Two prominent economists Alfred Cowles and Herbert Jones published an iconic academic research paper in 1937.

That analysed the performance of stocks listed on the New York Stock Exchange (NYSE) from 1920 through to 1935. They found that stocks which exceeded the median performance in one year also exceeded it in the following year (Cowles and Jones, 1937). This was a significant finding, which is the basis for the analysis of momentum as a factor in modern-day academic literature.

As the years have passed, many such studies have been conducted to ascertain whether momentum continues to remain relevant. Since momentum contradicts the Efficient Market Hypothesis (EMH), a lot of effort has been dedicated to proving that the effect of momentum has reduced with time. Unfortunately, this “proof” has not been forthcoming.

In 1993, Narasimhan Jegadeesh and Sheridan Titman published a seminal paper explaining the Momentum Effect, which is defined as the ability of an already rising (or falling) security to maintain that momentum and rise (or fall) further (Jegadeesh and Titman, 1993) The study labelled stocks that had performed well in the past as Winners and those which had performed badly as Losers. Based on data from 1965 to 1989, they found that a strategy that bought past Winners and sold past Losers generated significant excess returns. Their portfolio strategy, Winners Minus Losers (WML), which went long on stocks that performed well and simultaneously short on stocks which performed poorly generated largely positive monthly returns for upto 12 months from portfolio creation. A trading strategy that held positions for 6-months based on their past 6-months performance roughly generated an annualised excess return of 12.01%.

However, over a 36-month period, the difference between the monthly returns of Winners and Losers not only narrowed significantly but was also negative for several periods. This phenomenon of positive excess returns over the short term wearing out over an extended period of time can be attributed to mean reversion, which suggests that over long periods of time, stock prices revert to their long-term mean/average price level based on their fundamentals.

Mark Carhart extended the FF3F Model by incorporating a Monthly Momentum (MOM) Factor. The MOM portfolio, also referred to as the Up Minus Down (UMD) portfolio, is theoretically a zero-cost portfolio that goes long in past 12-month Winners (positive momentum stocks) and short in past 12-month Losers (negative momentum stocks). The inclusion of the UMD Factor increased the explanatory power of the FF3F model, further reinforcing the importance of the Momentum factor in making better investment decisions (Carhart, 1997).

These studies suggest that markets tend to let positive momentum stocks rise further and negative momentum stocks fall further due to the presence of irrationalities and behavioural biases. This makes the Momentum Effect extremely pervasive, yet transitory due to the aforementioned effect of mean reversion.

**Momentum over X months**

Although momentum can be defined in several different ways, the simplest and most prominent measures of momentum are returns over different time periods viz. 6-Month Total Return, 9-Month Total Return, 12-Month Total Return among others. Notably, many professionals may measure stocks’ momentum as defined by their price returns instead of total returns in an attempt to eradicate the effect of cash flows, such as dividends, from the returns and thus focus on the ‘true’ price momentum, which is largely governed by the demand and supply dynamics of the stocks. It is often calculated as follows

These measures can be used in many ways and while the most popular usage focuses on selecting one time period for analysis and comparison, more complex methods have emerged as well.

**Change in Momentum**

These include measures that ascertain the change in momentum to identify stocks in which it is intensifying as an advance indicator. This is calculated as follows

Where X< Y

A number greater than 1 indicates momentum that is intensifying and a number lower than 1 depicts slowing momentum.

While the momentum effect has remained relevant over the years, momentum portfolios can exhibit high levels of volatility. This led to it being shunned by many participants and over time, an alternative measure emerged to address this.

**Risk Adjusted Momentum**

Risk Adjusted Momentum is calculated as follows

*Stock Return can be defined as the stock’s price return or the stock’s total return.

Risk Adjusted Momentum subtracts a risk-free rate from the stock’s return and divides this excess return by the annualised standard deviation or volatility of that stock. This is very similar to the manner in which the Sharpe ratio is calculated and as such, this must be inferred in the same way as the Sharpe Ratio. Unlike other momentum indicators mentioned earlier, Risk Adjusted Momentum takes into account the stock’s volatility and can be perceived as a multi-factor metric that includes the low volatility factor along with the momentum factor.

In addition, there are several technical indicators such as bollinger bands, moving averages convergence divergence (MACD), and relative-strength index (RSI), that attempt to discern trends and patterns in the movements of security prices. However, these are typically used by short-term traders and may be of less interest to long-term investors since their effect tends to wear out quickly.