Stage 4 — From selected FMPs to a final portfolio

The alpha factory begins after validation. It does not simply take the first few rows of the FMP ranking and assign equal weights. It selects a set of credible, sufficiently distinct sleeves, estimates how they behave together, and solves for a combination that balances expected contribution against shared risk.

That FMP-level combination is then translated back into security weights and passed through the final portfolio constraints. The complete process is tested forward again, including turnover and costs.

What the animation shows

The left panel starts with FMPs that survived the promotion gates. Correlation and family checks prevent several versions of the same idea from occupying the whole allocation. Their training-window return histories form a matrix from which expected sleeve returns and cross-sleeve covariance are estimated.

In the center, the signal-space optimizer assigns weights to those sleeves. A high-scoring sleeve can receive less weight when it duplicates another sleeve; a modest but diversifying sleeve can remain useful. The weighted FMPs then map back to a target vector of security holdings.

The right panel applies the same asset risk model used during FMP construction, adds the mandate's position and exposure constraints, and produces the final portfolio. The last step runs the entire chain through unseen periods rather than backtesting only the final optimizer in isolation.

Estimate the sleeve opportunity set

For the selected set \(\mathcal{S}\), let \(F\) contain the training-window returns of the FMP sleeves. Estimate the expected-return vector \(\widehat{\mu}_F\) and the annualized covariance matrix \(\widehat{\Omega}_F\) from that window only:

\[\widehat{\mu}_F = \frac{1}{T}\sum_{t=1}^{T}F[t,:]^{\mathsf T},\]

\[\widehat{\Omega}_F = \frac{A}{T-1} \sum_{t=1}^{T} \left(F[t,:]^{\mathsf T}-\widehat{\mu}_F\right) \left(F[t,:]^{\mathsf T}-\widehat{\mu}_F\right)^{\mathsf T}.\]

Some configurations map ranking evidence such as ICIR into an allocation score. That mapping must be declared and calibrated; an ICIR value is not by itself an expected percentage return.

Combine the FMPs in signal space

The nominal sleeve-allocation problem is

\[\underset{\omega}{\operatorname{maximize}} \quad \widehat{\mu}_F^{\mathsf T}\omega -\lambda_\omega \omega^{\mathsf T}\widehat{\Omega}_F\omega.\]

Here \(\omega\) contains the allocations across FMP sleeves. Covariance is what makes this a portfolio problem rather than a score sort. Without constraints, the first-order solution is

\[\omega^* = \left(2\lambda_\omega\widehat{\Omega}_F\right)^{-1} \widehat{\mu}_F.\]

If \(H_t\) contains the current security weights of the selected pure FMPs, the combined target portfolio is

\[\boxed{h^*=H_t\omega^*.}\]

Map the target to asset-level alpha

The target is connected to the downstream asset optimizer through the same covariance model \(Q_t\) used to purify the individual FMPs:

\[\boxed{\alpha^*=Q_t h^*.}\]

This consistency has a useful consequence. In the unconstrained problem,

\[\underset{w}{\operatorname{maximize}} \quad (\alpha^*)^{\mathsf T}w -\lambda_h w^{\mathsf T}Q_t w,\]

the solution follows the direction of the FMP target,

\[w^*=\frac{1}{2\lambda_h}h^*.\]

The final optimizer can therefore add real-world constraints without changing the meaning of the target it received.

Apply the mandate and test the whole chain

The production solve may add a benchmark, long-only requirement, position bounds, sector and factor budgets, active-risk limits, liquidity, borrow, turnover, and transaction costs. These constraints decide which parts of the idealized target are feasible for a particular portfolio.

At every historical rebalance, StrategyNet freezes the selected FMP set, expected-return estimate, covariance estimate, sleeve allocation, implied alpha, and final positions before observing the next return. Net performance is

\[r_{p,t+1}^{\mathrm{net}} = w_t^{\mathsf T}r_{t+1} -\operatorname{Cost}(w_t-w_{t-1}).\]

The output is the complete portfolio record: positions, FMP contributions, risk exposures, turnover, costs, return, and drawdown. That record can be traced backward through the selected sleeves to the original versioned signals.