Market and Portfolio Drawdowns: Essays on Path-Dependent Risks

Abstract

Significant drawdowns have been around since the start of financial markets. While these "perfect storm" scenarios occur infrequently, their impact is often very significant. One can surely remember the recent market retracement in 2020, linked to COVID-19 of more than 30% for the S&P500 and 40% for the Euro Stoxx Index in less than a month. After a substantial recovery in 2021, the European benchmark retraced more than 20% between January and March 2022, following the escalation in the Russia-Ukraine conflict. The drawdown risk measure plays a crucial role in capturing these extreme events, which can have a significant impact on financial and emotional capital. Unlike traditional risk measures, drawdowns consider the sequence of events and reflect the path-dependent nature of risk. While drawdowns play a crucial role in practice, the research so far has been mainly focused on traditional risk measures. The overall aim of this dissertation is therefore to further develop the drawdown risk measure and find practical ways to use it in risk and portfolio management. This dissertation studies and categorizes the key risk metrics linked to drawdowns, performs an empirical study of drawdown risk for equity indices, foreign exchange, and commodity prices over various time periods, and develops a framework for analyzing drawdown risk for an investment or trading operation. The use of drawdown measures offers several advantages over traditional risk measures in risk management and portfolio asset allocation decisions. Drawdown measures capture downside risk more comprehensively and intuitively, considering the magnitude and duration of portfolio losses, which is crucial for risk management. Unlike static traditional risk measures, drawdown measures provide a dynamic and path-dependent perspective on risk, acknowledging the non-linear and time-varying nature of financial markets. This enables a more accurate assessment of the risk associated with sequential portfolio losses, allowing investors to evaluate potential cumulative losses and recovery times. This information is essential for setting risk limits, adjusting leverage levels, and evaluating the resilience of investment strategies during challenging market conditions. Drawdowns significantly influence the choices and strategies of both investors and fund managers. Effectively handling drawdowns is crucial for fund managers in order to preserve client confidence, secure new investments, and guarantee the sustained success of their business. Apart from financial drawdown, there is also the concept of emotional drawdown, referring to the mental impact of capital losses on investors. Extreme drawdowns, which can have a significant psychological impact, have often surprised risk-takers leading to forced liquidations near the bottom of a market. Human psychology thus plays a key role in decision-making. In a review on the future of behavioral economics, Thaler (2016) highlights three influential economists on the importance of psychology for the field of economics. One can go back to 1776 to notice that Adam Smith already talked about concepts such as loss aversion, overconfidence, and self-control. In 1906 Pareto wrote that the foundation of political economy, and, in general, of every social science, is evidently psychology. In 1936 Keynes observed that the daily fluctuations of share prices tend to have an absurd influence on the markets. In "The Alchemy of Finance", George Soros introduced the theory of reflexivity as a means to identify significant price movements in financial markets throughout history. According to Soros, the crucial factor in understanding market dynamics lies in the discrepancy between the actual state of affairs and the participants’ perceptions. This theory posits that participants’ biases and cognitive limitations often lead to distorted perceptions, which can have a profound impact on market behavior. These distortions create a feedback loop between market participants’ actions and the underlying fundamentals, resulting in self-reinforcing cycles of boom and bust. The behavioral finance literature describes several phenomena that might explain the creation of market bubbles. According to this theory, asset bubbles are a manifestation of behavioral biases. Some of the well-documented biases that have an implication on the formation of bubbles are over-optimism, herding behavior, extrapolation bias, and overconfidence. Many authors report on the presence of overreaction and underreaction in stock markets.1 The common theme within these publications is a phase of overreaction based on the extrapolation bias, followed by a period of under-reaction in which people take time to adjust their mental frame. Daniel et al. (1998) describe a model for security prices and show that continued overreaction causes momentum in prices, but that the momentum is eventually reversed as further public information gradually adjusts the price back to fundamentals. Based on the reported concepts of overreaction and extrapolation, it is conceivable that irrational bubbles could be created. Thaler (2016) believes that the only danger related to the Efficient Market Hypothesis is when people, especially policymakers, consider it to be true. Not being aware that bubbles may be possible, they may fail to take appropriate steps to dampen them. Usually, the aftermath of a bubble phase is a drawdown phase. Some down moves are gradual, while others can happen abruptly. Johansen and Sornette (2002), who measured drawdowns as consecutive daily down moves, found several outliers in the drawdown distribution when using a generalization of the exponential model and labeled these outliers as "market crashes". In a further analysis of these drawdowns, they found that the crashes originated in two ways. On the one hand, the crashes have an endogenous origin. In this case, imitation behavior leads to unsustainable bubbles. After this bubble follows a severe drop which restores market efficiency. On the other hand, the outliers are triggered by a surprising event of exogenous origin, which has a fundamental impact. These assumptions were further tested by Johansen (2004) by considering the origin of crashes in three US stock markets. In this paper, he considers drawdown behavior as "restoring market efficiency." Additional empirical studies related to drawdowns and financial bubbles can be found in Zhou and Sornette (2009), Rotundo and Navarra (2007) and Chang and Feigenbaum (2008). Drawdowns, by definition, provide a reference to the highest watermark that an investor has achieved over a certain investment period. Comparing the performance of an investment or portfolio to a given reference is labeled as anchoring. Knowing that people are loss averse, these reference points have a big impact on investor well-being. Let’s consider the following example: both Investors A and B start with an initial investment of 1,000. They both invest their proceeds in the stock market. After one year, the investment of Investor A is worth 3,000; the investment of Investor B is worth 1,500. After two years, both investments are worth 2,000. Considering the fact that people are loss averse and reset their references, there is a strong likelihood that Investor A will experience a feeling of regret and that Investor B will have a better feeling than Investor A after two years. In this simplified example, investor A experienced a drawdown of 1,000, whereas investor B, who experienced a consistent positive increase in wealth, experienced no drawdown. While reference points are different for people and thus are not necessarily always the high watermark of an investment2, it does reflect the relevance of the drawdown measure from the perspective of investor well-being. This example also illustrates the importance of the frequency at which the portfolio is observed. Managing downside risk and preventing big drawdowns is key for long-term success. McNeil et al. (2015) capture the general essence of risk management as ensuring resilience to future events. To be able to guard against future events, it is essential to be able to assess path-dependent risks. One of the key path-dependent risk measures is the drawdown risk measure, which captures the loss compared to the previous peak over a specific time interval.