用R实现滚动单因子模型

引言

单因子模型

滚动单因子模型的 R 代码

# 获取最新市场数据(2024-01-01至2025-05-15)
getSymbols(c("TSLA", "^IXIC"), from="2024-01-01", src="yahoo")
tsla_ret <- dailyReturn(Ad(TSLA))
nasdaq_ret <- dailyReturn(Ad(IXIC))

# 改进版滚动SFM函数
# 高效版滚动SFM函数
rollSFM <- function(Ra, Rb, window = 60) {
  # 输入验证
  n <- length(Ra)
  if (n != length(Rb)) stop("Ra和Rb的长度必须相同")
  if (n < window) stop("数据长度必须大于或等于窗口大小")
  
  # 预计算累积量用于快速计算
  cum_sum_x <- cumsum(Rb)
  cum_sum_y <- cumsum(Ra)
  cum_sum_xy <- cumsum(Ra * Rb)
  cum_sum_x2 <- cumsum(Rb^2)
  
  # 初始化结果向量
  result_size <- n - window + 1
  alpha <- numeric(result_size)
  beta <- numeric(result_size)
  r_squared <- numeric(result_size)
  
  # 计算每个窗口的统计量
  for (i in 1:result_size) {
    end_idx <- i + window - 1
    start_idx <- end_idx - window + 1
    
    # 快速计算窗口内的统计量
    sum_x <- cum_sum_x[end_idx] - if(start_idx > 1) cum_sum_x[start_idx - 1] else 0
    sum_y <- cum_sum_y[end_idx] - if(start_idx > 1) cum_sum_y[start_idx - 1] else 0
    sum_xy <- cum_sum_xy[end_idx] - if(start_idx > 1) cum_sum_xy[start_idx - 1] else 0
    sum_x2 <- cum_sum_x2[end_idx] - if(start_idx > 1) cum_sum_x2[start_idx - 1] else 0
    
    # 计算均值
    mean_x <- sum_x / window
    mean_y <- sum_y / window
    
    # 计算回归系数
    numerator <- sum_xy - sum_x * mean_y
    denominator <- sum_x2 - sum_x * mean_x
    
    # 避免除以零
    if (denominator == 0) {
      beta[i] <- NA
      alpha[i] <- NA
      r_squared[i] <- NA
    } else {
      beta[i] <- numerator / denominator
      alpha[i] <- mean_y - beta[i] * mean_x
      
      # 计算R²
      pred_y <- alpha[i] + beta[i] * Rb[start_idx:end_idx]
      ss_total <- sum((Ra[start_idx:end_idx] - mean_y)^2)
      ss_residual <- sum((Ra[start_idx:end_idx] - pred_y)^2)
      r_squared[i] <- 1 - (ss_residual / ss_total)
    }
  }
  
  # 返回结果数据框
  data.frame(
    Date = if(is.ts(Ra) || is.zoo(Ra)) index(Ra)[window:n] else window:n,
    Alpha = alpha,
    Beta = beta,
    R_squared = r_squared
  )
}

# 计算滚动参数
results <- rollSFM(tsla_ret, nasdaq_ret)
tail(results)  # 查看最近6个窗口结果



# 创建绘图主题
finance_theme <- theme_minimal() +
  theme(
    plot.title = element_text(size=14, face="bold"),
    axis.title = element_text(size=12),
    panel.grid.minor = element_blank(),
    legend.position = "top"
  )

# Beta系数时序图
ggplot(results, aes(x=Date, y=Beta)) +
  geom_line(color="#2b8cbe", size=1) +
  geom_hline(yintercept=1, linetype="dashed", color="#e34a33") +
  labs(title="TSLA相对NASDAQ的60日滚动Beta系数",
       x="日期", y="Beta系数") +
  scale_x_date(labels=date_format("%Y-%m")) +
  finance_theme

# Alpha-Beta联合分布图
ggplot(results, aes(x=Beta, y=Alpha)) +
  geom_point(aes(color=R_squared), size=3) +
  scale_color_gradient(low="#fee8c8", high="#e34a33", 
                      name="R平方值") +
  geom_vline(xintercept=1, linetype="dotted") +
  geom_hline(yintercept=0, linetype="dotted") +
  labs(title="TSLA Alpha-Beta分布（60日窗口）",
       x="系统性风险(Beta)", y="超额收益(Alpha)") +
  finance_theme