# Momentum Study Essay

Here, we specifically use a strategy that selects stocks on the basis of returns over the past M months (i.e. formation period) and holds them for N months (holding period). This is called as the M x N strategy. At the beginning of each month t, the candidate stocks are ranked in descending order on the basis of their returns in the past M months. The top decile portfolio is called the “winners” portfolio and the bottom decile is called the “losers” portfolio. This strategy involves, simultaneously buying the winner portfolio and selling the loser portfolio and then holding this position for N months (total number of months).

The strategies we have considered in our project involve selecting stocks based on their

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CR1= ln(P1/P0) + ln(P2/P1) + ln(P3/P2) + ln(P4/P3) + LN(P5/P4) + ln(P6/P5)

Where, P0, P1, P2, P3, P4, P5, P6 are adjusted monthly closing prices for January, February, March, April, May ,June and July respectively. The stocks are arranged in descending order. Based on these rankings, ten decile portfolios are formed. Each decile portfolio consists of stocks weighed equally in that decile. Top decile portfolio forms winner portfolio and bottom decile portfolio forms loser portfolio.

It is to be noted that a portfolio is constructed by going long on the winner portfolio and short on the loser portfolio. This is done on a monthly basis and the step is repeated 86 times for the period starting August 2003 and ending on August, 2011 as mentioned above.

Holding Period

After the winner and loser portfolios are identified in a given month for a given formation period, the following calculations are to be done for the holding period.

Step 1: Calculating month-on-month stock returns for all stocks selected in winner and loser portfolio

The first step involves calculating month-on-month returns for all candidate stocks in the winner and loser portfolio for