### Complete Portfolio Construction and Comparison Workflow

Source: https://context7.com/ardiad/riskportfolios/llms.txt

A comprehensive example demonstrating estimation of returns and covariance, portfolio construction, and performance comparison.

```r
library(RiskPortfolios)
data("Industry_10")
rets <- Industry_10

# ============================================
# STEP 1: Estimate expected returns
# ============================================
mu_naive <- meanEstimation(rets, control = list(type = 'naive'))
mu_bs <- meanEstimation(rets, control = list(type = 'bs'))

# ============================================
# STEP 2: Estimate covariance matrices
# ============================================
Sigma_naive <- covEstimation(rets, control = list(type = 'naive'))
Sigma_lw <- covEstimation(rets, control = list(type = 'lw'))
Sigma_const <- covEstimation(rets, control = list(type = 'const'))

# ============================================
# STEP 3: Estimate semideviation for risk-efficient portfolios
# ============================================
semiDev <- semidevEstimation(rets, control = list(type = 'naive'))

# ============================================
# STEP 4: Construct various portfolios
# ============================================

# Equal-weighted benchmark
n <- ncol(rets)
w_ew <- rep(1/n, n)

# Minimum variance with different covariance estimators
w_minvol_naive <- optimalPortfolio(Sigma = Sigma_naive,
  control = list(type = 'minvol', constraint = 'lo'))
w_minvol_lw <- optimalPortfolio(Sigma = Sigma_lw,
  control = list(type = 'minvol', constraint = 'lo'))
w_minvol_const <- optimalPortfolio(Sigma = Sigma_const,
  control = list(type = 'minvol', constraint = 'lo'))

# Mean-variance with Bayes-Stein inputs
w_mv_bs <- optimalPortfolio(mu = mu_bs, Sigma = Sigma_lw,
  control = list(type = 'mv', constraint = 'lo', gamma = 1))

# Equal-risk-contribution
w_erc <- optimalPortfolio(Sigma = Sigma_lw,
  control = list(type = 'erc', constraint = 'lo'))

# Maximum diversification
w_maxdiv <- optimalPortfolio(Sigma = Sigma_lw,
  control = list(type = 'maxdiv', constraint = 'lo'))

# Risk-efficient
w_riskeff <- optimalPortfolio(Sigma = Sigma_lw, semiDev = semiDev,
  control = list(type = 'riskeff', constraint = 'lo'))

# ============================================
# STEP 5: Compare portfolio characteristics
# ============================================

# Function to compute portfolio volatility
portfolio_vol <- function(w, Sigma) {
  sqrt(as.numeric(crossprod(w, Sigma %*% w)))
}

# Function to compute diversification ratio
div_ratio <- function(w, Sigma) {
  sig <- sqrt(diag(Sigma))
  weighted_vol <- sum(w * sig)
  port_vol <- portfolio_vol(w, Sigma)
  weighted_vol / port_vol
}

# Compare volatilities using Ledoit-Wolf covariance
portfolios <- list(
  "Equal-Weight" = w_ew,
  "Min-Vol (Naive)" = w_minvol_naive,
  "Min-Vol (LW)" = w_minvol_lw,
  "Min-Vol (Const)" = w_minvol_const,
  "Mean-Var (BS)" = w_mv_bs,
  "ERC" = w_erc,
  "Max-Div" = w_maxdiv,
  "Risk-Eff" = w_riskeff
)

# Print comparison
cat("Portfolio Comparison:\n")
cat("=" , rep("=", 50), "\n", sep = "")
for (name in names(portfolios)) {
  w <- portfolios[[name]]
  vol <- portfolio_vol(w, Sigma_lw) * sqrt(252) * 100  # Annualized %
  dr <- div_ratio(w, Sigma_lw)
  cat(sprintf("%-18s Vol: %5.2f%%  Div.Ratio: %.3f\n", name, vol, dr))
}
```

--------------------------------

### Construct Maximum Decorrelation Portfolios

Source: https://context7.com/ardiad/riskportfolios/llms.txt

Examples of constructing maximum decorrelation portfolios under different constraint scenarios.

```r
# Unconstrained maximum decorrelation
w_maxdec <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'maxdec'))

# Long-only maximum decorrelation
w_maxdec_lo <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'maxdec', constraint = 'lo'))

# Maximum decorrelation with bounds
w_maxdec_bounds <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'maxdec', constraint = 'user',
                 LB = rep(0.02, 10), UB = rep(0.80, 10)))
```

--------------------------------

### Construct Maximum Diversification Portfolio with Bounds

Source: https://context7.com/ardiad/riskportfolios/llms.txt

Constructs a maximum diversification portfolio using specific lower and upper bounds for asset weights.

```r
w_maxdiv_bounds <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'maxdiv', constraint = 'user',
                 LB = rep(0.02, 10), UB = rep(0.80, 10)))
```

--------------------------------

### Construct Risk-Efficient Portfolios

Source: https://context7.com/ardiad/riskportfolios/llms.txt

Constructs risk-efficient portfolios requiring semideviation estimation, available in unconstrained, long-only, and bounded variants.

```r
# Unconstrained risk-efficient (requires semideviation)
w_riskeff <- optimalPortfolio(Sigma = Sigma, semiDev = semiDev,
  control = list(type = 'riskeff'))

# Long-only risk-efficient
w_riskeff_lo <- optimalPortfolio(Sigma = Sigma, semiDev = semiDev,
  control = list(type = 'riskeff', constraint = 'lo'))

# Risk-efficient with bounds
w_riskeff_bounds <- optimalPortfolio(Sigma = Sigma, semiDev = semiDev,
  control = list(type = 'riskeff', constraint = 'user',
                 LB = rep(0.02, 10), UB = rep(0.80, 10)))
```

--------------------------------

### Compute Optimal Portfolio Weights

Source: https://context7.com/ardiad/riskportfolios/llms.txt

Generates portfolio weights based on risk-based methodologies. Supports various constraints like long-only, gross exposure, and user-defined bounds.

```r
library(RiskPortfolios)
data("Industry_10")
rets <- Industry_10

# Step 1: Estimate inputs
mu <- meanEstimation(rets)
Sigma <- covEstimation(rets)
semiDev <- semidevEstimation(rets)

# ============================================
# MEAN-VARIANCE PORTFOLIO
# ============================================

# Unconstrained mean-variance with default risk aversion gamma = 0.89
w_mv <- optimalPortfolio(mu = mu, Sigma = Sigma)
print(round(w_mv, 4))

# Mean-variance with custom risk aversion gamma = 1
w_mv_gamma1 <- optimalPortfolio(mu = mu, Sigma = Sigma,
  control = list(gamma = 1))

# Long-only mean-variance portfolio
w_mv_lo <- optimalPortfolio(mu = mu, Sigma = Sigma,
  control = list(type = 'mv', constraint = 'lo'))

# Mean-variance with user-defined bounds (2% to 80% per asset)
w_mv_bounds <- optimalPortfolio(mu = mu, Sigma = Sigma,
  control = list(type = 'mv', constraint = 'user',
                 LB = rep(0.02, 10), UB = rep(0.80, 10)))

# Mean-variance with gross exposure constraint (default 1.6 = 130/30)
w_mv_gross <- optimalPortfolio(mu = mu, Sigma = Sigma,
  control = list(type = 'mv', constraint = 'gross'))

# Mean-variance with custom gross exposure (1.2)
w_mv_gross12 <- optimalPortfolio(mu = mu, Sigma = Sigma,
  control = list(type = 'mv', constraint = 'gross', gross.c = 1.2))

# ============================================
# MINIMUM VARIANCE PORTFOLIO
# ============================================

# Unconstrained minimum variance
w_minvol <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'minvol'))

# Long-only minimum variance
w_minvol_lo <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'minvol', constraint = 'lo'))

# Minimum variance with bounds
w_minvol_bounds <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'minvol', constraint = 'user',
                 LB = rep(0.02, 10), UB = rep(0.80, 10)))

# Minimum variance with gross exposure constraint
w_minvol_gross <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'minvol', constraint = 'gross', gross.c = 1.2))

# ============================================
# INVERSE VOLATILITY PORTFOLIO
# ============================================

# Inverse volatility weighted (no constraints needed)
w_invvol <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'invvol'))

# ============================================
# EQUAL-RISK-CONTRIBUTION (ERC) PORTFOLIO
# ============================================

# ERC with long-only constraint
w_erc <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'erc', constraint = 'lo'))

# ERC with user-defined bounds
w_erc_bounds <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'erc', constraint = 'user',
                 LB = rep(0.02, 10), UB = rep(0.80, 10)))

# ============================================
# MAXIMUM DIVERSIFICATION PORTFOLIO
# ============================================

# Unconstrained maximum diversification
w_maxdiv <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'maxdiv'))

# Long-only maximum diversification
w_maxdiv_lo <- optimalPortfolio(Sigma = Sigma,
  control = list(type = 'maxdiv', constraint = 'lo'))
```

--------------------------------

### Estimate Semideviation with RiskPortfolios

Source: https://context7.com/ardiad/riskportfolios/llms.txt

Calculates downside risk using naive or EWMA methods. Requires the RiskPortfolios library and historical return data.

```r
library(RiskPortfolios)
data("Industry_10")
rets <- Industry_10

# Naive semideviation estimation
semiDev_naive <- semidevEstimation(rets)
print(round(semiDev_naive, 6))
#     NoDur     Durbl     Manuf     Enrgy     HiTec     Telcm     Shops     Hlth      Utils     Other
# 0.029841 0.044218 0.032672 0.038142 0.041563 0.033891 0.032108 0.031242 0.025674 0.035421

# Explicit naive estimation
semiDev_naive2 <- semidevEstimation(rets, control = list(type = 'naive'))

# EWMA semideviation with default lambda = 0.94
semiDev_ewma <- semidevEstimation(rets, control = list(type = 'ewma'))

# EWMA semideviation with custom lambda = 0.90
semiDev_ewma_fast <- semidevEstimation(rets, control = list(type = 'ewma', lambda = 0.90))
```

--------------------------------

### Expected Returns Estimation in R

Source: https://context7.com/ardiad/riskportfolios/llms.txt

Computes expected returns using arithmetic mean, EWMA, Bayes-Stein shrinkage, and Martellini implied returns. Bayes-Stein shrinks estimates toward the global minimum variance portfolio return.

```r
library(RiskPortfolios)
data("Industry_10")
rets <- Industry_10

# Naive arithmetic mean estimation
mu_naive <- meanEstimation(rets)
print(round(mu_naive, 6))
```

```r
# Explicit naive estimation
mu_naive2 <- meanEstimation(rets, control = list(type = 'naive'))
```

```r
# EWMA mean with default lambda = 0.94
# More weight on recent observations
mu_ewma <- meanEstimation(rets, control = list(type = 'ewma'))
```

```r
# EWMA with faster adaptation (lower lambda)
mu_ewma_fast <- meanEstimation(rets, control = list(type = 'ewma', lambda = 0.90))
```

```r
# Bayes-Stein shrinkage estimation
# Shrinks sample mean towards minimum variance portfolio return
mu_bs <- meanEstimation(rets, control = list(type = 'bs'))
```

```r
# Martellini implied returns (uses volatility as proxy for expected return)
mu_mart <- meanEstimation(rets, control = list(type = 'mart'))
```

--------------------------------

### Covariance Matrix Estimation in R

Source: https://context7.com/ardiad/riskportfolios/llms.txt

Estimates covariance matrices using various methods like naive sample, EWMA, Ledoit-Wolf shrinkage, factor models, and Bayes-Stein. Supports ten estimation types, with shrinkage being useful when assets outnumber observations.

```r
library(RiskPortfolios)
data("Industry_10")
rets <- Industry_10

# Naive (sample) covariance estimation - standard unbiased estimator
Sigma_naive <- covEstimation(rets)
print(round(Sigma_naive[1:3, 1:3], 6))
```

```r
# EWMA estimation with default decay lambda = 0.94 (RiskMetrics standard)
Sigma_ewma <- covEstimation(rets, control = list(type = 'ewma'))
```

```r
# EWMA with custom lambda = 0.90 for faster adaptation to recent data
Sigma_ewma_fast <- covEstimation(rets, control = list(type = 'ewma', lambda = 0.90))
```

```r
# Ledoit-Wolf shrinkage towards one-factor model (market)
# Well-conditioned even when N > T
Sigma_lw <- covEstimation(rets, control = list(type = 'lw'))
```

```r
# Factor model estimation with K = 3 factors
Sigma_factor <- covEstimation(rets, control = list(type = 'factor', K = 3))
```

```r
# Shrinkage towards constant correlation matrix
Sigma_const <- covEstimation(rets, control = list(type = 'const'))
```

```r
# Ledoit-Wolf shrinkage towards constant correlation (alternative)
Sigma_cor <- covEstimation(rets, control = list(type = 'cor'))
```

```r
# Shrinkage towards one-parameter matrix (equal variances, zero covariances)
Sigma_oneparm <- covEstimation(rets, control = list(type = 'oneparm'))
```

```r
# Shrinkage towards diagonal matrix (zero covariances)
Sigma_diag <- covEstimation(rets, control = list(type = 'diag'))
```

```r
# Large-dimensional estimator - optimal for high-dimensional data
Sigma_large <- covEstimation(rets, control = list(type = 'large'))
```

```r
# Bayes-Stein covariance estimation
Sigma_bs <- covEstimation(rets, control = list(type = 'bs'))
```

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