Strategic and tactical allocation with HCGL covariance (ROSAA)

Author: Artur Sepp

A case study of the framework that OptimalPortfolios implements. Software citation: CITATION.cff.

Overview

Sepp, Ossa and Kastenholz (2026) describe a framework for the robust optimisation of strategic and active asset allocation (ROSAA) of multi-asset portfolios. It has three layers:

  1. a covariance matrix from a factor model whose loadings are estimated by a hierarchical clustering group LASSO (HCGL) on multi-asset tradable factors;

  2. a strategic allocation (SAA) by risk budgets under that covariance;

  3. a tactical allocation (TAA) that maximises alpha against the strategic allocation under a tracking-error budget.

This page reports the study as the article states it, maps each layer to the package, and runs the same configuration offline on a synthetic panel with known factor loadings. The script reproduces the mechanism, not the article’s numbers.

        flowchart LR
    A["Factor prices<br/>and asset returns"] --> B["HCGL factor<br/>covariance"]
    B --> C["Strategic<br/>allocation by<br/>risk budgets"]
    B --> D["Tactical<br/>allocation: alpha<br/>over tracking error"]
    C -- "benchmark" --> D
    E["Alpha scores"] --> D

In words: one covariance, refitted each quarter, feeds both layers; the strategic allocation meets its risk budgets, and the tactical allocation tilts away from it in the direction of the alphas, within a tracking-error budget measured with the same covariance.

Study design and data

The article’s empirical application covers:

  • Strategic universe. Eleven sub-asset classes proxied by indexes: five fixed-income classes, equity and five alternatives, under a top-level target of 25% fixed income, 35% equity and 40% alternatives (Exhibits 1 and 2).

  • Tactical universe. 28 index-proxied instruments, 13 in fixed income, 5 in equity and 10 in alternatives, each with bounds, a turnover group and a monthly or quarterly rebalancing frequency (Exhibit 5).

  • Sample. Data from 31 December 1999; the backtest runs from 31 December 2004 to 30 June 2025.

  • Factors. Seven multi-asset tradable factors built from futures and investable trackers, each targeted to 10% volatility: equity, rates, credit, carry, inflation, commodities and a private-equity premium factor.

  • Covariance. EWMA spans of 36 months for liquid and 12 quarters for illiquid instruments, and a group-LASSO penalty of \(10^{-5}\) chosen on a grid. Clusters come from Ward linkage on EWMA correlations, and private-asset returns are unsmoothed before estimation.

  • Strategic layer. Constrained risk budgeting, rebalanced quarterly, with budgets per sub-asset class set so that the backtest’s average weights match the target allocation (Exhibit 3).

  • Tactical layer. Rebalanced monthly against the strategic allocation, with a 3% tracking-error limit per core asset class, group turnover limits and 20 basis points of transaction costs per traded volume.

  • Reference. A static benchmark rebalanced quarterly to fixed weights.

Configuration

Each layer of the article maps to one call of the package. The configuration below is that of the canonical script, examples/docs/app_rosaa_multi_asset_allocation.py, on a synthetic panel of three factors and eight asset classes, monthly from December 2004 to June 2025.

The covariance is refitted at every quarter end with the hierarchical-clustering group LASSO of FactorLasso, with the article’s span of 36 months and penalty of \(10^{-5}\):

estimator = op.FactorCovarEstimator(
    lasso_model=LassoModel(model_type=LassoModelType.HIERARCHICAL_CLUSTER_GROUP_LASSO,
                           reg_lambda=1e-5, span=36, warmup_period=24),
    factor_returns_freq='ME', factor_covar_span=36, rebalancing_freq='QE')
covar_dict = estimator.fit_rolling_covars(
    risk_factor_prices=factor_prices, asset_returns_dict={'ME': asset_returns},
    time_period=qis.TimePeriod('2014-12-31', '2025-06-30'))

The strategic allocation solves the risk-budgeting problem at each date:

budgets = pd.Series(RISK_BUDGETS, index=ASSETS)
saa = op.rolling_risk_budgeting(prices=asset_prices, constraints=op.Constraints(),
                                risk_budget=budgets, covar_dict=covar_dict)

Insight

A risk budget is a share of risk, not of capital. In the script, government bonds take 41% of capital for a 10% risk budget, because each unit of capital in them adds little risk to the portfolio.

The tactical allocation maximises alpha against the strategic allocation under a 3% ex-ante tracking error. The article sets the limit per asset class, which the package expresses with GroupTrackingErrorConstraint; the script uses one total limit:

alphas = alpha_scores(list(covar_dict), rng)
taa = op.rolling_maximise_alpha_over_tre(
    prices=asset_prices, alphas=alphas, benchmark_weights=saa, covar_dict=covar_dict,
    constraints=op.Constraints(tracking_err_vol_constraint=TRACKING_ERROR))

The script then asserts the mechanism at all 43 quarter ends:

  • every strategic allocation meets its risk budgets;

  • every tactical allocation has an ex-ante tracking error of 3% against it;

  • the active weights follow the alphas.

Left: risk budgets and the strategic weights that meet them for eight asset classes; governmentbonds take 41% of capital for a 10% risk budget. Right: active tactical weights against alphascores at 43 quarter ends, rising with the alpha, at a 3% ex-ante tracking error throughout.

Figure: the two allocation layers on the synthetic panel of the canonical script. The strategic weights meet the risk budgets, not the capital shares, and the tactical tilts spend the tracking-error budget in the direction of the alphas. The analytics gallery lists the exhibit’s provenance.

Pitfall

FactorCovarEstimator.fit_rolling_covars accepts residual_var_weight, which scales the residual variance of the assembled covariance. It is an option of the package, not part of the article’s method: the article measures tracking error with the full covariance, residual variance included. A weight below one understates the tracking error of a given tilt, so the tactical layer takes larger tilts than its budget intends.

Results

The article’s Exhibit 14 reports, for the backtest from 31 December 2004 to 30 June 2025:

Portfolio

Return p.a.

Volatility

Sharpe ratio

Maximum drawdown

Alpha against the static benchmark

Turnover

Static benchmark

6.7%

11.0%

0.61

−38%

–

–

Strategic allocation

6.9%

8.6%

0.80

−30%

1.2%

28%

Tactical allocation

8.3%

8.8%

0.95

−24%

2.5%

202%

Both allocations have a beta of about 0.79 to the static benchmark. In the text of the Empirical Application, the strategic allocation adds about 0.2% a year and roughly 30% in Sharpe ratio over the static benchmark, and the tactical allocation adds about 1.4% a year and roughly 20% in Sharpe ratio over the strategic allocation; both alphas are significant at the 1% level.

The Brinson attribution of Exhibit 16 places most of the active return in selection rather than in allocation across asset classes. Exhibits 18 and 19 show the ex-ante tracking error by asset class and the turnover by group, with the equity tracking error often at its 3% limit.

What the study does and does not show

  • It shows one historical path of index proxies, net of 20 basis points of costs, on which the risk-budgeted strategic allocation had lower volatility and drawdown than a static benchmark, and the tactical allocation added return at a turnover of about 200% a year.

  • It does not compare covariance estimators in a backtest. Exhibit 12 compares the loadings of a regression, an independent LASSO and HCGL qualitatively; the article makes no claim that one estimator gives more stable weights than another.

  • The universe uses indexes rather than investable funds, residuals are assumed uncorrelated, and the article lists regimes, liquidity risk and transaction-cost models as future work.

  • The synthetic reproduction on this page shows only that the package implements the three layers as described. Its numbers are those of a simulation and say nothing about performance.

Reproduce

The canonical script runs offline and asserts the mechanism above:

python -m examples.docs.app_rosaa_multi_asset_allocation

The paper folder papers/robust_optimisation_jpm_2026 holds a methodological example of the covariance and strategic layers. It downloads ETF prices with yfinance and differs from the article: it uses two price factors, equal risk budgets and 10 basis points of costs, and has no tactical layer. It uses the article’s spans of 36 months for the betas and the factor covariance and writes its factsheet to the configured output directory. The article’s own inputs are licensed index histories that the repository does not hold.

See also

References