Instruction

Evaluating the performance of Goldman Sachs and DFA over the period from January 2000 through December 2004. The data for the Fama-French portfolios are taken from Ken French’s website

Load data

multi_factor_models  <-  read_excel(here::here("data","Problem_Set_4_data.xls"), # Excel filename
                   sheet="Question 5", # Sheet name
                   skip=4) # Number of rows to skip

#clean name
multi_factor_models = multi_factor_models %>% 
  rename("GOLDMAN"="GOLDMAN...11",
         "DFA"="DFA...12",
         "SMB"="SMB...15",
         "mkt_rf"="Mkt - Rf...14",
         "HML"="HML...16",
         "MOM"="MOM...17",
         "rf"="Rf...18") %>% 
  select("MONTH",
         "GOLDMAN",
         "DFA",
         "SMB",
         "mkt_rf",
         "HML",
         "MOM",
         "rf")

Summarize the returns data for each of the funds

favstats(~GOLDMAN, data = multi_factor_models)

min	Q1	median	Q3	max	mean	sd	n	missing
-0.171	-0.05	-0.0015	0.0315	0.134	-0.00722	0.0616	60	0

favstats(~DFA, data = multi_factor_models)

min	Q1	median	Q3	max	mean	sd	n	missing
-0.162	-0.0203	0.0125	0.0517	0.116	0.014	0.0582	60	0

DFA performed better as it has higher mean and lower std

#CAPM model

#GOLDMAN
model_multi_factor_models_GOLDMAN=lm(I(GOLDMAN-rf)~ mkt_rf, data= multi_factor_models)

#DFA
model_multi_factor_models_DFA=lm(I(DFA-rf)~ mkt_rf, data= multi_factor_models)

#table together
huxreg(model_multi_factor_models_GOLDMAN, model_multi_factor_models_DFA,
       statistics = c('#observations' = 'nobs', 
                      'R squared' = 'r.squared', 
                      'Adj. R Squared' = 'adj.r.squared', 
                      'Residual SE' = 'sigma'), 
       bold_signif = 0.05, 
       stars = c(`***` = 0.001, `**` = 0.01, `*`=0.05)) %>% 
  set_caption('CAPM') %>% 
  set_contents(1,2,"GOLDMAN") %>% 
  set_contents(1,3,"DFA")

CAPM
	GOLDMAN	DFA
(Intercept)	-0.007 *	0.014 **
	(0.003)	(0.004)
mkt_rf	1.167 ***	0.975 ***
	(0.059)	(0.086)
#observations	60	60
R squared	0.871	0.688
Adj. R Squared	0.869	0.683
Residual SE	0.022	0.033
* p < 0.001; p < 0.01; * p < 0.05.

Using CAPM, GOLDMAN’s alpha is higher

#3-factor model

#GOLDMAN
model_multi_factor_models_GOLDMAN_2=lm(I(GOLDMAN-rf)~ mkt_rf + SMB + HML, data= multi_factor_models)

#DFA
model_multi_factor_models_DFA_2=lm(I(DFA-rf)~ mkt_rf + SMB + HML, data= multi_factor_models)

#table together
huxreg(model_multi_factor_models_GOLDMAN_2, model_multi_factor_models_DFA_2,
       statistics = c('#observations' = 'nobs', 
                      'R squared' = 'r.squared', 
                      'Adj. R Squared' = 'adj.r.squared', 
                      'Residual SE' = 'sigma'), 
       bold_signif = 0.05, 
       stars = c(`***` = 0.001, `**` = 0.01, `*`=0.05)) %>% 
  set_caption('Fama-French 3-factor') %>% 
  set_contents(1,2,"GOLDMAN") %>% 
  set_contents(1,3,"DFA")

Fama-French 3-factor
	GOLDMAN	DFA
(Intercept)	0.001	-0.001
	(0.002)	(0.002)
mkt_rf	0.994 ***	1.181 ***
	(0.049)	(0.049)
SMB	-0.225 ***	0.629 ***
	(0.051)	(0.051)
HML	-0.492 ***	0.782 ***
	(0.065)	(0.065)
#observations	60	60
R squared	0.937	0.928
Adj. R Squared	0.933	0.924
Residual SE	0.016	0.016
* p < 0.001; p < 0.01; * p < 0.05.

#4-factor model

#GOLDMAN
model_multi_factor_models_GOLDMAN_3=lm(I(GOLDMAN-rf)~ mkt_rf + SMB + HML + MOM, data= multi_factor_models)

#DFA
model_multi_factor_models_DFA_3=lm(I(DFA-rf)~ mkt_rf + SMB + HML +MOM, data= multi_factor_models)

#table together
huxreg(model_multi_factor_models_GOLDMAN_3, model_multi_factor_models_DFA_3,
       statistics = c('#observations' = 'nobs', 
                      'R squared' = 'r.squared', 
                      'Adj. R Squared' = 'adj.r.squared', 
                      'Residual SE' = 'sigma'), 
       bold_signif = 0.05, 
       stars = c(`***` = 0.001, `**` = 0.01, `*`=0.05)) %>% 
  set_caption('Fama-French 4-factor') %>% 
  set_contents(1,2,"GOLDMAN") %>% 
  set_contents(1,3,"DFA")

Fama-French 4-factor
	GOLDMAN	DFA
(Intercept)	0.001	-0.000
	(0.002)	(0.002)
mkt_rf	0.981 ***	1.170 ***
	(0.051)	(0.052)
SMB	-0.201 **	0.649 ***
	(0.058)	(0.059)
HML	-0.490 ***	0.783 ***
	(0.065)	(0.065)
MOM	-0.031	-0.027
	(0.036)	(0.036)
#observations	60	60
R squared	0.938	0.928
Adj. R Squared	0.933	0.923
Residual SE	0.016	0.016
* p < 0.001; p < 0.01; * p < 0.05.

#Conclusion Using CAPM, GOLDMAN’s alpha is higherBut when using Fama-French, their alphas are close to zero and GOLDMAN’s is higherThe adjusted R squared is high and the factors are significantThis means, compared to the same type of funds, both of them performed good