Fama Macbeth Regression

Step 0: Estimate N Time Series Regression

step0 <- data %>% 
  nest(data = c(date,ri,MKT,SMB,HML)) %>% 
  mutate(estimates = map(
    data,
    ~tidy(lm(ri ~ MKT + SMB + HML, data = .x))
  )) %>% 
  unnest(estimates) %>% 
  select(symbol, estimate, term) %>% 
  pivot_wider(names_from  = term,
              values_from = estimate) %>% 
  select(symbol, 
         b_MKT = MKT, 
         b_HML = HML, 
         b_SMB = SMB)


step0 <- data %>% 
  left_join(step0, by = "symbol")

Step 0: Estimate N Time series Regression

symbol	date	ri	MKT	SMB	HML	b_MKT	b_HML	b_SMB
AAPL	4-Jan-11	0.0052063	-0.0013139	-0.0065	0.0008	0.9000063	-0.0578213	0.0685351
AAPL	5-Jan-11	0.0081463	0.0049947	0.0018	0.0013	0.9000063	-0.0578213	0.0685351
AAPL	6-Jan-11	-0.0008082	-0.0021252	0.0001	-0.0025	0.9000063	-0.0578213	0.0685351
AAPL	7-Jan-11	0.0071361	-0.0018465	0.0022	-0.0006	0.9000063	-0.0578213	0.0685351
AAPL	10-Jan-11	0.0186573	-0.0013773	0.0041	0.0039	0.9000063	-0.0578213	0.0685351
AAPL	11-Jan-11	-0.0023682	0.0037182	0.0016	0.0036	0.9000063	-0.0578213	0.0685351

Step 1: Estimate T Cross-sectional regression

step1 <- step0 %>% 
    nest(data = c(symbol, ri, b_MKT, b_SMB, b_HML)) %>% 
  mutate(estimates = map(
    data,
    ~tidy(lm(ri ~ b_MKT + b_SMB + b_HML, data = .x))
  )) %>%
  unnest(estimates) %>% 
  select(date, estimate, term) %>% 
  pivot_wider(names_from  = term,
              values_from = estimate) %>% 
  select(date, b_MKT, b_HML, b_SMB)

Step 1: Estimate T Cross-sectional regression

date	b_MKT	b_HML	b_SMB
4-Jan-11	0.0416292	0.0573720	-0.0255197
5-Jan-11	-0.0113470	0.0628473	-0.1580455
6-Jan-11	0.0373012	-0.1732343	0.0070293
7-Jan-11	0.0127224	-0.0642265	0.0322688
10-Jan-11	-0.0366313	0.0586457	0.0171230
11-Jan-11	0.0040892	0.0898581	-0.0953614

Step 2: Estimate time series averages

# Step2: Estimate time series averages
t.test(step1$b_MKT, mu=0)

## 
##  One Sample t-test
## 
## data:  step1$b_MKT
## t = -0.37879, df = 1256, p-value = 0.7049
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -0.002546371  0.001722208
## sample estimates:
##     mean of x 
## -0.0004120813

t.test(step1$b_SMB, mu=0)

## 
##  One Sample t-test
## 
## data:  step1$b_SMB
## t = 0.97712, df = 1256, p-value = 0.3287
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -0.003711466  0.011076953
## sample estimates:
##   mean of x 
## 0.003682744

t.test(step1$b_HML, mu=0)

## 
##  One Sample t-test
## 
## data:  step1$b_HML
## t = -0.18044, df = 1256, p-value = 0.8568
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -0.005541205  0.004607776
## sample estimates:
##     mean of x 
## -0.0004667146