WilliamWJHuang Portfolio Construction & Optimization
Modern Portfolio Theory & Beyond
When asked to construct an optimal portfolio:
Start with mean-variance as a baseline, but always acknowledge its limitations:
- Estimation error in expected returns dominates the optimization
- Small changes in inputs produce dramatically different allocations
- Covariance matrices estimated from historical data can be unreliable
Use robust methods to mitigate estimation error:
- Black-Litterman model to blend views with equilibrium
- Shrinkage estimators for covariance (Ledoit-Wolf)
- Resampled efficient frontier for stability
- Risk parity as a less input-sensitive alternative
Diversification depth: Don't just count assets. True diversification requires understanding correlation structure, factor exposures, sector concentration, and tail dependence. In crises, correlations spike — assets that look diversified in normal times may all fall together.
Rebalancing
Portfolio rebalancing requires balancing drift risk against transaction costs:
- Calendar-based: rebalance monthly/quarterly regardless of drift
- Threshold-based: rebalance when allocation drifts beyond tolerance bands
- Tax-aware rebalancing: harvest losses when rebalancing, avoid wash sales
- Higher frequency reduces drift risk but increases transaction/tax costs
Benchmark Selection
Always match the benchmark to the strategy:
- An equity long/short fund should not be compared to the S&P 500
- Use style-matched, investable benchmarks
- Track tracking error and information ratio for active strategies
Risk Management
Value at Risk (VaR) & Beyond
VaR answers "what's the worst loss at X% confidence?" but has critical limitations:
- Tail risk: VaR says nothing about losses beyond the threshold. Expected Shortfall (CVaR) measures the average loss in the tail.
- Fat tails: Financial returns are non-normal with excess kurtosis. Parametric VaR assuming normality underestimates extreme losses.
- Correlation breakdown: In crises, correlations spike toward 1. Historical covariance matrices become unreliable.
When to use what
- Parametric VaR: Quick estimate, good for normal-ish distributions
- Historical simulation: No distributional assumption, but limited by data
- Monte Carlo VaR: Most flexible, handles complex portfolios
- Always complement with: stress testing, scenario analysis, Expected Shortfall
Stress Testing
Run stress tests using both historical and hypothetical scenarios:
- Historical: 2008 GFC, COVID crash, dot-com bust, 1998 LTCM
- Hypothetical: rates +300bps, equity -40%, correlation → 1
- Reverse stress test: what scenario causes the portfolio to lose X%?
Risk-Adjusted Returns
The Sharpe ratio is a starting point but not sufficient:
- Sortino ratio: Only penalizes downside deviation (better for asymmetric returns)
- Maximum drawdown: Peak-to-trough loss — what's the worst pain?
- Calmar ratio: Annualized return / maximum drawdown
- Information ratio: Active return / tracking error vs. benchmark
Backtesting
Critical Biases to Address
Look-Ahead Bias
Never use information that wouldn't have been available at the time of the simulated decision. This includes:
- Point-in-time fundamentals (use lagged data, not restated)
- Index reconstitution (use point-in-time index membership, not current constituents)
- Event timing (earnings dates, splits are known in advance in databases)
Survivorship Bias
Use survivorship-bias-free datasets that include delisted and bankrupt companies. Testing only on currently listed securities inflates returns by silently excluding the failures.
Transaction Costs & Market Impact
Always account for:
- Commissions and fees
- Bid-ask spread (especially for small-caps and illiquid assets)
- Market impact (your own trades move the price)
- Slippage between signal and execution
Net-of-cost returns are the only returns that matter.
Overfitting to Historical Data
- Use walk-forward validation or expanding window cross-validation
- Keep the number of tuned parameters small relative to the data
- Run out-of-sample tests on genuinely held-out data
- Be suspicious of strategies with too-good-to-be-true Sharpe ratios (> 2.0)
- Combinatorial purged cross-validation (CPCV) for financial data
Multiple Testing Bias
When evaluating many strategies or parameter combinations:
- The best-performing backtest is likely inflated by selection bias
- Use the deflated Sharpe ratio (López de Prado) to correct for data mining
- Apply family-wise error rate corrections (Bonferroni, Holm)
- Report false discovery rate (FDR) when screening many signals
Valuation
DCF (Discounted Cash Flow)
Always run sensitivity analysis on:
- WACC (discount rate): A 1% change can move the valuation by 20%+
- Terminal growth rate: Must be ≤ long-term GDP growth (2-3%)
- Terminal value: Usually represents 60-80% of total DCF — flag this
Present a range of values, not a single point estimate. DCF gives a range of reasonable valuations, not "the right answer."
Comparable Analysis
Peer selection matters enormously:
- Match industry, growth profile, and risk characteristics
- Normalize for accounting differences (operating leases, R&D capitalization)
- Use forward multiples when available (less backward-looking)
- Consider EV-based multiples for capital structure neutrality
Options Pricing
Black-Scholes assumptions rarely hold in practice:
- Constant volatility (reality: volatility smile/skew)
- Continuous trading (reality: discrete, with gaps)
- Log-normal returns (reality: fat tails, jumps)
Consider binomial trees for American options, Monte Carlo for path-dependent payoffs, and stochastic volatility models for better smile fitting.
Time Series & Forecasting
Stationarity
Never fit ARIMA or regression on raw price levels without checking stationarity.
- Augmented Dickey-Fuller (ADF) or Phillips-Perron tests first
- Use log-returns or first differences for modeling
- Cointegration tests (Johansen, Engle-Granger) for pairs trading
Regime Changes
Markets exhibit regime shifts (bull/bear, high/low volatility):
- GARCH models capture volatility clustering
- Markov switching models for regime detection
- Always ask: "would this model work in a different market regime?"
Return Distributions
Financial returns are not normally distributed:
- Fat tails (excess kurtosis) — extreme events are more common than Gaussian predicts
- Skewness — downside moves tend to be larger than upside
- Volatility clustering — captured by GARCH family models
- Consider Student-t or generalized hyperbolic distributions
General Finance Best Practices
Return Calculations
- Use geometric (compound) returns for multi-period performance
- Arithmetic returns only for single-period expected value
- Time-weighted returns (TWR) for manager evaluation
- Money-weighted returns (IRR) for investor experience
- Don't annualize by multiplying monthly by 12 — compound properly
Inflation Adjustment
For any analysis spanning more than 2-3 years:
- Distinguish nominal vs. real returns
- Use CPI or PCE deflator for purchasing power comparisons
- Retirement planning MUST use real returns
Tax Awareness
- Short-term vs. long-term capital gains have different rates
- Tax-loss harvesting can offset gains (watch wash sale rules)
- After-tax returns can differ dramatically from pre-tax
- High-turnover strategies incur significant tax drag
Market Efficiency
Before claiming alpha or outperformance:
- What informational or structural edge does the strategy exploit?
- Why hasn't it been arbitraged away?
- What's the capacity (can it scale)?
- Is the edge decaying as more capital pursues it?
Regulatory Awareness
- Investment advice is regulated — include appropriate disclaimers
- Know your customer (KYC) and anti-money laundering (AML) requirements
- Fiduciary duty: act in the client's best interest
- Suitability: recommendations must match client risk tolerance and objectives
Disclaimer: This skill provides educational guidance on financial methodology. It is not financial advice. Consult qualified professionals for investment decisions.