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The January effect is an argument against weak-form efficiency (that prices quickly reflect market data), but certainly is not an argument against strong-form efficiency (that markets quickly reflect all data, public and private).  The January effect has nothing to do with insider information.

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I disagree. Dogs and Cheshire cats are not in a subset-superset relationship like strong form and weak form.
There would be no January effect if a strong form, semi-strong form or weak form efficiency held.
In other words, if “–” denotes “implies”
strong form – weak form – technical analysis useless – no January effect.
Reverse this chain (if not A implies not B then B implies A)
Januarry effect – technical analysis works – no weak form – no strong form.

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