Rolling Mean-Variance Optimization for Portfolio Weights

Summary

The document asks whether portfolio theory can accommodate weights that change frequently, including at a tick-level timescale. The answer describes a rolling mean-variance procedure: estimate asset returns and their covariance matrix from historical data, then choose weights by minimizing portfolio variance subject to a full-investment constraint and a target-return constraint. The resulting allocation is framed as a forecast for the next period, after which the inputs and weights can be updated.

This connects changing portfolio weights to repeated optimization rather than to a fixed allocation. The answer is brief and does not explain how to estimate expected returns or covariance reliably, choose a lookback window, account for transaction costs, or handle practical trading constraints. Its small historical sample example illustrates the setup but provides no performance evidence. Re-optimizing at very high frequency can produce unstable allocations, a limitation the document does not address.

Key ideas

• Mean-variance optimization can be repeated as new return data arrive.
• The described allocation minimizes variance subject to a target return and a full-investment constraint.
• The optimized weights are treated as an allocation for the next period.
• The answer does not address estimation error, transaction costs, or the risks of frequent rebalancing.

Tags

# Time varying weights in a portfolio


# Time varying weights in a portfolio












As I have seen in my portfolio theory class, we define the weights of some assets and quantify the risk and return of the whole portfolio. In this setup, the weights do not change in time. What if the weights vary in time, like every second... Is this out of the scope of portfolio theory? What should I study?

Thanks

## Answer by Tosh (score 0)

https://quant.stackexchange.com/a/53856

Suppose you are given the historical data of 20 days. You calculate the asset returns and covariance matrix. Then you minimise the variance $$ Min \ \sigma^2 = w\Sigma w^T \\ s.t. wI^T = 1 \\ and \ w\mu^T = r_p \\ $$ Where $\mu$ is the asset returns and $r_p$ is the target return, to find the optimal weight allocation. This is a prediction of what your weight allocation should be for the 21st day. So if you are studying ticks by data, that is how stock prices change every second, you can experience change in weights. Hope this helps.

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