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This article aims to measure market efficiency without an information model. The intuition is that an efficient market leaves no arbitrage opportunities for active traders, so the measure of efficiency (MOE) is the proportion of profits available to passive traders for a given level of transaction costs. It is expressed as a percentage score and defined symmetrically with a measure of inefficiency (MOI). It can be computed sequentially from a price series and a round-trip transaction cost. The measure of efficiency is shown to increase with diversification, reduce in longer time periods, and have an inverse relation with volatility. It is shown to be a leading indicator of price movements on a day-to-day basis and ahead of the financial crisis of 2008.
This article presents a measure of efficiency that is a proxy for market efficiency without requiring a model of information value. Intuitively it compares the potential profits from passive and active trading. When a market is efficient in valuing price-sensitive information, it leaves no further room for arbitrageurs to make abnormal profits, and the active traders cannot beat the passive traders. When a market is inefficient, the active trading opportunities should exceed those of passive trading, and the extent of their advantage gives a measure of the inefficiencies.
The measure of efficiency MOE is computed as the ratio of the maximum profits that could have been made by passive trading to those of active trading over the time period of interest and for a specified level of transaction costs. It is a scale rather than a binary test, with a range from 0% (fully inefficient) to 100% (fully efficient). There is a complementary measure of inefficiency MOI with the reverse scale, so the two measures sum to 100%.
When transaction costs are high, there are fewer opportunities to profit, and the MOE is high. When costs are low, mean-reverting strategies can trade profitably on smaller price oscillations and the MOE is lower. The MOE also increases with diversification, decreases with the time interval over which it is measured, and has an inverse relationship with volatility. It is shown to be higher ahead of price corrections, both on a short-term day-to-day scale, and the longer term pattern around the 2008 financial crisis.
The measure of efficiency MOE is a proxy for market efficiency that can be calculated from readily available price information, and it exhibits many of the properties that we require. While debate will inevitably continue as to whether markets are efficient, numerical measures such as this should help facilitate research questions of how efficient markets are, rather than whether or not they are efficient to particular information sets, which will enable relative comparisons between different markets and different time periods.