如何基于含NA值的季度收益率序列计算年化收益率？

Hey Roger, let's break down why your rolling annualized return calculations aren't matching what you expected, especially with those NA values cluttering up your quarterly return data.

The Core Issue #

Your current code uses rollapply() with Return.annualized() from the PerformanceAnalytics package, but the default behavior doesn't handle NA values the way you probably want it to. When a rolling window includes NAs:

• Return.annualized() either ignores them entirely (if you set na.rm=TRUE) but still uses a fixed scale=4 (assuming 4 full quarters), which skews the result
• Or it returns NA (if na.rm=FALSE), which might not be what you're after either

Let's Fix This #

We'll create custom functions to handle NAs properly, depending on your exact needs.

First, let's recap your sample data and original code for context:

library(zoo)
library(PerformanceAnalytics)

# Your sample data
df <- data.frame(v1 = c(0.01, 0.03, 0.02,0.05, 0.06,0.03,0.01, NA), V2 = c(NA, 0.1, 0.02,NA,0.03,0.05,0.11, 0.2))

# Your original code
df_annual <- rollapply(df, width = 4, Return.annualized, scale =4, align = "right", fill = NA)

Option 1: Calculate Annualized Returns Using Valid Quarters in the Window

If you want to compute the return using whatever valid (non-NA) quarters are present in the 4-quarter window, then scale it to annualized based on the number of valid periods:

# Custom function to handle NAs by using valid returns and scaling appropriately
calc_annualized_with_na <- function(x) {
  # Filter out NA values from the window
  valid_returns <- x[!is.na(x)]
  num_valid <- length(valid_returns)
  
  # Return NA if there are no valid returns in the window
  if (num_valid == 0) return(NA)
  
  # Calculate geometric mean return, then annualize based on valid quarters
  total_growth <- prod(1 + valid_returns)
  annualized_return <- total_growth^(4 / num_valid) - 1
  
  return(annualized_return)
}

# Apply the custom function to your data
df_annual_adjusted <- rollapply(df, width = 4, FUN = calc_annualized_with_na, align = "right", fill = NA)

For example, take the 4th row of your V2 column (window: NA, 0.1, 0.02, NA):

• Valid returns are 0.1 and 0.02 (2 quarters)
• Calculation: (1.1 * 1.02)^(4/2) - 1 = 1.258884 - 1 = 0.258884 (matches your original result, but this logic explicitly accounts for the missing quarters)

Option 2: Only Calculate Returns for Full, Non-NA Windows

If you only want annualized returns when a 4-quarter window has no NA values (ignoring partial windows), use this stricter function:

# Custom function that only computes returns for complete, non-NA windows
calc_annualized_full_window <- function(x) {
  # Return NA if any value in the window is NA
  if (any(is.na(x))) return(NA)
  
  # Use standard annualization for a full 4-quarter window
  Return.annualized(x, scale = 4)
}

# Apply to your data
df_annual_full <- rollapply(df, width = 4, FUN = calc_annualized_full_window, align = "right", fill = NA)

This will return NA for any window that includes even one NA value, which might be what you expected if you only wanted full-year calculations.

Wrap-Up #

Pick the option that aligns with your business logic:

• Use Option 1 if you want to make use of partial valid data in each window
• Use Option 2 if you only trust full, complete 4-quarter periods

内容的提问来源于stack exchange，提问作者Roger