The portfolio construction model is the arbitrator that hears three competing inputs — the alpha model (expected returns), the risk model (expected variances and correlations), and the transaction cost model (cost of any trade) — and outputs the target portfolio weights. A strategy with excellent alpha but a poor portfolio construction model delivers suboptimal live results: allocating the most capital to the worst signals, or taking unintended sector bets, or trading so often that costs erode the alpha.
This note covers the two families of portfolio construction approach. Rule-based models are simpler, more robust to estimation error, and easier to debug. Optimisers are more flexible but sensitive to the quality of the covariance matrix and alpha estimates — which are both noisy. The practical question is not which is better in theory, but which survives contact with the noise in your estimates.
Learning objectives. By the end of this note you should be able to:
- describe equal-dollar, equal-risk, and signal-proportional weighting and state the argument for each;
- formulate the optimiser objective function and identify the three input models it balances;
- explain why covariance matrix estimation error causes optimisers to concentrate positions (the "error maximiser" problem);
- state the Kelly formula for multi-strategy capital allocation and interpret ;
- articulate the key constraints (sector, leverage, turnover, hard-to-borrow) and how they enter the optimiser.
In this lesson
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- The goal of portfolio construction
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- Rule-based portfolio construction
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- The optimiser approach
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- Kelly formula for multi-strategy allocation
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- Key constraints in a stat-arb optimiser
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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