Calculating Returns for Overlapping Momentum Portfolios
Summary
The document explains how to calculate monthly strategy returns when a momentum strategy forms a new winner portfolio each month and holds each one for K months. Under the equal-subportfolio buy-and-hold method associated with Jegadeesh and Titman, the strategy has K active sub-portfolios in a given calendar month, each at a different stage of its holding period. The strategy's return for that month is the average of the returns earned by those K sub-portfolios during that same month.
This is distinct from multiplying a sequence of K-month holding-period returns as if they were successive calendar-month returns. The answer presents the averaging rule for the overlapping portfolio construction and notes that the method approximates real investing. It also mentions monthly rebalancing as another approach, without detailing its calculation or reporting a comparison. The guidance therefore applies to the described equal-weighted subportfolio setup; transaction costs and other implementation details are not addressed.
Key ideas
- Form a new momentum sub-portfolio each month and hold it for K months.\nEach calendar month's strategy return averages the contemporaneous returns of its K active sub-portfolios.\nThe equal-subportfolio buy-and-hold method is associated with Jegadeesh and Titman.\nThe described calculation is an approximation and does not cover implementation costs.
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# Momentum strategy cumulation of K-monthly returns over multiple months # Momentum strategy cumulation of K-monthly returns over multiple months In a momentum strategy, every month you form a portfolio of winners. Each of these portfolio you hold for K months. So after K months you sell the 1st portfolio, after K+1 months you sell the next and so on. This results in a K-monthly return, every month. How do you cumulate these returns over time? Imagine you keep every portfolio 12 months. After 1 year you start selling these portfolios every month, resulting in returns (1+r) of for example 1.07 , 1.065 , 1.067, ... What is the cumulative return? 1.07 x 1.065 x 1.067 x ... ? Or something else? Thank you in advance! ## Answer by Alex C (score 0, accepted) https://quant.stackexchange.com/a/34318 There are various ways to do this calculation. The "K equal sub-portfolios, buy and hold" method was used by Jegadeesh and Titman in their 1993 paper (they also mentioned another method, the "monthly rebalancing" method but did not show results from that method in the paper). The method is relatively simple, but only an approximation of real investing. At the end of each month you form a sub-portfolio and hold it for K months. This generates K numbers, which are the buy and hold portfolio returns for each of the next K months. Now consider how to determine the returns for the strategy for a specific calendar month, such as May 2017. During this month you hold K sub-portfolios: The newest is the sub-portfolio that was formed at the end of April 2017, then there is one a little older that was formed in March 2017, and so on, until you get to a sub-portfolio formed K months ago, which is about to be liquidated at the end of this month. Jegadeesh and Titman assume that you hold these sub-portfolios with equal weights, so they find they the return for the strategy for May 2017 by simply averaging the May 2017 returns for these K sub-portfolios.
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