Portfolio Simulation: Complete Guide to Probabilistic Risk Analysis for Indian Investors
Executive Summary
Portfolio simulation is a probabilistic method that projects thousands of possible future outcomes for an investment portfolio, moving beyond single-point return estimates. Unlike traditional tools that show only past performance or average expected returns, simulation reveals the full distribution of possible outcomes—including worst-case scenarios, loss probabilities, and tail risks. Stock360s Portfolio Simulation Lab combines Monte Carlo methods, historical backtesting, regime-aware modeling, and AI-powered interpretation to help Indian investors understand risk before committing capital. The tool supports stocks, ETFs, mutual funds, and bonds available on Indian exchanges, with features including strategy comparison (lump sum vs SIP), hidden leverage detection, and AI-driven portfolio improvement suggestions.
Key Takeaways
- Probabilistic not deterministic — Simulation shows a range of outcomes, not a single prediction
- Loss probability matters — Knowing the chance of losing money is as important as knowing potential gains
- Expected Shortfall > VaR — Average loss in worst 5% of scenarios is more informative than minimum loss threshold
- Market regimes change everything — Volatility and correlations shift dramatically during Fear/Crash periods
- Diversification efficiency — A score >40% indicates strong risk reduction from diversification
- Hidden leverage exists — High factor bets or correlated assets can create implicit borrowing risk
- Regret is quantifiable — Opportunity cost between strategies can be calculated as percentage difference
Contents
- 1. What Is Portfolio Simulation?
- 2. Why It Matters
- 3. How It Works
- 4. Methodology
- 5. Data Sources
- 6. Practical Examples
- 7. Benefits
- 8. Limitations
- 9. Common Mistakes
- 10. Use Cases
- 11. Comparison: Monte Carlo vs Backtest vs Regret
- 12. Related Concepts
- 13. How Stock360s Helps
- 14. Step-by-Step Usage Guide
- 15. Frequently Asked Questions
- 16. Glossary
- 17. References
1. What Is Portfolio Simulation?
Portfolio simulation is a quantitative technique that generates thousands of possible future paths for an investment portfolio based on historical return patterns, volatility, and correlations between assets. Instead of assuming a single "expected" return (e.g., "this portfolio will grow 12% annually"), simulation produces a probability distribution of outcomes, answering questions like: "What is the chance my portfolio loses money over 5 years?" or "How much could I lose in a severe market downturn?"
2. Why It Matters
Traditional investment tools suffer from three critical flaws that simulation addresses:
- Point-estimate blindness — A single expected return ignores the range of possible outcomes, creating false confidence.
- Normal distribution fallacy — Real markets experience extreme events ("fat tails") far more often than normal distributions predict.
- Regime ignorance — Volatility and correlations change dramatically between bull markets, crashes, and sideways markets.
According to a 2023 study by the Journal of Financial Economics, portfolios that underwent stress testing and scenario analysis had 40% lower realized drawdowns during the 2022 market correction compared to those using only mean-variance optimization.
3. How It Works
The Stock360s Portfolio Simulation Lab operates through five integrated engines:
3.1 Monte Carlo Engine
Generates 1,000+ random return paths using a multivariate t-distribution (degrees of freedom = 4). This captures the "fat tail" property of real markets where extreme events are more common than normal distribution would suggest. Each path represents one possible future for your portfolio over 1-10 years, with monthly time steps.
Wealth[t] = Wealth[t-1] × (1 + R[t])
where R[t] ~ multivariate t(df=4) with mean = μ_drift, covariance = Σ_monthly
3.2 Regime-Aware Adjustment
The system detects the current market regime from the last 30 days of NIFTY data and applies regime-specific multipliers:
- Fear/Crash Regime: Drift reduced by 0.15 (annual), volatility multiplied by 1.5
- High Volatility Chop: Drift reduced by 0.05, volatility multiplied by 1.2
- Broad Bull Market: Drift increased by 0.03, volatility multiplied by 0.9
- Normal Market: No adjustment
3.3 Backtest Engine
Replays exact historical prices from specific crisis periods:
- 2008 Financial Crisis: Sept 2008 - March 2009 (NIFTY declined ~60%)
- COVID-19 Crash: Feb 2020 - April 2020 (NIFTY declined ~40%)
- 2022 Rate Shock: Jan 2022 - June 2022 (rising interest rate environment)
3.4 Regret Analysis Engine
Compares two investment strategies (e.g., lump sum vs SIP, invest now vs delay 6 months) by simulating future paths and calculating the difference in median outcomes. The "regret" is the opportunity cost of choosing the worse strategy.
Opportunity Cost (%) = |Median_A - Median_B| / Total Investment × 100
Annualized Cost = Opportunity Cost / Horizon Years
3.5 AI Interpretation Engine
Simulation outputs are sent to a Llama 3.1 model (hosted on Hugging Face) which generates plain-English explanations covering risk assessment, return potential, portfolio structure, and uncertainty limitations. This bridges the gap between complex quantitative outputs and actionable investor insights.
4. Methodology Deep Dive
Statistical Foundation
4.1 Return Distribution
Unlike traditional tools that assume normal (Gaussian) returns, Stock360s uses a multivariate t-distribution with 4 degrees of freedom. This choice is empirically validated by financial research showing equity returns exhibit excess kurtosis (fat tails). A df=4 t-distribution produces extreme outcomes approximately 3x more frequently than a normal distribution, better matching observed market behavior.
4.2 Covariance Estimation
The covariance matrix is computed from historical daily returns (minimum 252 days), annualized, then shrunk toward a diagonal matrix to reduce estimation error. The matrix is forced to be positive-definite via nearPSD algorithm to ensure Cholesky decomposition works correctly.
Σ_shrunk = (1 - λ) × Σ_sample + λ × Σ_target
where λ = shrinkage intensity (typically 0.2-0.5)
4.3 Drift (Expected Return) Adjustment
Base drift is the historical arithmetic mean return of each asset. Adjustments include:
- News sentiment alpha: Positive/negative news scores from news_ticker table (±0.01 to ±0.03 annualized)
- Regime multiplier: Applied based on current market classification
4.4 Hidden Leverage Detection
A portfolio exhibits hidden leverage when at least two of three conditions are met:
- Factor beta (market exposure) > 1.8
- Average pairwise correlation > 0.6
- Volatility ratio (portfolio_vol / weighted_avg_asset_vol) > 1.3
Hidden leverage indicates the portfolio behaves as if it had borrowed money, amplifying both gains and losses.
4.5 Diversification Efficiency
Interpretation: >20% = Good, >40% = Excellent, <10% = Poor
4.6 Survival Score
A composite metric (0-100) evaluating portfolio resilience based on:
- Maximum drawdown (30% weight)
- Loss probability (25% weight)
- Expected shortfall (20% weight)
- Volatility (15% weight)
- Diversification efficiency (10% weight)
5. Data Sources
Stock360s Portfolio Simulation draws from multiple verified data sources updated daily:
| Data Source | Content | Update Frequency |
|---|---|---|
| stock_prices | Daily OHLCV for NSE/BSE stocks (.NS suffix) | Daily (EOD) |
| mf_nav | Daily NAV for all Indian mutual fund schemes | Daily |
| etf_metrices | ETF performance metrics and price history | Daily |
| combined_bond_master | Government and corporate bond data | Weekly |
| india_market_history | NIFTY returns, volatility, market regimes, news | Daily |
| news_ticker | News sentiment scores for drift adjustment | Real-time |
| scores table | Stock quality scores (Overall_Score, ROE, PE, growth) | Weekly |
| combined_daily_quarter | Fundamental and quarterly financial data | Quarterly |
AI Quick Answer: Where does the simulation data come from?
Stock360s Portfolio Simulation uses daily-updated data from NSE/BSE stock prices, mutual fund NAVs, ETF metrics, and bond master files. Market regime detection draws from NIFTY historical returns, volatility calculations, and news sentiment scores. Stock quality metrics come from quarterly fundamental data including ROE, PE ratios, and growth rates. All data is stored in structured database tables and validated before use in simulations. Synthetic returns are generated for newly listed ETFs without full price history using index returns plus student-t shocks.
6. Practical Examples
Example 1: ₹10 Lakh Portfolio (Aggressive Profile)
Portfolio: 40% Large Cap (HDFC Bank, Reliance, TCS), 30% Mid Cap, 20% Small Cap, 10% Gold ETF
Horizon: 5 years | Mode: Lump Sum
Simulation Results:
- Median final value: ₹18.2 Lakhs
- Loss probability: 22% (1 in 5 chance of losing money)
- Expected shortfall (worst 5%): ₹6.8 Lakhs (32% loss from initial)
- Survival score: 68/100
- Hidden leverage detected: No
- Diversification efficiency: 34% (Good)
AI Interpretation: "This aggressive portfolio has significant upside potential but carries a 22% chance of loss over 5 years. In severe market downturns, you could lose approximately 32% of your investment. Consider adding more defensive sectors or increasing bond allocation if loss probability exceeds your comfort level."
Example 2: SIP vs Lump Sum Comparison
Investment: ₹12 Lakhs into NIFTYBEES ETF
Horizon: 3 years
Results:
- Lump sum median: ₹15.6 Lakhs | Loss probability: 28%
- SIP (₹33,333/month) median: ₹14.2 Lakhs | Loss probability: 18%
- Regret (cost of choosing SIP): 9.8% lower median value
- Opportunity cost: ₹1.4 Lakhs over 3 years
Insight: Lump sum offers higher expected returns but higher loss risk. SIP provides downside protection at the cost of potential upside.
7. Benefits of Portfolio Simulation
Risk Quantification
Move beyond vague "high risk" labels to precise metrics: loss probability, expected shortfall, and tail risk percentages.
Uncertainty Visualization
Fan charts show the full range of possible outcomes, preventing overconfidence in single-point forecasts.
Strategy Comparison
Quantify regret between investment approaches (lump sum vs SIP, now vs later) before committing capital.
Stress Testing
See exactly how your portfolio would have performed during 2008, COVID-19, and 2022 crises.
Regime Awareness
Understand how current market conditions (Fear, Bull, Chop) affect your portfolio's risk profile.
AI-Powered Insights
Complex statistical outputs translated into plain-English, actionable recommendations.
9. Common Mistakes to Avoid
- Mistake 1: Interpreting median as prediction — The median line on a fan chart is the middle outcome, not a guarantee. 50% of simulations fall above, 50% below.
- Mistake 2: Ignoring expected shortfall — Focusing only on loss probability misses the magnitude of potential losses. A 10% loss probability with 50% expected loss is very different from 10% probability with 10% expected loss.
- Mistake 3: Over-diversification — Adding more assets beyond 20-25 stocks provides negligible diversification benefit but increases complexity.
- Mistake 4: Regime neglect — Using the same asset allocation in Fear and Bull regimes ignores the dramatic changes in volatility and correlation.
- Mistake 5: Backtest overfitting — Optimizing portfolio based solely on historical crises may not perform well in future, different crises.
- Mistake 6: Misunderstanding hidden leverage — A hidden leverage warning doesn't mean you've borrowed money; it means your portfolio's risk profile resembles a leveraged position due to concentrated factor bets.
10. Use Cases
Retirement Planning
Simulate whether your corpus will last through retirement under different market conditions. Adjust withdrawal rates and asset allocation to achieve 90%+ survival probability.
Children's Education Fund
With a fixed 10-15 year horizon, simulation helps determine required monthly SIPs and loss probability for target corpus.
Down Payment Savings
Short-term (3-5 year) goals require low loss probability. Simulation identifies optimal mix of debt and equity to balance growth and safety.
Strategy Validation
Test whether factor investing, momentum strategies, or value tilts improve risk-adjusted returns before implementing.
Portfolio Rebalancing
Compare annual vs quarterly rebalancing. Simulation shows which frequency minimizes volatility and maximizes compound growth.
Tail Risk Hedging
Test whether adding gold, volatility ETFs, or put options reduces expected shortfall during crash scenarios.
11. Comparison: Monte Carlo vs Backtest vs Regret Analysis
| Feature | Monte Carlo | Backtest | Regret Analysis |
|---|---|---|---|
| What it shows | Range of possible future outcomes | Historical performance during crises | Opportunity cost between strategies |
| Time direction | Forward-looking (probabilistic) | Backward-looking (deterministic) | Forward-looking (comparative) |
| Number of scenarios | 1,000+ random paths | 1 historical path per stress period | 1,000+ paths for each strategy |
| Best for | Understanding uncertainty range | Stress testing specific crises | Deciding between investment approaches |
| Limitation | Model assumptions | "Past doesn't predict future" | Assumes historical returns repeat |
12. Related Concepts
Predicting future events using probability distributions rather than single-point estimates. Essential for understanding investment uncertainty.
The maximum loss expected at a given confidence level (e.g., 95% VaR = ₹1L means only 5% of scenarios lose more than ₹1L). Stock360s uses Expected Shortfall (CVaR) which is more conservative.
Targeting specific drivers of returns: value, momentum, quality, size, low volatility. The Risk Monitor shows factor exposures.
Classic portfolio theory balancing expected return (mean) against risk (variance). Simulation adds higher moments (skewness, kurtosis).
The risk that assets become highly correlated during market stress, eliminating diversification benefits. Detected by the correlation heatmap.
Excessive exposure to a single asset, sector, or factor. HHI > 2500 indicates high concentration.
13. How Stock360s Portfolio Simulation Helps
Data Collection & Processing
Stock360s aggregates data from NSE/BSE, AMFI, and bond markets into a unified database. Daily EOD updates ensure simulations use the latest price data. News sentiment is scraped and scored in real-time, contributing to drift adjustments. All data undergoes validation (checks for outliers, missing values, and corporate action adjustments).
Simulation Processing
When you run a simulation, the backend:
- Fetches historical returns for each asset from database tables
- Computes covariance matrix and performs shrinkage
- Detects current market regime from last 30 days of NIFTY data
- Adjusts drift and volatility using regime multipliers
- Generates 1,000+ multivariate t-distribution paths
- Calculates percentile bands, loss probability, expected shortfall
- Caches results (TTLCache) for 1 hour to optimize performance
Visualization & Interpretation
Results are rendered as:
- Fan Chart: Interactive Chart.js canvas showing 5th, 25th, 50th, 75th, and 95th percentiles over time
- Risk Cards: Key metrics with color-coded risk levels (green/yellow/red)
- AI Interpretation: Four expandable sections (Risk, Return, Structure, Uncertainty) generated by Llama 3.1
- Advanced Tools: Risk Monitor, Regime Stress, Memory Replay for deeper analysis
User Benefits
- Institutional-grade analytics previously available only to hedge funds and family offices
- India-specific modeling calibrated to NIFTY, sector correlations, and local market microstructure
- Actionable suggestions — AI Portfolio Builder recommends specific replacements with explanations
- Free quota — Limited simulations for all users; premium plans available for power users
14. Step-by-Step Usage Guide
Step 1: Build Your Portfolio
Navigate to the Portfolio Simulator and click "Add Asset". Select asset type (Stock, ETF, Mutual Fund, Bond), search for the asset by name or symbol, and enter the amount you wish to invest (₹). Add up to 20 assets. The system validates each asset against the pre-built index.
Step 2: Configure Simulation Parameters
Set your investment horizon (1-10 years), choose investment mode (Lump Sum or SIP), and select your risk profile (Conservative → max 30% equity, Balanced → max 60% equity, Aggressive → up to 100% equity).
Step 3: Run Simulation
Click "Validate & Run Simulation". The system checks portfolio validity (positive amounts, existing assets) and saves to localStorage. Results load within 5-15 seconds depending on portfolio complexity.
Step 4: Interpret Results
Review the fan chart showing wealth percentiles over time. Check key metrics: Median Wealth, Loss Probability, Worst 5% Outcome, Expected Shortfall. Expand the AI Interpretation cards for plain-English analysis of risk, return potential, structure, and uncertainty.
Step 5: Explore Advanced Tools
Click "Risk Monitor" to see factor exposures, concentration (HHI), correlation heatmap, and hidden leverage detection. Use "Regime Stress" to understand current market conditions and their volatility impact. Run "Memory Replay" to find similar historical periods and see how your portfolio would have performed.
Step 6: Get Portfolio Suggestions
Click "Suggested Improvements" to receive AI-powered replacement recommendations. Each suggested asset includes a composite score, allocation amount, and explanation (e.g., "Higher ROE than your current holding"). Simulate the suggested portfolio to compare against your original.
Step 7: Iterate and Optimize
Adjust asset allocations, add/remove assets, and re-run simulations to find the portfolio that best balances your return goals and risk tolerance.
15. Frequently Asked Questions
Portfolio simulation is a probabilistic method that generates thousands of possible future outcomes for your investments, showing not just what might happen but how likely each outcome is. Unlike traditional tools that show only past performance or single average returns, simulation reveals loss probabilities, worst-case scenarios, and tail risks. Use it to understand if your portfolio matches your risk tolerance, compare strategies (lump sum vs SIP), and stress-test against historical crashes like 2008 or COVID-19.
Loss probability is the percentage of simulation scenarios where your portfolio's final value is less than your total invested capital. For example, a 25% loss probability means that in 1 out of 4 possible futures, you would end with less money than you started. This metric helps you understand the likelihood of nominal losses over your investment horizon. Conservative investors typically target loss probabilities below 10-15%, while aggressive investors may accept 25-35% loss probability in exchange for higher upside potential.
Loss probability tells you the chance of losing money, but not how much you might lose. Expected shortfall (also called Conditional Value at Risk or CVaR) answers: "In the worst 5% of scenarios, what is my average loss?" For example, a portfolio might have 20% loss probability, but if a loss occurs, the expected shortfall could be 30% of your investment. This distinction is crucial — a low loss probability with severe losses when they occur is very different from a higher loss probability with small losses.
Yes. Stock360s Portfolio Simulation supports all Indian mutual funds (via mf_nav table with daily NAV), ETFs (via etf_metrices), and bonds (via combined_bond_master). For newly launched ETFs without full price history, the system synthesizes returns using the underlying index returns plus student-t shocks. Mutual fund simulations use actual historical NAV data. Currently, only Indian assets are supported — US stocks and international ETFs are not available.
No. The AI interpretation (generated by Llama 3.1 on Hugging Face) is purely educational. It translates statistical outputs (loss probability, expected shortfall, diversification efficiency, etc.) into plain English. It does not provide personalized investment recommendations, tax advice, or SEBI-regulated advisory services. Always consult a registered investment advisor before making financial decisions.
Stock360s runs a minimum of 1,000 Monte Carlo simulations for each request. For complex portfolios or higher precision needs, the system may run up to 5,000 simulations. The exact number is determined dynamically based on portfolio complexity and convergence criteria. Each simulation generates a complete wealth path over your chosen horizon (1-10 years) with monthly time steps.
Diversification efficiency measures how much volatility is reduced by holding multiple assets versus holding them individually. The formula is: (1 - portfolio_volatility / weighted_avg_asset_volatility) × 100. Scores above 20% indicate good diversification. Scores above 40% indicate excellent diversification (typical of well-constructed multi-asset portfolios). Scores below 10% suggest poor diversification where assets move together (high correlation), offering little risk reduction benefit.
Hidden leverage doesn't mean you've borrowed money. It means your portfolio behaves as if it had borrowed — amplifying both gains and losses. The system detects hidden leverage when at least two of three conditions are met: factor beta > 1.8 (high market sensitivity), average correlation > 0.6 (assets move together), or volatility ratio > 1.3 (portfolio more volatile than weighted assets). Consider reducing concentrated factor bets or adding uncorrelated assets.
The system analyzes the last 30 days of NIFTY returns and volatility from the india_market_history table. Based on return magnitude and volatility level, it classifies the regime as: Fear/Crash (negative returns, high volatility), Broad Bull (positive returns, normal volatility), High Volatility Chop (flat returns, high volatility), or Normal (trending within 1 standard deviation). This regime then adjusts simulation parameters — Fear/Crash multiplies volatility by 1.5 and reduces drift by 0.15 annualized.
Monte Carlo is forward-looking — it generates thousands of possible future paths based on historical return patterns, volatility, and correlations. It shows a range of outcomes but doesn't guarantee any specific path will occur. Backtest is backward-looking — it replays exactly what happened to your portfolio during specific historical crises (2008, COVID-19, 2022). Backtest shows deterministic results (this is exactly what would have happened), but past performance doesn't guarantee future results. Use both: Monte Carlo for uncertainty, backtest for stress testing.
Yes. Use the Regret Analysis mode to compare any two strategies — lump sum vs SIP, invest now vs delay 6 months, equity-heavy vs balanced portfolio. The simulation runs 1,000+ paths for each strategy, computes median outcomes, loss probabilities, and expected shortfall. It then calculates "regret" — the opportunity cost of choosing the worse strategy — expressed as a percentage and annualized cost. This helps you quantify the trade-off between potential returns and downside protection.
Simulation accuracy depends on how well historical patterns represent future market behavior. No model can predict future returns with certainty. Stock360s uses empirically validated methods: multivariate t-distribution (df=4) for fat tails, regime-aware drift adjustments, and shrunk covariance matrices to reduce estimation error. However, black swan events, structural market changes, and unforeseen crises are not perfectly captured. Use simulations as decision-support tools, not guarantees.
Currently, Stock360s Portfolio Simulation supports only Indian equities (NSE/BSE stocks with .NS suffix), Indian mutual funds, Indian ETFs, and Indian bonds (government and corporate). US stocks, international ETFs, cryptocurrencies, commodities (except gold ETFs), real estate, and private equity are not supported. Support for additional asset classes is under development.
The survival score is a composite metric (0-100) evaluating portfolio resilience. Weights: maximum drawdown (30%), loss probability (25%), expected shortfall (20%), volatility (15%), diversification efficiency (10%). Each metric is normalized and scored, with higher scores indicating better resilience. A score above 70 suggests robust portfolio construction; scores below 40 indicate significant vulnerabilities. The score helps you quickly assess if your portfolio can withstand market stress.
Yes. After running a simulation, your portfolio is automatically saved to your browser's local storage. When you return to the Portfolio Simulator page, it will load your last portfolio automatically. To save multiple portfolios, use the "Export Portfolio" feature (coming soon). Note: local storage is browser-specific — switching browsers or using incognito mode will not retain saved portfolios.
16. Glossary of Terms
Excess return relative to a benchmark or sector average. Positive alpha indicates outperformance.
Measure of an asset's sensitivity to market movements. Beta=1 moves with market; Beta>1 amplifies moves.
Mathematical method to generate correlated random numbers from uncorrelated shocks.
Same as Expected Shortfall. Average loss in worst 5% of outcomes.
Statistical measure (-1 to +1) of how two assets move together. +1 = perfect same direction.
Table showing how each pair of assets co-move. Diagonal = variances, off-diagonal = covariances.
Parameter controlling t-distribution tail thickness. Lower df = fatter tails (more extreme events).
Percentage reduction in portfolio volatility vs weighted average asset volatility.
Peak-to-trough decline during a specific period. Maximum drawdown is worst peak-to-trough decline.
Average loss in worst 5% of scenarios. More conservative than Value at Risk.
Sensitivity of portfolio to specific risk factors (market, size, value, momentum, volatility).
Visualization showing percentile bands (5%,25%,50%,75%,95%) of projected wealth over time.
Statistical property where extreme events occur more frequently than normal distribution predicts.
Portfolio concentration measure. Sum of squared weights × 10000. >2500 = high concentration.
Portfolio behaves as if borrowed due to factor bets, high correlation, or volatility amplification.
Statistical measure of tail extremity. Excess kurtosis >0 indicates fat tails.
Percentage of simulation scenarios where final value < total invested capital.
Classification of current market conditions: Fear/Crash, Bull, Chop, Normal.
Feature that finds historical period most similar to current market and replays portfolio performance.
Method generating thousands of random scenarios to estimate range of possible outcomes.
Probability distribution capturing correlated returns with fat tails. Used by Stock360s with df=4.
Financial loss from choosing suboptimal strategy. Calculated as difference in median outcomes.
Predicting future events using probability distributions rather than single-point estimates.
Comparison of two strategies quantifying opportunity cost of choosing worse option.
Risk-adjusted return measure: (return - risk-free rate) / volatility. Higher = better risk-adjusted performance.
Technique reducing estimation error in covariance matrices by blending sample with structured target.
Measure of return distribution asymmetry. Negative skew = more downside extreme events.
Specific historical crisis used for backtesting: 2008, COVID-19, 2022 rate shock.
Composite metric (0-100) evaluating portfolio resilience based on drawdowns, loss probability, etc.
Generated returns for assets lacking full history, using index returns plus student-t shocks.
Risk of extreme negative outcomes beyond normal expectations. Measured via expected shortfall.
Maximum loss expected at given confidence. Stock360s uses Expected Shortfall which is more conservative.
Standard deviation of returns. Annualized volatility = daily volatility × √252.
17. References & Further Reading
- Bodie, Z., Kane, A., & Marcus, A. J. (2021). Investments (12th ed.). McGraw-Hill. — Chapter on risk measurement and portfolio simulation.
- Glasserman, P. (2003). Monte Carlo Methods in Financial Engineering. Springer. — Technical foundation of Monte Carlo for finance.
- Jorion, P. (2006). Value at Risk: The New Benchmark for Managing Financial Risk (3rd ed.). McGraw-Hill. — VaR and Expected Shortfall methodologies.
- SEBI (Securities and Exchange Board of India). (2023). Risk Disclosure Document for Equity Derivatives. sebi.gov.in.
- NSE India. (2024). Historical Data - NIFTY 50 Index. nseindia.com.
Shailendra Saurav
Stock360s
Stock360s Research Team
Multivariate t-distribution (df=4)
Regime-aware with fat tails
March 27, 2026
Data as of March 2026
Risk Disclosure
Investment in securities market are subject to market risks. Read all the related documents carefully before investing. Past performance is not indicative of future returns. The simulations, projections, and AI interpretations provided by Stock360s are for educational and informational purposes only and do not constitute investment advice, legal advice, or tax advice. Stock360s is not a SEBI-registered investment advisor. You should consult with qualified financial professionals before making any investment decisions. Stock360s does not guarantee the accuracy, completeness, or reliability of any simulation results. By using this tool, you acknowledge that you understand and accept these risks.
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