# Momentum Strategies

Pinto, Henry, Robinson and Stowe (2010) define momentum indicators as valuation indicators that are based on the relationship between price or another fundamental, earnings for example, to a time series of its historical performance or to the fundamental’s expected future performance values. When the strategy uses earnings then it is an earnings momentum strategy and in the case of using price then it is a momentum strategy. Momentum strategies can either be relative or absolute. Relative strategies compare the momentum of different assets to each other and absolute momentum is not concerned with the performance of other assets as it only focuses on that stocks past return in predicting future returns.

Momentum strategies may use past returns or earnings surprises (earnings momentum strategies) as a basis for predicting future returns (Chan, Jegadeesh & Lakonishok, 1996). Momentum strategies may also use a historical time series of a stock’s fundamentals (price or earnings) relative to itself to predict expected returns and this is known as absolute momentum. Momentum may alternatively use a historical time series of a stock’s fundamental such as price or earnings and compare it to that of another stock’s fundamentals and that gives rise to cross sectional or relative strength momentum.

The rest of the article will explore the different momentum strategies and the indicators that are used in creating momentum strategies.

## Earnings Momentum

It has been shown that future returns can be predicted from previous news about earnings (Chan et al., 1996). Earnings momentum refers to the rate of acceleration or deceleration in the earnings per share of a company. If the earnings grow from one period to the next, usually measured over a quarter, then the company earnings will be showing momentum in their earnings. One cannot look at earnings in solitude. A closer look at the financials of a company, particularly statement of financial position and statement of comprehensive income, is required to complement the analysis of the earnings momentum. This is done to understand the financial health of a company because accelerating earnings in most instances occur contemporaneously with increased revenues which are usually a result of cost improvements, increases in sales or upward markets amongst other things. If the earnings multiplier (price to earnings ratio) is on an upward trend that could be an indicator that the earnings of that company are going to continue on an upward trend. This should impel the price of company upward over time but the level of increase in the price is dependent on the level of earnings momentum (Ord).

Earnings momentum is studied with the intention of understanding the impact of unexpected earnings on price. Furthermore, earnings momentum is studied in relation to earnings announcements.

One of the most commonly used indicators in calculating earnings momentum is the standardised unexpected earnings calculated as follows:

Another earnings indicator as used in their paper by Chan et al. (1996) is the abnormal stock return around the most recent announcement date of earnings up to month t.

Abnormal earnings is a measure of how much the stock’s returns are above the expected return and may be measured in a number of ways, above is the formula that Chan et al. (1996) use in their paper in calculating earnings momentum. Other ways of calculating earnings momentum include using a market model or equilibrium asset pricing model such as CAPM (Princeton University, 2003).

In addition to the research by Jegadeesh and Titman (1993) and Chan et al. (1996) that confirms that future returns in the near term can be predicted using past performance, Hou, Xiong and Peng (2009) also find that earnings momentum profit has a negative relationship with turnover. Additionally, earnings momentum show no sign of reversal after 13-36 months after portfolio formation. This could be a consequence of investor underreacting to earnings announcements. On the other hand they observed that price momentum could be the consequence of a strong overreaction to the same earnings announcement.

## Price Momentum

A price momentum strategy uses the price to create trading indicators that may be used to create the momentum strategy. Chan et al. (1996) for example, used the six month prior return of a stock as their indicator for their price momentum strategy. It has been shown in research that momentum is more worthwhile in up markets than down markets.

In terms of buying stocks: investors should expect that the stocks bought should return an above average return over the following three to twelve months given that the same stocks had previously shown relatively high returns over the past three to twelve months. In the same vein, in terms of selling stocks: investors should expect that any stocks that have had a poor return over the previous three to twelve months will continue to have below average returns over the following three to twelve months. Therefore one can expect to earn above average returns by buying winners and selling losers (Jegadeesh & Titman, 1993).

**Note: The formulas for Price and Risk adjusted momentum were sourced from www.gestaltu.com, you can find more about them in the reference list.**

The most basic form of calculating momentum is simple and shown below:

This calculation is too simple as it is not normalised. To normalise the formula a rate of change value can be calculated as shown below:

Other price momentum indicators that may be used to calculate price momentum are as follows:

This formula uses the difference between the long SMA and the short SMA to calculate price momentum.

In this formula the only difference is in terms of the variables used in calculation. The short term SMA is replaced with price and thus the price momentum is measured by the difference in price and the long term SMA.

Uses the rate of change of the SMA, the difference between yesterday’s SMA and today’s SMA.

Price percent rank highlights where the current price of the asset is in relation to the asset’s price over a specified look back period.

Z Score relates the price to the mean of prices of the asset.

Z Distribution shows the cumulative probability that relates to a particular z score.

T distribution is similar to the normal distribution but allows for a higher level of uncertainty.

GestaltU (2013a) used the above indicators in their analysis of price momentum.

The idea behind using multiple price momentum strategies is that no single indicator is as useful on its own as it would be in combination with other indicators or strategies. For instance research has shown that momentum and contrarian investment strategies can complement each other to bring about above average return.

Analysts may also make use of moving averages to calculate price momentum. For example equations 6 and 7 make use of a simple moving average. Another example of a moving average is the exponential moving average (EMA). Moving averages can be used to create buy and sell signals. When the short term moving average goes above the long term moving average a buy signal is triggered and vice versa. Also important to note is that momentum should be used in conjunction with other indicators to be an effective buy or sell indicator.

Price momentum is shown to have a positive relationship with turnover (a measure of the relationship between sellers and buyers of a particular stock). Some of the momentum profit may be a result of overreaction (Hou* et al.*, 2009). Daniel, Hirshleifer and Subrahmanyam (1998), on the other hand, attribute it to overconfidence bias and self-attribution bias. The former leads to overreaction and self-attribution fuels overconfidence.

Price momentum may be calculated on either a cross-sectional basis (relative strength momentum) or on a time series basis (absolute momentum).

## Relative Strength Momentum

Relative strength is the most commonly used momentum strategy. Relative strength is based on price (Pinto* et al.*, 2010) and this is why in some cases when investors mention that they are using a price momentum strategy it is usually on a relative momentum basis. This strategy is based on buying past winners and selling past losers as found in the research by Jegadeesh and Titman (1993) who showed that this strategy tends to return above average returns in the short to medium term.

If the relative strength portfolio uses long and short positions contemporaneously, as is in cross sectional momentum, the concern with regard to up and down markets is eliminated as the short momentum positions protect against long momentum positions and vice versa.

## Absolute Momentum

Momentum may also be applied on a time series or absolute basis, that is, the security’s past performance is used to predict its future performance unlike in relative strength momentum where the security’s relative performance to its peers is used as a predictive tool for future performance. Absolute momentum only looks at the historical excess returns of the security in question over a determined look back period (Antonacci, 2014). Furthermore, this is a trend following strategy as it a more direct way of analysing and using market trends in predicting price continuation (Antonacci, 2014).

The predictive power of absolute momentum is rooted in the significant positive auto-covariance that exists between the asset’s future returns and its returns in the past 12 months as shown in the study by Moskowitz, Ooi and Pedersen (2012)

Time series momentum is simpler to apply and has benefits for long-only investing (overweighting winners and underweighting losers) by decreasing the downside exposure that comes with long-only investing. It may also be applied to any individual security or portfolio of securities without sacrificing any of the value contributed by the other securities to the portfolio (Antonacci, 2013; Antonacci, 2014). Additionally, time series momentum by being able to recognise regime changes and thus it is capable of reducing the accompanying downside risk. Lastly, it has shown that it works in extreme markets and across different asset classes.

## Dual Momentum

Dual momentum combines the benefits of both relative and absolute momentum in creating a trading strategy. Just to give a better perspective of both relative and absolute momentum an example will be used. Consider that you have two assets, asset A and asset B. If asset A appreciates more than asset B then in this case asset A has positive relative momentum. If, for instance, both asset A and asset B depreciate over time then what has been exhibited in this instance would be negative absolute momentum. It follows then, that it can happen that an asset may exhibit both positive relative momentum and negative absolute momentum. Furthermore, an asset will have positive absolute momentum over a given historical period if its excess return over the said historical time horizon is positive regardless of how it performs in comparison to other assets (Antonacci, 2013).

In creating their dual momentum portfolio Antonacci (2013) use a two layer approach. First, they use relative strength momentum in asset selection and if the selected assets do not contemporaneously exhibit positive absolute momentum they are not selected and instead Treasury bills are chosen until the said asset is performing better than the Treasury bills. Price momentum does not perform well in down markets and thus using treasury bills as an alternative proxy when the asset does not have positive momentum leads to risk reduction in the portfolio. Using a dual momentum strategy has the added benefit of diversification. Diversification would not pose as a problem if using absolute momentum as a portfolio could be created with multiple assets. If one were to use relative momentum on its own the disadvantage would be that underperforming assets may be left out of the portfolio and the remaining top performers would have high correlations thus reducing diversification benefits (Antonacci, 2013).

The results from Antonacci (2013) show that with using dual momentum the risk is reduced and this had a corresponding increase in the Sharpe ratios. Dual momentum also led to a reduction in drawdown. In terms of creating the portfolio as long only it would be advisable to do that when both relative and absolute momentum are positive this is because long only momentum returns are highly dependent on regime changes (Antonacci, 2013).

## Risk Adjusted Momentum

In momentum investing the strategy uses an average of historically realised returns to create trading signals and therefore ignores fluctuating stochastic volatility that creates a noise in the data. This method of averaging past returns could possibly be inefficient because the actual expected return could be a noisy estimate (Dudler, Gmuer & Malamud, 2014). The risk adjusted momentum by Dudler* et al.* (2014) is different from the time series momentum by (Moskowitz* et al.*, 2012) only in that instead of using unadjusted averages of historical returns, they adjust these returns by a measure of realised volatility giving rise to risk adjusted momentum. Risk adjusted momentum, in simpler terms, standardises momentum returns by an appropriate risk measure (Dudler* et al.*, 2014; Shaik, 2011).

In comparing the risk factor of momentum in relation to the other risk factors as shown in the Fama and French model it is shown that the Sharpe ratio of momentum is higher than that of the market, size and value factors.

Moreover, momentum shows that it has a negative correlation to the market and value factors. Even though momentum has shown potential for creating abnormal returns it has been victim of crashes, case in point, year 1932 momentum produced a -91.59% return over a period of two months another crash occurred more recently in 2009. Managing the risk that comes with momentum will lead to better momentum returns (Barroso & Santa-Clara, 2015). Research by both Barroso and Santa-Clara (2015) and Dudler* et al.* (2014) shows that by normalizing momentum returns by the momentum volatility enhances the risk profile of momentum returns.

GestaltU (2013b) go further in analysing risk momentum by creating different risk adjusted momentum indicators that they use across multiple asset classes. Below are some of the risk adjusted metrics that were also applied by (GestaltU, 2013b) in their analysis.

**Note: The formulas for Price and Risk adjusted momentum were sourced from www.gestaltu.com, you can find more about them in the reference list.**

The most common and popular risk measure is the Sharpe ratio created by William Sharpe.

Measures the excess return per unit of volatility

Omega ratio measures the likelihood of achieving a certain return. The higher the omega value the higher the chance that the return will be met or surpassed. This measure of risk adjusted return is relevant because the omega ratio does not use a theoretical normal distribution, which in fact returns don’t follow as they have a skewed distribution. The ratio instead uses the actual return distribution and thus is a more realistic reflection of the historical performance of the asset being analysed.

Sortino ratio a modification to the Sharpe ratio that takes into account the standard deviation of negative returns. This is done to separate the harmful volatility from normal volatility. A high Sortino ratio is indicative of a lower probability of a large loss.

Ulcer index is an indicator of the downside risk relating to both the depth and also the duration of price declines. The Ulcer performance index uses the ulcer index in calculating risk adjusted returns.

Fractal Efficiency looks at the relationship between the market speed and volatility and its relevance is in its ability to filter choppy or flat stocks. Calculated by dividing the net change in the movement of price over a specified number of periods by the total of the absolute values of individual moves.

## Conclusion

Momentum strategies have shown their strength in generating higher returns but the general consensus coming from research over multiple asset classes and markets is that it is prone to work over a short to medium term horizon. After that momentum shows a return reversal. Instead of using momentum on its own, combining it with another trading strategy such as contrarian investing can prove to be useful. Combining multiple momentum strategies also leads to a higher average return. For example by using dual momentum that combines relative momentum and absolute momentum an investor can achieve better average return. Furthermore, using risk adjusted returns in creating momentum strategies will add to the increase in returns of the momentum strategies.

## References

Antonacci, G. 2013. Risk Premia Harvesting Through Dual Momentum. *Available at SSRN 2042750*.

Antonacci, G. 2014. Absolute momentum: a simple rule-based strategy and universal trend-following overlay. *Available at SSRN 2244633*.

Barroso, P. & Santa-Clara, P. 2015. Momentum has its moments. *Journal of Financial Economics, *116(1):111-120.

Chan, L.K.C., Jegadeesh, N. & Lakonishok, J. 1996. Momentum Strategies. *The Journal of Finance, *51(5):1681-1713.

Daniel, K., Hirshleifer, D. & Subrahmanyam, A. 1998. Investor psychology and security market under‐and overreactions. *the Journal of Finance, *53(6):1839-1885.

Dudler, M., Gmuer, B. & Malamud, S. 2014. Risk Adjusted Time Series Momentum. *Available at SSRN 2457647*.

GestaltU. 2013a. *Dynamic Asset Allocation for Practitioners Part 1: The Many Faces of Momentum*. [Online] Available from: http://gestaltu.com/2013/05/dynamic-asset-allocation-for-practitioners-part-1-the-many-faces-of-momentum-2.html [Accessed: 26 June 2015].

GestaltU. 2013b. *Dynamic Asset Allocation for Practitioners Part 2: Risk Adjusted Momentum*. [Online] Available from: http://gestaltu.com/2013/06/dynamic-asset-allocation-for-practitioners-part-2-risk-adjusted-momentum.html [Accessed: 2 July ].

Hou, K., Xiong, W. & Peng, L. 2009. A tale of two anomalies: The implications of investor attention for price and earnings momentum. *Available at SSRN 976394*.

Jegadeesh, N. & Titman, S. 1993. Returns to buying winners and selling losers: Implications for stock market efficiency. *The Journal of finance, *48(1):65-91.

Money-zine.com. 2009. *Understaning Price Momentum*. [Online] Available from: http://www.money-zine.com/investing/stocks/understanding-price-momentum/ [Accessed: 15 July ].

Moskowitz, T.J., Ooi, Y.H. & Pedersen, L.H. 2012. Time series momentum. *Journal of Financial Economics, *104(2):228-250.

Ord, T. *Earnings Momentum Definition and Trading Strategies*. [Online] Available from: http://www.mysmp.com/fundamental-analysis/earnings-momentum.html [Accessed: 15 July].

Pinto, J.E., Henry, E., Robinson, T.R. & Stowe, J.D. 2010. Equity asset valuation. *CFA Institute Investment Books, *2010(1):1-441.

Princeton University. 2003. *Value Relevance of Analysts’ Earnings Forecasts *[Online] Available from: http://www.princeton.edu/~markus/teaching/Eco467/04Lecture/04Event%20Study%20Description.pdf [Accessed: 14 July].

Shaik, R. 2011. *Risk-Adjusted Momentum:*

*A Superior Approach to Momentum Investing.* [Online] Available from: http://dorseywrightmm.com/downloads/hrs_research/Momentum%20White%20Paper%202011%20Fall.pdf [Accessed: 1 July 2015].

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