Ups and (draw) downs
提出一个测量框架，通过两个马尔可夫链过程描述资产价格相对于历史高点和低点的领先时间，用于分析回撤和回升的时间序列特征，并开发了识别牛熊市阶段的新算法。
The concept of a drawdown quantifies the potential loss in the value of a financial asset when it deviates from its historical peak. It plays an important role in evaluating market risk, portfolio construction, assessing risk-adjusted performance, and trading strategies. We consider a novel measurement framework that produces, along with the drawdown and its dual (the drawup), two Markov chain processes representing the current lead time with respect to the running maximum and minimum, i.e. the number of time units elapsed from the most recent peak and trough. Together with the distribution of asset returns, they determine the properties of the drawdown and drawup time series, in terms of size, serial correlation, persistence, and duration. Furthermore, they form the foundation of a new algorithm for dating the peaks and troughs of the price process delimiting bear and bull market phases. We then turn our attention to the problem of predicting the drawdown out-of-sample.