Calculating Returns for Momentum Strategies with Overlapping Cohorts

Summary

The document describes a stock momentum strategy that buys the strongest recent performer and shorts the weakest, while using overlapping holding periods. Each month, one cohort is replaced, so the portfolio contains positions initiated at different dates. Its example uses a six-month ranking period and three overlapping cohorts, with the oldest position liquidated as a new one is opened.

The author asks how to combine the cohorts’ monthly returns, whether to average or compound them, how to annualize the result, and what annual cohort rebalancing means mathematically. The document poses these implementation questions but supplies no answer, formula, or performance evidence. Any calculation therefore needs to define cohort weights, return timing, portfolio rebalancing, and the treatment of compounding before an annualized figure can be interpreted. The strategy description is useful for framing those choices, but it does not provide enough detail to reproduce or evaluate results.

Key ideas

• The strategy takes long positions in recent winners and short positions in recent losers.
• Overlapping holding periods create multiple investment cohorts that begin at different dates.
• A cohort is replaced as its holding period ends, while other cohorts remain invested.
• The document raises questions about cohort aggregation, compounding, annualization, and annual rebalancing but does not resolve them.

Tags

# How to calculate monthly Return from a Momentum Strategy with overlapping Holdingperiods?


# How to calculate monthly Return from a Momentum Strategy with overlapping Holdingperiods?












I replicate a Momentum Strategy from Rey and Schmid (2007) "Feasible momentum strategies" based on the idea from Jegadeesh and Titman (1993). I only buy the single stock with the highest past return while, by the same time, the stock with the lowest return is sold short. The momentum strategies include portfolios with overlapping holding periods. Each month, thus, 1/K of the holdings is revised. For example, in month t, the J = 6 / K = 3 portfolio of winner stocks consists of three investment cohorts: a position carried over from an investment at the end of month t − 3 in the stock with the highest average return over the respective past 6 months and two positions resulting from investments in the topperforming stocks at the end of months t − 2 and t − 1, respectively. At the end of month t , the first of these investment cohorts is liquidated and replaced with a new investment in the stock with the highest 6-month average return as of time t .The K different investment cohort are rebalanced annualy.

How do i calculate the monthly returns correctly? Am I allowed to just sum the discrete Returns vertically and divide them by 3? Or do I have to take compounding returns? How can i annualize these returns? What does the annually rebalancing means in a mathematical way?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.