Seminal work by Jegadeesh and Titman (1993) found that past winners outperform past losers over a horizon of 3-12 months. Investors thus take a long position on winner stocks and a short position on loser stocks in order to realise anomalous profits. This strategy is widely adopted and appears to be timeless in terms periodically not functioning but never completely disappearing. This paper sets to investigate what happens when the strategy does not work, i.e. when momentum crashes.
Explaining Momentum Crashes
A momentum crash occurs in times of market stress followed by a market rebound. Momentum fat tail distribution makes the strategy susceptible to crashing. Momentum strategies are known to be negatively skewed with excess kurtosis. One possible cause of the excess kurtosis of momentum is time-varying risk and this makes the strategy vulnerable to periodically crashing. Daniel and Moskowitz (2013) show that momentum strategies exhibit infrequent but strong strings of negative returns, causing their distribution to be negatively skewed. This normally follows a severe bear market when volatility is still high and the market is beginning to recover. These setbacks can be attributed to the effect of the stocks’ beta or exposure to the market. When you buy winners and sell losers, you are picking stocks that are more sensitive to overall market swings. Some of the smaller momentum crashes can also be identified using the 20% peak-to-trough rule. An increase in the stock market level of at least 20% from the previous low constitutes a bull market, whereas a minimum decline of 20% from the last high marks a bear market. This definition yields similar market cycles and covers some of the smaller crashes that occurred in the past, Bohl, Czaja and Kaufmann (2015).
Daniel and Moskowitz (2013) attribute these crashes to the conditional betas and call option-like features of loser portfolio. The option-like payoffs associated with the past losers in bear markets, and that the value of this option is not adequately reflected in the prices of past losers. The past loser portfolio have generally suffered severe losses and are therefore potentially much closer to a level where the option convexity is strong. The past winners, in contrast, would not have suffered the same losses, and would still be “in-the-money”. Another interpretation is that the loser stocks will be “out-of-the-money” in the pre-rebound phase and thus are not exercised by investors and thus keep losing. As the market rebounds, the loser stocks become “in-the-money”. In this situation, past losers outperform past winners in the rebound period since investors change their position on the loser stocks from going short to going long realising gains in excess of the prior winners. A possible reason for this optionality is that for a firm with debt in its capital structure, a share of common stock is a call option on the underlying firm value (Merton 1990).
The down-market betas of the past losers are low during bear markets, but the up-market betas are high. The returns on the loser portfolio will thus be larger on the market upswing. For example, in the rebound period after the Great Depression, in July and August of 1932, the market actually rose by 82%. Over these two months, the winner decile rose by 30%, but the loser decile was up by 236%. Similarly, over the three month period from March to May of 2009, when the market was recovering from the sub-prime mortgage crises, the market was up by 29%, but the loser decile was up by 156%.
Since these crashes occur at pivotal moments in the economy they ordinarily coincide with the end of a bear market, when stocks suddenly rebound. A bear market is defined as six or more consecutive months of generally declining stock prices, where any interim increase in the stock index level does not establish a new high. After a prolonged bear market hits bottom, the loser portfolio is mostly composed of highly volatile and leveraged small-cap stocks. Bohl, Czaja and Kaufmann (2015) show that the way trend-following strategies are constructed make them likely to load positively on systematic risk factors that performed well over the formation period and to load negatively on factors that performed poorly. This implies for loser stocks that their market beta is expected to substantially increase towards the end of a bear market and around market rebounds. As a result, the market beta should be largely negative for the long-short price momentum strategy and thus contributes to the prominent momentum crash.
A bull market occurs if the market moves upward for at least six months, while any interim decrease does not mark a new low. Bohl, Czaja and Kaufmann (2015) show that transitions from bear to bull markets are usually accompanied by a pronounced recovery of stock prices. U.S. retail investors are slow to sell loser stocks during optimistic periods, which subsequently lead to strong negative momentum in the short leg. Maheu and McCurdy (2000) and Gonzalez et al. (2005) document that returns earned at the beginning of a bull market are significantly higher than those obtained during the remaining months of an upward moving market.
Predicting Momentum Crashes
Barroso and Santa Clara (2014) find that the risk of momentum is highly variable over time and estimated the risk of momentum by the realized variance of daily returns and found that it is highly predictable. It can therefore be assumed that variables that capture these incidents can be used to predict when the momentum strategy is likely to fail. Daniel and Moskowitz (2014) use momentum volatility, the state of the economy using indicators such as a falling equity market and market volatility as a predictor of a market rebound. Market volatility in the formation dates of almost all of the momentum crashes is more than twice its mean as well as market return rebound in most of the momentum crash events. Avramov, Cheng and Hameed (2013) use market illiquidity for momentum prediction. The effect of high market-wide illiquidity and the broadening illiquidity gap between loser and winner stocks appears to induce momentum crashes. They argue that market illiquidity is critical for momentum profitability. In the presence of illiquid market states, low investor overconfidence in association with a widening illiquidity gap between loser and winner stocks appears to trigger low and often strongly negative momentum payoffs. Heidari (2015) went on to further investigate three additional momentum predictors, namely the cross-sectional dispersion of stock returns, change in market return, and change in momentum volatility which he argues have higher predictive power and are more successful at capturing market rebound.
The momentum strategy has time-varying exposure to market risk by construction (Grundy and Martin, 2001). Kothari and Shanken (1992) also documented the time variation in betas of return sorted portfolios and argued that, by their nature, past-return sorted portfolios will have significant time-varying exposure to systematic elements. The momentum strategy and the returns it generates are therefore sensitive to changes in the market conditions that occur as time effluxes. This suggests the possibility that changing market betas play a hand in momentum crashes. Consequently, if a variable can capture market rebound states, it can be used in momentum crash prediction.
When a market falls, losers fall more than winners. Then, when the market rebounds, stocks that have experienced higher drops will rise more than those that did not drop as much. The loser portfolio’s return will therefore be higher than the winner portfolio’s. This can rationalize why momentum crashes occur in panic periods and how market volatility and return can be used for momentum prediction.
Cooper, Gutierrez and Hameed (2004) and Asem and Tian (2010) also suggest that momentum profits crucially depend on the state of the market, either because of time variation in the factor-related return component or due to a changing impact of behavioural biases.
Momentum Crash Risk Management
The worst and most prominent momentum crashes in history occurred in 1932 after the Great Depression and in 2009 after the sub-prime mortgage crises and the collapse of Lehman Brothers (refer Fig 1 and 2). The two periods ensuing these two crashes represent the two largest and sustained drawdown periods for the momentum strategy. These crashes occurred as the market rebounded following large previous declines. One explanation for this pattern is the time-varying systematic risk of the momentum strategy. As an investment strategy, momentum has the worst crashes making the strategy unappealing to investors with reasonable risk aversion. In 1932 the momentum strategy dropped 92% in just 2 months and in 2009 dropped 73% in 3 months. The benefits of managing the risk of a crash are therefore immense, especially with regards to the benefits of higher expected returns, a lower standard deviation, a higher Sharpe ratio and reduced crash risk, thus making it more attractive to the risk-averse investor.
Risk-managed momentum achieves greater cumulative returns than the ordinary momentum strategy (refer fig 3). Barroso and Santa Clara (2014) opted to categorize momentum risk into systematic risk and specific risk and they found that the major source of risk does not come from systematic risk but from specific risk. This is because systematic risk focuses on the smaller and less predictable part of total risk. Systematic risk constituted 23% of the total risk therefore specific risk is the greater part of total risk. Managing specific risk therefore virtually eliminates crashes and nearly doubles the Sharpe ratio of the momentum strategy. Risk managed momentum reduces the kurtosis and the left skew of the strategy significantly. Barroso and Santa-Clara (2014) found that through risk management, kurtosis dropped from 18.24 to just 2.68 and the negative skew dropped from -2.47 to -0.42 and this significantly reduces crash risk.
The momentum strategy, by shorting losers to buy winners, has by construction a significant time-varying beta: positive after bull markets and negative after bear markets. Grundy and Martin (2001) show that momentum has significant negative beta following bear markets and argue that by hedging this negative exposure, the potential losses can be significantly alleviated, but Pedro and Barroso argue that managing time-varying betas fails because it focuses on the smaller and less predictable part of the risk and these time-varying betas are not the main source of predictability in momentum risk. Daniel and Moskowitz (2011) also went on to show that using betas in real time does not avoid the crashes. A further advantage of hedging specific risk rather than systematic risk is that it helps eliminate forward looking bias.
Fig 1: Momentum Crash Post Great Depression of WML Portfolio
Fig 2: Momentum Crash Post Sub-Prime Mortgage Crises of WML Portfolio
Fig 3: Risk Managed Momentum (WML*) vs. Ordinary Momentum (WML) 1927-2011
In this paper, I set out to explain momentum crashes, find variables to predict them as well as explore strategies to hedge against losses sustained during the crash period. Major momentum crashes are far an few between but the losses are immense when they do happen. The benefits of hedging against crashes should therefore not be ignored.
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