Both are concepts based on widely accepted (and researched) market beliefs:

1) Stocks that are currently being bid up by traders tend to do well in the near future. This is momentum, and can be thought of in the same way as we do everyday objects; an object in motion tends to stay in motion.

2) Stocks that are sold off by the market will probably be sold off more than they “deserve”, and hence can be bought on the cheap. Which is of course the basis of the entire Graham-Dodd (+ Buffett) school of thought. Note that “deserve” here refers to  a very subjective individual determination of the asset’s intrinsic value. 

For better or worse, the explanation above is about as precise as it gets. The reason for this is everyone has a different way of deciding what constitutes value, and what momentum looks like. What one classifies as “value” may be considered as still too expensive by another; and what one thinks is a stock with strong momentum might be spurned by someone else.

A trader might choose to define a value stock as one trading with a P/E ratio of less than it’s industry average; while defining a momentum stock as one trading at “overbought” or “oversold” levels on a technical indicator like the Relative Strength Index (RSI).

Of course, these simple examples are only the starting point, and traders more often than not include a number of other metrics or indicators in their analysis, which illustrates the broader reality that a stock’s return is affected by numerous variables. Traders (or investors) who study what these variables are, and their relationship with a stock’s price, are colloquially known as “quants”.

“Quant” being, of course, an abbreviation of “quantitative analyst”, which is an individual who analyzes financial products through a mathematical lens. With regards to stocks, this involves the construction of a multivariate regression, which is a fancy name for a model that reduces a stock’s return into a set of variables, more commonly referred to as “factors”. For example:

Return = X(Value Factor) + Y(Momentum Factor) + Z(Volatility Factor) + Alpha

X, Y, and Z are coefficients that measure how sensitive an asset’s price is to that particular factor, and Alpha a measurement of how much (on average) returns cannot be attributed to exposure to this set of factors.

Quant regressions work well for as long as its set of factors drive prices, but inevitably come to a point where they are no longer useful because factor relationships change with the market.

Value and momentum, as factors, are no different; a stock that is “value” today can become “momentum” very quickly, and vice versa. This is because a value stock that everyone thinks is trading cheaply is quickly bought up by value investors. When this buying gets to a point which catches the mainstream’s attention, more and more people will pile into the trade, making it a momentum play. Likewise, a momentum stock that has had its time in the limelight will get sold off, often to the point where some investors will deem it to be a value stock and start buying it.

Rather than thinking of value and momentum as diametrically opposite concepts with a clear dividing line, perhaps it might be more helpful to think of them as two sides of the same emotional coin?