9. Empirical Results
9.3 Results for Momentum Strategies Adjusted for Transaction Costs
reliance on single assets and lack of diversification is considered an unattractive characteristic in any investment strategy.
Besides from the substantial increase in volatility, the market-‐capitalization weighting scheme also adds what some might see as unnecessary transaction costs. The entire point of adding additional stocks to a portfolio is basically lost, if they don’t have any noteworthy influence on the portfolio’s expected return and risk. For all the strategies in this section, there are several months in which the portfolio composition is such that 5 or more stocks only have a
portfolio weight of 1% or less; one example of this is the 12/9-‐strategy, where 35% of the monthly portfolios bought have 5 or more stocks with a weight of 1% or less. Consequently, buying stocks with insignificant weights, and thereby, insignificant impact on the portfolio itself, will only introduce a somewhat unnecessary transaction cost to the investor. Furthermore, these
transaction costs are an even bigger issue for smaller investors, because many brokers require a minimum transaction fee for smaller investments. Thus, applying these strategies on a small scale will make the transaction costs relatively more expensive compared to larger investments, and make the strategies less profitable in the end.
Given these considerations about the market-‐capitalization weighting scheme, we believe that applying an equal weighting scheme to the momentum strategies is the better alternative, since this eliminates the issues presented above. Therefore, the rest of this analysis will focus on the strategies employing equal weights to the assets traded each month.
Furthermore, using equally weighted portfolios for the rest of the analysis also makes our findings easier to compare to previous studies that predominantly employed an equal weighting scheme.
adjusts the results from the winner and zero-‐cost strategies employing equal portfolio weights in section 9.1, and investigates whether these strategies still produce significant returns.
Table 9.5: Returns on winner, loser and zero-‐cost portfolios (adjusted for transaction costs)
The table shows the average monthly return for the winner portfolios for all of the 16 distinct momentum strategies adjusted for transaction costs, while the numbers in parentheses are the standard deviations. The table also includes indicators from 3 different tests all testing whether the average monthly return on the winner portfolios are
significantly larger than the average monthly return on the benchmark for the same time periods. Test 1 (T1):
Student’s t-‐test, Test 2 (T2): Welch’s t-‐test, Test 3 (T3): Adjusted Welch’s t-‐test.
* Significant at the 0.10 significance level.
** Significant at the 0.05 significance level.
*** Significant at the 0.01 significance level.
The strategies and their returns in this section have all been adjusted to include the transaction costs induced in both the start and the end of each holding period, as outlined in the methodology section. The strategy returns are then compared to a ‘buy and hold’ strategy on the benchmark, just like in the previous sections, to see if the average monthly return is significantly bigger than that of the benchmark. It should be noted however, that the returns on the
benchmark are not adjusted for transaction cost, simply because these are assumed to be insignificant, given that the transaction costs for a buy and hold strategy would only occur twice,
3 6 9 12
3 Winner 1,21% *** 1,20% *** 1,25% *** 1,35% ***
(0,061) (0,056) (0,058) (0,054)
Zero-‐C 0,92% ** 0,96% *** 1,06% *** 1,08% ***
(0,061) (0,05) (0,043) (0,039)
6 Winner 1,42% *** 1,58% *** 1,58% *** 1,51% ***
(0,06) (0,061) (0,058) (0,057)
Zero-‐C 1,12% ** 1,35% *** 1,37% *** 1,20% ***
(0,071) (0,067) (0,059) (0,052)
9 Winner 1,69% *** 1,71% *** 1,68% *** 1,75% ***
(0,056) (0,057) (0,057) (0,057)
Zero-‐C 1,51% *** 1,54% *** 1,47% *** 1,24% ***
(0,077) (0,071) (0,066) (0,061)
12 Winner 1,81% *** 1,74% *** 1,89% *** 1,77% ***
(0,06) (0,059) (0,059) (0,058)
Zero-‐C 1,47% *** 1,42% *** 1,37% *** 1,20% ***
(0,078) (0,073) (0,07) (0,066)
Holding (K)
Formation (J)
once when the index portfolio is bought and then again when it is sold at the end of the analysis period. While this lack of adjustment is not in line with reality, it should not decrease the validity of the results in any significant way since only 2 out of 170+ observations are affected slightly.
As expected the introduction of transaction costs decrease the average monthly return on the momentum strategies substantially, as evident in 9.5. On average, the monthly return for all the winner strategies is 1.57%, which is a decrease compared to the 1.66% in section 9.1, while the standard deviation doesn’t change much. The change in return is most significant in the strategies with a shorter holding period, which is at least partly explained by the increasing number of transactions that follow from using a strategy with shorter holding periods. But while the average monthly return decreases, the winner and zero-‐cost portfolios still manage to produce significantly positive results.
Furthermore, unlike in section 9.1, not all winner strategies significantly outperform the benchmark when transaction costs are accounted for, as evident in table 9.6. Three strategies with a 3-‐month formation period fail to significantly outperform the benchmark. The relatively less impressive outcomes are also reflected in the results from the student’s-‐ and Welch’s t-‐tests when comparing with table 9.2. However, the adjusted Welch’s t-‐test, shows that all winner strategies with a formation period of 6 months or longer produces an average monthly return that is significantly larger than the benchmark. Lastly, because of the transaction costs, the best performing strategy is no longer the 12/3, but the 12/9-‐strategy.
So far we have seen that a large part of the winner strategies proved to be profitable and outperformed the benchmark even after accounting for transaction costs, but the same cannot be said about the zero-‐cost strategies in table 9.6. None of the 16 distinct zero-‐cost
strategies significantly outperform the benchmark. Especially the zero-‐cost strategies with a short formation period perform poorly when compared to a simple ‘buy and hold’ strategy holding the benchmark. On average, the monthly return of the 16 zero-‐cost strategies is 1.27% compared to 1.45% in section 9.1, while the average standard deviation stays close to the same. The 9/3-‐
strategy is once again among the best performing zero-‐cost strategies, like in section 9.1, with an average monthly return of 1.51%, just about 0.4 %-‐point less than the best strategies based solely on winner portfolios. Since the zero-‐cost strategies do not significantly outperform a simple ‘buy
and hold’ strategy, it makes them somewhat less desirable, given that an investor could get an average monthly return close to the zero-‐cost portfolios, but with much less transaction costs, both time-‐ and moneywise. Nonetheless, the zero-‐cost strategies still pose as an interesting investment strategy. Although they fail to significantly outperform the benchmark, they still produce significant positive returns, while only requiring relatively little initial financing.
Table 9.6: Excess return on winner and zero-‐cost portfolios (adjusted for transaction costs)
The table shows the average monthly excess return for the winner and zero-‐cost portfolios for all of the 16 distinct momentum strategies, while the numbers in parentheses are the standard deviations. Furthermore, the table includes indicators from 3 different tests, all testing whether the average monthly return on the portfolios are significantly larger than the average monthly return on the benchmark. Test 1 (T1): Student’s t-‐test, Test 2 (T2): Welch’s t-‐test, Test 3 (T3): Adjusted Welch’s t-‐test.
* Significant at the 0.10 significance level.
** Significant at the 0.05 significance level.
*** Significant at the 0.01 significance level.
3 (T1) (T2) (T3) 6 (T1) (T2) (T3) 9 (T1) (T2) (T3) 12 (T1) (T2) (T3)
3 Winner 0,35% 0,34% 0,31% 0,39% *
(0,061) (0,056) (0,058) (0,054)
Zero-‐C 0,06% 0,10% 0,11% 0,11%
(0,061) (0,05) (0,043) (0,039)
6 Winner 0,62% * ** 0,67% * ** 0,60% * ** 0,56% * **
(0,06) (0,061) (0,058) (0,057)
Zero-‐C 0,32% 0,43% 0,39% 0,25%
(0,071) (0,067) (0,059) (0,052)
9 Winner 0,83% ** * *** 0,76% ** * *** 0,70% * *** 0,66% * **
(0,056) (0,057) (0,057) (0,057)
Zero-‐C 0,66% 0,59% 0,49% 0,16%
(0,077) (0,071) (0,066) (0,061)
12 Winner 0,93% ** * *** 0,80% ** * *** 0,78% ** * *** 0,70% * **
(0,06) (0,059) (0,059) (0,058)
Zero-‐C 0,59% 0,47% 0,26% 0,14%
(0,078) (0,073) (0,07) (0,066)
Holding (K)
Formation (J)