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Basic theory of momentum strategies

Systematic momentum trading is a major alternative risk premium strategy across asset classes. Time series momentum motivates trend following; cross section momentum gives rise to ‘winners-minus-losers strategies’. Trend following is a market directional strategy that promises ‘convex beta’ and ‘good diversification’ for outright long and carry portfolios as it normally performs well in protracted good and bad times alike. It works best if the underlying assets earn high absolute (positive or negative) Sharpe ratios and display low correlation. By contrast, cross section momentum strategies benefit from high absolute correlation of underlying contracts and are more suitable for trading assets of a homogeneous class. The main pitfalls of both momentum strategies are jump events and high costs of ‘gamma trading’ conjoined with high leverage.

Roncalli, Thierry (2017), “Keep Up The Momentum”, December 2017

The post ties in with SRSV’s lecture on setback risk.
The below are excerpts from the paper. Emphasis and cursive text have been added.

Background and definitions

“The idea of alternative risk premia is to group individual securities in another way in order to define new risk factors…to build a better diversified portfolio than a traditional stock-bond asset mix policy…Carry and momentum are the most relevant alternative risk premia since they are present across different asset classes…Momentum is one of the oldest and most popular trading strategies…[Momentum strategies are] risk premium strategies [that] assume that the past trend is a predictor of the future trend.”

“We have to make the distinction between two generic [momentum] strategies: time-series and cross-section

  • The time-series momentum is called…trend-following strategy…because it assumes that assets with a current positive trend will continue to have a future positive trend and assets with a current negative trend will continue to have a future negative trend…The portfolio is long on assets with a positive past trend and short on assets with a negative past trend… The time-series momentum strategy is intensively used by CTAs with a multi-asset universe and is generally implemented with equity, bond, currency and commodity futures contracts.
  • A cross-section momentum is called a winners-minus-losers strategy. It assumes that the current winners will continue to outperform the current losers in the future… building a portfolio that is long on assets that have outperformed and short on assets that have underperformed…The net exposure of a cross-section momentum is equal to zero…The cross-section momentum strategy is one of the pillars when a fund manager builds an equity multi-factor portfolio by mixing size, value, momentum, low risk and quality stocks.”

“Like the theory of options, the theory of momentum is then based on several trade-offs: trend versus volatility, delta gain versus gamma cost, long-term volatility versus short term-volatility.”

[Since] the Global Financial Crisis…[alternative] risk factors have…been seen as dependent on traditional asset classes. The reason is that most of them are beta strategies, meaning that their performance also depends on the performance of the market. If alternative risk premia are beta strategies…the traditional diversification approach is not appropriate….It must…be replaced by the payoff diversification approach….Volatility is not the right risk measure of long-term investors, which are more sensitive to expected drawdowns…Volatility risk is a tactical asset allocation decision, whereas skewness risk is a strategic asset allocation decision.”

“By differentiating convexity and concavity in the portfolio, alternative risk premia reshuffle the notion of ‘bad’ and ‘good’ diversification. A bad diversification…will help in bad times, but that will also destroy performance in good times…This is the example of systematically buying put options…A good diversification…will help in bad times without compromising the long-run performance. This can only be achieved with a risk premium strategy that exhibits a time-varying beta: a positive beta in good times and a negative beta in bad times. This is exactly the [historical] beta profile of momentum risk premia.”

The attraction of momentum strategies

“[Simulations] demonstrate that the payoff of the trend-following strategy is convex and is similar to a long exposure on a straddle option… Convex beta [with limited downside and unlimited upside] is precious and scarce. Among risk premia, momentum is one of the few strategies to offer this…asymmetry.”

To trend is to diversify in bad times. In good times, trend-following strategies offer no significant diversification power….This is not a problem, since investors do not need to be diversified at all times. In particular, they do not need diversification in good times, because they do not want that the positive returns generated by some assets to be cancelled out by negative returns on other assets. This is why diversification may destroy portfolio performance in good times. Investors only need diversification in bad economic times and stressed markets.”

Conditions for successful momentum trading

“Trend-following strategies [are based on] market anomalies…The loss is bounded, but the gain may be infinite, even if the asset has a zero Sharpe ratio. These generic results are impacted by three main parameters [1] the duration of the moving average that estimates the trends; [2] the Sharpe ratio of the assets that compose the investment universe; [2] the correlation matrix of asset returns…

  • The P&L of short-term trend-following strategies has a larger volatility than the P&L of long-term trend-following strategies. This result is not so obvious, because we may have the feeling that risk management of short-term trading is easier than risk management of long-term trading. In fact, this result is related to the fact that short-term trends are more difficult to estimate than long-term trends. This explains that short-term trend-following strategies are more sensitive to trading recipes, proprietary models and the “savoir-faire” of the management team. This result is also confirmed by the broader dispersion of returns that is observed between short-term CTAs than between long-term CTAs.
  • The performance of the trend-following strategy does not depend on the sign of the Sharpe ratio, but only on its absolute value. Therefore, we obtain a symmetry property: a negative Sharpe ratio has the same impact than a positive Sharpe ratio…The Sharpe ratio is a statistic that combines the trend and the volatility. In order to perform, momentum strategies need significant trends compared to the volatility. What does it mean? In fact, we can show that momentum strategies have a negative vega, implying that the investor pays a systematic premium because of the short exposure on the short-term volatility. This is why the momentum risk premium does not like that the volatility increases. Therefore, the Sharpe ratio is a relative measure of the strength of the trend. When considering a momentum strategy, the investor needs to be convinced that assets in the investment universe will exhibit trends, whatever the direction. This explains that the investment universe of a buy-and-hold or constant-mix portfolio is generally composed of stocks and bonds, whereas the investment universe of a momentum portfolio also includes currencies and commodities that are not risk premia.
  • The third important parameter is the correlation between asset returns… the time-series momentum does not like (positively or negatively) correlated assets… The best case is when the correlation is equal to zero, because we have two independent trends…In the case of a long/short investment portfolio, the case of negative correlation is symmetric to the case of positive correlation. For instance, if we consider the two extreme cases, a correlation of +100% between two assets is equivalent to a correlation of -100% in a long/short momentum portfolio. In this later case, if we observe a positive trend on one asset, this implies a negative trend on the second asset.”

“[By contrast] correlation is…the friend of cross-section momentum…The return of the portfolio depends on the relative difference between asset trends. If assets are weakly correlated, the dispersion of the P&L is very high. The outcome of the strategy is then very uncertain…Cross-section momentum makes sense for a universe of homogeneous securities, for instance the stocks of an equity index that is focused in one country or one region.”

Pitfalls of momentum trading

“Each traditional and alternative risk premium has its own bad times…Momentum strategy is not an exception…Trend followers lose more often than they gain…This is due to the fact that big trends are not so frequent in financial markets. Most of the time, gamma costs [trading costs due to market volatility] dominate implying that the performance of the momentum strategy is poor, but sometimes there is a big trend and the momentum strategy posts an outstanding performance.”

“[A momentum strategy’s] loss is bounded [but only] under two conditions. The first one assumes that the momentum strategy uses a reasonable leverage….The problem comes from the costs induced by gamma trading, which are not linear with respect to portfolio’s leverage. In particular, we can show that too much leverage can be harmful for the strategy….The second condition assumes that there is no jump or discontinuity in asset prices. Without this assumption, the payoff is not necessarily convex and the loss is not bounded.”

“There is a misconception…Many people think that CTAs [institutional trend followers] are good strategies for hedging the skewness risk of the stock market. In reality, trend-following strategies help to hedge drawdowns due to volatility risk. For instance, CTAs did a very good job in 2008, because the Global Financial Crisis is more a high- volatility event than a pure skewness-risk event. However, it is not obvious that CTAs may post similar performances when facing skewness events. For instance, the performance of CTAs was disappointing during the Eurozone crisis in 2011 and the Swiss CHF chaos in January 2015.”


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