DEFINITION of 'Entropy'

Entropy is a measure of randomness. Much like the concept of infinity, entropy is used to help model and represent the degree of uncertainty of a random variable. It is used by financial analysts and market technicians to determine the chances of a specific type of behavior by a security or market.


Entropy has long been a source of study and debate by market analysts and traders. It is used in quantitative analysis and can help predict the probability that a security will move in a certain direction or according to a certain pattern. Volatile securities have greater entropy than stable ones that remain relatively constant in price. The concept of entropy is explored in "A Random Walk Down Wall Street."

Entropy as a Measure of Risk

Like beta and volatility, entropy is used to measure financial risk as a measure of randomness. In the world of finance, risk is both bad and good depending on the needs of the investor; however, it is generally assumed that greater risk creates a higher probability for enhanced growth. Investors seeking higher growth are taught to seek out high beta or high volatility stocks. Entropy is used in the same way. A stock with a high level of entropy is considered riskier than others. Some analysts believe entropy provides a better model of risk than beta. It has been shown that entropy, like beta, and standard deviation go down when the number of assets or securities in a portfolio increases.

Entropy Usage

The main issue with using entropy is the calculation itself. Among analysts there are many different theories about the best way to apply the concept in computational finance. For example, in financial derivatives, entropy is used as a way to identify and minimize risk. In the traditional Black-Scholes capital asset pricing model, the model assumes all risk can be hedged. That is, all risk can be determined and accounted for. This is not always a realistic model. The concept of entropy can be applied and represented by a variable to eliminate the randomness created by the underlying security or asset, which allows the analyst to isolate the price of the derivative. In other words, entropy is used as a way to identify the best variable for which to define risk within a given system or financial instrument arrangement. The best variable is the one that deviates the least from physical reality. In finance, this can be represented with the use of probabilities and expected values. While the calculation itself is evolving, the purpose is clear; analysts are using the concept to find a better way to price complex financial instruments.

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