Week 40 Day 4: Maximum Drawdown: The Pain Metric That Matters Most

Maximum drawdown = the biggest drop from a peak to the following trough. If a stock went from $100 to $150 to $60 to $120, the maximum drawdown is from $150 to $60 = -60%. It does not matter that the stock eventually recovered to $120. The maximum drawdown was -60%, and anyone who bought at $150 experienced a 60% loss before recovery.

Maximum drawdowns of common investments (approximate): U.S. T-bills: approximately -1% (negligible). Intermediate bonds (BND): approximately -18% (2022 rate shock). U.S. stocks (VTI/S&P 500): approximately -51% (2007-2009). International stocks (VXUS): approximately -58% (2007-2009). Small-cap value: approximately -60% (2007-2009). REITs (SCHH): approximately -68% (2007-2009). Individual stocks: -100% is possible (Enron, Lehman, Pets.com). Bitcoin: approximately -83% (2017-2018), approximately -76% (2021-2022). Leveraged ETFs (3x): -90%+ is not uncommon. Why maximum drawdown matters more than standard deviation to REAL investors: standard deviation is an abstract number. Maximum drawdown is an emotional experience -- the worst period of losses you will actually live through. If you cannot tolerate a 50% drawdown (the historical worst case for VTI), you need to reduce your stock allocation until the expected maximum drawdown matches your emotional capacity. Using drawdown for allocation: (a) 100% stocks (VTI): expected max drawdown approximately -50%. (b) 80/20 stocks/bonds: expected max drawdown approximately -40%. (c) 60/40 stocks/bonds: expected max drawdown approximately -30%. (d) 40/60 stocks/bonds: expected max drawdown approximately -20%. Choose the allocation where the expected maximum drawdown would NOT cause you to sell. Better to earn 7% and hold than to target 10% and panic-sell at the worst time.

Maximum drawdown (MDD) is a path-dependent risk metric that captures the investor's worst-case experience and is therefore more behaviorally relevant than standard deviation (which is path-independent). Formally, MDD = max_t [max_s<=t (P_s) - P_t] / max_s<=t (P_s), where P_t is the portfolio value at time t. The recovery time (time from trough to recovery of the previous peak) is a complementary metric: MDD tells you how deep the hole is, and recovery time tells you how long you are in it. For the S&P 500: 2000-2002 crash: MDD = -49%, recovery time = 7 years (2000-2007). 2007-2009 crash: MDD = -51%, recovery time = 5.5 years (2009-2013). 2020 crash: MDD = -34%, recovery time = 5 months. Grossman and Zhou (1993) derived the optimal portfolio policy for a drawdown-constrained investor and showed that it involves dynamic de-risking as the drawdown deepens (reducing equity exposure as losses increase), which is the formal justification for the bucket strategy's behavior of spending from cash/bonds during drawdowns rather than selling equities. Chekhlov, Uryasev, and Zabarankin (2005) developed the Conditional Drawdown-at-Risk (CDaR) measure, which calculates the expected drawdown in the worst alpha% of scenarios -- a tail-risk metric more relevant to investor experience than VaR. For practical purposes, multiplying the historical maximum drawdown by 1.5 provides a conservative estimate of the worst drawdown the portfolio might experience in the future (since future crises may exceed historical precedents).