Figure 4 demonstrates that the strategy of buying winners only still
outperforms the relevant benchmark, proving the contention made earlier that
the pattern of momentum profits is split evenly between winning and loosing
stocks. In Figure 4 the momentum a portfolio of buying winners exhibits
exactly the same pattern of profits as the full momentum strategy reported in
Figures 1 - 3.
Given the apparent relationship between size cohorts and momentum evident
in Figures 1 - 4, the returns to a momentum strategy based on size sorted
portfolios were computed. The following procedure was used to construct size
portfolios.
1. In each month the capital rank of the stock based on the last recorded
price is assigned. It is also a requirement that the stock have a valid
return in the previous month (so that prices at time t and t-1 both
exist). Table 2 reports the average number of stocks within size cohorts
that pass this criterion in each time period.
2. Nine (9) portfolios were constructed from the ranked stocks spanning
ranks from 1 - 900 in increments of 100.
3. The momentum strategy is implemented as described previously using
the returns on the size portfolios. The strategy involves short selling
the three worst performing portfolios of the previous six months and
buying the three best performing portfolios.
It is important to emphasize that step 1 in the selection strategy is based on
the trades observed in the month leading to portfolio formation and hence
involves no sample selection. An easy trap to fall into is to form portfolios to
only include stocks with observed current period returns (between t and t+1).
The problem with the latter criterion is that it uses information not available
at the time of portfolio formation and would potentially introduce sample
selection bias into measured average returns. However, it also important to
point out that the filter in step 1 also implies that implementing the portfolio
returns reported on the figure 5 requires portfolio rebalancing in latter periods
t+1, t+2, etc. (unlike the reported momentum strategies that freeze the
portfolio at time t). For example to form a portfolio in period t+1 (for the
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