Portfolio Optimization — Quantitative Approaches

Why This Matters

Level 2 taught you to construct a portfolio using common sense and rules of thumb. Level 3 introduces the mathematical framework that institutional investors use — Modern Portfolio Theory (Teoria Moderna de Portfólios). Understanding these concepts allows you to build portfolios that maximize return for a given level of risk, or minimize risk for a given return target. In Angola’s market, where every percentage point counts against 15.7% inflation, optimization matters.

Modern Portfolio Theory Foundations

Harry Markowitz’s insight, which earned him a Nobel Prize: the risk of a portfolio is not simply the weighted average of individual asset risks. Because assets are imperfectly correlated, combining them reduces total portfolio risk below what you would expect.

Key variables for each asset:

• Expected return (μ): Your forecast of the asset’s annual return
• Standard deviation (σ): A measure of return volatility — higher σ means more uncertain returns
• Correlation (ρ): How closely two assets move together. ρ = 1 means perfect co-movement; ρ = -1 means perfect inverse movement; ρ = 0 means no relationship

The portfolio return: Weighted average of individual returns. Simple. The portfolio risk: Depends on individual risks AND correlations. This is where the magic happens.

Correlation in Angola’s Market

Estimated correlation matrix for Angola’s main asset classes:

Key insight: USD bonds have low correlation (0.15-0.30) with all other Angolan assets because they are driven by USD factors while domestic assets respond to Kwanza/oil dynamics. This makes USD bonds an excellent diversifier — adding them to a portfolio reduces total risk more than their individual volatility would suggest.

The Efficient Frontier

The efficient frontier is the set of portfolios that deliver the maximum possible return for each level of risk. Portfolios below the frontier are suboptimal — you could get more return for the same risk or less risk for the same return.

For Angola’s four asset classes:

Using the risk/return/correlation estimates:

• Kz Bonds: Return 20%, Volatility 8%
• USD Bonds: Return 8%, Volatility 5%
• Equities: Return 25%, Volatility 20%
• Deposits: Return 16%, Volatility 2%

The efficient frontier curves from the minimum-risk portfolio (heavy deposits/USD bonds, ~12% return, ~4% volatility) to the maximum-return portfolio (heavy equities, ~25% return, ~18% volatility).

The Sharpe Ratio: (Portfolio Return - Risk-Free Rate) / Portfolio Volatility. The portfolio with the highest Sharpe ratio is the optimal risk-adjusted allocation. In Angola, with the risk-free rate at approximately 18.5% (91-day BT), the Sharpe ratio optimization favors portfolios heavy in bonds with moderate equity exposure.

Practical Optimization for Angola

Given the constraints of BODIVA (limited stocks, moderate liquidity), practical optimization means:

1. Define Your Return Target

What do you need to beat? Inflation (15.7%) is the ultimate benchmark. A portfolio targeting 20% nominal return needs to optimize for the least risk to achieve this.

2. Set Constraints

• Maximum 30% in any single asset
• Minimum 20% in liquid assets (deposits + short bonds)
• Maximum 40% in equities (liquidity constraint on BODIVA)
• Minimum 20% in USD-indexed assets (currency hedge)

3. Optimize Within Constraints

Using the efficient frontier with constraints, the optimal moderate-risk portfolio for Angola approximately:

Sharpe Ratio: (17.45 - 18.5) / 8 = -0.13. A negative Sharpe ratio reflects the reality that Angola’s risk-free rate (18.5%) is extremely high — beating it risk-adjusted is genuinely difficult.

This highlights an important point: in Angola’s current rate environment, the risk-free treasury bill is hard to beat on a risk-adjusted basis. The equity premium needs to be substantial to justify the additional volatility.

Worked Example: Optimizing a Kz 30 Billion Institutional Portfolio

A pension fund manager must achieve at least a 19% nominal return with maximum volatility of 10%.

Optimization result:

• 35% Kwanza OTs (3-7 year ladder): 7.35% return contribution, ~2.5% risk
• 20% USD-indexed OTs: 1.6% return contribution, ~1.0% risk
• 30% BODIVA equities (diversified): 7.5% return contribution, ~6.0% risk
• 15% term deposits: 2.4% return contribution, ~0.3% risk

Portfolio metrics:

• Expected return: 18.85% — slightly below 19% target
• Expected volatility: ~8.5% — within 10% limit
• Maximum drawdown (stress scenario): approximately -12%

To reach 19%, the manager can: increase equity to 35% (accepting ~9.5% volatility), or extend duration on Kwanza bonds to capture curve steepness.

Key Takeaways

• Modern Portfolio Theory shows that diversification reduces risk more than expected due to imperfect correlations
• The efficient frontier maps the best possible risk-return tradeoffs
• USD-indexed bonds are the best diversifier in Angola due to low correlation with Kwanza assets
• The Sharpe ratio measures risk-adjusted return — in Angola, the very high risk-free rate makes beating it hard
• Practical optimization requires constraints (liquidity, concentration limits, regulatory)
• Quantitative tools complement but do not replace qualitative judgment — models rely on estimates that can be wrong

Common Mistakes

Over-relying on historical correlations — Correlations change during crises. In a severe Kwanza depreciation, all Kwanza assets may move together more than historical data suggests.

Precision illusion — An optimizer says 32.7% Kwanza bonds is optimal. But the inputs (expected returns, volatilities, correlations) are estimates. Small input changes can produce very different outputs. Use optimization as a guide, not a gospel.

Ignoring implementation costs — The theoretical optimal portfolio may require frequent rebalancing. In Angola’s less liquid market, trading costs can erode the optimization benefit.

What’s Next

Optimization is a framework. Macro trading is where you apply economic views to position portfolios. The next lesson covers how global and domestic macro factors create trading opportunities in Angola.

Next Lesson: Macro Trading — Economic Views as Investment Strategy

Build optimized portfolios with the Portfolio Builder. Review risk metrics for each asset class.