Momentum Risk Premium Theory

What makes momentum investing tick? In their September 2017 paper entitled “Understanding the Momentum Risk Premium: An In-Depth Journey Through Trend-Following Strategies”, Paul Jusselin, Edmond Lezmi, Hassan Malongo, Côme Masselin, Thierry Roncalli and Tung-Lam Dao present a theoretical analysis of the momentum risk premium. They assume that asset prices generally exhibit geometric Brownian motion (randomness) with constant volatility, but with a time-varying trend. They examine momentum strategy performance based on this model and test some conclusions empirically on a multi-class set of asset indexes. Based on mathematical derivations and using monthly returns for a universe of four equity, four government bond, three interest rate, five currency and four commodity indexes during January 2000 through July 2017, they find that:

• Based on mathematical analysis of the momentum model:
  • The optimal trend metric is an exponentially weighted moving average (EMA).
  • The ratio of trend volatility to asset volatility indicates the optimal trend measurement frequency.
  • Long-term momentum strategies inherently have higher Sharpe ratios than short-term momentum strategies. Also, probability of ruin is higher for short-term than long-term momentum.
  • The penalty for picking a suboptimal lookback interval for momentum measurement is not large. For example, estimating a 4-month trend with a 6-month or a 3-month moving average does not make much difference.
  • Overall, momentum traders lose more often than they gain, but the expected gain is larger than the expected loss. When the Sharpe ratio of the asset being traded (measured using the duration of the momentum lookback interval) is very negative or very positive, the probability of gain may be higher than the probability of loss.
  • Momentum is unique among risk premiums in having positive return skewness, and is therefore a candidate for hedging tail risk. However, sharp drops in asset prices defeat the hedging power.
  • The momentum risk premium involves a trade-off between trend strength and volatility. A very strong trend with high volatility is not necessarily better than a medium-strength trend with very low volatility.
  • For intrinsic (absolute or time series) momentum:
    • Performance is best when assets in the universe have zero return correlations with each other (independent trends).
    • Increasing the number of uncorrelated assets has no impact on average return, but reduces volatility and thereby increases Sharpe ratio.
    • Performance is better for a small number of assets with very high or very low individual Sharpe ratios than for a large number of assets with low-magnitude Sharpe ratios.
  • In contrast, for relative (cross-sectional) momentum:
    • Performance is better when assets in the universe have positive and high return correlations with each other.
    • Performance is better when the dispersion of asset Sharpe ratios is high, but the magnitude of asset Sharpe ratios is unimportant.
    • Relative momentum is more prone to crashes than intrinsic momentum.
• Empirically, for a multi-class universe of indexes:
  • The optimal EMA is generally in the range one to four months, longer for commodities than equities. However, results are very sensitive to the sample period. For example:
    • Over the last five years, average duration of equity trends is four months.
    • Over the last 10 years, average duration of government bond trends is 12 months.
  • Interest rate, government bond and equity indexes exhibit much higher momentum risk premiums than currency and commodity indexes.
  • Trend-following hedges for individual assets generally reduce extreme losses, but may increase intermediate losses.

In summary, theoretical analysis indicates different success criteria for intrinsic momentum (zero return correlations and extreme Sharpe ratios among assets) and relative momentum (high positive return correlations and large dispersion of Sharpe ratios among assets).

Cautions regarding findings include:

• As noted in the paper, the simple model of momentum used for theoretical analysis is imperfect. Geometric Brownian motion with trends does not fully describe actual asset price behaviors.
• Neither theoretical analyses nor empirical tests account for implementation frictions/barriers, including:
  • Using indexes as assets ignores implementation costs/fees of creating liquid funds that track the indexes. These costs/fees may vary considerably across asset classes.
  • Monthly portfolio turnover may be high, generating additional material costs.
  • Shorting may in some cases be costly/infeasible due to lack of assets to borrow for shorting. Using futures rather than underlying assets eliminates this concern, but momentum may work differently for futures versus underlying assets.
• The sample period used for empirical tests is short in terms of variety of market conditions, especially considering overlap of momentum lookback intervals.