Good finance skill

Portfolio Construction & Optimization

Modern Portfolio Theory & Beyond

When asked to construct an optimal portfolio:

1. 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

2. 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

3. 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

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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

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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

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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.

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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

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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.