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Volatility analysis of an index

Source: R/fct_volatility.R
volatility_analysis.Rd

Is the index's recent volatility normal? The analysis looks at the daily log returns, log(close(t) / close(t-1)), from the close of one trading day to the next, in two ways. All the windows count trading days, and a year is 252 of them.

The last month (month_days trading days, 21 by default): its volatility, the standard deviation of the daily returns times sqrt(252), against the year before it and against every past period of the same length; an F test and the Fligner-Killeen test, which is robust to a few extreme days, of whether its variance is larger than the year before; its largest daily move, in standard deviations of the year before; and its return against every past period of the same length.

The last days (recent_days days): their return against every past period of as many days; the same, in standard deviations of the year before; a GARCH(1,1) model with Student-t errors (see garch_fit()), fitted to the garch_years years before them, which judges each day against the volatility the model expected for it given the days before; and each day's volume against the volume_days days before it (see volume_ratio()), judged by how often the index's volume was as far from usual.

The next days (forecast_days days): the same model, with its variance brought up to the last day, forecasts the volatility and the range of the price (see garch_forecast()), and gives the value at risk and the expected shortfall of the next day (see garch_risk()). A Kupiec test (see kupiec_test()) checks how often the model's value at risk was exceeded over the last year. The value at risk and expected shortfall of the last year's daily returns are given without the model too.

Usage

volatility_analysis(
  history,
  month_days = 21,
  recent_days = 2,
  garch_years = 4,
  forecast_days = 5,
  level = 0.95,
  volume_days = 21
)

Arguments

history

Price history of one index from get_history(), sorted by date. The comparisons use the whole history, so pass all of it.

month_days

Trading days of the volatility window, the "month": 21, or for example 5 for the last week or 63 for the last quarter.

recent_days

Trading days in the recent move, such as 1 for the last day alone.

garch_years

Years of history to fit the GARCH model to.

forecast_days

Trading days to forecast, the weekdays after the last day.

level

Probability of the forecast ranges, and of the value at risk: 0.95 is the 95% range and the worst 5% of days.

volume_days

Trading days before each day whose median volume the day's volume is compared with.

Value

NULL when the history is not longer than a year and the longer of month_days and recent_days, or the price did not move at all in the year before the month or the last days, otherwise a list with

  • index, first_date and last_date;

  • month: a list of the month's measures, see the code;

  • recent: a list of the measures of the last days, with a days data frame of each day's return, GARCH measures, volume, volume_ratio and volume_one_in_days (NA without volume);

  • garch: the fitted model, or NULL when it could not be fitted or there are fewer than 500 days before the last days;

  • forecast: NULL without a model, otherwise a list with days, a data frame with a row per day ahead: its date, sigma (the daily standard deviation the model expects, in percent) and the closes low, low_50, median, high_50 and high of the ranges (see garch_forecast()); sigma and sigma_long_run, the daily standard deviation expected for the next day and in the long run; half_life, the days for the volatility to get half-way back to the long run; var and es, the value at risk and expected shortfall of the next day; and backtest, the days, exceedances and p_value of the Kupiec test;

  • history_risk: var and es of the daily returns of the last days (252) trading days, in percent;

  • series: a data frame with a row per day and the columns date, close, volume, return_pct, volume_ratio (see volume_ratio()), volatility_month (of the month_days days up to the day, annualized, in percent), garch_sigma (the daily standard deviation the model expected, in percent), garch_z (the day's move in those standard deviations) and garch_var (the model's value at risk for the day, in percent);

  • settings: month_days, recent_days, garch_years, forecast_days, level and volume_days.

Examples

if (FALSE) { # interactive()
spx <- get_history("S&P 500", as.Date("1950-01-01"))
analysis <- volatility_analysis(spx)
analysis$month$level
analysis$recent$days
analysis$forecast$days
volatility_text(analysis)
# the volatility of the last week, and the move of the last day
volatility_text(volatility_analysis(spx, month_days = 5, recent_days = 1))$month$headline
}