Load all data sheets from the Excel file: client portfolio, risk model, index data, and FX rates. Filter to working days only (Monday-Friday).

data <- load_data()
tbl_client_portfolio <- data$tbl_client_portfolio
tbl_risk_model <- data$tbl_risk_model
tbl_idx_data <- data$tbl_idx_data
tbl_fx_data <- data$tbl_fx_data

# load_data() reads 4 sheets:
# - tbl_client_portfolio: Portfolio holdings and weights
# - tbl_risk_model: Factor definitions and mappings
# - idx_data: Index time series (filtered to working days)
# - fx_data: FX spot rates (filtered to working days)

Build ID-to-currency and ID-to-name lookup tables for consistent referencing across portfolio and risk model data.

mappings <- create_mapping_tables(tbl_client_portfolio, tbl_risk_model)
tbl_map_id_currency <- mappings$tbl_map_id_currency
tbl_map_id_name <- mappings$tbl_map_id_name

# ID to currency mapping combines portfolio and risk model currencies
# ID to name mapping uses factor_name from risk model, falls back to name

Define the base currency (EUR) and identify the cash index for excess return calculations.

to_currency <- "EUR"
cli::cat_bullet(glue::glue("Basiswahrung: {to_currency}"), bullet_col = "red")

cash_id <- tbl_client_portfolio |>
  dplyr::filter(name == glue::glue("Cash {to_currency}")) |>
  dplyr::pull(id)

# Output: "Cash Index: Cash EUR"

Convert all indices to base currency EUR and calculate excess returns over the cash index. Also convert Trade-Weighted Index (TWI) data.

tbl_idx_data_base <- convert_to_excess_returns(
  tbl_idx_data, tbl_fx_data, tbl_client_portfolio,
  tbl_risk_model, tbl_map_id_currency, to_currency, cash_id
)

tbl_twi_data_base <- convert_twi_to_base(
  tbl_idx_data, tbl_fx_data, tbl_risk_model, to_currency
)

# Excess returns: value_excess = value_base / value_cash
# TWI indices inverted and converted to EUR

Combine time series, determine date ranges (10-year lookback), and filter portfolio/risk model IDs based on data availability.

ts_prep <- prepare_time_series(
  tbl_idx_data_base, tbl_twi_data_base,
  tbl_client_portfolio, tbl_risk_model,
  lookback_years = 10
)

start_date <- ts_prep$start_date
end_date <- ts_prep$end_date
id_port <- ts_prep$id_port    # Portfolio IDs
id_rm <- ts_prep$id_rm        # Risk model IDs
id <- ts_prep$id              # All IDs

# Output: "Gesamtzeitraum der Daten: 2014-01-03 bis 2024-01-03"

Build the date x ID index matrix, compute log returns, and calculate 22-day rolling returns for covariance estimation.

returns <- create_index_matrix_and_returns(
  ts_prep$tbl_ts_data, start_date, end_date, id, id_rm,
  period_length = 22L
)

idx_date_id <- returns$idx_date_id       # Index matrix
ret_date_id <- returns$ret_date_id       # Daily log returns
ret22_date_id <- returns$ret22_date_id   # 22-day rolling returns
annualization_factor <- returns$annualization_factor  # ~11.86

# Working days per year: 365.2425 / 7 * 5 = 260.89
# Annualization factor: 260.89 / 22 = 11.86

Core algorithm: Iteratively estimate covariance with GARCH-based time-decay weights. Uses eigenvalue decomposition to create orthogonal risk factors.

cov_est <- estimate_iterative_covariance(ret22_date_id, id, id_rm, period_length)

Q_emp <- cov_est$Q_emp           # Empirical covariance matrix
Q_rm <- cov_est$Q_rm             # Scaled risk model covariance
Q_rm_comp <- cov_est$Q_rm_comp   # Component covariance
weight <- cov_est$weight         # Time-decay weights
idx_rm_comp <- cov_est$idx_rm_comp  # Component indices

# Algorithm:
# 1. Initialize linear time weights
# 2. Compute weighted covariance Q_emp
# 3. Scale risk model, eigenvalue decomposition
# 4. Fit GARCH(1,1) to first component
# 5. Update weights: weight = time^(1-s) * garch^s
# 6. Repeat until convergence

Visualize the converged time-decay weights and the first 5 principal risk factors.

plot_weights(weight)
plot_risk_factors(idx_rm_comp, n = 5)

# Weights: Higher in recent periods, lower in older periods
# Risk factors: Orthogonal components explaining portfolio variance

Display annualized volatility for each portfolio asset from the empirical covariance matrix.

plot_volatility_barplot(
  Q_emp[id_port, id_port],
  tbl_map_id_name,
  annualization_factor,
  "Annualized Volatility of 22-Day Returns"
)

# Volatility = sqrt(diag(Q_emp) * annualization_factor)

Estimate the factor model with beta decomposition. Select components explaining 95% of variance and compute shrinkage-adjusted covariance.

factor_model <- estimate_factor_model(Q_rm_comp, Q_emp, cov_est$ei, id_port,
                                       variance_threshold = 0.95)

n_comp <- factor_model$n_comp                  # Number of components
id_comp <- factor_model$id_comp                # Component IDs
beta_id_port_id_comp.fit <- factor_model$beta_id_port_id_comp.fit  # Betas
Q_shrink <- factor_model$Q_shrink              # Shrinkage covariance

# Q_shrink = Q_fit + Q_res
# Q_fit = beta' * Q_comp * beta (systematic risk)
# Q_res = diag(Q_emp - Q_fit) (idiosyncratic risk)

# Output: "Anzahl relevanter Risk Model Faktoren: 7"

Fit GARCH(1,1) models to residuals and components for forward-looking volatility forecasts.

garch_results <- fit_garch_models(
  idx_rm_comp, beta_id_port_id_comp.resid,
  id_port, id_comp,
  prediction_horizon, workday_per_year
)

sd_resid <- garch_results$sd_resid  # Residual volatilities
sd_comp <- garch_results$sd_comp    # Component volatilities

# For each component/residual:
# 1. Fit GARCH(1,1) specification
# 2. Forecast h=prediction_horizon steps ahead
# 3. Annualize: sd * sqrt(workday_per_year)

Visualize GARCH-forecasted volatilities for each risk model component.

barplot(
  sd_comp / sqrt(annualization_factor),
  main = "Annualized Volatility of Risk Model Components"
)
abline(h = 0.01)  # Reference line at 1% volatility

Construct the forward-looking GARCH covariance matrix using forecasted component and residual volatilities.

q_shrink <- calculate_garch_covariance(
  beta_id_port_id_comp.fit, sd_comp, sd_resid, id_port
)

# Q_garch = beta' * diag(sd_comp^2) * beta + diag(sd_resid^2)
# This is the forward-looking covariance matrix

Display GARCH-forecasted annualized volatility for each portfolio asset.

plot_volatility_barplot(
  q_shrink,
  tbl_map_id_name,
  1,  # Already annualized
  "Annualized Volatility of Portfolio IDs from Estimated Covariance Matrix"
)

Extract the three final covariance matrices for portfolio assets: empirical, shrinkage-adjusted, and GARCH-forecasted.

Q_port_emp <- Q_emp[id_port, id_port]       # Empirical (historical)
Q_port_shrink <- Q_shrink[id_port, id_port] # Shrinkage (factor model)
Q_port_garch <- q_shrink[id_port, id_port]  # GARCH (forward-looking)

# All three matrices are:
# - Symmetric
# - Positive semi-definite
# - Portfolio-sized (n_assets x n_assets)

Compare volatilities across the three estimation methods using scatter plots.

plot_volatility_comparisons(Q_port_emp, Q_port_shrink, Q_port_garch, annualization_factor)

# Creates two scatter plots:
# 1. Empirical vs Shrinkage volatility
# 2. Empirical vs GARCH volatility
# Red line = 45-degree reference (perfect agreement)

Output the correlation matrices (subset) for validation and comparison.

print_final_correlations(Q_port_emp, Q_port_shrink, Q_port_garch)

# Prints 3x3 correlation matrices for assets 6-8
# Example output:
#      [,1] [,2] [,3]
# [1,] 1.00 0.42 0.35
# [2,] 0.42 1.00 0.28
# [3,] 0.35 0.28 1.00