Momentum risk premium is one of the most important alternative risk premia, Since it is considered a market anomaly, it is not always well understood. (Page 1)

In particular, we revisit the payoff of trend-following strategies, and analyze the impact of the asset universe on the risk/return profile. We also compare empirical stylized facts with the theoretical results obtained from our model. Finally, we study the hedging properties of trend-following strategies. (Page 1)

Momentum is one of the oldest and most popular trading strategies in the investment industry. For instance, momentum strategies are crucial to commodity trading advisors (CTAs) and managed futures (MFs) in the hedge funds industry. (Page 2)

Indeed, it is well-known that the manufacturing of structured products is based on momentum strategies. Hedging demand from retail and institutional investors is therefore an important factor explaining the momentum style. (Page 2)

There is strong evidence that trend-following investing is one of the more profitable styles, generating positive excess returns for a very long time. (Page 2)

This is particularly true for equities and commodities. For these two asset classes, the momentum risk factor has been extensively documented by academics since the end of nineteen-eighties. (Page 2)

They found that buying stocks that have performed well over the past three to twelve months and selling stocks that have performed poorly produces abnormal positive returns. (Page 2)

However, the nature of momentum strategies in commodity markets is different than in equity markets, because of backwardation and contango effects (Miffre and Rallis, 2007). More recently, academics have investigated momentum investing in other asset classes and also found evidence in fixed-income and currency markets (Moskowitz et al., 2012; Asness et al., 2013). (Page 2)

The recent development of alternative risk premia impacts the place of momentum investing for institutional investors, such as pension funds and sovereign wealth funds (Ang,2014; Hamdan et al., 2016). Since they are typically long-term and contrarian investors, momentum strategies were relatively rare among these institutions. (Page 2)

Today, many institutional investors build their strategic asset allocation (SAA) using a multi-factor portfolio that is exposed to size, value, momentum, low beta and quality risk factors (Cazalet and Roncalli, 2014). (Page 2)

Fung and Hsieh (2001) developed a general methodology to show that “trend followers have nonlinear, option-like trading strategies”. In particular, they showed that a trend following strategy is similar to a lookback straddle option, and exhibits a convex payoff. They then deduced that it has a positive skewness. Moreover, they noticed a relationship between a trend-following strategy and a long volatility strategy. (Page 3)

The P&L of trend-following strategies has an asymmetric right-skewed distribution. They also focused on the hit ratio (or the fraction of winning trades), and showed that the best case is obtained when the asset volatility is low. (Page 3)

This is why they concluded that “trend followers lose more often than they gain”. Since the average P&L per trade is equal to zero in their model, Potters and Bouchaud (2006) also showed that the average gain is larger than the average loss. Therefore, they confirmed the convex option profile of the momentum risk premium. (Page 3)

The paper of Dao et al. (2016) goes one step further by establishing the relationship between trend-following strategies and the term structure of realized volatility. More specifically, the authors showed that “the performance of the trend is positive when the long-term volatility is larger than the short-term volatility”. Therefore, trend followers have to risk manage the short-term volatility in order to exhibit a positive skewness and a positive convexity. (Page 4)

They demonstrated that the payoff of the trend-following strategy is similar to the payoff of an equally-weighted portfolio of ATM strangles. (Page 4)

The authors finally concluded that “even if options provide a better hedge, trend following is a much cheaper way to hedge long-only (Page 4)

It is remarkable that only the magnitude of the trend, and not the direction, is important. This symmetry property holds because the trend-following strategy makes sense in a long/short framework. (Page 8)

We also notice that the maximum loss is a decreasing function of A, or equivalently an increasing function of the average duration of the moving average. This implies that short-term momentum is less risky than long-term momentum. This result is obvious since long-term momentum is more sensitive to reversal trends, and short-term momentum is better to capture a break in the trend. (Page 8)

In Figure 29, we report the cumulative performance of V;, G; and g; in the case of the Eurostoxx 50 Index. For this, we follow Bruder and Gaussel (2011) who prefer to perform the trend-following (Page 34)

strategy on the volatility targeted index rather than on the index itself. We consider a 20% volatility target strategy and we assume that the parameter A is equal to 2, meaning that the average momentum duration is six months, whereas the leverage a is set to 1. (Page 35)

We also confirm that most of the performance of the momentum strategies comes from the trading impact, while the contribution of the option profile is not significant. (Page 35)

For some assets, we notice that the exposure is mainly positive except for some short periods. It follows that the momentum risk premium can then benefit from two main patterns: trends and risk premia. In the first case, the asset must exhibit strong trends in order to obtain good performance. This is less relevant in the second case, since the momentum risk premium comes from the capacity to leverage or deleverage traditional risk premia. (Page 39)

Tail risk management is generally associated with portfolio insurance, which can be implemented using the CPPI method (Black and Perold, 1992; Perold and Sharpe 1995) or the OPBI approach (Leland, 1980; Rubinstein and Leland; 1981). The constant proportion portfolio insurance (CPPI) method is a dynamic trading strategy that allocates investments between the underlying asset and the reserve (or risk-free) asset. (Page 41)

Today, asset managers and banks also propose a new spectrum of other methodologies, in particular managed volatility strategies (Hocquard et al., 2013) and volatility overlay methods (Whaley, 2013). (Page 43)

The first point is related to the difference between passive and dynamic asset allocation. Even if the strategic asset allocation (SAA) is very well-diversified, investors must be active if they want to control their tail risk (Page 43)

Since trend-following strategies have a convex option profile, they are good candidates for hedging tail risk. The empirical works of Fung and Hsieh (2001) and the 2008 Global Financial Crisis (GFC) have pushed asset owners and managers to use CTAs as a tail protection. (Page 44)

Dao et al. (2016) show that there is a link between convexity and diversification. In particular, they notice that a diversified trend-following strategy provides a hedge for a multi-asset risk parity portfolio. (Page 50)

It is obvious that using the same allocation scheme helps. More generally, the hedging gain depends on the correlation between the diversified portfolio and the equivalent long only portfolio deduced from the trend following strategy. (Page 50)

In fact, we think that there is a misconception about CTAs. Many people think that CTAs are good strategies for hedging the skewness risk of the stock market. In reality, trend-following strategics help to hedge drawdowns due to volatility risk. (Page 53)

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. (Page 53)

The momentum risk premium has been extensively documented by academics and professionals. There is no doubt that momentum strategies have posted impressive (real or simulated) past performance. (Page 54)

With the emergence of alternative risk premia, momentum is now under the scrutiny of sophisticated institutional investors, in particular pension funds and sovereign wealth funds. (Page 54)

The momentum risk premium has two main risks. The first one is obvious, and concerns trend reversals. This point has been already observed by Daniel and Moskowitz (2016), who showed that investors may face momentum crashes, especially when they use a cross-section implementation. This point is also related to the coherency between the duration of the trend and the duration of the moving average. The second risk is less obvious because it is associated with the leverage effect. At first sight, leverage may be viewed as a homogencous scaling mechanism. In the case of CPPI products, we know that the scaling is not homogenous and that an excessively high leverage (Page 55)

dramatically destroys the performance of such products. For momentum strategies, we observe a similar effect, because the gamma costs may be prohibitive when we exceed a certain level of leverage and when the asset volatility is high. As a consequence, even if the ruin probability of a momentum strategy is significantly lower than for value and contrarian strategies, investors may pay attention to the leverage risk. (Page 56)

Since a trend-following strategy has a negative vega, the momentum risk premium does not like volatility to increase. This result is the opposite of that obtained with value and contrarian strategics. (Page 56)

Our model shows that a strong trend with a high volatility is not necessarily better than a medium trend with a very low volatility. This is why a momentum risk premium faces a trade-off between trend and volatility. A famous example is the Global Financial Crisis in 2008. Some people think that the incredible performance of trend-following strategies in 2008 is mainly due to short exposures on the equity market. This is not true, because even though we had a very strong negative trend on stocks, the volatility of this market was also very high. Because the performance of stocks and bonds was negatively correlated during this period, trend-following strategies benefited from the positive trend on sovereign bonds, whose volatility was contained. In the end, long fixed-income exposures contributed more to the momentum risk premium in 2008 than short equity exposures. (Page 56)

In the case of a long-only investment portfolio, the best case for diversification is when some assets are negatively correlated to other assets. This explains why the stock/bond asset mix policy is certainly the most well-known diversified portfolio. However, the case of negative correlation is symmetric to the case of positive correlation. (Page 56)

In fact, the concept of diversification is more complex for momentum strategies than for long-only investment portfolios. In particular, we must distinguish time-series momentum and cross-section momentum. (Page 56)

In contrast, a cross-section momentum prefers highly correlated assets to independent assets. (Page 56)

In the multivariate case, the allocation matrix becomes a key parameter for understanding the performance. For a time-series momentum strategy, weight dive reduces the expected gain. (Page 56)

When a big trend appears, the time-series strategy should concentrate its exposure on this bet rather than diversify the bets. This is not the case of the cross-section strategy, because it should be exposed to many relative bets. (Page 56)

Generally, time-series momentum is implemented with a multi-asset universe in order to have decorrelated assets and absolute bets, whereas cross-section momentum is implemented within a single-asset class in order to have correlated assets and relative bets. (Page 56)

They understood that their diversification power comes from the short exposure and depends on the market regime. In particular, they observed that they have the tendency to perform well in a period of stressed equity markets (Fung and Hsieh, 2001). Since the concepts of diversification and hedging are related, some asset owners and managers then considered that trend-following strategies could be hedging strategies. (Page 57)

In reality, building a robust trend-following strategy is much more complex than the theoretical model we have developed in this paper. This model is enough to understand the behavior of the momentum risk premium, but it remains a toy model if the objective is to build an investment product that aims to fully capture the momentum risk premium. (Page 57)