Determining bottom price-levels after a speculative peak

During a stock market peak the price of a given stock ($i$) jumps from an initial level $p_1(i)$ to a peak level $p_2(i)$ before falling back to a bottom level $p_3(i)$. The ratios $A(i)=p_2(i)\mathrm{/}{p}_1(i)$ and $ B(i)= p_3(i)/p_1(i) $ are referred to as the peak- and bottom-amplitude respectively. The paper shows that for a sample of stocks there is a linear relationship between $A(i)$ and $B(i)$ of the form: $B=0.4A+b$. In words, this means that the higher the price of a stock climbs during a bull market the better it resists during the subsequent bear market. That rule, which we call the resilience pattern, also applies to other speculative markets. It provides a useful guiding line for Monte Carlo simulations.