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Autonomous Sparse Mean-CVaR Portfolio Optimization
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Proposes Autonomous Sparse Mean-CVaR (ASMCVaR), approximating the l0-constrained mean-CVaR portfolio model via a tailed approximation of the m-sparse indicator, solved by PALM with nested FPPA, and reports higher cumulative wealth and Sharpe ratios than sparse and non-sparse baselines on six Kenneth French datasets.
Problem
Portfolio optimization with an exact l0 cardinality constraint on mean-CVaR is NP-hard and existing combinatorial (branch-and-bound) solvers are computationally expensive and need commercial optimizers.
Approach
Replace the l0 constraint's indicator function with a tailed approximation (quadratic penalty on coefficients outside the m largest in magnitude, weighted by 1/(2gamma)), yielding a three-term model solvable by PALM with an FPPA inner loop; approximation becomes arbitrarily accurate as gamma tends to 0.
Key results
- ASMCVaR (m=10) final cumulative wealth 973.23 on FF25 vs 440.32 for Mean-CVaR-l1 and 333.41 for Mean-CVaR
- ASMCVaR Sharpe ratios on FF25EU about 45.7% higher than Mean-CVaR and Mean-CVaR-l1
- On average more than 89% of selected assets overlap between sparsity levels m=10, 15, 20
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use ASMCVaR with m=10 instead of the strongest listed baseline, Mean-CVaR-ℓ1 | portfolio optimization · FF25 | final cumulative wealth: 440.32 -> 973.23 | Helped |
| use ASMCVaR with m=10 instead of Mean-CVaR | portfolio optimization · FF25EU | final cumulative wealth: 18.60 -> 122.82 | Helped |
| use ASMCVaR with m=10 instead of Mean-CVaR-ℓ1 | portfolio optimization · FF32 | final cumulative wealth: 332.55 -> 1122.76 | Helped |
| use ASMCVaR with m=10 instead of Mean-CVaR-ℓ1 | portfolio optimization · FF49 | final cumulative wealth: 178.93 -> 758.66 | Helped |
| use ASMCVaR with m=15 instead of m=10 (ablation) | ASMCVaR · FF25EU | final cumulative wealth: 122.82 -> 123.13 | Helped |
| use ASMCVaR with m=20 instead of m=10 (ablation) | ASMCVaR · FF32 | final cumulative wealth: 1122.76 -> 1317.01 | Helped |
| use ASMCVaR with m=20 instead of m=10 (ablation) | ASMCVaR · FF49 | final cumulative wealth: 758.66 -> 767.61 | Helped |
| use ASMCVaR with m=15 instead of m=10 (ablation) | ASMCVaR · FF100 | final cumulative wealth: 966.32 -> 1126 | Helped |
| use ASMCVaR with m=10 instead of Mean-CVaR-ℓ1 | portfolio optimization · FF25 | Sharpe ratio: 0.2392 -> 0.2610 | Helped |
| use ASMCVaR with m=15 instead of Mean-CVaR-ℓ1 | portfolio optimization · FF25EU | Sharpe ratio: 0.1862 -> 0.2765 | Helped |
| use ASMCVaR with m=10 instead of Mean-CVaR | portfolio optimization · FF32 | Sharpe ratio: 0.2375 -> 0.2638 | Helped |
| use ASMCVaR with m=10 instead of Mean-CVaR-ℓ1 | portfolio optimization · FF100 | Sharpe ratio: 0.1815 -> 0.2446 | Helped |
Surprising findings
- The l0-constrained Mean-CVaR-l0 cutting-plane baseline could not be run because the models were too large for the authors' setup
Limitations
- Approximation guarantees rely on gamma tending to zero; the experiments use gamma=1e-5 and no convergence to global optimum is proven for the nonconvex problem
- Evaluation is limited to six monthly Kenneth French datasets with a single 60-month window and no runtime comparison
- Mean-CVaR-l0 exact baseline not run because of model size
Experimental setup
Datasets: Kenneth R. French FF25 FF25EU FF32 FF49 FF100 FF100MEOP
Benchmarks: FF25 FF25EU FF32 FF49 FF100 FF100MEOP
Metrics: final cumulative wealth alpha factor Sharpe ratio overlap proportion of assets cumulative wealth under transaction cost
Baselines: SSMP SSPO SPOLC S1 S2 S3 Mean-CVaR Mean-CVaR-l1 MT-CVaR 1/N
Builds on: mean-CVaR linear programming proximal alternating linearized minimization fixed-point proximity algorithm l0-constrained mean-CVaR branch-and-bound
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