asset-allocation

Asset Allocation

Purpose

Provides frameworks for determining how to distribute capital across asset classes and strategies. Covers strategic and tactical allocation, mean-variance optimization, Black-Litterman, risk parity, glide paths, and practical implementation approaches. Asset allocation is the primary driver of long-term portfolio performance and risk.

Layer

4 — Portfolio Construction

Direction

both

When to Use

• Setting long-term strategic asset allocation targets
• Making tactical allocation decisions based on market views
• Running mean-variance optimization with constraints
• Implementing Black-Litterman to blend market equilibrium with investor views
• Building risk parity or equal risk contribution portfolios
• Designing glide paths for target-date or lifecycle strategies
• Evaluating core-satellite portfolio structures
• Matching assets to liabilities for pensions or insurance portfolios

Core Concepts

Strategic Asset Allocation (SAA)

The long-term policy portfolio based on an investor's risk tolerance, return objectives, time horizon, and constraints. SAA determines the baseline target weights (e.g., 60% equity / 30% bonds / 10% alternatives) and is the dominant driver of long-term portfolio returns. SAA should be revisited when investor circumstances change, not in response to market movements.

Tactical Asset Allocation (TAA)

Short-to-medium-term deviations from the SAA based on market views, valuations, or momentum signals. TAA requires a disciplined process to avoid becoming ad hoc market timing. Key considerations:

• Define allowable deviation bands (e.g., +/- 10% from SAA)
• Have a clear signal framework (valuation, momentum, macro)
• Set reversion rules: when to return to SAA weights

Mean-Variance Optimization (MVO)

Markowitz's framework for finding optimal portfolio weights that maximize risk-adjusted return:

max w'*mu - (lambda/2) * w'Sigmaw

subject to: sum(w_i) = 1, w_i >= 0 (if long-only), and any additional constraints.

Where:

• w = weight vector
• mu = expected return vector
• Sigma = covariance matrix
• lambda = risk aversion parameter

MVO requires three inputs: expected returns, the covariance matrix, and risk aversion. The solution is highly sensitive to expected return inputs.

Black-Litterman Model

Combines market equilibrium returns with investor views to produce more stable, intuitive portfolio weights. Two-step process:

Step 1 — Implied Equilibrium Returns: Pi = lambda * Sigma * w_mkt

where w_mkt is the market-capitalization weight vector, lambda is the risk aversion parameter, and Sigma is the covariance matrix. These are the returns the market implicitly expects given current prices.

Step 2 — Blending with Views: E(R) = [(tau*Sigma)^(-1) + P'*Omega^(-1)P]^(-1) * [(tauSigma)^(-1)*Pi + P'*Omega^(-1)*Q]

where:

• tau = scalar (uncertainty of equilibrium, typically 0.025-0.05)
• P = pick matrix (identifies assets in each view)
• Q = view vector (expected returns from views)
• Omega = diagonal matrix of view uncertainties

The result is a posterior expected return vector that tilts away from equilibrium toward the investor's views, proportional to confidence.

Risk Parity

Equalizes the risk contribution from each asset (or factor) rather than equalizing capital allocation:

RC_i = w_i * (Sigma*w)_i / sigma_p

Set RC_i = RC_j for all i, j.

In a simple two-asset case with no correlation: w_i is proportional to 1/sigma_i

Risk parity portfolios allocate more capital to lower-volatility assets (typically bonds) and often require leverage to achieve competitive return targets.

Glide Path

An age-based or time-based allocation that systematically shifts from growth assets to defensive assets as the investor ages or the target date approaches:

Common rule of thumb: Equity % = 110 - Age

Target-date fund glide paths typically:

• Start at 90% equity for young investors
• Decrease by ~1-2% per year
• Reach 30-40% equity at retirement
• Continue to "through" allocation post-retirement

Core-Satellite

A hybrid approach combining:

• Core (60-80%): Low-cost, broadly diversified index funds or ETFs
• Satellites (20-40%): Active strategies, factor tilts, alternatives, or concentrated positions

This structure captures the market return efficiently (core) while allowing alpha generation or specific exposures (satellites).

Asset-Liability Matching

For investors with defined liabilities (pensions, insurance, endowments with spending rules):

• Match asset duration and cash flows to liability duration and timing
• Surplus optimization: optimize the portfolio relative to liabilities, not absolute return
• Liability-driven investing (LDI): hedge liability risk with duration-matched bonds, invest surplus in return-seeking assets

Key Formulas

Formula	Expression	Use Case
MVO Objective	max w'*mu - (lambda/2)*w'Sigmaw	Optimal portfolio weights
Equilibrium Returns	Pi = lambda * Sigma * w_mkt	Black-Litterman starting point
BL Posterior	E(R) = [(tau*Sigma)^(-1) + P'*Omega^(-1)P]^(-1) * [(tauSigma)^(-1)*Pi + P'*Omega^(-1)*Q]	Blended expected returns
Risk Contribution	RC_i = w_i * (Sigma*w)_i / sigma_p	Risk parity target
Risk Parity Condition	RC_i = RC_j for all i, j	Equal risk contribution
Glide Path Rule	Equity % = 110 - Age	Age-based allocation

Worked Examples

Example 1: Three-Asset Mean-Variance Optimization

Given:

• Assets: US Equity (mu=8%, sigma=16%), Int'l Equity (mu=7%, sigma=18%), US Bonds (mu=3%, sigma=4%)
• Correlations: US/Intl Equity = 0.75, US Equity/Bonds = 0.10, Intl Equity/Bonds = 0.05
• Risk aversion: lambda = 4
• Constraints: long-only, fully invested

Calculate: Optimal weights

Solution:

Covariance matrix:

• Cov(US,US) = 0.16^2 = 0.0256
• Cov(Intl,Intl) = 0.18^2 = 0.0324
• Cov(Bond,Bond) = 0.04^2 = 0.0016
• Cov(US,Intl) = 0.75 * 0.16 * 0.18 = 0.0216
• Cov(US,Bond) = 0.10 * 0.16 * 0.04 = 0.00064
• Cov(Intl,Bond) = 0.05 * 0.18 * 0.04 = 0.00036

MVO with lambda=4 (solving numerically or via quadratic programming):

Optimal weights (approximate):

• US Equity: 35%
• Int'l Equity: 15%
• US Bonds: 50%

Portfolio: expected return = 5.25%, volatility = 7.8%

Note: The high bond allocation results from the optimization penalizing variance heavily (lambda=4). Reducing lambda or adding a minimum equity constraint would shift toward equities.

Example 2: Black-Litterman with a View on Emerging Markets

Given:

• Market-cap weights: US 55%, Developed Ex-US 30%, EM 15%
• Equilibrium returns (from Pi = lambdaSigmaw_mkt): US 6.5%, Dev Ex-US 5.8%, EM 7.2%
• Investor view: EM will outperform US by 2% (medium confidence)
• tau = 0.05

Calculate: Posterior expected returns and implied weight shift

Solution:

View specification:

• P = [-1, 0, 1] (EM minus US)
• Q = [2%] (EM outperforms US by 2%)
• Omega = [0.001] (medium confidence; lower = higher confidence)

After applying the Black-Litterman formula:

Posterior expected returns (approximate):

• US: 6.2% (decreased from 6.5%)
• Dev Ex-US: 5.9% (slight increase due to correlation effects)
• EM: 7.8% (increased from 7.2%)

The posterior tilts returns toward the view. When these posterior returns are fed into MVO, the resulting weights shift from market-cap weights toward EM and away from US, but the shift is moderate and proportional to confidence, avoiding the extreme concentrations that raw MVO can produce.

Common Pitfalls

• MVO is highly sensitive to expected return inputs and has been called an "error maximizer" — small changes in returns produce large changes in weights
• Unconstrained MVO often produces extreme, concentrated positions — always add constraints (long-only, max weight, turnover limits)
• Black-Litterman requires the analyst to specify confidence in views (Omega), which is itself uncertain
• Risk parity portfolios require leverage to achieve equity-like returns, introducing borrowing costs and leverage risk
• Ignoring implementation costs: transaction costs, bid-ask spreads, and taxes can significantly erode theoretical optimal returns
• Ignoring liquidity constraints: some asset classes (private equity, real estate) cannot be rebalanced quickly
• Glide paths assume a generic investor — individual circumstances may require customization
• Over-reliance on historical covariance matrices that may not reflect future relationships

Cross-References

• historical-risk (wealth-management plugin, Layer 1a): volatility and correlation inputs for mean-variance optimization
• forward-risk (wealth-management plugin, Layer 1b): expected return forecasts and scenario analysis for portfolio optimization
• diversification (wealth-management plugin, Layer 4): diversification principles underpin all allocation frameworks
• bet-sizing (wealth-management plugin, Layer 4): position sizing within the allocated asset classes
• rebalancing (wealth-management plugin, Layer 4): maintaining allocation targets over time
• quantitative-valuation (wealth-management plugin, Layer 3): valuation signals can inform TAA decisions

Reference Implementation

See scripts/asset_allocation.py for computational helpers.