JPMorgan Data Science Analyst Interview: Technical Questions & Solutions

The bias-variance tradeoff describes the relationship between model complexity and prediction error. Bias is the error from overly simplistic assumptions, while variance is the error from sensitivity to small fluctuations in training data. In financial modeling: High bias (underfitting) occurs with simple models that miss important market patterns. High variance (overfitting) occurs with complex models that capture noise as signal. Optimal complexity minimizes total error $ = $ bias² $ + $ variance $ + $ irreducible error. For financial applications, we often prefer slightly higher bias to reduce variance due to market volatility and limited historical data. Techniques like cross-validation, regularization (L1/L2), and ensemble methods help achieve optimal balance.

VaR (Value at Risk) of $1M at 95% confidence means there's a 5% probability of losing more than $1M in one day under normal market conditions. Validation methods: 1) Backtesting $ - $ compare actual losses to VaR predictions over historical periods, expect ~5% of days to exceed VaR, 2) Statistical tests like Kupiec's POF test for correct failure rate, 3) Independence test to ensure violations aren't clustered, 4) Stress testing under extreme scenarios, 5) Model validation through out-of-sample testing, 6) Comparison with Expected Shortfall (average loss beyond VaR). Key limitations: assumes normal market conditions, doesn't capture tail risk beyond confidence level, and may underestimate risk during market stress.

```python

```sql

WITH daily_returns AS (

SELECT

stock_symbol,

trade_date,

close_price,

LAG(close_price) OVER (PARTITION BY stock_symbol ORDER BY trade_date) as prev_close,

(close_price $ - $ LAG(close_price) OVER (PARTITION BY stock_symbol ORDER BY trade_date))

/ LAG(close_price) OVER (PARTITION BY stock_symbol ORDER BY trade_date) as daily_return

FROM stock_prices

WHERE trade_date >= CURRENT_DATE $ - $ INTERVAL '60 days'

),

rolling_volatility AS (

SELECT

stock_symbol,

trade_date,

daily_return,

STDDEV(daily_return) OVER (

PARTITION BY stock_symbol

ORDER BY trade_date

ROWS BETWEEN 29 PRECEDING AND CURRENT ROW

) as rolling_30d_volatility,

COUNT(daily_return) OVER (

PARTITION BY stock_symbol

ORDER BY trade_date

ROWS BETWEEN 29 PRECEDING AND CURRENT ROW

) as window_size

FROM daily_returns

WHERE daily_return IS NOT NULL

)

SELECT

stock_symbol,

AVG(rolling_30d_volatility) as avg_30d_volatility,

MAX(rolling_30d_volatility) as max_30d_volatility,

COUNT(*) as observation_count

FROM rolling_volatility

WHERE window_size $ = $ 30

AND trade_date >= CURRENT_DATE $ - $ INTERVAL '30 days'

GROUP BY stock_symbol

HAVING COUNT(*) >= 20

ORDER BY avg_30d_volatility DESC

LIMIT 5;

```

Expected Shortfall (ES), also called Conditional VaR (CVaR), measures the average loss beyond the VaR threshold. For 95% confidence, ES is the average of the worst 5% of outcomes. ES advantages over VaR: 1) Coherent risk measure $ - $ satisfies subadditivity, monotonicity, positive homogeneity, and translation invariance, 2) Captures tail risk $ - $ provides information about severity of extreme losses, 3) Optimization-friendly $ - $ convex function enabling portfolio optimization, 4) Regulatory preference $ - $ Basel III uses ES for market risk capital requirements. Calculation: ES $ = $ E[Loss

Structural break detection methods: 1) Chow test $ - $ tests for parameter stability across subsamples, 2) CUSUM test $ - $ detects gradual parameter changes, 3) Bai-Perron test $ - $ identifies multiple unknown breakpoints, 4) Recursive estimation $ - $ monitors parameter stability over time, 5) Regime-switching models $ - $ allow for different states. Handling approaches: 1) Dummy variables for known breaks (e.g., financial crises), 2) Regime-switching models (Markov-switching), 3) Time-varying parameter models, 4) Robust estimation methods, 5) Subsample analysis excluding break periods. In financial applications, common breaks occur during: market crashes, policy changes, technological shifts. Model validation should include out-of-sample testing across different regimes and stress testing under various market conditions.

Mean-variance optimization limitations: 1) Requires accurate estimates of expected returns, covariances (estimation error), 2) Assumes normal distributions (ignores skewness, kurtosis), 3) Single-period framework, 4) No transaction costs or constraints, 5) Unstable solutions sensitive to input changes, 6) Concentrated portfolios in practice. Alternative approaches: 1) Black-Litterman model $ - $ incorporates market equilibrium and investor views, 2) Risk parity $ - $ equal risk contribution from each asset, 3) Minimum variance portfolios $ - $ focus on risk reduction, 4) Factor-based optimization $ - $ target specific risk factors, 5) Robust optimization $ - $ accounts for parameter uncertainty, 6) Behavioral portfolio theory $ - $ incorporates investor psychology, 7) Multi-period optimization with rebalancing costs. Practical implementations often use constraints (position limits, turnover limits) and robust estimation techniques.

Black-Scholes assumptions: 1) Constant risk-free rate, 2) Constant volatility, 3) Log-normal stock price distribution, 4) No dividends, 5) European exercise only, 6) No transaction costs, 7) Continuous trading, 8) No arbitrage opportunities. Violations and practical implications: 1) Volatility smile/skew $ - $ implied volatility varies with strike/time, addressed by local volatility models, 2) Interest rate changes $ - $ use stochastic interest rate models, 3) Dividends $ - $ adjust for discrete dividend payments, 4) Early exercise $ - $ use binomial/trinomial trees for American options, 5) Transaction costs $ - $ wider bid-ask spreads, 6) Jump risk $ - $ use jump-diffusion models (Merton), 7) Stochastic volatility $ - $ Heston, SABR models. Market makers use these extensions and calibrate models to market prices rather than relying on theoretical values.

PD model development process: 1) Data collection $ - $ financial statements, market data, macroeconomic variables, default history, 2) Feature engineering $ - $ financial ratios (leverage, profitability, liquidity), market-based indicators (equity volatility, CDS spreads), 3) Target definition $ - $ default events within specific time horizon (1-year typical), 4) Model selection $ - $ logistic regression (interpretable), random forest, gradient boosting, neural networks, 5) Validation $ - $ out-of-time testing, cross-validation, discrimination (AUC), calibration (Hosmer-Lemeshow), 6) Regulatory compliance $ - $ Basel requirements for IRB models. Key features: debt-to-equity ratio, interest coverage, current ratio, ROA, market cap, sector indicators. Model monitoring includes population stability index (PSI), characteristic stability index (CSI), and regular backtesting against actual defaults.

Market impact is the price movement caused by a trade, consisting of temporary and permanent components. Temporary impact reflects liquidity provision costs and typically reverts. Permanent impact reflects information content and persists. Impact models: 1) Square-root law $ - $ impact ∝ √(trade size/average volume), 2) Linear models for small trades, 3) Nonlinear models for large trades. Factors affecting impact: trade size, market volatility, liquidity, time of day, market conditions. Algorithmic trading strategies to minimize impact: 1) TWAP (Time-Weighted Average Price) $ - $ spread trades over time, 2) VWAP (Volume-Weighted Average Price) $ - $ match historical volume patterns, 3) Implementation Shortfall $ - $ balance market impact vs. timing risk, 4) Participation rate strategies $ - $ limit percentage of market volume. Advanced techniques include machine learning for impact prediction and optimal execution under stochastic models.

Stress testing framework components: 1) Scenario design $ - $ historical scenarios (2008 crisis, COVID-19), hypothetical scenarios (interest rate shocks, credit spreads widening), 2) Risk factor mapping $ - $ identify key drivers (equity indices, FX rates, credit spreads, volatilities), 3) Shock calibration $ - $ magnitude based on historical percentiles or regulatory requirements, 4) Portfolio revaluation $ - $ full revaluation vs. sensitivity-based approaches, 5) Aggregation $ - $ across asset classes, geographies, business lines. Implementation: 1) Monte Carlo simulation for complex portfolios, 2) Historical simulation using crisis periods, 3) Sensitivity analysis for key risk factors, 4) Reverse stress testing $ - $ find scenarios causing specific losses. Governance: regular testing frequency, escalation procedures, capital planning integration, regulatory reporting (CCAR, ICAAP). Results inform risk limits, hedging strategies, and capital allocation decisions.

NLP sentiment analysis pipeline: 1) Data collection $ - $ financial news APIs (Bloomberg, Reuters), SEC filings, social media, 2) Text preprocessing $ - $ tokenization, stop word removal, stemming/lemmatization, named entity recognition, 3) Feature extraction $ - $ TF-IDF, word embeddings (Word2Vec, GloVe), BERT embeddings, 4) Sentiment scoring $ - $ lexicon-based (VADER, TextBlob), machine learning (SVM, Random Forest), deep learning (LSTM, Transformer models), 5) Financial domain adaptation $ - $ finance-specific dictionaries, domain fine-tuning. Model architecture: combine sentiment scores with technical indicators, use attention mechanisms for important phrases, incorporate temporal dynamics with RNNs. Challenges: sarcasm detection, context understanding, market-specific language. Evaluation: correlation with price movements, trading strategy performance, Sharpe ratio improvement. Production considerations: real-time processing, model drift monitoring, regulatory compliance for automated trading.

Factor models decompose asset returns into systematic (factor) and idiosyncratic components: R_i $ = $ α_i $ + $ β_i1*F_1 $ + $ β_i2*F_2 $ + $ ... $ + $ ε_i. Types: 1) Fundamental factors $ - $ based on company characteristics (size, value, profitability, growth), 2) Macroeconomic factors $ - $ interest rates, inflation, GDP growth, 3) Statistical factors $ - $ principal components, independent component analysis. Construction process: 1) Factor identification $ - $ economic theory, statistical analysis, 2) Factor portfolio construction $ - $ long-short portfolios, 3) Factor loading estimation $ - $ time-series or cross-sectional regression, 4) Model validation $ - $ R-squared, factor significance, residual analysis. Popular models: Fama-French 3/5-factor, Carhart 4-factor, Barra risk models. Applications: risk attribution, performance attribution, portfolio construction, alpha generation. Implementation considerations: factor timing, transaction costs, capacity constraints, factor decay over time.

Pairs trading algorithm components: 1) Pair selection $ - $ cointegration testing (Engle-Granger, Johansen), correlation analysis, fundamental similarity, 2) Spread construction $ - $ price ratio or log price difference, 3) Mean reversion testing $ - $ Augmented Dickey-Fuller test, half-life estimation, 4) Signal generation $ - $ z-score thresholds (typically ±2), Bollinger bands, Kalman filter for dynamic parameters. Trading logic: Enter long spread when z-score $ < $ -2, enter short spread when z-score $ > $ +2, exit when z-score crosses zero or reaches profit target. Risk management: 1) Stop-loss levels, 2) Maximum holding period, 3) Position sizing based on volatility, 4) Correlation breakdown detection. Implementation: ```python

Real-time market data pipeline architecture: 1) Data ingestion $ - $ Apache Kafka for high-throughput streaming, multiple brokers for redundancy, 2) Stream processing $ - $ Apache Spark Streaming or Apache Flink for low-latency processing, 3) Data storage $ - $ time-series databases (InfluxDB, TimescaleDB), distributed storage (HDFS, S3), 4) Message queuing $ - $ Redis for caching, RabbitMQ for reliable delivery. Components: 1) Feed handlers $ - $ normalize different data formats, handle connection failures, 2) Data validation $ - $ schema validation, outlier detection, missing data handling, 3) Enrichment $ - $ reference data joins, calculated fields, 4) Distribution $ - $ WebSocket APIs, message queues for downstream consumers. Scalability: horizontal scaling with partitioning, load balancing, auto-scaling based on volume. Monitoring: latency metrics, throughput monitoring, data quality checks, alerting for failures. Technologies: Python/Java for processing, Docker/Kubernetes for deployment, Prometheus/Grafana for monitoring. Disaster recovery: multi-region deployment, data replication, failover procedures.

Common behavioral biases affecting models: 1) Momentum $ - $ herding behavior creates price trends, 2) Mean reversion $ - $ overreaction leads to reversals, 3) Anchoring $ - $ prices stick to reference points, 4) Loss aversion $ - $ asymmetric risk preferences, 5) Overconfidence $ - $ excessive trading, underestimation of risk. Model adjustments: 1) Regime-switching models $ - $ different parameters for different market states, 2) Behavioral factors $ - $ momentum, reversal, sentiment indicators, 3) Adaptive models $ - $ time-varying parameters, machine learning for pattern recognition, 4) Volatility clustering $ - $ GARCH models for volatility persistence, 5) Fat-tailed distributions $ - $ Student's t, skewed distributions. Practical implementation: 1) Sentiment indicators from news, social media, 2) Technical indicators capturing momentum/reversal, 3) Options market data for implied volatility skew, 4) Survey data (AAII sentiment, VIX), 5) Insider trading patterns. Model validation should include behavioral regime identification and out-of-sample testing across different market conditions.

MiFID II algorithmic trading requirements: 1) Risk controls $ - $ pre-trade risk limits, maximum order values, position limits, 2) Circuit breakers $ - $ automatic halt mechanisms for erroneous orders, 3) Conformance testing $ - $ algorithm testing in non-production environments, 4) Business continuity $ - $ backup systems, disaster recovery procedures, 5) Governance $ - $ clear accountability, regular review processes. Technical requirements: 1) Kill switches $ - $ ability to cancel all orders immediately, 2) Throttling mechanisms $ - $ limit order submission rates, 3) Self-assessment $ - $ annual compliance review, 4) Record keeping $ - $ detailed logs of algorithm decisions, 5) Market making obligations $ - $ continuous quotes, maximum spreads. Implementation: 1) Real-time monitoring systems, 2) Automated compliance checks, 3) Regular stress testing, 4) Staff training and certification, 5) Third-party validation. Documentation requirements: algorithm descriptions, risk management procedures, testing results, incident reports. Penalties for non-compliance include fines up to 10% of annual turnover and trading suspensions.

Term structure modeling approaches: 1) Parametric models $ - $ Nelson-Siegel, Svensson for yield curve fitting, 2) Equilibrium models $ - $ Vasicek, CIR for short rate dynamics, 3) No-arbitrage models $ - $ Hull-White, Black-Karasinski for derivative pricing, 4) Multi-factor models $ - $ capturing level, slope, curvature factors. Key concepts: 1) Spot rates $ - $ zero-coupon yields, 2) Forward rates $ - $ implied future rates, 3) Par yields $ - $ coupon-bearing bond yields, 4) Yield curve shapes $ - $ normal, inverted, humped. Bond pricing implications: 1) Duration $ - $ price sensitivity to yield changes, 2) Convexity $ - $ second-order price sensitivity, 3) Key rate durations $ - $ sensitivity to specific maturity points, 4) Scenario analysis $ - $ parallel shifts, steepening/flattening. Implementation: ```python

MLOps pipeline for credit scoring: 1) Model development $ - $ feature engineering, model training, validation, 2) Model registry $ - $ versioning, metadata tracking, approval workflows, 3) Deployment $ - $ containerization (Docker), orchestration (Kubernetes), A/B testing framework, 4) Monitoring $ - $ model performance, data drift, concept drift, 5) Retraining $ - $ automated pipelines, trigger conditions, rollback procedures. Infrastructure: 1) Feature store $ - $ centralized feature management, 2) Model serving $ - $ REST APIs, batch scoring, real-time inference, 3) Data pipeline $ - $ ETL processes, data quality checks, 4) Logging $ - $ prediction logs, feature values, model versions. Monitoring metrics: 1) Model performance $ - $ AUC, precision, recall, calibration, 2) Data quality $ - $ missing values, outliers, distribution shifts, 3) Business metrics $ - $ approval rates, default rates, profitability, 4) System metrics $ - $ latency, throughput, error rates. Governance: 1) Model validation $ - $ independent validation, regulatory approval, 2) Bias testing $ - $ fairness across demographics, 3) Explainability $ - $ SHAP values, LIME, 4) Documentation $ - $ model cards, validation reports. Tools: MLflow, Kubeflow, SageMaker, DataRobot.

Cryptocurrency volatility modeling approaches: 1) GARCH models $ - $ capture volatility clustering, leverage effects, 2) Stochastic volatility models $ - $ allow for volatility of volatility, 3) Jump-diffusion models $ - $ account for sudden price movements, 4) Regime-switching models $ - $ different volatility regimes. Unique characteristics: 1) 24/7 trading $ - $ no overnight gaps, continuous price discovery, 2) High volatility $ - $ much higher than traditional assets, 3) Thin liquidity $ - $ large price impacts, 4) Regulatory uncertainty $ - $ policy announcements cause jumps, 5) Technological risks $ - $ exchange hacks, network issues. Data considerations: 1) Multiple exchanges $ - $ price differences, volume weighting, 2) Market microstructure $ - $ bid-ask spreads, order book depth, 3) On-chain metrics $ - $ transaction volumes, active addresses, 4) Sentiment data $ - $ social media, news sentiment. Model implementation: ```python

ESG integration approaches: 1) ESG scoring $ - $ standardized metrics across companies, 2) Factor construction $ - $ ESG momentum, ESG quality factors, 3) Portfolio optimization $ - $ ESG constraints, tilting, 4) Risk modeling $ - $ ESG-related risks, stranded assets. Data sources: 1) ESG rating agencies $ - $ MSCI, Sustainalytics, Refinitiv, 2) Alternative data $ - $ satellite imagery, news sentiment, supply chain data, 3) Company disclosures $ - $ sustainability reports, CDP submissions, 4) Regulatory filings $ - $ climate risk disclosures. Quantitative methods: 1) ESG factor models $ - $ decompose returns into ESG components, 2) Machine learning $ - $ predict ESG improvements, identify ESG leaders, 3) Natural language processing $ - $ analyze ESG-related text data, 4) Network analysis $ - $ supply chain ESG risks. Implementation challenges: 1) Data quality $ - $ inconsistent methodologies, reporting gaps, 2) Greenwashing $ - $ distinguishing genuine vs. superficial ESG efforts, 3) Materiality $ - $ identifying ESG factors relevant to financial performance, 4) Time horizons $ - $ ESG benefits may be long-term. Performance measurement: ESG-adjusted Sharpe ratios, tracking error attribution, impact measurement alongside financial returns.

Low-latency system design: 1) Hardware optimization $ - $ FPGA for ultra-low latency, high-frequency CPUs, RDMA networking, 2) Software optimization $ - $ kernel bypass, lock-free programming, memory pre-allocation, 3) Network optimization $ - $ co-location, direct market access, microwave/laser networks, 4) Algorithm optimization $ - $ simplified logic, pre-computed decisions, minimal branching. Latency sources: 1) Network latency $ - $ physical distance, routing, 2) Processing latency $ - $ algorithm complexity, system calls, 3) Market data latency $ - $ feed processing, normalization, 4) Order management $ - $ risk checks, position updates. Measurement: 1) End-to-end latency $ - $ market data to order submission, 2) Jitter $ - $ latency variability, 3) Percentile analysis $ - $ 99th percentile latency, 4) Clock synchronization $ - $ GPS/PTP timestamps. Architecture: ```

Market Data → Feed Handler → Strategy Engine → Risk Manager → Order Gateway → Exchange

``` Risk management: 1) Pre-trade checks $ - $ position limits, order size limits, 2) Real-time monitoring $ - $ P&L, position tracking, 3) Kill switches $ - $ immediate order cancellation, 4) Circuit breakers $ - $ automatic trading halts. Regulatory compliance: market making obligations, best execution, audit trails.

Satellite data evaluation framework: 1) Data quality assessment $ - $ resolution, frequency, coverage, weather interference, 2) Signal validation $ - $ correlation with known events, ground truth verification, 3) Timeliness $ - $ data latency, update frequency, 4) Cost-benefit analysis $ - $ data costs vs. alpha generation potential. Use cases: 1) Retail analytics $ - $ parking lot car counts, store traffic, 2) Commodity trading $ - $ crop yield estimation, oil storage levels, 3) Real estate $ - $ construction activity, land use changes, 4) Economic indicators $ - $ industrial activity, shipping traffic. Processing pipeline: 1) Image preprocessing $ - $ cloud removal, atmospheric correction, 2) Feature extraction $ - $ object detection, change detection, 3) Time series analysis $ - $ seasonal patterns, trend analysis, 4) Signal generation $ - $ anomaly detection, predictive modeling. Technical implementation: ```python

``` Challenges: 1) Weather dependency $ - $ cloud cover, seasonal variations, 2) Resolution limitations $ - $ distinguishing objects, 3) Processing costs $ - $ computational requirements, 4) Regulatory restrictions $ - $ privacy, national security. Integration: combine with traditional data, ensemble modeling, risk-adjusted position sizing.

Risk budgeting allocates portfolio risk across assets, strategies, or factors rather than capital. Key concepts: 1) Risk contribution $ - $ each position's contribution to total portfolio risk, 2) Marginal risk $ - $ additional risk from increasing position size, 3) Component risk $ - $ risk decomposition by asset/factor. Mathematical framework: Portfolio variance $ = $ Σᵢ Σⱼ wᵢ wⱼ σᵢⱼ, Risk contribution of asset i $ = $ wᵢ × (∂σₚ/∂wᵢ) $ = $ wᵢ × Σⱼ wⱼ σᵢⱼ $ / $ σₚ. Implementation approaches: 1) Equal risk contribution (ERC) $ - $ each asset contributes equally to portfolio risk, 2) Risk parity $ - $ risk-weighted allocation, 3) Targeted risk budgets $ - $ allocate specific risk amounts to strategies. Optimization problem: Minimize Σᵢ (RCᵢ $ - $ RBᵢ)² subject to Σᵢ wᵢ $ = $ 1, where RCᵢ is risk contribution and RBᵢ is risk budget. Benefits: 1) Better diversification $ - $ avoids concentration in low-volatility assets, 2) Risk transparency $ - $ clear understanding of risk sources, 3) Dynamic rebalancing $ - $ maintains risk targets over time. Challenges: estimation error in covariance matrix, transaction costs, constraints handling.

Common backtesting pitfalls: 1) Look-ahead bias $ - $ using future information, 2) Survivorship bias $ - $ excluding delisted stocks, 3) Data snooping $ - $ over-optimization on historical data, 4) Transaction cost underestimation $ - $ ignoring market impact, slippage, 5) Regime changes $ - $ strategy performance varies across market conditions. Avoidance strategies: 1) Point-in-time data $ - $ use data available at decision time, 2) Out-of-sample testing $ - $ reserve data for final validation, 3) Walk-forward analysis $ - $ rolling optimization and testing periods, 4) Monte Carlo simulation $ - $ test strategy robustness, 5) Paper trading $ - $ live testing without capital risk. Realistic assumptions: 1) Transaction costs $ - $ bid-ask spreads, commissions, market impact, 2) Execution delays $ - $ order processing time, partial fills, 3) Capacity constraints $ - $ strategy scalability, 4) Borrowing costs $ - $ short selling fees, margin requirements. Statistical validation: 1) Sharpe ratio significance testing, 2) Maximum drawdown analysis, 3) Tail risk measures, 4) Correlation with market factors. Implementation: ```python

Greeks calculation and management: 1) Delta $ - $ price sensitivity, hedge with underlying or futures, 2) Gamma $ - $ delta sensitivity, manage with options, 3) Theta $ - $ time decay, natural short for option sellers, 4) Vega $ - $ volatility sensitivity, hedge with volatility products, 5) Rho $ - $ interest rate sensitivity, hedge with bonds/swaps. Portfolio Greeks: Aggregate individual option Greeks weighted by position size. For complex portfolios: ΔPortfolio $ = $ Σᵢ Δᵢ × Positionᵢ. Dynamic hedging: 1) Delta hedging $ - $ maintain delta-neutral portfolio, 2) Gamma scalping $ - $ profit from gamma while maintaining delta neutrality, 3) Volatility trading $ - $ manage vega exposure. Risk limits: 1) Gross exposure limits $ - $ maximum notional exposure, 2) Net exposure limits $ - $ directional risk limits, 3) Greeks limits $ - $ maximum delta, gamma, vega, 4) Scenario analysis $ - $ stress testing under extreme moves. Implementation: ```python

Market efficiency testing approaches: 1) Random walk tests $ - $ variance ratio tests, runs tests, 2) Autocorrelation tests $ - $ serial correlation in returns, 3) Unit root tests $ - $ stationarity of price series, 4) Cointegration tests $ - $ long-run relationships, 5) Event studies $ - $ abnormal returns around announcements. Weak-form efficiency: 1) Autocorrelation function $ - $ test for serial dependence, 2) Ljung-Box test $ - $ joint test for multiple lags, 3) Variance ratio test $ - $ compare variances at different horizons, 4) BDS test $ - $ nonlinear dependence. Semi-strong form: 1) Event study methodology $ - $ abnormal returns $ = $ actual $ - $ expected, 2) Regression analysis $ - $ CAR $ = $ α $ + $ β × Market $ + $ ε, 3) Cross-sectional tests $ - $ risk-adjusted abnormal returns. Strong-form efficiency: 1) Insider trading analysis $ - $ abnormal returns before announcements, 2) Mutual fund performance $ - $ risk-adjusted returns, 3) Technical analysis profitability $ - $ moving averages, momentum strategies. Statistical implementation: ```python

Robo-advisor algorithm components: 1) Risk profiling $ - $ questionnaire-based assessment, behavioral analysis, 2) Asset allocation $ - $ strategic allocation based on risk tolerance, 3) Portfolio construction $ - $ ETF selection, tax optimization, 4) Rebalancing $ - $ threshold-based or time-based rebalancing, 5) Tax-loss harvesting $ - $ realize losses to offset gains. Risk assessment: 1) Time horizon $ - $ investment period, liquidity needs, 2) Risk capacity $ - $ financial ability to take risk, 3) Risk tolerance $ - $ psychological comfort with volatility, 4) Goals-based approach $ - $ specific financial objectives. Algorithm design: ```python

``` Features: 1) Automatic deposits $ - $ dollar-cost averaging, 2) Goal tracking $ - $ progress monitoring, 3) Tax optimization $ - $ asset location, harvesting, 4) Behavioral coaching $ - $ prevent emotional decisions. Regulatory considerations: fiduciary duty, disclosure requirements, cybersecurity, data privacy.

Momentum factor construction: 1) Universe definition $ - $ investable stocks, liquidity filters, 2) Signal calculation $ - $ price momentum (3-12 months), earnings momentum, analyst revisions, 3) Portfolio formation $ - $ long top decile, short bottom decile, 4) Weighting scheme $ - $ equal weight, cap weight, risk-adjusted. Signal variations: 1) Price momentum $ - $ cumulative returns excluding most recent month, 2) Risk-adjusted momentum $ - $ returns scaled by volatility, 3) Cross-sectional momentum $ - $ relative to market/sector, 4) Time-series momentum $ - $ absolute trend following. Implementation: ```python

``` Validation methods: 1) Out-of-sample testing $ - $ different time periods, markets, 2) Decay analysis $ - $ signal strength over time, 3) Turnover analysis $ - $ transaction cost impact, 4) Risk decomposition $ - $ factor loadings, residual risk. Risk management: 1) Sector neutrality $ - $ control for sector effects, 2) Size neutrality $ - $ control for market cap bias, 3) Volatility scaling $ - $ risk-adjusted positions, 4) Capacity analysis $ - $ strategy scalability.

Basel III market risk capital calculation: 1) Standardized Approach (SA) $ - $ risk weights by asset class, 2) Internal Models Approach (IMA) $ - $ VaR and Expected Shortfall models, 3) Fundamental Review of Trading Book (FRTB) $ - $ new framework. SA calculation: Capital $ = $ Σᵢ (Risk Weight × Exposure × 8%), Risk weights vary by asset class: government bonds (0-150%), corporate bonds (20-150%), equities (100-400%). IMA requirements: 1) VaR model $ - $ 99% confidence, 10-day horizon, 2) Stressed VaR $ - $ calibrated to stress period, 3) Expected Shortfall $ - $ 97.5% confidence, replaces VaR, 4) Default Risk Charge $ - $ jump-to-default risk. FRTB components: 1) Sensitivities-Based Method (SBM) $ - $ delta, vega, curvature risks, 2) Default Risk Charge (DRC) $ - $ credit jump risk, 3) Residual Risk Add-On (RRAO) $ - $ exotic risks. Implementation: ```python