Rolling annualized tracking differences

For each fund–index pair in fund_index_map, computes rolling, annualized tracking differences over a backward-looking window of n_days calendar days. Both log-return and CAGR forms are returned.

Usage

roll_diffs(
  df,
  n_days,
  fund_index_map,
  date_col = "date",
  index_level = c("net", "gross"),
  annual_days = 365,
  messages = c("roll", "skip"),
  gross_suffix = "-GR"
)

Arguments

df: Data frame containing a date column, fund columns, and benchmark/index columns referenced in fund_index_map.
n_days: Rolling lookback window in calendar days.
fund_index_map: Named character vector mapping fund column names to their corresponding benchmark/index base column names.
date_col: Name of the date column in df. Defaults to "date". Must be of class Date and sorted in ascending order.
index_level: Which index level to use, one of "net" or "gross". If "gross", gross_suffix is appended to the mapped index base name before lookup in df. Defaults to "net".
annual_days: Number of days used for annualization. Defaults to 365.
messages: Character vector controlling emitted messages. Any of "roll" (per-pair progress) and "skip" (skip reasons). Use messages = "roll" to show only progress, messages = "skip" to show only skip reasons, or messages = character() or NULL to silence all messages. Defaults to c("roll", "skip").
gross_suffix: Suffix appended to the mapped index base name when index_level = "gross". Defaults to "-GR".

Value

A named list with two data frames, log and cagr. Each data frame contains date_col followed by one column per fund (named as in fund_index_map), holding the rolling annualized tracking differences.

Details

For each date $t$, an anchor date $t_0$ is chosen as the last available observation at or before $t - n\_days$ where both fund and index values are present. Let $\Delta = t - t_0$ in calendar days.

The annualized tracking differences are:

Log-return difference: $$\left[\ln\left(\frac{f_t}{f_{t_0}}\right) - \ln\left(\frac{i_t}{i_{t_0}}\right)\right] \times \frac{annual\_days}{\Delta}$$
CAGR difference: $$\left(\frac{f_t}{f_{t_0}}\right)^{annual\_days/\Delta} - \left(\frac{i_t}{i_{t_0}}\right)^{annual\_days/\Delta}$$

Values are NA when an anchor cannot be found, required inputs are missing, $\Delta \le 0$, or values are invalid for the chosen formula (e.g. non-positive inputs for log returns).