In a multiperiod pure exchange world with investors displaying HARA-preferences, conditions for period-by-period application of one-period asset pricing models are derived first. The future investment opportunity set may be uncertain, provided that in every period a specific market portfolio variable depending on preferences is known as of the preceding date. This variable need not be completely deterministic.
Second, conditions for a serially independent market excess return are derived. These conditions render serial independence very unlikely. Hence estimation methods assuming serial independence are likely to yield biased results.