casemark/conducting-monte-carlo-portfolio-analysis

Conducting Monte Carlo Portfolio Analysis

Runs Monte Carlo simulations for portfolio analysis, producing return distributions, tail-risk metrics, and path-dependent scenario evaluations for multi-asset portfolios.

When To Use

• Estimating the probability distribution of portfolio returns over a defined horizon (1-month to 30-year)
• Quantifying tail risk (CVaR/ES, max drawdown distributions, left-tail probabilities)
• Evaluating path-dependent features: sequence-of-returns risk, cash-flow overlays, rebalancing triggers, or option-like payoffs
• Stress-testing portfolio allocations under regime-switching or fat-tailed assumptions
• Comparing allocation candidates when closed-form analytics are insufficient (e.g., non-normal returns, leverage constraints, dynamic hedging)

Inputs To Gather

• Asset universe and weights — tickers or asset classes, target allocation, and any constraints (min/max bounds, sector caps)
• Return assumptions — historical lookback window OR forward capital-market assumptions (expected return, volatility, correlation matrix)
• Distribution model — normal, Student-t (specify degrees of freedom), skew-normal, or empirical bootstrap [VERIFY: confirm distributional choice suits the asset classes]
• Simulation parameters — number of paths (default: 10,000; use 50,000+ for stable tail estimates), time step (daily/monthly), horizon length
• Correlation structure — static Pearson matrix, DCC-GARCH, copula specification (Gaussian vs. Clayton/Gumbel for tail dependence) [VERIFY: copula choice with portfolio manager]
• Path-dependent rules — rebalancing frequency and bands, cash inflows/outflows, drawdown-triggered de-risking, tax-loss harvesting logic
• Risk-free rate and inflation assumption — for real-return or Sharpe-ratio computations
• Benchmark (optional) — index or liability stream for relative-return analysis

Workflow

1. Validate inputs

   • Confirm the correlation matrix is positive semi-definite; apply nearest-PSD correction if not
   • Check for stale or missing return series; flag gaps > 5 trading days
   • Verify that weight vector sums to 1.0 (or intended leverage ratio)

2. Calibrate the return-generation model

   • Fit chosen distribution to each asset's return series (MLE or method-of-moments)
   • Estimate correlation/copula parameters; report goodness-of-fit (e.g., Anderson-Darling p-values)
   • If using regime-switching: estimate Hidden Markov Model states (bull/bear/crisis) with transition probabilities [VERIFY: number of regimes]

3. Generate simulation paths

   • Draw correlated random variates via Cholesky decomposition (normal) or copula sampling (non-normal)
   • Construct cumulative return paths for each asset; apply portfolio weights at each rebalancing step
   • Enforce path-dependent rules: execute rebalances, apply transaction costs, overlay cash flows

4. Compute output statistics

   • Distribution metrics — mean, median, standard deviation, skewness, kurtosis of terminal wealth or annualized return
   • Tail-risk metrics — VaR and CVaR at 95% and 99% confidence; maximum drawdown distribution (median, 95th percentile); probability of loss exceeding a user-defined threshold
   • Path statistics — median path, 5th/25th/75th/95th percentile fan chart; time-to-recovery distribution after drawdowns > X%
   • Scenario analysis — conditional statistics for worst 5% of paths (crisis regime analysis)

5. Sensitivity and robustness checks

   • Re-run with ±1 standard error on expected returns and volatilities to assess input sensitivity
   • Compare results across distribution assumptions (normal vs. Student-t vs. bootstrap)
   • Confirm convergence: verify that key metrics stabilize as path count doubles

6. Compile report

   • Present results in summary table plus fan-chart visualization specification
   • Highlight key risk findings: probability of failing a return threshold, worst-case drawdown, and left-tail scenarios
   • State all assumptions, model limitations, and data vintage

Output

• Summary statistics table — expected return (annualized), volatility, Sharpe ratio, VaR (95/99), CVaR (95/99), max drawdown (median and 95th percentile), probability of negative return, probability of meeting target return
• Distribution chart spec — histogram of terminal returns with VaR/CVaR markers; fan chart of cumulative wealth paths (5/25/50/75/95 percentile bands)
• Sensitivity matrix — key metrics under alternative return, volatility, and correlation assumptions
• Path-dependent analysis — impact of rebalancing frequency, cash-flow timing, and drawdown-triggered rules on terminal wealth distribution
• Assumption log — distribution model, calibration method, number of simulations, random seed (for reproducibility), data sources and dates

Quality Checks

• Simulation count is sufficient: tail metrics (99% CVaR) should not shift > 2% when re-run with a different random seed
• Mean simulated return approximates the input expected return within ±10 bps (sanity check on the generation engine)
• Correlation of simulated asset returns matches input matrix within ±0.02
• Path-dependent rules are verified against at least one manually traced scenario
• All [VERIFY] items are resolved or explicitly flagged as pending before delivery
• Results are not presented as forecasts — disclaim that outputs reflect model assumptions, not predictions of future performance