Are the Financial Markets Becoming More Efficient?

With the advent of negotiated commissions in 1975 and growing use of increasingly powerful computer based trading systems, the markets appear to be increasingly efficient. One way to measure market efficiency is by examining conditional returns: if conditional returns are trend persistent, profits can be made by betting with the trend; if conditional returns are mean regressive, profits can be had by betting on trend reversals. If conditional returns are too small to profit from, then the markets are efficient.

Our Bifurcation Parameter (BP) is a measure of the degree of trend persistence (when positive) or mean regression (when negative). It is defined as the 200 day sum of daily returns, R(t+1) after prior day returns in the interval 0.5% < R(t) < +3.5% minus the sum of daily returns after previous day returns in the interval -3.5% < R(0) < -0.5%. When this measure is greater than +10%, we consider the market to be trend persistent; when less than -10%, the market is mean regressive. Between these levels, the market is in a relatively efficient state.

Figure 1 illustrates the NASDAQ BP dating back to 1971. For much of this period, the NASDAQ BP was highly trend persistent, and hardly ever mean regressive with respect to daily returns. However, beginning roughly in the year 2000, the NASDAQ has become more efficient and more recently mean regressive, a highly volatile, disordered market state.


Figure 1. The NASDAQ has become more efficient over the past decade and more recently has become mean regressive. (Click on chart to expand).

Figure 2 summarizes the returns for each key market state. The mean regressive state has has the least data and is not statistically significant at the 95% level. The bifurcated bull and bear states are highly statistically significant. Statistical significance is based on excluding the probability that the returns in a particular state are the same as for the efficient state.


Figure 2. The NASDAQ returns in the bull and bear state are statistically significant. (Click on chart to expand).

The Dow Jones Industrial Average has also become more efficient since about 1975. Figure 3 summarizes the Bifurcation Parameter dating back to the Crash of 1929. During the post World War II period the markets were highly trend persistent as the economy boomed. However, in the post 1975 period, the DJIA BP has also steadily declined and currently remains at levels not seen since the Crash of 1929.


Figure 3. The DJIA has become more efficient since 1975 and has recently become highly mean regressive. (Click on chart to expand).

Figure 4 summarizes the returns and their statistical significance for key DJIA market states. The mean regressive state is not statistically significant due to its high volatility and relatively little data. However the DJIA bull and bear states are highly statistically significant.


Figure 4. The DJIA returns in the bull and bear state are statistically significant. (Click on chart to expand).

Japan's NIKKEI Index provides an example of what to expect from an efficient market. It has been efficient on average since about 1991 (based on a quadratic fit to the NIKKEI Bifurcation Parameter). Figure 5 summarizes the NIKKEI Bifurcation Parameter dating back to 1984.


Figure 5. The NIKKEI has been fairly efficient since 1990. (Click on chart to expand).

Figure 6 summarizes the returns and their statistical significance for key NIKKEI market states. The mean regressive state is not statistically significant due to its high volatility and relatively little data. The DJIA bull and bear states are also not statistically significant. Therefore as the markets become more efficient, there will be fewer profitable trading opportunities.


Figure 6. The NIKKEI returns in the bull and bear state are not statistically significant. (Click on chart to expand).

Dow Jones Industrials Remain in Over Reaction, Mean Regressive State

The Bifurcation Parameter (BP) for the Dow Jones Industrial Average (DJIA) remains in negative territory at -38%. This market has been in an over reaction, mean regressive state that has often accompanied crisis markets. The BP is defined here.

Figure 1 summarizes the DJIA BP dating back to the Crash of 1929. For most of this period the BP has been indicating a bifurcated market in which investor sentiment is prone to under react and price is trend persistent. However, with the advent of computerized trading and negotiated commissions in 1975 the markets have become more efficient. An efficient market is defined here as one in which there is neither trend persistence nor mean regression is large enough to provide significant trading opportunities.


Figure 1. The Dow Jones Industrial Average Bifurcation Parameter suggests that the market has become more efficient since 1975. (Click on chart to enlarge).

The average return for the DJIA as a function of the average value of the BP for each market state is summarized in Figure 2. The t-test for each state provides the probability that the returns for a given state are equivalent to those from the efficient market state (when -10% < BP < +10%). Note that the crisis state (BP < -10%) is not statistically significant at the 95% level due to the limited amount of data, the recent market rally and the high volatility of this state. In contrast, the bifurcated bull state (BP >= +10% and R(0) >= 0) is statistically highly significant (p = 1.6E-9). Likewise the bear state (BP < -10% and R(0) < 0) is highly significant (p = 1.5E-5). However, if the markets have become more efficient, then these trend persistent states will be evident less frequently.


Figure 2. The Dow Jones Industrial Average market returns for the bull and bear state have been highly statistically significant. (Click on chart to enlarge).

NASDAQ Remains in Mean Regressive State

The Bifurcation Parameter for the NASDAQ Composite Index slipped back to -22% over the past few weeks (white arrow on the chart). Figure 1 summarizes the average daily return expected from each of the four key market states expected from the Bifurcation Parameter (and prior day return, R(0)).

NASDAQ Composite Index Returns for States Predicted by the NASDAQ Bifurcation Parameter (click on chart to enlarge)

The statistical significance of each state is based on a comparison with the efficient state (when -10% < BP < +10%). The statistical significance of the Crisis Market State is questionable at p = 0.1 which is below the 95% confidence level benchmark and approximately the same as found for the Dow Industrial as briefed in Zurich and shown on the briefing slides for that talk. In contrast, the Bull and Bear states are both highly statistically significant. For the Zurich talk, daily returns were annualized and the t-test was based on comparing each state with the buy and hold benchmark (as opposed to the efficient market state).