policy looser. Yet the appreciation in fact took place month-by-month, over four years (with investor expectations, as reflected in the forward discount, interest differential or survey data, all forecasting a depreciation).” [33]

As an example of this it is clear from Table 4 that there has been a substantial return from holding short-term $A nominal assets during the extended period of high real interest rates on these assets since late 84 (or late 85). [34]

Given covered interest parity, regressions of equation (3) support this statement. Both the regressions in Table 1, as well as most of those quoted by Goodhart (1988), Obstfeld (1988), Thorpe et. al. (1988) and many others, find negative estimates of β – although they are usually insignificantly different from zero. These regressions suggest that a higher domestic nominal interest rate leads, on average over the next month or three months, to a higher (or perhaps unchanged) domestic nominal exchange rate than would otherwise have been the case. See also Meese and Rogoff (1988). [35]

“In many [uncertain] situations, people make estimates by starting from an initial value [the anchor] that is adjusted to yield the final answer. The initial value … may be suggested by the formulation of the problem, or it may be the result of a partial computation. In either case, adjustments are typically insufficient. That is, different starting points yield different estimates, which are biased toward the initial values.” Tversky and Kahneman (1974). Of course, expectations formed by such a process are not rational in an economist's sense. [36]

With reference to that argument, the average magnitude of depreciation predicted by the Australian market participants is close to that predicted by the forward rate (see Figure 2 and associated discussion). Note however that we find that the inflation differential dominates the forward rate as an explanator of market expectations (equation 6). [37]

An alternative candidate for the cause of a peso problem is a market perception that there is a non-negligible chance that Australian inflation will dramatically accelerate in the future and depreciate the nominal exchange rate. A belief in the possibility of either accelerated monetary expansion or the collapse of the Prices and Incomes Accord could be the source of this expectation. With the benefit of hindsight, although Australian inflation over the past four years has been substantially higher than comparable countries (see Figure 6) it has shown few signs of acceleration. If inflationary expectations were the source of a peso problem, agents should have been continuously surprised that the event(s) they were anticipating did not eventuate, and presumably have revised their expectations. Only one of the events in Table 10 seems related to inflation (the CPI announcement). [38]

Nevertheless, we remain impressed by the conclusions of Meese and Rogoff (1983, 1988) that macroeconomic fundamentals (and interest rate differentials in particular) have little significant capacity to explain movements in the nominal or real exchange rate, even over periods as long as a year. [39]

Derived using annual inflation rates which had been published when the expectations were formed – as for Figure 2. [40]

Interestingly, market participants' reaction to the previous rapid fall in the $A had been quite different. From the beginning of Feb to 8 Mar 85, the $A fell 16% against the $US and 13% against the TWI. Over the next ten Fridays, they predict an average appreciation of the $A at an annual rate of 8.8%. Perhaps the subsequent behaviour of the $A (and the terms of trade and current account deficit) changed their attitude. [41]