You want to construct an optimal portfolio.
Let's say you have an alpha signal that arrives with some period (say quarterly). The alpha signal predicts arithmetic returns one-year ahead. You have risk estimates that are updated daily.
The optimizer your utility function is maximizing is expected returns from the quarterly alpha signal (associated with a confidence level), minimizing risk from the daily risk model, and minimizing transaction costs. On Day 1 determining the optimal single-period strategy weights is easy -- just turn the crank on the optimizer.
However, let's say a week passes and you have an opportunity to re-balance. Security prices have changed partly reflecting noise and partly new information. Your alpha forecasts are increasingly stale until the next quarterly alpha signal.
Question - what is the optimal optimal re-balancing procdedure?
There are a couple approaches and it is not obvious which is best - a Bayesian update of alpha signal, shrinkage towards a prior as the alpha signal is increasingly stale, or some other rule-of-thumb re-balancing rule. (Some form of simplification is necessary here since truly the optimal re-balancing would be a multi-period dynamic programming problem that is not practically solvable.)
Here are some approaches:
Do nothing - ignore re-balancing opportunities. Cons: Security may have achieve the effective price targets or portfolio may have deviated from optimality (i.e. marginal returns per unit of risk is no longer balanced).
Naive case - At the next re-balancing period, optimize with the the beginning of period alpha forecasts and the new risk estimates. Drawback is that we have less confidence in the alpha forecast as time passes. Imagine a security that has impounded severe negative news -- your optimizer would load up on this security if you used your beginning-of-period alpha signal. This approach treats all price changes as non-informative.
Ratchet down the confidence of the alpha signal at each re-balancing period (until the next quarterly refresh) and allow the optimizer to shrink towards a prior such as the minimum variance portfolio.
Low the confidence in the alpha signal AND re-calibrate the alpha signal to account for security price changes. For example, if the original alpha forecast for a security is 8% annualized and the position is +10% already then your re-calibrated forecast would be -2% (short). Con: Alpha signals are never so precise. They are most effective at ranking opportunities and this approach might lead to scenarios where you are shorting your strongest candidates on an alpha signal sorted basis.
Somehow treat the price changes as informative and use Bayesian updating to adjust your alpha forecast after observing actual performance. Con: Lots of hand-waving here.
Do not use the optimizer in subsequent re-balancing -- just use your risk model. Specifically, sell securities that have a higher marginal contribution to risk, and buy securities that have a low marginal contribution to risk.
Ultimately this seems like an empirical question that has to be tested. The best answer would cite empirical research on asynchronous optimal re-balancing if it exists.