Fluctuation Phenomena: Leverage Could Be Positive and Negative

Abstract

Real stock markets are always full of fluctuations in prices. Overall fluctuations (i.e., volatility), which can be calculated by the variance of log returns of a time series of prices, can represent investment risks; extremely big fluctuations, which are indicated by fat tails in the probability distribution of these log returns, can incur financial crises. Therefore, it is particularly important to understand such fluctuations, especially in case of the introduction of new financial instruments like the leverage of borrowing money. Here we include this leverage into a kind of one-stock market in the laboratory, whose original version was experimentally shown to produce some stylized facts like scaling laws and clustering behavior in Chap. 3. When the leverage becomes higher (which means borrowing more money), our human experiments and computer simulations show that the value of overall fluctuations (or extremely big fluctuations) increases (or decreases), which is a negative (or positive) effect. The negative effect means that the investment risk of the whole market increases; the positive effect indicates that fat tails are shrunk, thus lowering the probability of the outbreak of financial crises in the market. We reveal that the underlying mechanism lies in the effect of margin calls. In addition, since wealth distribution affects the harmony and stabilization of a society, we also study the leverage effect on wealth distribution in the laboratory market, and report some interesting findings and mechanisms. This work not only helps to understand the leverage appropriately, but also helps to enrich fluctuation theory in statistical mechanics.