01 / OVERVIEW
Understand the downside.
2025-09-03 to 2026-10-07 · Four-company equal-weight study
2025-09-03to2026-10-07
The equal-weight sample's annualized historical volatility is 16.20%. Historical tail statistics use 275 actual daily returns and are estimates of this observed sample, not limits on future losses.
02 / MEASURES
Examine the result.
Calculated measures
| Measure | Result | Definition / status |
|---|---|---|
| Historical one-session VaR | 1.72 % loss | 95% empirical confidence; loss-positive |
| Historical expected shortfall | 2.18 % loss | Mean loss beyond 95% empirical VaR |
| Annualized sample volatility | 16.20% | Sample standard deviation × sqrt(252) |
| Maximum observed drawdown | -16.23% | Includes the initial wealth baseline |
The equal-weight sample's annualized historical volatility is 16.20%. Historical tail statistics use 275 actual daily returns and are estimates of this observed sample, not limits on future losses.
2025-09-03to2026-10-07
calculates this technical study from completed adjusted OHLCV sessions. Warm-up values remain unavailable; the indicator is descriptive, not a validated forecast.
2025-09-03to2026-10-07
calculates this technical study from completed adjusted OHLCV sessions. Warm-up values remain unavailable; the indicator is descriptive, not a validated forecast.
2025-09-03to2026-10-07
computes conversion/base high-low midpoints and the shifted technical cloud from observed adjusted OHLC prices. The leading spans are a technical display shift, not a calibrated price forecast; warm-up remains null.
Daily return correlation matrix
| symbol | AAPL | MSFT | JPM | BAC |
|---|---|---|---|---|
| AAPL | 1.0000 | 0.1325 | 0.1651 | 0.2386 |
| MSFT | 0.1325 | 1.0000 | 0.0935 | 0.1115 |
| JPM | 0.1651 | 0.0935 | 1.0000 | 0.7514 |
| BAC | 0.2386 | 0.1115 | 0.7514 | 1.0000 |
Pearson associations use common observed sessions. Correlation does not establish causation; the four-company selection is not the full market.
Company performance and exposure
| symbol | sample_return | starting_weight | beta |
|---|---|---|---|
| AAPL | 41.7007 | 25.0000 | 0.6835 |
| MSFT | 5.6928 | 25.0000 | 0.9702 |
| JPM | 12.7044 | 25.0000 | 0.7965 |
| BAC | 9.7980 | 25.0000 | 0.7268 |
Weights are explicitly fixed at 25% for the daily-rebalanced demonstration. Returns exclude costs and taxes.
Observed risk and performance measurements
| metric | symbol | value | unit | status |
|---|---|---|---|---|
| Annualized volatility | AAPL | 24.6106 | % | calculated |
| Annualized volatility | MSFT | 31.6368 | % | calculated |
| Annualized volatility | JPM | 22.0199 | % | calculated |
| Annualized volatility | BAC | 21.6425 | % | calculated |
| Annualized volatility | SPY | 12.5835 | % | calculated |
| Historical VaR (signed return) | AAPL | -2.0921 | % | calculated |
| Historical VaR (signed return) | MSFT | -2.7104 | % | calculated |
| Historical VaR (signed return) | JPM | -2.3703 | % | calculated |
| Historical VaR (signed return) | BAC | -2.4714 | % | calculated |
| Historical VaR (signed return) | SPY | -1.3361 | % | calculated |
| Expected shortfall (signed return) | AAPL | -3.5551 | % | calculated |
| Expected shortfall (signed return) | MSFT | -3.9555 | % | calculated |
| Expected shortfall (signed return) | JPM | -3.2490 | % | calculated |
| Expected shortfall (signed return) | BAC | -3.2547 | % | calculated |
| Expected shortfall (signed return) | SPY | -1.7467 | % | calculated |
| Maximum drawdown | AAPL | -13.7985 | % | calculated |
| Maximum drawdown | MSFT | -34.4984 | % | calculated |
| Maximum drawdown | JPM | -15.4717 | % | calculated |
| Maximum drawdown | BAC | -17.9317 | % | calculated |
| Maximum drawdown | SPY | -8.8850 | % | calculated |
| Skewness | AAPL | -0.4218 | dimensionless | calculated |
| Skewness | MSFT | 1.3287 | dimensionless | calculated |
| Skewness | JPM | -0.3626 | dimensionless | calculated |
| Skewness | BAC | -0.5277 | dimensionless | calculated |
| Skewness | SPY | -0.1754 | dimensionless | calculated |
| Kurtosis | AAPL | 3.1026 | dimensionless | calculated |
| Kurtosis | MSFT | 14.7356 | dimensionless | calculated |
| Kurtosis | JPM | 0.9112 | dimensionless | calculated |
| Kurtosis | BAC | 1.2118 | dimensionless | calculated |
| Kurtosis | SPY | 1.2024 | dimensionless | calculated |
| Ulcer | AAPL | 6.1185 | % | calculated |
| Ulcer | MSFT | 18.6815 | % | calculated |
| Ulcer | JPM | 6.5111 | % | calculated |
| Ulcer | BAC | 7.4075 | % | calculated |
| Ulcer | SPY | 2.0624 | % | calculated |
| Period Return | AAPL | 41.7007 | % | calculated |
| Period Return | MSFT | 5.6928 | % | calculated |
| Period Return | JPM | 12.7044 | % | calculated |
| Period Return | BAC | 9.7980 | % | calculated |
| Period Return | SPY | 22.3760 | % | calculated |
| Beta | AAPL | 0.6835 | dimensionless | calculated |
| Beta | MSFT | 0.9702 | dimensionless | calculated |
| Beta | JPM | 0.7965 | dimensionless | calculated |
| Beta | BAC | 0.7268 | dimensionless | calculated |
| Daily tracking error | AAPL | 1.4741 | % | calculated |
| Daily tracking error | MSFT | 1.8387 | % | calculated |
| Daily tracking error | JPM | 1.2456 | % | calculated |
| Daily tracking error | BAC | 1.2545 | % | calculated |
| Daily information ratio | AAPL | 0.0422 | ratio | calculated |
| Daily information ratio | MSFT | -0.0201 | ratio | calculated |
| Daily information ratio | JPM | -0.0188 | ratio | calculated |
| Daily information ratio | BAC | -0.0265 | ratio | calculated |
calculates daily-return risk and performance from the same completed source sessions. Volatility uses 252 sessions per year. VaR/expected-shortfall rows retain the library's signed-return convention; main risk cards show loss-positive values. Tracking error and information ratio retain daily units.
Complete FinanceToolkit technical indicator collection
| indicator | symbol | value | status | date |
|---|---|---|---|---|
| McClellan Oscillator | AAPL | 0.0312 | calculated | 2026-10-07 |
| Advancers - Decliners | AAPL | 1.0000 | calculated | 2026-10-07 |
| On-Balance Volume | AAPL | 1,313,063,900.0000 | calculated | 2026-10-07 |
| Accumulation/Distribution Line | AAPL | 878,307,790.6689 | calculated | 2026-10-07 |
| Chaikin Oscillator | AAPL | 2,170,709.3577 | calculated | 2026-10-07 |
| TRIN | AAPL | — | unavailable | 2026-10-07 |
| New Highs - New Lows | AAPL | 0.0000 | calculated | 2026-10-07 |
| Chaikin Money Flow | AAPL | 0.1175 | calculated | 2026-10-07 |
| Ease of Movement | AAPL | -3.9272 | calculated | 2026-10-07 |
| Negative Volume Index | AAPL | 1,167.2373 | calculated | 2026-10-07 |
| Positive Volume Index | AAPL | 1,213.9836 | calculated | 2026-10-07 |
| Money Flow Index | AAPL | 70.1801 | calculated | 2026-10-07 |
| Williams %R | AAPL | -44.3932 | calculated | 2026-10-07 |
| Aroon Indicator Up | AAPL | 21.4286 | calculated | 2026-10-07 |
| Aroon Indicator Down | AAPL | 71.4286 | calculated | 2026-10-07 |
| Commodity Channel Index | AAPL | 10.6996 | calculated | 2026-10-07 |
| Relative Vigor Index | AAPL | 0.4376 | calculated | 2026-10-07 |
| Force Index | AAPL | 20,786,317.9067 | calculated | 2026-10-07 |
| Ultimate Oscillator | AAPL | 46.5550 | calculated | 2026-10-07 |
| Percentage Price Oscillator | AAPL | 1.2801 | calculated | 2026-10-07 |
| Detrended Price Oscillator | AAPL | 5.5779 | calculated | 2026-10-07 |
| Average Directional Index | AAPL | 15.8370 | calculated | 2026-10-07 |
| Chande Momentum Oscillator | AAPL | -0.8373 | calculated | 2026-10-07 |
| Ichimoku Conversion Line | AAPL | 334.4000 | calculated | 2026-10-07 |
| Ichimoku Base Line | AAPL | 327.6200 | calculated | 2026-10-07 |
| Ichimoku Leading Span A | AAPL | 318.3487 | calculated | 2026-10-07 |
| Ichimoku Leading Span B | AAPL | 308.8936 | calculated | 2026-10-07 |
| Stochastic %K | AAPL | 55.6068 | calculated | 2026-10-07 |
| Stochastic %D | AAPL | 43.9666 | calculated | 2026-10-07 |
| MACD Line | AAPL | 3.2824 | calculated | 2026-10-07 |
| MACD Signal Line | AAPL | 4.1033 | calculated | 2026-10-07 |
| Relative Strength Index | AAPL | 57.6961 | calculated | 2026-10-07 |
| Balance of Power | AAPL | -0.0492 | calculated | 2026-10-07 |
| Awesome Oscillator | AAPL | 5.6747 | calculated | 2026-10-07 |
| Vortex Indicator VI+ | AAPL | 1.0185 | calculated | 2026-10-07 |
| Vortex Indicator VI- | AAPL | 0.9633 | calculated | 2026-10-07 |
| Elder Ray Bull Power | AAPL | 4.9499 | calculated | 2026-10-07 |
| Elder Ray Bear Power | AAPL | -0.9401 | calculated | 2026-10-07 |
| Rate of Change | AAPL | -0.0979 | calculated | 2026-10-07 |
| Choppiness Index | AAPL | 56.8613 | calculated | 2026-10-07 |
| Know Sure Thing | AAPL | 53.9446 | calculated | 2026-10-07 |
| Know Sure Thing Signal Line | AAPL | 60.9707 | calculated | 2026-10-07 |
| Simple Moving Average (SMA) | AAPL | 335.4921 | calculated | 2026-10-07 |
| Exponential Moving Average (EMA) | AAPL | 333.5358 | calculated | 2026-10-07 |
| Double Exponential Moving Average (DEMA) | AAPL | 336.0591 | calculated | 2026-10-07 |
| TRIX | AAPL | 0.1925 | calculated | 2026-10-07 |
| Triangular Moving Average | AAPL | 335.1629 | calculated | 2026-10-07 |
| Weighted Moving Average (WMA) | AAPL | 334.5491 | calculated | 2026-10-07 |
| Hull Moving Average (HMA) | AAPL | 332.0574 | calculated | 2026-10-07 |
| Kaufman Adaptive Moving Average (KAMA) | AAPL | 331.1829 | calculated | 2026-10-07 |
| Volume Weighted Average Price (VWAP) | AAPL | 335.5554 | calculated | 2026-10-07 |
| Parabolic SAR | AAPL | 341.8381 | calculated | 2026-10-07 |
| Pivot Point | AAPL | 332.8767 | calculated | 2026-10-07 |
| Pivot Point Resistance 1 | AAPL | 335.1333 | calculated | 2026-10-07 |
| Pivot Point Support 1 | AAPL | 331.3733 | calculated | 2026-10-07 |
| Fibonacci Retracement 50.0% | AAPL | 335.5750 | calculated | 2026-10-07 |
| Fibonacci Retracement 61.8% | AAPL | 333.2705 | calculated | 2026-10-07 |
| Bollinger Band Upper | AAPL | 342.2033 | calculated | 2026-10-07 |
| Bollinger Band Middle | AAPL | 335.4921 | calculated | 2026-10-07 |
| Bollinger Band Lower | AAPL | 328.7810 | calculated | 2026-10-07 |
| True Range | AAPL | 5.8900 | calculated | 2026-10-07 |
| Average True Range | AAPL | 6.5823 | calculated | 2026-10-07 |
| Supertrend | AAPL | 320.8583 | calculated | 2026-10-07 |
| Supertrend Trend Direction | AAPL | 1.0000 | calculated | 2026-10-07 |
| Keltner Channel Upper | AAPL | 346.7004 | calculated | 2026-10-07 |
| Keltner Channel Middle | AAPL | 333.5358 | calculated | 2026-10-07 |
| Keltner Channel Lower | AAPL | 320.3713 | calculated | 2026-10-07 |
| Donchian Channel Upper | AAPL | 345.3400 | calculated | 2026-10-07 |
| Donchian Channel Middle | AAPL | 335.5750 | calculated | 2026-10-07 |
| Donchian Channel Lower | AAPL | 325.8100 | calculated | 2026-10-07 |
The actual technicals controller collects all supported breadth, momentum, overlap and volatility indicators from observed adjusted OHLCV. Each latest value has its own calculated/unavailable state. Session volume is provider volume, not a fabricated order book.
Source and calculation coverage
| module | status | reason |
|---|---|---|
| ratios/models | unavailable | Financial statement ratios and DuPont require matching annual statement evidence; choose AQ06 for those calculations. |
| fixedincome | unavailable | No specific bond, coupon schedule or swaption market observations were supplied by this stock-market demonstration. Bond and swaption outputs are not invented. |
| economics | unavailable | No dated macro release/vintage dataset was selected. Market price returns are not substituted for economic releases. |
| portfolio/causal econometrics | unavailable | Portfolio optimization and causal research require explicit constraints, instruments and validation; this bounded demonstration does not imply those workflows ran. |
Unavailable measurements retain their specific missing evidence. A method being present in the library does not mean the required market inputs exist.
Measures that need additional evidence (4)
- ratios/models: Financial statement ratios and DuPont require matching annual statement evidence; choose AQ06 for those calculations.
- fixedincome: No specific bond, coupon schedule or swaption market observations were supplied by this stock-market demonstration. Bond and swaption outputs are not invented.
- economics: No dated macro release/vintage dataset was selected. Market price returns are not substituted for economic releases.
- portfolio/causal econometrics: Portfolio optimization and causal research require explicit constraints, instruments and validation; this bounded demonstration does not imply those workflows ran.
03 / SOURCES & METHOD
Follow the reasoning.
Calculation method
Public yfinance observations are requested through tomorrow because Yahoo's end date is exclusive.
Only verified completed XNYS sessions at selection time enter daily studies; incomplete current-day bars are excluded.
The selection date is fixed once in Africa/Tunis. The observed source cutoff is displayed separately.
methods receive observed input. Missing values are not filled or replaced with defaults.
Adjusted-close returns are descriptive provider-adjusted returns, not a point-in-time data-vintage backtest.
The four-company sample holds 25% per company and rebalances daily. SPY is an observed ETF comparison, not a complete global-market benchmark.
Source evidence
Scope and review
This is a bounded public-data research demonstration; no transaction execution, accounts or customer records are used.
Sources may be delayed or revised. Current observations and provider licensing must be reviewed before commercial redistribution.
Narratives are generated deterministically from calculated evidence. No language model is claimed to have authored this run.
The run date stays fixed for this selection. Market observations and financial reporting periods can precede that date. Estimates are research calculations; they are not observed future prices.