Applying Mean–Variance Allocation to Event-Driven Trading Signals
Summary
The document considers how to allocate capital among several assets when one trading strategy can generate signals for multiple assets on the same day. It proposes using historical daily returns to estimate each asset’s variance and cross-asset covariances, then choosing weights according to an objective such as minimizing the strategy’s return variance. Because signals occur conditionally and the set of active assets changes over time, the question is how to adapt ordinary portfolio optimization to this dynamic setting.
The response points to Merton’s portfolio problem, which studies allocation between a risky asset and a riskless asset while accounting for ongoing consumption. Under its basic assumptions, the optimal risky allocation coincides with the Markowitz result; changing assumptions, such as introducing market frictions, can produce different conclusions. This is a conceptual pointer rather than a worked solution: it does not specify how to model signal arrival, estimate conditional returns, or optimize weights across changing active sets. A practical implementation would need to define its objective and test the resulting allocation in a backtest.
Key ideas
- A strategy that signals on several assets can require a portfolio allocation decision on each active day.
- Historical return variances and covariances can inform a variance-based allocation objective.
- Conditional signal generation makes the allocation problem dynamic and stochastic.
- Merton’s portfolio problem is a useful starting point, and its basic optimal allocation matches Markowitz under its assumptions.
- Market frictions and other changed assumptions can alter the portfolio optimization result.
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# Portfolio diversification and Sharpe ratio # Portfolio diversification and Sharpe ratio I have a given trading strategy T and say 3 assets in my universe. The hold time is one day. The trading strategy can general signals for the 3 assets in any given day (so signal can trigger for any one or all 3). In case the signal is generated for more than one asset, the goal is to find the optimal capital allocation between the two (or three) assets, according to "some" criterion". One criterion could be minimizing overall return variance where return is the yearly return of the strategy say. We are given historical OHLC data for the 3 assets. So it is possible to compute daily return series, and the variance/covariance between the returns across the 3 assets. In general I want to apply mean variance to the problem but am a bit confused when it comes to treating the dynamic nature of the problem (its not as simple as optimizing a portfolio of assets). The signal generation is conditioned on some events being true so its stochastic. I can set up a backtest and compute the realized returns (keeping weights on the assets unknowns, in days where signals came for two/three assets say). I am curious if someone can help structure the problem or drop some pointers to set it up. Is this in the camp of Stochastic dynamic asset allocation? ## Answer by lehalle (score 1) https://quant.stackexchange.com/a/35976 You should start looking at Merton's Portfolio problem. A lot of papers elaborated on the top of it. The principle is "simple": - optimize the allocation between one risky asset (Brownian) and a riskless one; - such a way you maintain a portfolio from which you consume money (for instance to pay some expenses). The main result is the optimal allocation is the same as Markowitz one. It is probably why people did not focus that much on it. Nevertheless as soon as you change assumptions, you obtain very interesting results, like for instance in On portfolio optimization in markets with frictions.
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