The 12 portfolio optimization objectives, ranked by use case

The 12 portfolio optimization objectives MEDGE Capital ships, ranked by typical investor use case: Max Sharpe (textbook default), Max Sortino (loss-averse), Max Calmar (retirement targets), Max Omega (asymmetry-aware), Max Rachev (tail-symmetric), Min Vol (do-no-harm), Min CVaR 95/99 (institutionally-influenced), Min Drawdown (sleep-at-night), Min Ulcer Index (duration-aware), Risk Parity (diversification purist), Max Return (constraint-driven). Each comes with one common failure mode.

The product question users ask the most is "which one should I use?". The honest answer is "depends on what risk feels like to you" — and that is the lens this list ranks by. Objectives are grouped by the kind of investor profile they serve best, with the failure mode of each.

Risk-adjusted return maximisers (the "Sharpe family")

1. Max Sharpe — for textbook investors

The default. Maximises excess return per unit of total volatility. Failure mode: ignores skew and tails — a strategy that sells crash insurance dominates Max Sharpe until the day insurance pays out. Use only with CVaR reported alongside.

2. Max Sortino — for loss-averse investors

Like Sharpe but the denominator is downside deviation only — upside volatility is not penalised. Best for asymmetric strategies (trend-following, long convexity). Failure mode: silent on the magnitude of tail losses, just like Sharpe.

3. Max Calmar — for retirement-target investors

CAGR divided by absolute Maximum Drawdown. Penalises the single worst experience over the window. Failure mode: Calmar is unstable when the window is short — one new low drives it. Use 5+ years of data.

4. Max Omega — for asymmetry-aware investors

Probability-weighted gains-to-losses at a threshold. Captures the full distribution. Failure mode: the threshold choice is consequential; defaulting to zero hides cash-target investors.

5. Max Rachev — for tail-symmetric investors

Right-tail expected return divided by left-tail expected loss. Symmetric and skew-aware. Failure mode: ignores the bulk of the distribution; can prefer strategies with rare big wins and many small losses.

Risk minimisers (the "Min family")

6. Min Vol — for the "first do no harm" investor

Pure variance minimisation under the budget constraint. Reproducible, no behavioural surprises. Failure mode: low vol does not mean low loss — Min Vol can still drawdown 15% in a regime where it concentrates in a single sector.

7. Min CVaR 95% — for the institutionally-influenced

Penalises the expected loss in the worst 5% of cases. Convex, well-behaved, the literature standard since Rockafellar-Uryasev (2000). Failure mode: in-sample CVaR estimates are noisy below 200 observations.

8. Min CVaR 99% — for the extreme-event-conscious

Same as #7 but at the 99% level. Strongly favours diversification across uncorrelated risk drivers. Failure mode: requires very long history (1,000+ observations) for stable estimation.

9. Min Drawdown — for the "I want to sleep at night" investor

Targets the worst peak-to-trough decline. Non-convex; the solver uses sequential quadratic programming with multistart. Failure mode: dominated by the worst single event in the window; can over-fit to it.

10. Min Ulcer Index — for the duration-aware risk-averse

Minimises the RMS of drawdowns — penalises long underwater periods as much as deep ones. Failure mode: less prominent in academic literature; harder to communicate to a non-technical audience.

Allocation rules (not objectives in the strict sense)

11. Risk Parity — for diversification purists

Equal risk contribution across assets, leveraged to a target volatility. Conceptually different from the Sharpe family: it does not optimise expected return at all. Failure mode: assumes negative bond-equity correlation. 2022 broke this.

12. Max Return — for the "I know what I want" investor

Maximises mean return under the box constraints. The objective is so degenerate that the value of the exercise is purely in the constraint set — turnover caps, group limits, leverage bounds. Failure mode: if there are no constraints, it picks one asset.

Which one to pick

Three honest recommendations: (a) for a first portfolio, run BOTH Max Sharpe and Min CVaR 95% and compare. If they agree, the input universe is well-behaved. If they disagree, look at the disagreement. (b) For a retirement portfolio, Max Calmar or Min Ulcer Index match the lived experience better than Max Sharpe. (c) For an institutional mandate, Min CVaR is the literature standard and the easiest to defend.

In MEDGE

All 12 objectives operate on the same input universe and the same constraint set, so direct comparison is possible. The Compare module surfaces a side-by-side of any two strategies including the regime ribbon — useful when two different objectives produce different weights.