Entropy

What Is Entropy?

Entropy is a quantitative measure of randomness. Like the concept of noise, entropy is used to help model and represent the degree of uncertainty of a random variable, such as the prices of securities, in a market.

Understanding Entropy

The concept of entropy is used by financial analysts and market technicians to determine the probabilities that specific types of price action predicted of a security or market will come to fruition.

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."

One source of entropy in markets is due to noise. Noise, in the context of financial markets, refers to random, irrational, or misinformed activity that confuses, distorts, or misrepresents genuine underlying trends. This often comes from the trading behaviors of novice or retail investors that trade based on emotion, trend-chasing, or rumor. Entropy caused by market noise can make it challenging for investors to discern what's driving the trend and whether a trend is changing or merely experiencing short-term volatility.

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 beneficial and detrimental depending on the needs of the investor; however, it is generally assumed that greater risk can enhance growth. Investors seeking higher growth are taught to seek out high beta or high volatility stocks.

Entropy is used in a similar 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.

In finance, the holy grail has been to find the best way to construct a portfolio that exhibits growth and low draw-downs. Another way to say that is, maximum return for the least amount of risk. Lots of time and energy has been spent studying data sets and testing many variables. When looking for edge in portfolio construction, entropy optimization can be quite useful. Entropy is one way for analysts and researchers to isolate a portfolio's randomness, or expected surprise.

Computing Entropy

The main issue with using entropy is the calculation itself. Among analysts, there are several 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 (CAPM), the assumption is that 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 to define risk within a given system or financial instrument arrangement. This is usually 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.