Risk and Portfolio Analytics AI Prompts

Conduct a comprehensive drawdown analysis for this strategy or portfolio. Return series: {{returns}} Benchmark (optional): {{benchmark}} 1. Drawdown calculation: - Cumulative wealth index: W_t = ∏(1 + r_i) for i = 1 to t - Running maximum: M_t = max(W_1, W_2, ..., W_t) - Drawdown at time t: DD_t = (W_t - M_t) / M_t - Maximum drawdown (MDD): min(DD_t) over full period 2. Drawdown statistics: - Maximum drawdown: magnitude and the peak and trough dates - Average drawdown: mean of all drawdown episodes - Average drawdown duration: average time from peak to trough - Average recovery time: average time from trough to new high water mark - Number of drawdown episodes exceeding threshold (e.g. >5%, >10%, >20%) - Current drawdown: is the strategy currently in a drawdown? 3. Drawdown distribution: - Plot all drawdown episodes sorted by severity - Are large drawdowns rare events or do they cluster? - Drawdown at each percentile (50th, 75th, 90th, 95th) of episode severity 4. Underwater curve analysis: - Plot the cumulative return and the underwater curve (time spent in drawdown) on the same chart - What fraction of total time was the strategy in a drawdown? - Pain index: average drawdown × fraction of time in drawdown 5. Risk-adjusted return ratios involving drawdown: - Calmar ratio: annualized return / |MDD|. Higher is better. Benchmark: > 0.5 - Sterling ratio: annualized return / average of top 3 annual drawdowns - Burke ratio: annualized return / sqrt(sum of squared drawdowns) - Martin ratio (Ulcer index-based): annualized return / Ulcer_index Ulcer index = sqrt(mean(DD²)): penalizes both depth and duration of drawdowns 6. Drawdown comparison to benchmark: - Relative drawdown: active drawdown = portfolio DD - benchmark DD - Did the strategy protect capital better or worse than the benchmark during major drawdown periods? - Maximum relative drawdown and its timing Return: drawdown statistics table, underwater curve plot, drawdown episode list, ratio comparison, and benchmark relative analysis.

Step 1: Return data profiling — profile the return data quality. Check for missing dates, zero returns, extreme outliers, survivorship bias, and corporate action contamination. Compute basic statistics and confirm data is suitable for analysis. Step 2: Distributional analysis — test for normality, measure skewness and excess kurtosis, estimate tail behavior using EVT (GPD fitting). Determine which risk models are appropriate given the distributional properties. Step 3: VaR and CVaR — compute using all three methods (historical, parametric, Monte Carlo). Backtest VaR with Kupiec POF test and Christoffersen interval forecast test. Report which method is most appropriate. Step 4: Drawdown analysis — compute maximum drawdown, average drawdown, recovery time, and the full distribution of drawdown episodes. Report Calmar ratio, Ulcer index, and current drawdown status. Step 5: Factor decomposition — run factor model regression. Decompose total risk into systematic (factor) and idiosyncratic components. Identify the dominant factor exposures driving portfolio risk. Step 6: Stress testing — apply at least 3 historical stress scenarios and 3 hypothetical scenarios. For each: P&L impact, VaR comparison, and which positions contribute most to stress loss. Step 7: Risk report — write a 1-page risk summary: current risk level vs target, factor exposures of concern, tail risk assessment, liquidity profile, and top 3 risk management recommendations.

Assess the liquidity risk of this portfolio and estimate the cost and time required for liquidation. Portfolio holdings: {{holdings}} (positions and sizes) Market data: {{market_data}} (average daily volume, bid-ask spreads) Liquidation scenario: {{scenario}} 1. Liquidity metrics per position: - Average Daily Volume (ADV): 20-day and 60-day trailing ADV - Days-to-liquidate (DTL): position_size / (participation_rate × ADV) Standard assumption: participate at 20% of ADV to avoid significant market impact - Bid-ask spread cost: size × (ask - bid) / midprice - Amihud illiquidity ratio: |return| / dollar_volume. Higher = more illiquid. 2. Portfolio-level liquidity: - Asset-weighted average DTL for the full portfolio - DTL percentile distribution: what % of the portfolio can be liquidated in 1 day, 3 days, 1 week, 2 weeks? - Illiquid tail: which positions have DTL > 20 days? These are the most problematic under stress. 3. Market impact modeling: The square-root market impact model: Impact = η × σ × sqrt(Q / ADV) Where η ≈ 0.1 for equities, σ = daily volatility, Q = shares to trade, ADV = average daily volume - Estimate market impact for each position at 100% liquidation - Total liquidation cost = bid-ask spread cost + market impact cost - Liquidity-adjusted VaR: add expected liquidation cost to standard VaR 4. Stress scenario — forced liquidation: Scenario: forced to liquidate {{pct}}% of portfolio in {{days}} trading days - Which positions can be liquidated within the constraint? - What market impact will the liquidation create? - What is the expected slippage cost in dollars and as % of portfolio NAV? - Which positions will require extended liquidation beyond the constraint? 5. Liquidity mismatch risk: - If managing a fund: compare portfolio liquidity profile to fund redemption terms - What fraction of the portfolio could be liquidated within the fund's redemption notice period? - What are the implications if redemptions exceed the liquid portion? 6. Liquidity stress testing: - Scenario: ADV drops 50% (typical in a crisis). How does the DTL profile change? - Scenario: bid-ask spreads widen 5×. How does total liquidation cost change? Return: per-position liquidity metrics, portfolio liquidity distribution, market impact estimates, forced liquidation analysis, and liquidity stress test results.

Decompose portfolio performance into its sources using Brinson-Hood-Beebower (BHB) attribution. Portfolio: {{portfolio_weights_and_returns}} Benchmark: {{benchmark_weights_and_returns}} Period: {{period}} 1. BHB attribution framework: Total active return = Allocation effect + Selection effect + Interaction effect For each segment i: - Allocation effect: (w_p,i - w_b,i) × (R_b,i - R_b) Did we overweight/underweight the right segments? - Selection effect: w_b,i × (R_p,i - R_b,i) Did we pick better securities within each segment? - Interaction effect: (w_p,i - w_b,i) × (R_p,i - R_b,i) Did we concentrate in segments where we had good selection? Where: - w_p,i = portfolio weight in segment i - w_b,i = benchmark weight in segment i - R_p,i = portfolio return in segment i - R_b,i = benchmark return in segment i - R_b = total benchmark return 2. Segment definitions: Apply attribution at multiple levels: - Level 1: by asset class (equity, fixed income, alternatives) - Level 2: by sector (within equity: technology, healthcare, financials, etc.) - Level 3: by country or region (within global equity) 3. Attribution over time: - Monthly attribution: cumulative linking is required (simple addition creates geometric compounding error) - Geometric linking method: chain-link the single-period attributions - Plot cumulative allocation, selection, and interaction effects over the period 4. Factor attribution (alternative to BHB): Regress active returns on factor returns (Barra or Fama-French): - Factor contribution: β_factor × factor_return - Specific (residual) contribution: unexplained by factors - This tells you whether outperformance came from intentional factor tilts or from security selection 5. Risk-adjusted attribution: - Information ratio: active_return / tracking_error - t-statistic: is active return statistically significant? Require ≥ 3 years to assess significance. - Active risk decomposition: which bets contributed most to tracking error? 6. Pitfalls: - Currency effects: separate currency contribution from local return contribution for international portfolios - Geometric vs arithmetic: be explicit about which convention is used Return: BHB attribution table by segment, cumulative attribution plots, factor attribution, and information ratio analysis.

Construct an optimal portfolio from this asset universe using mean-variance optimization and robust alternatives. Assets: {{asset_universe}} Return estimates: {{return_estimates}} Covariance matrix: {{covariance_matrix}} Constraints: {{constraints}} 1. Classical mean-variance optimization (Markowitz): Solve: min w'Σw subject to w'μ = target_return, w'1 = 1, w ≥ 0 - Efficient frontier: trace the set of portfolios minimizing variance for each target return - Identify: minimum variance portfolio (MVP), maximum Sharpe ratio portfolio (tangency) - Report for each portfolio: weights, expected return, volatility, Sharpe ratio 2. The problem with classical MVO: - Estimation error: small changes in expected returns produce large weight changes - Input sensitivity: MVO is an 'error maximizer' — it concentrates in assets with the most overestimated returns - Demonstrate: perturb expected returns by ±1% and show how weights change 3. Robust optimization alternatives: Maximum Sharpe Ratio with shrinkage: - Shrink expected returns toward a common prior (e.g. equal returns for all assets or CAPM-implied returns) - Ledoit-Wolf shrinkage on the covariance matrix Minimum Variance Portfolio: - Avoids using expected return estimates entirely (which are the most error-prone input) - min w'Σw subject to w'1 = 1, w ≥ 0 - Historically outperforms on a risk-adjusted basis in many markets Risk Parity: - Each asset contributes equally to total portfolio variance - RC_i = w_i × (Σw)_i = Portfolio_variance / N - Implicit long duration bias (bonds are low vol); often levered to achieve return targets Maximum Diversification: - Maximize the ratio: w'σ / sqrt(w'Σw) where σ is the vector of individual asset volatilities - Maximizes diversification benefit relative to a weighted average of individual volatilities 4. Practical constraints: - Long-only: w ≥ 0 - Weight bounds: w_i ∈ [0, 0.20] (max 20% in any single asset) - Turnover constraints: |w_new - w_old| ≤ budget - Sector constraints: sum of sector weights within bounds 5. Out-of-sample evaluation: - Walk-forward portfolio construction: reoptimize annually, evaluate on the following year - Compare all methods: realized Sharpe, realized volatility, maximum drawdown, turnover Return: efficient frontier plot, portfolio weights for each method, sensitivity analysis, walk-forward performance comparison.

Construct and analyze a risk parity portfolio from this asset universe. Assets: {{assets}} Covariance matrix: {{covariance}} Target volatility: {{target_vol}} (e.g. 10% annualized) 1. Risk contribution framework: Marginal risk contribution (MRC): MRC_i = (Σw)_i = ∂σ_p/∂w_i Total risk contribution (TRC): TRC_i = w_i × MRC_i Portfolio variance: σ²_p = w'Σw = Σ_i TRC_i Risk contribution percentage: RC%_i = TRC_i / σ²_p Risk parity condition: RC%_i = 1/N for all assets i 2. Numerical solution: Risk parity has no closed-form solution for N > 2 assets. Use gradient-based optimization: min Σ_i Σ_j (TRC_i - TRC_j)² subject to w'1 = 1, w ≥ 0 Or alternatively, use Maillard et al. (2010) iterative algorithm: w_i ← w_i × σ_p / (N × MRC_i) → iterate until convergence 3. Risk parity portfolio analysis: - Report: asset weights, marginal risk contributions, percentage risk contributions - Verify: risk contributions are approximately equal across all assets - Compare weights to: equal-weight, min-variance, and 60/40 benchmark 4. Volatility targeting: - Scale the risk parity weights by: k = target_vol / σ_rp - This may require leverage if σ_rp < target_vol (common with bonds in the portfolio) - Report: leverage ratio, cost of leverage assumed (financing rate) 5. Sensitivity analysis: - How do weights change if equity volatility doubles? (Bonds get more weight) - How do weights change if bond-equity correlation goes from -0.3 to +0.3? - Risk parity is most sensitive to: changes in relative volatilities and correlation regime changes 6. Historical performance analysis: - Backtest the risk parity portfolio with monthly rebalancing - Compare to: equal-weight, 60/40, min-variance - Report: Sharpe ratio, Calmar ratio, max drawdown, monthly turnover - Notable: risk parity struggled in 2022 when bonds and equities both sold off simultaneously (positive correlation regime) 7. Limitations: - Risk parity is a risk-based, not return-based, allocation - It is implicitly long duration (bonds dominate in unlevered form) - Correlation instability undermines the equal risk contribution in practice Return: risk parity weights with risk contribution verification, comparison table, sensitivity analysis, and backtest performance.

Calculate Value at Risk (VaR) and Conditional Value at Risk (CVaR) for this portfolio using multiple methods. Portfolio returns: {{returns}} Confidence levels: 95% and 99% Holding period: 1-day and 10-day 1. Definitions: - VaR(α): the loss that will not be exceeded with probability α. If 1-day 99% VaR = $1M, there is a 1% chance of losing more than $1M in a single day. - CVaR(α) (also called Expected Shortfall, ES): the expected loss given that the loss exceeds VaR. Always ≥ VaR. More coherent risk measure — CVaR is sub-additive, VaR is not. 2. Method 1 — Historical simulation: - Sort the return series from worst to best - 95% VaR: the 5th percentile of the distribution (5% of worst returns) - 99% VaR: the 1st percentile - CVaR: mean of returns below the VaR threshold - Pros: non-parametric, captures empirical fat tails and asymmetry - Cons: limited by historical window length; past scenarios may not reflect future risks 3. Method 2 — Parametric (variance-covariance) approach: - Assume returns are normally distributed: VaR = μ - z_α × σ - z_{0.95} = 1.645, z_{0.99} = 2.326 - CVaR = μ - σ × φ(z_α) / (1 - α), where φ is the standard normal PDF - Pros: fast, analytical, easy to decompose by position - Cons: assumes normality — severely underestimates tail risk for fat-tailed assets 4. Method 3 — Monte Carlo simulation: - Fit a distribution to the returns (normal, t, or skew-t) - Simulate 100,000 scenarios from the fitted distribution - Compute VaR and CVaR from the simulated distribution - Pros: flexible distribution; can model complex portfolios - Cons: results depend heavily on the assumed distribution and model parameters 5. Scaling to multi-day horizons: - Square-root-of-time rule: 10-day VaR ≈ 1-day VaR × sqrt(10) - Caveat: this assumes i.i.d. returns. Volatility clustering violates this assumption. - Better: simulate 10-day paths and compute VaR directly from path-end P&L 6. Method comparison and recommendation: - Report VaR and CVaR from all three methods - Where do they differ most? Why? - Which method is most appropriate for this portfolio and why? - Backtesting VaR: count how many historical days exceeded the VaR. Should be ≈ 5% for 95% VaR. Return: VaR and CVaR table (method × confidence level), method comparison, scaling analysis, and backtesting results.