The Random Walk vs. Intuition

Economists generally think that prices on well--functioning financial markets are random walks. This means that the percentage change on any one day (i.e., the return) has no links to prices or price--changes in the past. When a price is a random walk, past and future returns have a zero correlation. Economists use the phrase "efficient market" when prices in a market accurately reflect information and forecasts about the future. They test for market efficiency by asking whether prices in the real world are, indeed, random walks.

The evidence, from all countries in the world, is fairly supportive of this hypothesis when two conditions are met: (a) trading takes place at exchanges, and (b) large scale market manipulation is not present. Small blemishes do undoubtedly exist. For example, the stock market index in India has a positive autocorrelation (of 0.15) between consecutive changes. If Nifty rises today, then there is good chance that it will rise tomorrow also (and vice versa). However, the practical significance of this dependance is limited -- forecasts using it only explain 3% of the variation of Nifty. It remains useful to think that Nifty is close to an idealised random walk.

The random walk serves as a benchmark for how market prices should behave when thinking about how India's markets are organised. For example, one reason to have futures and options on Nifty is that they would eliminate this correlation (of 0.15) in Nifty.

The behaviour of the random walk often proves to be highly uncomfortable in the "practical intuition" of many individuals. We will take up two examples of the gap between "obvious intuition" and the random walk: the years--high to years--low ratio on the stock market, and the dollar--rupee.

Years--high versus years--low.

Recently, there has been some discussion about the "sanity" (or lack thereof) of the gap between annual highs and lows observed on the stock market. For most individual stocks, the years--high seems to be twice the years--low. Do fluctuations of this magnitude "make sense"? Many feel it is "obvious" that the valuation of a company should not vary by this much over a year. This conundrum proves to be an example of how the random walk challenges human intuition.

The typical Indian stock has a daily standard deviation of 3%. When we work out the range of annual movements of an ideal random walk with daily volatility of 3%, it turns out that the annual high should be 2.1 times the annual low. Hence the observation that the years--high / years--low ratio in India is 2 (on average) is the same as the observation that the daily volatility of stocks in India is 3% per day. To human intuition, the latter is unremarkable, but the former elicits surprise. Yet, when prices are random walks, we cannot have one without the other!

The Dollar--Rupee

Some of the worst violations in tests of market efficiency, worldwide, are on currency markets. This has led many observers to criticise the regime of floating exchange rates, since it appears to be unable to deliver market efficiency. Two alternative explanations exist: (a) that the mechanism used in trading currencies, which consists of dealers talking to each other, without anonymity and without centralisation at an exchange, hurts price discovery, and (b) that market manipulation by central banks is responsible for these breakdowns of market efficiency.

Today, most governments feel that they should not have a say in prices of shares, or wheat. Yet, most governments feel that they should "manage" their exchange rates. It is only in the last five years that the US and German central banks have reduced the scale of their market interventions, and we are starting to see something approaching a true market rate on the dollar--mark.

In India's case, the dollar--rupee exchange rate differs from an ideal random walk. Over the period 1990--1997, the first four autocorrelations are statistically different from 0. The first is -0.27 (i.e., a rise yesterday is likely to be reversed today). The second is +0.31 (i.e., a rise the day before is likely to go with a rise today), the third is -0.09 and the fourth is -0.06. Forecasting models that use these relationships are able to explain 17% of the variation of the rupee.

In addition, there is acute "volatility clustering" in the dollar--rupee. The rupee enjoys many days of near--zero volatility, followed by sharp bursts of high volatility. This behaviour is perhaps owing to a significant extent of RBI intervention, which gives way to true equilibrium rates when the market exchange rate is seriously mispriced.

How would the rupee behave if it was a true random walk? We can sketch many properties of a true market rate assuming that the volatility is that observed over 1990--97, i.e. 0.7% per day. If the currency were a pure random walk, we would get a years--high to years--low ratio of 1.26 (on average). Many might find this confounding; newspaper editorials will ask how it is possible for the rupee to gain (or lose) 26% compared to the a year ago. This ratio would exceed 1.26, half the time. The rupee would move daily, and every change would be permanent (i.e. it would not be reversed in the near future). There would be no extended periods of little change, followed by periods of sharp change. In three weeks a year (on average), the one--week change would be larger than three percentage points.

These properties may defy intuition, which is perhaps what makes them so interesting. There are no bands in a random walk! In thinking about exchange--rate regimes and interventions, the aim of public policy should be to obtain prices which behave like the ideal efficient market, i.e. the rupee should be a random walk. In this case, the properties of the previous paragraph should emerge from the market under a proposed policy regime.

The crisis in East Asia powerfully illustrates the dangers of fixed exchange rates. Individuals embarking on trade or capital account transactions with the outside world fail to adequately hedge their exposures; indeed, currency derivatives markets do not blossom under currency stability. Suboptimal investments are undertaken in the real economy when agents believe the government will hold the exchange rate constant. All this generates a political constituency which favours keeping the currency where it is. When change comes to a stabilised currency, as it must, that change is painful. Change in the long term is inevitable. The random walk doles out a little change every day, which is less painful than sudden large changes.

In India, there is no serious proposal for a fixed exchange rate. What is widespread is an intuitive notion of "currency stability". This desire is inconsistent with the random walk. Government stabilisation programs, even when they are more flexible than Korea, go along with these ills on a smaller scale.

Currencies which are random walks yield a deeper sort of stability. The steady pace of small changes every day generates realistic expectations about currency risk and continual realignment in production processes in the economy. It avoids sudden changes, and keeps the currency out of the domain of politics. The random walk regime is sustainable without incurring serious distortions in the economy.

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