Many investment options, each with different expected return and risk, different correlations. The classical finance OR problem: Markowitz mean-variance optimization, from 1952.
In plain words
Sound familiar?
- The company has surplus cash; instead of leaving it in current account, the manager decides each month by intuition what to do with it.
- A bank relationship manager says 'these funds suit you'; we can't really test whether they fit us or whether other options are better.
- We have FX, gold, and stocks; the portfolio is 50% in USD and we don't measure the risk distribution.
- A retiring employee wants to invest their pension; they have no way to ask which fund mix suits them.
- Should we invest in the business, hold bonds, or buy a machine? We decide using a single number like 'historical stock return'.
- Our risk appetite changed โ we used to be aggressive, now we want conservative โ but we don't know how to revise the portfolio.
- Taxes, fees, minimum-investment thresholds โ we allocate without modeling how these affect the portfolio decision.
Why it matters
How it's solved
Technical depth
How it's solved
Technical depthOne-liner: Two investments moving in the same direction (high correlation) is not diversification โ it’s just a bigger bet. Real diversification comes from pairs where one rises when the other falls. Don’t only weigh expected returns; weigh how the assets offset each other.
This is the Portfolio Optimization Problem at the intersection of operations research (a discipline that uses math and computing to solve business-decision problems) and finance mathematics. The classical formulation is Markowitz Mean-Variance Optimization (1952). Solution in three stages:
1. Modeling. Candidate asset list (n assets), each asset’s expected return (ฮผแตข), pairwise covariances (ฯแตขโฑผ) โ the heart of the model. Constraints: weights sum to 1 (all capital invested), each weight โฅ 0 (no short-selling, if so), per-asset min/max (individual exposure control), upper limits on sector or region groups (concentration control). Objective: either maximize expected return for a given risk, or minimize variance for a given return.
2. Solver-driven decision. Markowitz is a quadratic-programming (QP) problem and modern solvers complete it in seconds. 5-50 assets: seconds; 100+: minutes. The efficient frontier โ the curve of maximum-return points for each risk level โ is delivered as output. Single-point solution: the tangent portfolio that maximizes Sharpe ratio. In practice, covariance-matrix estimation (the table of how each pair of assets moves together) is the hardest step; shrinkage estimators (a statistical method that smooths extreme numbers in historical data) and factor models are common.
3. Field integration. Output translates to weight-per-asset percentages for actual investment. The investor gets a rebalancing schedule (e.g., quarterly), risk-return visualization (efficient-frontier curve with current position), what-if scenarios (what if TRY falls 20%, what if rates rise 500 bps). Regular reports โ expected vs. realized return and tracking metrics (Sharpe, Treynor, max drawdown)."
Alternatives
Manual + bank relationship manager's advice
FreeFree (commission embedded in investment products)
Who it fits: Small capital (under 100K TRY), 1-3 investments
- + Zero software cost
- + Human contact, questions can be asked
- + Regulatory compliance handled by the bank
- โ Bank conflict of interest โ pitches its own products
- โ No numerical optimization
- โ Risk appetite not personally measured
- โ Doesn't scale
Robo-advisor / digital wealth-management platforms
Enterprise0.5-1.5% annual portfolio fee, or 100-2000 TRY/year fixed
Who it fits: Individual or small SMB, 100K-5M TRY
- + Automatic rebalancing
- + Markowitz or Black-Litterman-based algorithm
- + Lower commission, transparent
- โ Limited options in TR
- โ Doesn't integrate private assets (business reinvestment)
- โ Customization limited
Professional portfolio-management firm (institutional)
Enterprise1-2% annual management fee + performance fee
Who it fits: 5M+ TRY portfolio, institutional investor
- + Professional team, analysis, reporting
- + Professional risk management
- + Regulatory compliance, audit
- โ Expensive
- โ Minimum-investment thresholds high (1-5M TRY)
- โ Transparency varies
Open-source solver + financial Python libraries
Open SourceLicense free; in-house build 4-8 weeks or 100K-300K TRY consulting
Who it fits: Finance-literate SMB or individual; advanced
- + Full control, customizable
- + Markowitz, Black-Litterman, risk-parity available in open-source
- + No license
- โ Finance + Python knowledge required
- โ Data feeds (price history) may be paid
- โ Self-maintained
Recommendation
Ask in the meeting
- Which portfolio optimization method do you use? Are options like Markowitz, Black-Litterman, risk parity available?
- Which covariance estimator? (e.g., shrinkage, factor model, raw sample)
- How do you measure my risk appetite (volatility tolerance)? Survey, past behavior, simulation?
- Are transaction costs (fees, taxes, spreads) included in the optimization?
- How is rebalancing frequency set? Quarterly, semi-annual, or threshold-based (drift)?
- Do you support stress testing and scenario analysis (e.g., rates +500 bps, TRY -20%)?
- Is the 3-5 year historical portfolio performance reported transparently?
- If we stop working with you, how do we get our position history and reports in standard format?
Technical details
Editor’s note
Colloquially this is called “asset allocation”, “portfolio diversification”, or “investment mix”. Academically it is the Portfolio Optimization Problem or Markowitz Mean-Variance Optimization. Without knowing the difference, you’d accept a bank’s fund proposal without being able to question under which assumptions (return estimate, covariance estimate, risk-appetite measurement) it was optimized.
The most-skipped point in the industry: estimation of the covariance matrix. Estimating expected returns is relatively easy (the error is big but it’s done); estimating covariances is much harder because of the matrix dimension โ 50 assets means 1275 parameters to estimate, and observation counts may not suffice. Naive sample estimators perform poorly; modern approaches (shrinkage, factor models) are necessary. Without answering which estimator the software uses, you cannot evaluate its quality.
Step-by-step path โ for the SMB
Stage 1 โ Measure yourself first. Risk appetite: how much volatility (annual standard deviation) is acceptable? Horizon: 1 year, 5 years, 10 years? Liquidity needs: when and how much cash might be needed? Tax situation: income tax bracket, corporate tax.
Stage 2 โ Define the asset universe. Typical for Turkey: TRY deposits, equities (BIST), FX (USD, EUR), gold, government bonds, REIT funds, business reinvestment. Historical returns (5-10 years minimum) and correlations needed for each.
Stage 3 โ Pilot. Run optimization on paper, track a virtual portfolio for 3-6 months. Success criteria: at target volatility, expected return improves by at least 2 percentage points.
Stage 4 โ Implementation. Move to real money, regular rebalancing (quarterly or semi-annual). Annual review to update for macro changes and risk-appetite changes.
Risks โ what can go wrong
- Expected-return estimation error. Past returns โ future returns. Estimation error can be 30-50%; this error in the optimization causes the output to swing dramatically. Fix: Bayesian / Black-Litterman to combine with expert views.
- Correlations shift over time. In crisis periods all assets fall together (correlation โ 1); diversification benefit temporarily disappears. Test via stress testing.
- Liquidity ignored. On paper, real estate could be 30% of the optimum portfolio; when cash is needed, real estate can’t be sold. Liquidity constraint must be added to the model.
- Tax and regulatory change. Turkey’s tax regime changes frequently. Optimize after-tax return, not pre-tax."
Solution method โ a technical look
| Approach | Typical scale | Solve time | Guaranteed optimum? |
|---|---|---|---|
| Quadratic Programming (classical Markowitz) | 5-100 assets | seconds | Yes |
| Black-Litterman (Bayesian extension) | 5-100 assets | minutes | Yes (Bayesian sense) |
| Risk Parity | Any scale | seconds | No (heuristic) |
| Monte Carlo + scenario optimization | Stochastic | minutes | No |
| Robust optimization | Uncertain parameters | seconds-minutes | Worst-case optimum |
Objective function choice:
- Objective 1 โ Maximum Sharpe ratio: Most common academic objective.
- Objective 2 โ Maximum return for given risk: When investor sets a volatility cap.
- Objective 3 โ Maximum-drawdown limit: Cap on worst-case loss.
- Objective 4 โ Minimum risk for target return: When a specific income target exists."
For a Turkish investor: after-tax return + TRY-based real return (inflation-adjusted) is critical."
Academic references
See the sources field in the frontmatter.
Sources
- Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77โ91. Foundational paper of modern portfolio theory, Nobel-prize-winning.
- Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425โ442. CAPM, an extension of portfolio theory.
- Ledoit, O. and Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2), 365โ411. Modern reference for covariance estimation.
- Turkish Capital Markets Board (SPK) โ annual reports and regulatory documents. Reference for the TR financial market.
- Turkish CoHE (YรK) Thesis Center โ keyword ‘portfรถy optimizasyonu’ โ 80+ Turkish theses. tez.yok.gov.tr
Glossary
- Portfolio Optimization
- Allocating capital across multiple investment options under a risk-return trade-off.
- Mean-Variance Analysis
- The classical finance framework, due to Markowitz, that analyses investment decisions in the expected-return (mean) vs. risk (variance) plane.
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