# Quant Investing: The Momentum-based Beta Strategy (I) (中文)

本文主旨為介紹利用動能為基礎的產業配置策略，並且透過其他相關指標進行改良，獲得績效大幅優於大盤的純多頭策略。

Elastic Asset Allocation (2014) is a momentum-based strategy published by Wouter J. Keller that only uses a geometrically weighted average of the historical returns, volatility, and correlation, but the backtest results are pretty good during his out-of-sample period from 1964 to 2014. Also, after we extend the strategy to 2022, it is still good enough according to its return, Sharpe ratio, and max drawdown.

In this article, we present a sector allocation strategy based on the generalized momentum analysis proposed in Elastic Asset Allocation (hereafter, EAA). And our universe is ETF rather than individual stocks.

The formula of generalized momentum analysis is :

W_{i} ~ Z_{i} = R_{i}^{wR} **•** (1-C_{i})^{wC} / V_{i}^{wV}

where Z_{i} is the generalized momentum score, W_{i} >0 is the optimal weighted, R_{i} is the momentum, C_{i} is the correction to the equal-weighted portfolio of the universe, V_{i} is the volatility, and (wR, wC, wV) are positive constants that we can decide.

Also using crash protection ratio mentioned in the same paper to regard the percentage of assets with negative momentum (CP%) as the weighted of the defensive position (e.g Cash or Bond).

For empirical, we use Select Sector SPDRs as our sector universe, and {BIL, SHY, IEF, TIP} as our defensive position. Contact us to get the full version of the quantitative report for Jan 2023 to get the setting detail of how we use it.

Figure 1 is the cumulative return of EAA sector allocation, the green line is the offensive asset which is the sector rotation using generalized momentum analysis without crash protects constraint, and the orange line is the defensive asset which chooses the higher momentum between our defensive universe. Figure 2 is weighted of holding in EAA Sector Allocation from 2008 Jan. to 2022 Dec.

For the EAA portfolio, we can observe that the drawdowns are smaller than the benchmark, and the volatility also which leads the Sharpe ratio of the EAA portfolio to have a higher Sharpe and Sortino ratio. However, cause of the de-leverage mechanism of crash protection, the recovery rate is too slow after the big drawdowns (2008,2018,2020) which causes the cumulative return start from 2008 to be only similar to the SPY.

To improve the recovery rate after the big drawdown, we can consider the indicator (hereafter, AMA) which is the percentage of the names of SPX components whose market price is above the 200-day moving average. When AMA is in a low-value situation and starts to raising, we can regard it as recovery timing. More Detail is in our quantitative report for Jan 2023.

Figure 3 shows the recovery timing that identifies by the AMA indicator, and figure 4 shows the performance of the EAA strategy after the adjustment by AMA timing. We can see that after solving the recovery problem, the cumulative return is much better than the benchmark. At the same time, it still keeps the advantage of the EAA strategy (low volatility and small drawdown).

Table 1 shows the performance matrix of these strategies. The momentum-based strategy with crash protection and recovery adjustment ( EAA & AMA in the table) has a Sharpe ratio almost twice as high as the benchmark (SPY). Also, the max drawdown is only one-third of our benchmark. Exceptional, the beta against SPY is only 0.42 which means the correlation between strategy and market is quite low and also shows that it had considerable protection in times of market decline.

On the left of figure 5, it shows the yearly return of the strategy and benchmark. And the right-hand side is the 1-year trailing return which is the histogram of the cumulative return for holding the strategy hole year for any month you started. We can observe that our strategy reduces a lot of tail risk and the return is more independent of the starting time of investment.

From 2008 to now, the market has experienced financial crises, long bull, QE, COVID-19, QT, and inflation issues. But all of the evidence we show above can tell us that this momentum-based portfolio is a robust strategy to beat the market with higher returns and lower volatility.

Elastic Allocation is a powerful and straightforward momentum-based allocation method. It has a great performance in the universe of US sector and bond ETFs. The strategy reduces the tail risk by switching between offensive and defensive assets, at the same time, it keeps the same level of cumulative return with lower risk. After solving the momentum crash when the market starts to recover, it has a wonderful performance against SPY.

Although the strategy has a very great performance, it still has something to improve. we will give the result and the detail that how we improve this strategy in the second episode of this topic.

Yu-Chin Lin

*Junior Quantitative Analyst, Quantitative Finance*, **Gamma Paradigm**