aggregate-volatility-asset-pricing

library(readxl)
library(dplyr)
library(tseries)
library(psych)
library(moments)
df <- read_excel("C:/Users/Cindy/Desktop/毕业论文/data/data_daily.xlsx")

####ADF test
adf.test(df$VIX)
adf.test(df$`Mkt-RF`)
adf.test(df$`SMB(FF3)`)
adf.test(df$HML)

adf.test(df$LO20_EXCESS)
adf.test(df$QNT2_EXCESS)
adf.test(df$QNT3_EXCESS)
adf.test(df$QNT4_EXCESS)
adf.test(df$HI20_EXCESS)
adf.test(df$`SMB(FF5)`)
adf.test(df$RMW)
adf.test(df$CMA)

####describtion
vars <- df[, c(
  "VIX",
  "Mkt-RF",
  "SMB(FF3)",
  "SMB(FF5)",
  "HML",
  "RMW",
  "CMA",
  "COVID",
  "LO20_EXCESS",
  "QNT2_EXCESS",
  "QNT3_EXCESS",
  "QNT4_EXCESS",
  "HI20_EXCESS"
)]
desc_table <- data.frame(
  Variable = names(vars),
  Mean = sapply(vars, mean, na.rm = TRUE),
  Std.Dev = sapply(vars, sd, na.rm = TRUE),
  Min = sapply(vars, min, na.rm = TRUE),
  Max = sapply(vars, max, na.rm = TRUE),
  Skewness = sapply(vars, skewness, na.rm = TRUE),
  Kurtosis = sapply(vars, kurtosis, na.rm = TRUE)
)

desc_table[, -1] <- round(desc_table[, -1], 4)

desc_table

###FF3
ff3 <- lm(
  LO20_EXCESS ~ `Mkt-RF` + `SMB(FF3)` + HML,
  data = df
)

summary(ff3)

portfolios <- c(
  "LO20_EXCESS",
  "QNT2_EXCESS",
  "QNT3_EXCESS",
  "QNT4_EXCESS",
  "HI20_EXCESS"
)

for (p in portfolios) {
  
  model <- lm(
    as.formula(
      paste(p, "~ `Mkt-RF` + `SMB(FF3)` + HML")
    ),
    data = df
  )
  
  cat("\n====================\n")
  cat(p, "\n")
  cat("====================\n")
  
  print(summary(model))
}



###FF5
ff5 <- lm(
  LO20_EXCESS ~ `Mkt-RF` + `SMB(FF5)` + HML + RMW + CMA,
  data = df
)

summary(ff5)

portfolios <- c(
  "LO20_EXCESS",
  "QNT2_EXCESS",
  "QNT3_EXCESS",
  "QNT4_EXCESS",
  "HI20_EXCESS"
)

for (p in portfolios) {
  
  model <- lm(
    as.formula(
      paste(p, "~ `Mkt-RF` + `SMB(FF5)` + HML + RMW + CMA")
    ),
    data = df
  )
  
  cat("\n====================\n")
  cat(p, "\n")
  cat("====================\n")
  
  print(summary(model))
}


###FF3 and VIX
portfolios <- c(
  "LO20_EXCESS",
  "QNT2_EXCESS",
  "QNT3_EXCESS",
  "QNT4_EXCESS",
  "HI20_EXCESS"
)

for (p in portfolios){
  
  cat("\n====================\n")
  cat(p,"\n")
  cat("====================\n")
  
  model <- lm(
    as.formula(
      paste(
        p,
        "~ `Mkt-RF` + `SMB(FF3)` + HML + VIX"
      )
    ),
    data=df
  )
  
  print(summary(model))
}


results_ff3_vix <- data.frame()

for (p in portfolios){
  
  model <- lm(
    as.formula(
      paste(
        p,
        "~ `Mkt-RF` + `SMB(FF3)` + HML + VIX"
      )
    ),
    data=df
  )
  
  results_ff3_vix <- rbind(
    results_ff3_vix,
    data.frame(
      Portfolio = p,
      Alpha = coef(model)[1],
      Beta_MKT = coef(model)[2],
      Beta_SMB = coef(model)[3],
      Beta_HML = coef(model)[4],
      Gamma_VIX = coef(model)[5],
      Adj_R2 = summary(model)$adj.r.squared,
      AIC = AIC(model),
      BIC = BIC(model)
    )
  )
}

results_ff3_vix

for (p in portfolios){
  
  model <- lm(
    as.formula(
      paste(
        p,
        "~ `Mkt-RF` + `SMB(FF3)` + HML + VIX"
      )
    ),
    data = df
  )
  
  cat("\n====================\n")
  cat(p,"\n")
  cat("====================\n")
  
  print(
    coef(summary(model))["VIX", ]
  )
}

###FF5 and VIX
portfolios <- c(
  "LO20_EXCESS",
  "QNT2_EXCESS",
  "QNT3_EXCESS",
  "QNT4_EXCESS",
  "HI20_EXCESS"
)

for (p in portfolios){
  
  cat("\n====================\n")
  cat(p,"\n")
  cat("====================\n")
  
  model <- lm(
    as.formula(
      paste(
        p,
        "~ `Mkt-RF` + `SMB(FF5)` + HML + RMW + CMA + VIX"
      )
    ),
    data = df
  )
  
  print(summary(model))
}


results_ff5_vix <- data.frame()

for (p in portfolios){
  
  model <- lm(
    as.formula(
      paste(
        p,
        "~ `Mkt-RF` + `SMB(FF5)` + HML + RMW + CMA + VIX"
      )
    ),
    data = df
  )
  
  results_ff5_vix <- rbind(
    results_ff5_vix,
    data.frame(
      Portfolio = p,
      Alpha = coef(model)[1],
      Beta_MKT = coef(model)[2],
      Beta_SMB = coef(model)[3],
      Beta_HML = coef(model)[4],
      Beta_RMW = coef(model)[5],
      Beta_CMA = coef(model)[6],
      Gamma_VIX = coef(model)[7],
      Adj_R2 = summary(model)$adj.r.squared,
      AIC = AIC(model),
      BIC = BIC(model)
    )
  )
}

results_ff5_vix


for (p in portfolios){
  
  model <- lm(
    as.formula(
      paste(
        p,
        "~ `Mkt-RF` + `SMB(FF5)` + HML + RMW + CMA + VIX"
      )
    ),
    data = df
  )
  
  cat("\n====================\n")
  cat(p,"\n")
  cat("====================\n")
  
  print(
    coef(summary(model))["VIX", ]
  )
}

###VIX_COVID
df$VIX_COVID <- df$VIX * df$COVID

###return
portfolios <- c(
  "LO20_EXCESS",
  "QNT2_EXCESS",
  "QNT3_EXCESS",
  "QNT4_EXCESS",
  "HI20_EXCESS"
)
results <- data.frame()

for(p in portfolios){
  
  model <- lm(
    as.formula(
      paste(
        p,
        "~ `Mkt-RF` + `SMB(FF5)` + HML + RMW + CMA + VIX + COVID + VIX_COVID"
      )
    ),
    data = df
  )
  
  coef_table <- summary(model)$coefficients
  
  results <- rbind(
    results,
    data.frame(
      
      Portfolio = p,
      
      Alpha = coef_table["(Intercept)", "Estimate"],
      
      Beta_MKT = coef_table["`Mkt-RF`", "Estimate"],
      Beta_SMB = coef_table["`SMB(FF5)`", "Estimate"],
      Beta_HML = coef_table["HML", "Estimate"],
      Beta_RMW = coef_table["RMW", "Estimate"],
      Beta_CMA = coef_table["CMA", "Estimate"],
      
      Gamma_VIX = coef_table["VIX", "Estimate"],
      P_VIX = coef_table["VIX", "Pr(>|t|)"],
      
      Gamma_COVID = coef_table["COVID", "Estimate"],
      P_COVID = coef_table["COVID", "Pr(>|t|)"],
      
      Gamma_Interaction = coef_table["VIX_COVID", "Estimate"],
      P_Interaction = coef_table["VIX_COVID", "Pr(>|t|)"],
      
      Adj_R2 = summary(model)$adj.r.squared,
      
      AIC = AIC(model),
      BIC = BIC(model)
    )
  )
}
results_table <- results

results_table[, -1] <- round(
  results_table[, -1],
  4
)

results_table

star <- function(p){
  
  if(p < 0.01){
    return("***")
  }else if(p < 0.05){
    return("**")
  }else if(p < 0.10){
    return("*")
  }else{
    return("")
  }
  
}

paper_table <- data.frame(
  
  Portfolio = results$Portfolio,
  
  VIX =
    paste0(
      round(results$Gamma_VIX,4),
      sapply(results$P_VIX, star)
    ),
  
  COVID =
    paste0(
      round(results$Gamma_COVID,4),
      sapply(results$P_COVID, star)
    ),
  
  Interaction =
    paste0(
      round(results$Gamma_Interaction,4),
      sapply(results$P_Interaction, star)
    ),
  
  Adj_R2 = round(results$Adj_R2,4),
  
  AIC = round(results$AIC,2),
  
  BIC = round(results$BIC,2)
)

paper_table

library(openxlsx)

write.xlsx(
  paper_table,
  "FF5_VIX_COVID_Interaction.xlsx",
  rowNames = FALSE
)



###logVIX
df$logVIX <- log(df$VIX)
df$logVIX_COVID <- df$logVIX * df$COVID
portfolios <- c(
  "LO20_EXCESS",
  "QNT2_EXCESS",
  "QNT3_EXCESS",
  "QNT4_EXCESS",
  "HI20_EXCESS"
)

results <- data.frame()

for(p in portfolios){
  
  model <- lm(
    as.formula(
      paste(
        p,
        "~ `Mkt-RF` + `SMB(FF5)` + HML + RMW + CMA + logVIX + COVID + logVIX_COVID"
      )
    ),
    data = df
  )
  
  coef_table <- summary(model)$coefficients
  
  results <- rbind(
    results,
    data.frame(
      
      Portfolio = p,
      
      Alpha = coef_table["(Intercept)", "Estimate"],
      
      Beta_MKT = coef_table["`Mkt-RF`", "Estimate"],
      Beta_SMB = coef_table["`SMB(FF5)`", "Estimate"],
      Beta_HML = coef_table["HML", "Estimate"],
      Beta_RMW = coef_table["RMW", "Estimate"],
      Beta_CMA = coef_table["CMA", "Estimate"],
      
      Gamma_logVIX =
        coef_table["logVIX", "Estimate"],
      
      P_logVIX =
        coef_table["logVIX", "Pr(>|t|)"],
      
      Gamma_COVID =
        coef_table["COVID", "Estimate"],
      
      P_COVID =
        coef_table["COVID", "Pr(>|t|)"],
      
      Gamma_Interaction =
        coef_table["logVIX_COVID", "Estimate"],
      
      P_Interaction =
        coef_table["logVIX_COVID", "Pr(>|t|)"],
      
      Adj_R2 =
        summary(model)$adj.r.squared,
      
      AIC = AIC(model),
      BIC = BIC(model)
    )
  )
}

star <- function(p){
  
  if(p < 0.01){
    return("***")
  }else if(p < 0.05){
    return("**")
  }else if(p < 0.10){
    return("*")
  }else{
    return("")
  }
  
}


paper_table <- data.frame(
  
  Portfolio = results$Portfolio,
  
  logVIX =
    paste0(
      round(results$Gamma_logVIX,4),
      sapply(results$P_logVIX, star)
    ),
  
  COVID =
    paste0(
      round(results$Gamma_COVID,4),
      sapply(results$P_COVID, star)
    ),
  
  Interaction =
    paste0(
      round(results$Gamma_Interaction,4),
      sapply(results$P_Interaction, star)
    ),
  
  Adj_R2 =
    round(results$Adj_R2,4),
  
  AIC =
    round(results$AIC,2),
  
  BIC =
    round(results$BIC,2)
)

paper_table


###△VIX
library(dplyr)

df <- df %>%
  arrange(Date) %>%
  mutate(
    DeltaVIX = VIX - lag(VIX)
  )

summary(df$DeltaVIX)
df2 <- na.omit(df)
df2$DeltaVIX_COVID <- df2$DeltaVIX * df2$COVID


portfolios <- c(
  "LO20_EXCESS",
  "QNT2_EXCESS",
  "QNT3_EXCESS",
  "QNT4_EXCESS",
  "HI20_EXCESS"
)

results <- data.frame()

for(p in portfolios){
  
  model <- lm(
    as.formula(
      paste(
        p,
        "~ `Mkt-RF` + `SMB(FF5)` + HML + RMW + CMA +
           DeltaVIX + COVID + DeltaVIX_COVID"
      )
    ),
    data = df2
  )
  
  coefs <- summary(model)$coefficients
  
  results <- rbind(
    results,
    data.frame(
      Portfolio = p,
      
      DeltaVIX = coefs["DeltaVIX","Estimate"],
      P_DeltaVIX = coefs["DeltaVIX","Pr(>|t|)"],
      
      COVID = coefs["COVID","Estimate"],
      P_COVID = coefs["COVID","Pr(>|t|)"],
      
      Interaction =
        coefs["DeltaVIX_COVID","Estimate"],
      P_Interaction =
        coefs["DeltaVIX_COVID","Pr(>|t|)"],
      
      Adj_R2 = summary(model)$adj.r.squared,
      
      AIC = AIC(model),
      BIC = BIC(model)
    )
  )
}

results

star <- function(beta,p){
  
  if(p < 0.01){
    paste0(round(beta,4),"***")
  } else if(p < 0.05){
    paste0(round(beta,4),"**")
  } else if(p < 0.10){
    paste0(round(beta,4),"*")
  } else {
    round(beta,4)
  }
  
}

paper_table <- data.frame(
  Portfolio = results$Portfolio,
  
  DeltaVIX =
    mapply(star,
           results$DeltaVIX,
           results$P_DeltaVIX),
  
  COVID =
    mapply(star,
           results$COVID,
           results$P_COVID),
  
  Interaction =
    mapply(star,
           results$Interaction,
           results$P_Interaction),
  
  Adj_R2 = round(results$Adj_R2,4),
  AIC = round(results$AIC,2),
  BIC = round(results$BIC,2)
)

paper_table



###Δln(VIX)
library(dplyr)

df <- df %>%
  mutate(
    logVIX = log(VIX),
    DlogVIX = logVIX - lag(logVIX)
  )
df2 <- na.omit(df)
df2$DlogVIX_COVID <- df2$DlogVIX * df2$COVID



portfolios <- c(
  "LO20_EXCESS",
  "QNT2_EXCESS",
  "QNT3_EXCESS",
  "QNT4_EXCESS",
  "HI20_EXCESS"
)

results <- data.frame()

for(p in portfolios){
  
  model <- lm(
    as.formula(
      paste(
        p,
        "~ `Mkt-RF` + `SMB(FF5)` + HML + RMW + CMA +
         DlogVIX + COVID + DlogVIX_COVID"
      )
    ),
    data = df2
  )
  
  coefs <- summary(model)$coefficients
  
  results <- rbind(
    results,
    data.frame(
      Portfolio = p,
      
      DlogVIX =
        coefs["DlogVIX","Estimate"],
      
      COVID =
        coefs["COVID","Estimate"],
      
      Interaction =
        coefs["DlogVIX_COVID","Estimate"],
      
      P_DlogVIX =
        coefs["DlogVIX","Pr(>|t|)"],
      
      P_COVID =
        coefs["COVID","Pr(>|t|)"],
      
      P_Interaction =
        coefs["DlogVIX_COVID","Pr(>|t|)"],
      
      Adj_R2 =
        summary(model)$adj.r.squared,
      
      AIC =
        AIC(model),
      
      BIC =
        BIC(model)
    )
  )
}

results
star <- function(x){
  
  if(x < 0.01) return("***")
  if(x < 0.05) return("**")
  if(x < 0.10) return("*")
  
  return("")
}

table_out <- data.frame(
  
  Portfolio = results$Portfolio,
  
  DlogVIX =
    paste0(
      round(results$DlogVIX,4),
      sapply(results$P_DlogVIX, star)
    ),
  
  COVID =
    paste0(
      round(results$COVID,4),
      sapply(results$P_COVID, star)
    ),
  
  Interaction =
    paste0(
      round(results$Interaction,4),
      sapply(results$P_Interaction, star)
    ),
  
  Adj_R2 =
    round(results$Adj_R2,4),
  
  AIC =
    round(results$AIC,2),
  
  BIC =
    round(results$BIC,2)
)

table_out

###HI20 - LO20


df <- df %>%
  mutate(
    HI20_LO20 = HI20_EXCESS - LO20_EXCESS
  )


T_obs  <- nrow(df)
nw_lag <- ceiling(T_obs^(1/3))

run_model <- function(formula, label){
  
  model <- lm(formula, data=df)
  
  nw <- coeftest(
    model,
    vcov = NeweyWest(
      model,
      lag = nw_lag,
      prewhite = FALSE
    )
  )
  
  cat("\n=================================\n")
  cat(label,"\n")
  cat("=================================\n")
  
  print(nw)
  
  cat(
    sprintf(
      "\nAdjusted R² = %.4f\n",
      summary(model)$adj.r.squared
    )
  )
  
  return(model)
}

###FF5

m1 <- run_model(
  
  HI20_LO20 ~
    `Mkt-RF` +
    HML +
    RMW +
    CMA,
  
  "FF5"
)

###FF5 + VIX
m2 <- run_model(
  
  HI20_LO20 ~
    `Mkt-RF` +
    HML +
    RMW +
    CMA +
    VIX,
  
  "FF5 + VIX"
)

###FF5 + VIX + COVID
m3 <- run_model(
  
  HI20_LO20 ~
    `Mkt-RF` +
    HML +
    RMW +
    CMA +
    VIX +
    COVID,
  
  "FF5 + VIX + COVID"
)


cat("\n==============================\n")
cat("Alpha comparison\n")
cat("==============================\n")

alpha1 <- coef(m1)[1]
alpha2 <- coef(m2)[1]
alpha3 <- coef(m3)[1]

print(
  data.frame(
    
    Model = c(
      "FF5",
      "FF5+VIX",
      "FF5+VIX+COVID"
    ),
    
    Alpha = c(
      alpha1,
      alpha2,
      alpha3
    )
  )
)



coefs <- summary(m3)$coefficients

data.frame(
  Portfolio   = "HI20_LO20",
  VIX         = round(coefs["VIX","Estimate"],4),
  COVID       = round(coefs["COVID","Estimate"],4),
  Interaction = round(coefs["VIX:COVID","Estimate"],4),
  Adj_R2      = round(summary(m3)$adj.r.squared,4),
  AIC         = round(AIC(m3),2),
  BIC         = round(BIC(m3),2)
)

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