Economic Complexity Limits Accuracy of Price Probability Predictions by Gaussian Distributions

Abstract

The accuracy of predictions of price and return probabilities substantially determines the reliability of asset pricing and portfolio theories. We develop successive approximations that link up predictions of the market-based probabilities of price and return for the whole stock market with predictions of price and return probabilities for stocks of a particular company and show that economic complexity limits the accuracy of any forecasts. The economic origin of the restrictions lies in the fact that the predictions of the m-th statistical moments of price and return require descriptions of the economic variables composed by sums of the m-th powers of economic or market transactions during an averaging time interval. The attempts to predict the n-th statistical moments of price and return of stocks that are under the action of a single risk result in estimates of the n-dimensional risk rating vectors for economic agents. In turn, the risk rating vectors play the role of coordinates for the description of the evolution of economic variables. The lack of a model description of the economic variables composed by sums of the 2-d and higher powers of market transactions causes that, in the coming years, the accuracy of the forecasts will be limited at best by the first two statistical moments of price and return, which determine Gaussian distributions. One can ignore existing barriers and limits but cannot overcome or resolve them. That significantly reduces the reliability and veracity of modern asset pricing and portfolio theories. Our results could be essential and fruitful for the largest investors and banks, economic and financial authorities, and market participants.