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At first, Lo and MacKinlay (When are Contrarian Profits Due to Stock Market Overreaction?, 1990) didn't do it for momentum precisely. However,Kyung-In Park and Dongcheol Kim (Sources of Momentum Profits in International Stock Markets, 2011) use it to identify and analyse the difference in the momentum effect across different countries. Here is the exact part that I would like to understand:

The purpose of this paper is to examine the differences in the underlying forces determining momentum profits between countries exhibiting and non-exhibiting the momentum phenomenon and to induce which component(s) drives momentum profits. In order to determine the underlying forces of momentum profits, we use the decomposition method of momentum profits by Lo and MacKinlay (1990). They decompose momentum profits into three components; (1) the first-order serial covariance of market returns, (2) the average of first-order serial covariances of all individual assets, and (3) the cross-sectional dispersion in unconditional mean returns of individual assets. The total momentum profit equals minus (1) plus (2) plus (3) [i.e., 􏰀􏰁1􏰂 􏰃 􏰁2􏰂 􏰃 􏰁3􏰂􏰄. That is, the first term contributes negatively, and the second and third terms contribute positively to momentum profits. The first two components reflect the intertemporal behavior [􏰀􏰁1􏰂 􏰃 􏰁2􏰂], and the third component reflects the cross- sectional behavior of asset returns [􏰃􏰁3􏰂].

As you can see, Kim and Park have subsumed the 3 parts into 2 parts: the inter temporal behavior and the cross-sectional behaviour of asset returns.

More precisely, in the conclusion of the article we can find:

Momentum profits can be decomposed into two parts; the part reflecting the cross-sectional difference in unconditional expected returns and the part reflecting the intertemporal behavior of asset returns.

So my question can rewritten like this: what is exactly the part reflecting the cross-sectional difference in unconditional expected returns and the part reflecting the intertemporal behavior of asset returns ?

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  • $\begingroup$ the formulas copied incorrectly $\endgroup$ – pyCthon Jul 2 '15 at 22:30
  • $\begingroup$ I don't understand your comment, can you be more specific please? Just to make sure, I didn't copy anything, it is a copy paste from the article. $\endgroup$ – Pierre Jul 3 '15 at 15:19
  • $\begingroup$ I can't read the formulas $\endgroup$ – Alex C Jul 3 '15 at 20:39
  • $\begingroup$ This is because there is formula, just words. $\endgroup$ – Pierre Jul 7 '15 at 11:35
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As a simple example: if stock A went up a lot in 2014 and also went up a lot in 2015 it could be: (a) that Stock A is a high Beta stock and the market was up in both years. This is the cross sectional property of expected returns. Some stocks, in this case high beta stocks go up more than others when the market goes up. (b) Somehow the fact that Stock A went up the first year caused it to go up the next year. This is the intertemporal behavior of asset returns. In this case there is a true momentum effect and stocks that increase one year are likely to go up the next.

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