Calculating Returns for Overlapping Momentum Portfolios
Summary
The document asks how to calculate monthly returns for a Jegadeesh and Titman style momentum strategy with overlapping portfolios. Each month, a new tranche is formed and held alongside earlier tranches that have not yet reached the end of their holding periods. The example considers a three month formation period and a three month holding period, and contrasts averaging the constituent tranches’ returns each month with recording returns when individual tranches are liquidated.
The answer describes the monthly strategy return as the average of the monthly returns of all active tranches for that month. It clarifies that each tranche’s contribution is its return over the current month, even though the tranche began earlier and remains invested across multiple months. This supports a time series of monthly portfolio returns rather than combining a liquidation observation with a separate composite portfolio observation. The response calls the convention simple while noting that other calculation methods may be used; it does not provide implementation details or fully specify portfolio weighting and rebalancing assumptions.
Key ideas
- An overlapping strategy has several active investment tranches in each month.
- Calculate each active tranche’s return for the current month.
- The strategy’s monthly return is the average of the active tranches’ monthly returns.
- Do not treat a tranche’s full holding-period return as an extra monthly observation alongside the composite return.
- Other return calculation conventions may be possible, depending on the intended methodology.
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# Calculate Returns of Momentum Strategy (Overlapping Portfolios - Jegadeesh and Titman 1993) # Calculate Returns of Momentum Strategy (Overlapping Portfolios - Jegadeesh and Titman 1993) I want to implement a Momentum Strategy, followed by Jegadeesh and Titman (1993) with overlapping Portfolios. I want to duplicate their results. Quick Link to the paper (Unfortunately the Method is poorly described): http://www.business.unr.edu/faculty/liuc/files/BADM742/Jegadeesh_Titman_1993.pdf First of all: I work with discrete monthly Returns. But I don't know which returns I have to calculate to implement my Momentum Strategy properly. Let's consider Formationperiod J=3 and Holdingperiod K=3 In this case I have a composite Portfolio consisting of the Portfolio initiated in JAN (Tranche 1), a Portfolio initiated in FEB (Tranche 2, hold for 2 Periods) and the portfolio initiated in MAR (Tranche 3, hold for 1 Period). What Returns do I have to calculate now to duplicate the Method of Jegadeesh and Titman (1993)? My attempt would be: In March, I calculate the Return of Tranche 1. This Portfolio was acutally held for 3 Months and so we liquidate it and measure it's Return with the Geometric Mean (Because I have discrete Returns). This is the first observation of my Strategy. But I can also calculate the Return of the composite Portfolio (vertical aggregation) for the month March. I calculate the Return of the composite Portfolio (Consisting 3 Sub-Portfolios) in March and divide it by 3 (Arimethic Mean) so that I have the average Returns of all 3 Sub-Portfolios for the Month March in my Composite Portfolio. This results in having for March 2 Observations, the Return of my liquidated Sub-Portfolio and the Return of my Composite Portfolio for the Month. In April I have the monthly Return of Tranche 2 and the composite Portfolio (Consisting Tranche2, 3 and the new Tranche 1). For every Month I sum up these two observations and take the Mean. This continues every Month. At the end I sum every Return of each Month up and take the mean of that to have the Monthly Returns of my actual Strategy. Is this the proper way to calculate the Returns of a Momentum Strategy? Or do I just calculate composite Portfolio Returns? I would really appreciate your help! With kind regards! ## Answer by nbbo2 (score 1) https://quant.stackexchange.com/a/36096 In Jegadeesh and Titman, and the papers that follow it, the monthly return to the strategy for the month of March is found by averaging the monthly return for Tranche 1 in March, the avg return for Tranche 2 in March and the monthly return for Tranche 3 in March. As shown in the diagram Tranche 1 consists of those stocks bought at the end of December and held in Jan, Feb, Mar and so on for the other tranches. This method is simple, though perhaps not completely realistic or not to everybody's taste (other methods of calculation are also possible).
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.