- For TS strategies, all earn positive excess returns that tend to increase with the length of the ranking period. However, not all CS strategies have positive excess returns, with returns generally being negative for sorts with both shorter ranking and holding periods and for both longer ranking and holding periods.
- The differences in returns between TS and CS strategies exhibit a U-shaped pattern, with the largest differences at the long and short ends, where TS strategies tend to outperform CS strategies.
- As an example, a CS strategy with a one-month ranking period and one-month holding period (1 x 1) earned -5.09%, which is consistent with the evidence of short-term reversal patterns shown in prior research on CS momentum. In comparison, a 1 x 1 TS strategy earned 4.03%.
- The 60 x 60 CS strategy earned -2.00%, which is also consistent with long-horizon return reversals shown in prior research on CS momentum, while a 60 x 60 TS strategy earned 7.71%.
- Both CS and TS 6 x 6 strategies earn significantly positive excess returns—the TS strategy earned 5.79%, and the CS strategy earned 3.90%.

Goyal and Jegadeesh attribute these differences in returns between TS and CS strategies in U.S. stocks to both market timing and time-varying net long holdings of TS strategies. The authors attribute market timing as being responsible for differences in returns for short ranking and holding periods, and time-varying net long investments in risky assets of TS strategies being responsible for differences in returns for longer ranking and holding periods.

**Adjusting For Time-Varying Net Long Exposure **

Given that TS strategies are not zero-dollar investment strategies like CS strategies and will be either net long or short at any given time, to make these strategies directly comparable, the authors add to CS strategies a time-varying investment in the equity market.

This investment is equal to the dollar value of the difference between the long and short sides of the TS strategy each month (we’ll call this the “time-varying market” or “TVM-CS strategy”). If the performances of TS strategies and TVM-CS strategies are similar, it would be a stretch to view TS momentum as a distinct source of return.

The authors find that both TS and TVM-CS strategies perform similarly within U.S. individual stocks for the horizons over which momentum strategies have been shown to be profitable. Following are highlights from their findings:

- The return differences between TS and TVM-CS strategies are small and mostly statistically insignificant.
- For ranking periods of 1 x 1 and 60 x 60, the differences in returns between TS and TVM-CS strategies are 1.18% and 0.51%, respectively.
- For strategies when ranking period equals holding period—3 x 3, 6 x 6 and 12 x 12—the alphas for the differences in returns between TS and TVM-CS strategies, using the Fama-French three-factor model, are statistically insignificant, or not different from zero.

The authors suggest that when momentum works, TS strategies pick winners and losers among individual stocks in the same manner that CS strategies do.

This is because returns are similar for TS and TVM-CS strategies over horizons where CS momentum has been shown to provide positive returns—thus, the seemingly superior performance of TS strategies over CS strategies that Moskowitz, Ooi and Pedersen claim is due entirely to TS strategies’ time-varying net long positions in the market.

Given this, and contrary to Moskowitz, Ooi and Pedersen’s claims, the authors suggest that TS momentum is not a distinct source of return and that TS strategies do not subsume CS strategies in individual stocks.

**Adjusting For Scale Differences **

Goyal and Jegadeesh also look at TS and CS strategies across international asset classes. Specifically, the authors look at 55 different futures markets across four broad asset classes of equities, bonds, commodities and currencies over the period 1985 through 2013.

The authors first compare TS and CS strategies across international asset classes that are scaled similarly, as before, for U.S. stocks to have total positions, both long and short, equal to two dollars. They find that excess returns for both strategies are similar and positive for all periods, and the differences between excess returns of TS and CS strategies are not statistically different than zero. This is consistent with the authors’ assertion that TS and CS momentum are not distinct sources of return.