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)/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.