Module 07 · AAPL risk
The Apple left tail, measured two ways.
Historical VaR from eight annual returns is a small-sample confession. Parametric VaR uses the live-blended σ.
Annual σ
27.1%
blend · annual μ + live realized σ
S0
$313.45
Live tape
Hist. 95% VaR
26.9%
One-year
CVaR 95%
26.9%
Expected shortfall
Workbook correlation
Hover a cell.
| Revenue | Net | Gross | Services | Op. | EPS | Price | |
|---|---|---|---|---|---|---|---|
| Revenue | |||||||
| Net income | |||||||
| Gross margin | |||||||
| Services | |||||||
| Op. income | |||||||
| EPS | |||||||
| Price |
Recomputed from the AAPL prints
Hover a cell.
| Revenue | Net | Gross | Services | Op. | EPS | Price | |
|---|---|---|---|---|---|---|---|
| Revenue | |||||||
| Net income | |||||||
| Gross margin | |||||||
| Services | |||||||
| Op. income | |||||||
| EPS | |||||||
| Price |
Services versus the stock is the series to watch in the matrix. If you only watch the rest of the mix, you are watching the wrong line.
Value at risk
| Metric | Value | Note |
|---|---|---|
| Historical VaR 90% | 26.9% | Empirical percentile, n=7 returns |
| Historical VaR 95% | 26.9% | Thin tail sample |
| CVaR 95% | 26.9% | Mean of the worst 5% |
| CVaR 99% | 26.9% | Mean of the worst 1% |
| Parametric VaR 90% | 6.4% | Normal, live σ |
| Parametric VaR 95% | 16.2% | Normal, live σ |
| Parametric VaR 99% | 34.7% | Normal, live σ |
| Drift μ | 28.3% | Mean log-return, 10-K |
| Live daily σ | 18.4% | Annualized from the open feed |
| $1M dollar VaR 95% | $268,581 | Position sizing |
Diagnostics (workbook)
| Test | Stat | p | Reading |
|---|---|---|---|
| Shapiro–Wilk | 0.910 | 0.395 | Cannot reject normality |
| Jarque–Bera | 0.803 | 0.669 | Cannot reject normality |
| Kolmogorov–Smirnov | 0.210 | 0.861 | Cannot reject normality |
| Lag-1 autocorrelation | 0.088 | — | Low serial dependence |
| Hurst exponent | 0.500 | — | Random-walk-like at annual frequency |
AAPL Bayesian revenue