In previous sections, the transaction costs that have been estimated using LOT Y-split model are those for the marginal investor. One deficiency of this approach is that not all investors face the same transaction costs and so the transaction costs that we report above do not apply across the whole investor spectrum. One way to address this issue is to calculate the break-
"DOWN" MARKETS NO. OF MONTHS DIFFERENCE JxH Weight Construction Raw return (W) Cost - W Net return (W) Raw return (W) Cost - W Net return (W) TSM - CSM AUSTRALIA 50 9x3 MW BHAR(0) 3.37% 0.78% 2.59% 1.13% 0.69% 0.44% 2.15% 2.5150 4.1022 1.9827 1.1899 4.3293 0.4577 2.5108
AUSTRIA 68 12x3 IVOL CAR(0) 0.41% 0.32% 0.09% 0.15% 0.27% -0.12% 0.22%
0.6717 12.4876 0.1510 0.5805 14.2588 -0.4812 0.4196
BELGIUM 61 6x12 IVOL BHAR(0) -0.43% 0.15% -0.59% -0.36% 0.14% -0.50% -0.08%
-0.8007 2.3010 -1.0770 -0.6442 2.2902 -0.8924 -0.4438 CANADA 22 9x3 MW CAR(0) 2.37% 0.85% 1.53% 0.60% 0.69% -0.09% 1.61% 1.4578 12.9951 0.9463 0.3028 14.4676 -0.0453 1.5816 DENMARK 55 9x3 MW CAR(1) 1.24% 0.53% 0.71% 1.15% 0.33% 0.82% -0.11% 0.9144 11.7788 0.5194 1.4578 12.1888 1.0385 -0.1213 FINLAND 71 6x12 MW BHAR(0) 0.67% 0.15% 0.52% 0.01% 0.12% -0.11% 0.63% 0.4317 2.3284 0.3304 0.0073 2.3189 -0.0787 0.9322
FRANCE 58 9x9 IVOL BHAR(0) 0.15% 0.32% -0.17% 0.01% 0.30% -0.28% 0.11%
0.3122 2.8964 -0.3313 0.0257 2.8860 -0.5752 0.6030 GERMANY 62 6x12 MW BHAR(0) -0.13% 0.36% -0.50% -0.04% 0.31% -0.35% -0.14% -0.1250 2.5905 -0.4657 -0.0464 2.5985 -0.3641 -0.4318 GREECE 98 3x12 MW BHAR(1) -0.17% 0.17% -0.34% -1.05% 0.10% -1.15% 0.81% -0.1572 2.6189 -0.3240 -1.1798 2.8519 -1.2981 1.0161 HONGKONG 48 9x9 MW BHAR(0) 3.08% 0.44% 2.64% 1.31% 0.37% 0.94% 1.70% 1.5799 2.6611 1.3447 0.7791 2.5878 0.5533 1.3866 IRELAND 40 6x12 MW BHAR(0) 0.28% 0.21% 0.07% 0.41% 0.18% 0.23% -0.16% 0.1298 1.5553 0.0329 0.2072 1.4947 0.1164 -0.3182 ISRAEL 53 9x3 MW BHAR(1) 4.32% 0.93% 3.39% 2.04% 0.41% 1.63% 1.76% 2.3229 3.9083 1.8123 2.0378 4.3058 1.6394 1.1123 ITALY 80 12x9 MW BHAR(0) -0.14% 0.12% -0.26% 0.11% 0.08% 0.03% -0.29% -0.1381 2.9310 -0.2572 0.1440 2.8017 0.0415 -0.3136 JAPAN 106 3x12 MW BHAR(0) 0.65% 0.15% 0.50% 0.57% 0.13% 0.43% 0.07% 0.8211 3.3274 0.6335 0.7589 3.3428 0.5857 0.2609
NETHERLANDS 50 9x6 IVOL BHAR(0) 2.33% 0.42% 1.86% -0.33% 0.32% -0.65% 2.51%
1.1956 3.0719 0.9779 -0.4228 3.1430 -0.8020 1.6083
NEWZEALAND 20 6x3 MW CAR(0) 2.23% 0.57% 1.66% -0.30% 0.37% -0.67% 2.33%
1.1571 15.8270 0.8635 -0.3314 17.2220 -0.7446 1.2881
NORWAY 56 9x6 MW BHAR(1) 1.11% 0.44% 0.68% 1.29% 0.33% 0.96% -0.29%
0.6674 3.1819 0.4149 1.0628 3.2972 0.8124 -0.2781
PORTUGAL 75 6x9 IVOL BHAR(1) 0.86% 0.24% 0.62% 0.41% 0.23% 0.19% 0.43%
0.8279 2.8947 0.5986 0.4592 2.6689 0.2086 0.5330
SINGAPORE 63 12x6 IVOL BHAR(1) 1.40% 0.47% 0.93% 0.20% 0.31% -0.12% 1.04%
0.9274 3.5173 0.6116 0.2201 3.5282 -0.1285 0.8910 SPAIN 85 12x6 MW BHAR(0) 0.99% 0.14% 0.64% 0.39% 0.15% 0.24% 0.40% 1.4869 3.1000 1.2052 0.5761 3.2287 0.3560 0.6237 SWEDEN 56 3x9 MW BHAR(1) -0.75% 0.29% -1.04% 0.19% 0.18% 0.01% -1.04% -0.5207 2.3535 -0.7181 0.1385 2.5353 0.0039 -1.4185 SWITZERLAND 57 12x3 MW BHAR(0) 1.17% 0.44% 0.66% 0.09% 0.28% -0.18% 0.84% 0.9326 4.2962 0.5514 0.1402 4.7557 -0.2744 0.8887 UK 38 12x6 IVOL BHAR(0) 0.51% 0.39% 0.11% 0.15% 0.31% -0.16% 0.27% 0.4221 2.8163 0.0945 0.1554 2.7733 -0.1555 0.7872 US 26 6x12 EW BHAR(0) 1.17% 0.13% 1.04% 1.39% 0.13% 1.25% -0.22% 0.4939 1.4374 0.4372 0.5967 1.4432 0.5378 -1.0861 OPTIMAL IMPLEMENTATION TSM CSM
146 even transaction costs for each implementation of the two momentum strategies. The break- even transaction cost is that rate which would reduce the return on the implementation to zero based on the “actual” turnover generated by the implementation (Yufeng, H., Ke, Y., & Guofu, Z., 2013), One particular advantage of this approach is that it allows every investors to compare their estimate of their own transaction costs with the break-even transaction cost in order to see whether they might expect to earn a profit from implementing the momentum strategy.
The “actual” turnover is based on the difference in weights between stocks in the portfolio at the end of one holding period and the weights in targeted portfolio at the beginning of the subsequent period. Knowing these two portfolios, the purchases and sale of stocks can be calculated and they equate with the actual transactions that would take place if the strategy was being implemented. Then, the break-even transaction cost is estimating by dividing the before-transaction cost return obtained from Chapter five by the aggregate of the actual turnover for both the winner and loser portfolios. The actual turnover and break-even transaction costs for each implementation are reported in the Table 7.7 – 7.9 in the Appendix.
Table 7.15 below compares the actual turnovers and break-even transaction costs of the time- series (TSM) and cross-sectional (CSM) momentum strategies for what we refer to as the optimal implementations (see table 5.11). One important observation to be taken from Table 7.15 is that the level of turnover generated by time-series momentum is about 10% higher than what it is for cross-sectional momentum. Indeed, time-series momentum proves to have the higher turnover in 22 of the 24 with the exceptions being in Finland and Ireland. Despite typically having the higher turnover, time-series momentum has the higher break-even transaction costs in 19 of the 24 markets. However, the higher turnover ratio has little impact on the superior performance of the time-series momentum strategy in terms of the break-even
147 transaction costs. The last column in the table reports the difference in break-even transaction costs between the time-series and cross-sectional momentum strategies. In the case of time- series momentum strategies it can be seen that the break-even costs are higher than cross- sectional momentum strategies in 19 markets with the exceptions being Belgium, Denmark, Germany, Switzerland and the UK. This is consistent with our previous finings that time- series momentum remains the better performing strategy after incorporating transactions costs even through the extent of its superiority is eroded by their introduction
Table 7.15. Break-even transaction costs for optimal time-series and cross-sectional strategies
The optimal implementations are based on before-transaction costs returns in table 5.11. The column (W-L) shows the raw returns, T/O represents the actual turnover ratio for the winner and loser portfolios. The column (Breakeven) shows the Break-even transaction costs, where the costs is calculated by the raw return over the sum of actual turnover ratios on the winner and loser portfolios. The last column shows the difference in break- even costs between the time-series and cross-sectional momentum strategies under optimal implementation for each market.
Country Breakeven Difference
JxH Weight Construction W - L T/O (L) (T/O) W Breakeven W - L T/O (L) (T/O) W Breakeven TSM - CSM AUSTRALIA 9x3 MW BHAR(0) 2.76% 47.21% 39.33% 3.19% 1.86% 43.28% 39.03% 2.26% 0.93% AUSTRIA 12x3 IVOL CAR(0) 1.57% 40.46% 40.11% 1.95% 1.40% 38.30% 37.46% 1.84% 0.11% BELGIUM 12x3 IVOL CAR(1) 1.79% 37.87% 36.88% 2.39% 1.63% 30.68% 29.25% 2.72% -0.32% CANADA 9x3 MW BHAR(0) 3.13% 47.24% 39.50% 3.61% 2.06% 42.37% 35.80% 2.63% 0.98% DENMARK 9x3 IVOL BHAR(1) 2.00% 41.51% 37.32% 2.54% 1.74% 30.86% 30.47% 2.83% -0.30% FINLAND 12x6 MW BHAR(0) 2.85% 21.15% 19.62% 6.98% 1.72% 23.32% 21.89% 3.80% 3.19% FRANCE 9x3 IVOL CAR(1) 1.43% 42.13% 43.29% 1.68% 1.11% 38.66% 38.25% 1.44% 0.24% GERMANY 12x3 IVOL CAR(0) 1.85% 38.09% 36.91% 2.46% 1.62% 32.30% 30.73% 2.57% -0.11% GREECE 3x12 MW BHAR(1) 1.71% 43.48% 44.04% 1.96% 1.38% 36.50% 35.53% 1.91% 0.04% HONGKONG 6x3 MW BHAR(0) 2.21% 53.67% 50.01% 2.13% 1.34% 49.53% 44.77% 1.42% 0.71% IRELAND 6x12 MW BHAR(0) 3.52% 27.94% 27.40% 6.36% 2.36% 30.23% 29.09% 3.98% 2.38% ISRAEL 9x12 MW BHAR(0) 2.02% 46.92% 42.31% 2.26% 1.66% 44.68% 37.12% 2.03% 0.23% ITALY 12x6 MW BHAR(0) 2.26% 40.25% 37.45% 2.91% 1.38% 27.91% 27.34% 2.49% 0.42% JAPAN 3x12 MW BHAR(0) 1.09% 15.37% 14.81% 3.60% 0.24% 14.23% 14.45% 0.85% 2.75% NETHERLANDS 9x3 EW BHAR(1) 2.40% 41.31% 43.41% 2.83% 1.58% 31.20% 31.63% 2.52% 0.31% NEWZEALAND 12x3 IVOL BHAR(0) 2.82% 44.88% 44.08% 3.17% 1.73% 41.11% 40.65% 2.12% 1.05% NORWAY 9x3 IVOL BHAR(0) 2.07% 43.31% 41.96% 2.43% 1.57% 35.94% 35.03% 2.21% 0.22% PORTUGAL 6x6 MW BHAR(1) 2.08% 28.45% 30.05% 3.56% 0.89% 29.04% 28.27% 1.55% 2.00% SINGAPORE 9x3 IVOL BHAR(0) 1.64% 43.75% 44.07% 1.87% 0.87% 35.96% 34.73% 1.23% 0.64% SPAIN 12x6 EW BHAR(0) 1.29% 20.99% 22.04% 3.01% 1.00% 18.84% 19.39% 2.61% 0.40% SWEDEN 12x3 IVOL BHAR(1) 2.81% 38.27% 37.01% 3.73% 1.37% 31.00% 29.99% 2.25% 1.48% SWITZERLAND 12x3 EW CAR(0) 1.75% 37.84% 36.37% 2.36% 1.32% 26.10% 26.07% 2.52% -0.16% UK 12x3 IVOL CAR(0) 2.15% 36.45% 36.34% 2.95% 1.85% 32.27% 30.22% 2.96% -0.01% US 9x3 MW CAR(1) 0.87% 48.07% 40.22% 0.99% 0.64% 42.72% 36.23% 0.82% 0.17%
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7.9.
Conclusion
Previous chapters have found that both momentum strategies produce positive returns for the 24 markets but that the time-series momentum strategy produces the best investment outcomes largely driven by its better performance during period when markets are performing poorly. In order to investigate whether the apparent profitability of these strategies is exploitable by investors, we have repeated much of the previous analysis but this time is on an after-transaction costs basis.
From a practical perspective, some studies question the viability of momentum strategies for two reasons. One is that momentum strategies may not be profitable after transaction costs are considered (Lesmond et al., 2004). The other is that momentum strategies may not be profitable if short sales are prohibited (Alexander, 2000). This chapter examines both momentum strategies after addressing these concerns. Compared with the study in Lesmond et al. (2004), this study investigates a large number of implementation approaches that have been employed in the majority of momentum literature for each market and applies the more precise transaction cost measurement model used by Goyenko et al. (2009).
We find that based on our 192 implementations, both of the time-series and cross-sectional momentum strategies can still be profitable but this is conditioned on means for implementation used. The findings suggest that in most markets the aggregate of the formation period and holding period in the two momentum strategies should be extended to between 15 and 18 months (as compared with the previous 12 and 15 months) as a result of taking into account transaction costs. We also find in most markets that buy-and-hold portfolio construction along with market weighting is consistent with achieving superior investment outcomes.
149 We find that optimal implementation of the time-series momentum strategy yields average profits 1.34% per month over the 24 markets and it is significant in 19 markets. The cross- sectional momentum strategy is also found to be profitable in all but the Hong Kong (0.12% loss per month) and yields an average return of 0.87% per month. The transaction costs from the time-series momentum strategy are higher than the costs from the cross-sectional momentum strategy which is largely a consequence of time-series momentum strategy selecting smaller and growth stocks, and generating a higher turnover over a market cycle.
Comparing the differences between the performance of the two momentum strategies before and after the transaction costs, we find that the time-series momentum strategy continues to outperform cross-sectional momentum strategy in 21 of the 24 markets. However, the outperformance is only now significant in seven markets (Canada, Ireland, Japan, the Netherlands and Sweden at 5% level and Finland and New Zealand at 10% level) compared to 13 markets previously. The consistent results that the eroded outperformance in the time- series momentum strategy has been found based on the long-only portfolio of the winning stocks, which in the case when short-sale is restricted.
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