程式
金融：投資組合 - 多空投資組合建構
我正在嘗試在 R 中建構一個多頭/空頭投資組合。假設我有兩個投資組合
Tech，Mature並且我想在投資組合上做多Tech並在投資組合上做空Mature。我使用以下方式收集和下載數據：
tickers <- c("GOOG", "MSFT", "GE", "WAL") library(tidyquant) library(dplyr) library(tidyverse) library(glue) data <- tq_get(tickers, get = "stock.prices", from = "2010-01-01", to = "2015-01-01") %>% group_by(symbol) %>% tq_transmute(select = adjusted, mutate_fun = periodReturn, period = "monthly", type = "arithmetic") %>% mutate(portfolio = case_when( symbol == "GOOG" ~ "Tech", symbol == "MSFT" ~ "Tech", symbol == "GE" ~ "Mature", symbol == "WAL" ~ "Mature" ), date = ceiling_date(date, "month") - days(1)) %>% # set the date to the end of the month group_by(portfolio, date) %>% summarise( Port_Monthly_Rets = mean(monthly.returns) )看起來像：
# A tibble: 120 x 3 # Groups: portfolio [2] portfolio date Port_Monthly_Rets <chr> <date> <dbl> 1 Mature 2010-01-31 0.173 2 Mature 2010-02-28 0.0639 3 Mature 2010-03-31 0.0605 4 Mature 2010-04-30 0.283 5 Mature 2010-05-31 -0.104 6 Mature 2010-06-30 -0.111 7 Mature 2010-07-31 0.0659 8 Mature 2010-08-31 -0.130 9 Mature 2010-09-30 0.113 10 Mature 2010-10-31 -0.0563 # ... with 110 more rows我還下載了 Fama French Factors：
# Collect Fama French Factors: temp <- tempfile() base <- "http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/" factor <- "North_America_3_Factors" format<-"_CSV.zip" full_url <-glue(base,factor,format,sep ="") download.file(full_url,temp,quiet = TRUE) FF_Factors <- read_csv(unz(temp, "North_America_3_Factors.csv"), skip = 6) %>% rename(date = X1) %>% mutate_at(vars(-date), as.numeric) %>% mutate(date = rollback(ymd(parse_date_time(date, "%Y%m") + months(1)))) %>% drop_na(date) %>% rename(Mkt_Rf_3 = `Mkt-RF`, SMB_3 = SMB, HML_3 = HML, RF_3 = RF)我將所有內容連接在一起併計算超額收益：
# Join factors with portfolios df <- data %>% left_join(FF_Factors, by = "date") %>% mutate(R_excess = Port_Monthly_Rets - RF_3)現在看起來像：
# A tibble: 120 x 8 # Groups: portfolio [2] portfolio date Port_Monthly_Rets Mkt_Rf_3 SMB_3 HML_3 RF_3 R_excess <chr> <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> 1 Mature 2010-01-31 0.173 -3.63 0.45 0.89 0 0.173 2 Mature 2010-02-28 0.0639 3.71 0.86 2.35 0 0.0639 3 Mature 2010-03-31 0.0605 6.27 1.5 1.48 0.01 0.0505 4 Mature 2010-04-30 0.283 1.92 3.73 1.9 0.01 0.273 5 Mature 2010-05-31 -0.104 -7.86 0.74 -2.32 0.01 -0.114 6 Mature 2010-06-30 -0.111 -5.5 -1.07 -3.73 0.01 -0.121 7 Mature 2010-07-31 0.0659 6.95 0.02 1.03 0.01 0.0559 8 Mature 2010-08-31 -0.130 -4.44 -1.61 -2.35 0.01 -0.140 9 Mature 2010-09-30 0.113 9.47 3.67 -1.85 0.01 0.103 10 Mature 2010-10-31 -0.0563 3.89 0.98 -1.55 0.01 -0.0663 # ... with 110 more rows我對我的投資組合進行 Fama French 回歸：
summary(lm(R_excess ~ Mkt_Rf_3 + SMB_3 + HML_3, data = subset(df, portfolio == "Mature"))) summary(lm(R_excess ~ Mkt_Rf_3 + SMB_3 + HML_3, data = subset(df, portfolio == "Tech")))例如，
Tech投資組合如下所示：Call: lm(formula = R_excess ~ Mkt_Rf_3 + SMB_3 + HML_3, data = subset(df, portfolio == "Mature")) Residuals: Min 1Q Median 3Q Max -0.10673 -0.03100 -0.01297 0.02820 0.18958 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.010782 0.007560 1.426 0.15934 Mkt_Rf_3 0.009913 0.002130 4.654 0.0000204 *** SMB_3 0.008572 0.004173 2.054 0.04463 * HML_3 0.011192 0.004137 2.705 0.00903 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.05491 on 56 degrees of freedom Multiple R-squared: 0.5271, Adjusted R-squared: 0.5018 F-statistic: 20.81 on 3 and 56 DF, p-value: 0.00000000349我想做多
tech投資組合，做空mature投資組合。這是我創建多空組合的嘗試。LS_Portfolio <- df %>% select(-Port_Monthly_Rets) %>% pivot_wider(names_from = portfolio, values_from = c(R_excess)) %>% mutate(Long_Short = Tech - Mature) summary(lm(Long_Short ~ Mkt_Rf_3 + SMB_3 + HML_3, data = LS_Portfolio))哪個輸出：
Call: lm(formula = Long_Short ~ Mkt_Rf_3 + SMB_3 + HML_3, data = LS_Portfolio) Residuals: Min 1Q Median 3Q Max -0.248952 -0.027568 0.003106 0.029772 0.191031 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.017876 0.009873 -1.810 0.07559 . Mkt_Rf_3 0.002387 0.002782 0.858 0.39457 SMB_3 -0.018172 0.005450 -3.334 0.00152 ** HML_3 -0.012778 0.005404 -2.365 0.02154 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.07171 on 56 degrees of freedom Multiple R-squared: 0.2307, Adjusted R-squared: 0.1895 F-statistic: 5.597 on 3 and 56 DF, p-value: 0.001983在我看來這是錯誤的，
Mkt_Rf_3應該很重要。當我將其應用於更大的股票投資組合時，我得到了非常相似的回歸結果。我的問題與程式無關，但鑑於我在每個投資組合中有許多股票，我應該如何建構多頭/空頭投資組合。
我要做的是：
1）根據一些標準形成股票組合
計算每個投資組合的平均月收益
通過獲取平均每月投資組合收益並從 Fama French 數據中去除無風險利率來計算投資組合的超額收益
取
tech投資組合收益並減去mature投資組合收益。5）執行我的回歸分析（表現不佳）。
我只想知道我的邏輯哪裡出錯了。
你不會在任何地方“出錯”。當你說回歸執行不佳時，這表明你的投資組合的回報並沒有被 fama french 因素很好地解釋（這對你的風險因素來說是一件積極的事情，idk 為什麼你稱之為窮人）。
當您做多兩隻股票時，您創建的投資組合風險低於個別股票（我假設股票的相關性是正的，通常是）。如果您願意，風險較小可能是由於對各種參數或因素的敏感性發生變化。在您的情況下，投資組合回報對市場 (mkt_rf) 是中性的，這非常有意義。