Dow Jones Case Study
Melissa, Joe, Steven, Torey Tonche
3/22/2021
#Data
Input data and view structure:
Dow_Jones = read.csv(here("Data/dow_jones_index.data"))
str(Dow_Jones)## 'data.frame': 750 obs. of 16 variables:
## $ quarter : int 1 1 1 1 1 1 1 1 1 1 ...
## $ stock : chr "AA" "AA" "AA" "AA" ...
## $ date : chr "1/7/2011" "1/14/2011" "1/21/2011" "1/28/2011" ...
## $ open : chr "$15.82" "$16.71" "$16.19" "$15.87" ...
## $ high : chr "$16.72" "$16.71" "$16.38" "$16.63" ...
## $ low : chr "$15.78" "$15.64" "$15.60" "$15.82" ...
## $ close : chr "$16.42" "$15.97" "$15.79" "$16.13" ...
## $ volume : int 239655616 242963398 138428495 151379173 154387761 114691279 80023895 132981863 109493077 114332562 ...
## $ percent_change_price : num 3.79 -4.43 -2.47 1.64 5.93 ...
## $ percent_change_volume_over_last_wk: num NA 1.38 -43.02 9.36 1.99 ...
## $ previous_weeks_volume : int NA 239655616 242963398 138428495 151379173 154387761 114691279 80023895 132981863 109493077 ...
## $ next_weeks_open : chr "$16.71" "$16.19" "$15.87" "$16.18" ...
## $ next_weeks_close : chr "$15.97" "$15.79" "$16.13" "$17.14" ...
## $ percent_change_next_weeks_price : num -4.428 -2.471 1.638 5.933 0.231 ...
## $ days_to_next_dividend : int 26 19 12 5 97 90 83 76 69 62 ...
## $ percent_return_next_dividend : num 0.183 0.188 0.19 0.186 0.175 ...Clean Data
The date variable was changed from a character string to a date format. All of the variables with currency values (open, high, low, close, next_weeks_open, and next_weeks_close) were converted to numeric variables, by first removing the $ from all the strings.
Dow_Jones$date = as.Date(Dow_Jones$date, format = "%m/%d/%Y")
# these currency variables will look as if they have been rounded, but they are not; that is just how the str() function represents the values
Dow_Jones$open = as.numeric(str_remove(Dow_Jones$open, "[$]"))
Dow_Jones$high = as.numeric(str_remove(Dow_Jones$high, "[$]"))
Dow_Jones$low = as.numeric(str_remove(Dow_Jones$low, "[$]"))
Dow_Jones$close = as.numeric(str_remove(Dow_Jones$close, "[$]"))
Dow_Jones$next_weeks_open = as.numeric(str_remove(Dow_Jones$next_weeks_open, "[$]"))
Dow_Jones$next_weeks_close = as.numeric(str_remove(Dow_Jones$next_weeks_close, "[$]"))
str(Dow_Jones)## 'data.frame': 750 obs. of 16 variables:
## $ quarter : int 1 1 1 1 1 1 1 1 1 1 ...
## $ stock : chr "AA" "AA" "AA" "AA" ...
## $ date : Date, format: "2011-01-07" "2011-01-14" ...
## $ open : num 15.8 16.7 16.2 15.9 16.2 ...
## $ high : num 16.7 16.7 16.4 16.6 17.4 ...
## $ low : num 15.8 15.6 15.6 15.8 16.2 ...
## $ close : num 16.4 16 15.8 16.1 17.1 ...
## $ volume : int 239655616 242963398 138428495 151379173 154387761 114691279 80023895 132981863 109493077 114332562 ...
## $ percent_change_price : num 3.79 -4.43 -2.47 1.64 5.93 ...
## $ percent_change_volume_over_last_wk: num NA 1.38 -43.02 9.36 1.99 ...
## $ previous_weeks_volume : int NA 239655616 242963398 138428495 151379173 154387761 114691279 80023895 132981863 109493077 ...
## $ next_weeks_open : num 16.7 16.2 15.9 16.2 17.3 ...
## $ next_weeks_close : num 16 15.8 16.1 17.1 17.4 ...
## $ percent_change_next_weeks_price : num -4.428 -2.471 1.638 5.933 0.231 ...
## $ days_to_next_dividend : int 26 19 12 5 97 90 83 76 69 62 ...
## $ percent_return_next_dividend : num 0.183 0.188 0.19 0.186 0.175 ...We are creating three variables that essential breakdown the date into month, year, and week within the month. We may need the month and week of month variables to create lagged variables.
Dow_Jones = Dow_Jones %>% mutate(Month = month(date),
Week_of_Month = if_else(day(date) <= 7, 1,
if_else(day(date) <= 14, 2,
if_else(day(date) <= 21, 3,
if_else(day(date) <= 28, 4, 5))))
)Feature engineering
Calculating return.
Dow_Jones = Dow_Jones %>% group_by(stock) %>%
arrange(date) %>%
mutate(stock_return = (close - lag(close)) / lag(close)) %>%
ungroup()converting high and open to relative values of open and close.
Dow_Jones$Percent_change_high_open = (Dow_Jones$high / Dow_Jones$open - 1) * 100
Dow_Jones$Percent_change_high_close = (Dow_Jones$high / Dow_Jones$close - 1) * 100
Dow_Jones$Percent_change_low_open = (Dow_Jones$low / Dow_Jones$open - 1) * 100
Dow_Jones$Percent_change_low_close = (Dow_Jones$low / Dow_Jones$close - 1) * 100Lag Analysis and Variables
Show general time dependent nature of target variable
plot(Dow_Jones$date, Dow_Jones$percent_change_next_weeks_price) +
abline(lm(Dow_Jones$percent_change_next_weeks_price ~ Dow_Jones$date), col = 'red')
## integer(0)Check correlations for all lag variables up to lag 6.
Dow_Jones <- Dow_Jones[order(Dow_Jones$stock),]
for (j in 4:ncol(Dow_Jones)){
print(names(Dow_Jones[j]))
for (i in 1:6){
print(cor(lag(Dow_Jones[,j], n = i), Dow_Jones$percent_change_next_weeks_price, use = 'complete.obs'))
}
}## [1] "open"
## [,1]
## open 0.059279
## [,1]
## open 0.03720391
## [,1]
## open 0.03643353
## [,1]
## open 0.04112611
## [,1]
## open 0.02736256
## [,1]
## open 0.02883202
## [1] "high"
## [,1]
## high 0.05856215
## [,1]
## high 0.03590202
## [,1]
## high 0.03672582
## [,1]
## high 0.03873521
## [,1]
## high 0.02337338
## [,1]
## high 0.02802601
## [1] "low"
## [,1]
## low 0.05808992
## [,1]
## low 0.03850403
## [,1]
## low 0.0365267
## [,1]
## low 0.04152299
## [,1]
## low 0.024095
## [,1]
## low 0.03117969
## [1] "close"
## [,1]
## close 0.05553115
## [,1]
## close 0.0352073
## [,1]
## close 0.03669212
## [,1]
## close 0.04105935
## [,1]
## close 0.02007615
## [,1]
## close 0.0266617
## [1] "volume"
## [,1]
## volume -0.09518982
## [,1]
## volume -0.08741669
## [,1]
## volume -0.08554534
## [,1]
## volume -0.1244597
## [,1]
## volume -0.04210884
## [,1]
## volume -0.05558134
## [1] "percent_change_price"
## [,1]
## percent_change_price -0.06135933
## [,1]
## percent_change_price -0.03382854
## [,1]
## percent_change_price 0.0001703799
## [,1]
## percent_change_price -0.01037548
## [,1]
## percent_change_price -0.166845
## [,1]
## percent_change_price -0.04636764
## [1] "percent_change_volume_over_last_wk"
## [,1]
## percent_change_volume_over_last_wk 0.04212278
## [,1]
## percent_change_volume_over_last_wk 0.03024644
## [,1]
## percent_change_volume_over_last_wk 0.04925272
## [,1]
## percent_change_volume_over_last_wk -0.2431635
## [,1]
## percent_change_volume_over_last_wk 0.05017883
## [,1]
## percent_change_volume_over_last_wk -0.04473876
## [1] "previous_weeks_volume"
## [,1]
## previous_weeks_volume -0.0896915
## [,1]
## previous_weeks_volume -0.09220271
## [,1]
## previous_weeks_volume -0.1324579
## [,1]
## previous_weeks_volume -0.0458884
## [,1]
## previous_weeks_volume -0.06306201
## [,1]
## previous_weeks_volume -0.04776301
## [1] "next_weeks_open"
## [,1]
## next_weeks_open 0.05581352
## [,1]
## next_weeks_open 0.03694355
## [,1]
## next_weeks_open 0.03669992
## [,1]
## next_weeks_open 0.04200098
## [,1]
## next_weeks_open 0.01797055
## [,1]
## next_weeks_open 0.026202
## [1] "next_weeks_close"
## [,1]
## next_weeks_close 0.05758584
## [,1]
## next_weeks_close 0.03235717
## [,1]
## next_weeks_close 0.03448398
## [,1]
## next_weeks_close 0.04405015
## [,1]
## next_weeks_close 0.01735498
## [,1]
## next_weeks_close 0.02007517
## [1] "percent_change_next_weeks_price"
## [,1]
## percent_change_next_weeks_price 0.05064951
## [,1]
## percent_change_next_weeks_price -0.0584009
## [,1]
## percent_change_next_weeks_price -0.04279636
## [,1]
## percent_change_next_weeks_price 0.03375161
## [,1]
## percent_change_next_weeks_price 0.003300199
## [,1]
## percent_change_next_weeks_price -0.1309721
## [1] "days_to_next_dividend"
## [,1]
## days_to_next_dividend -0.009258347
## [,1]
## days_to_next_dividend -0.009016315
## [,1]
## days_to_next_dividend 0.03427167
## [,1]
## days_to_next_dividend 0.0324008
## [,1]
## days_to_next_dividend 0.0349644
## [,1]
## days_to_next_dividend -0.01834739
## [1] "percent_return_next_dividend"
## [,1]
## percent_return_next_dividend 0.1030057
## [,1]
## percent_return_next_dividend 0.1074255
## [,1]
## percent_return_next_dividend 0.1079997
## [,1]
## percent_return_next_dividend 0.1099141
## [,1]
## percent_return_next_dividend 0.1021779
## [,1]
## percent_return_next_dividend 0.09235505
## [1] "Month"
## [,1]
## Month 0.04969544
## [,1]
## Month 0.07141836
## [,1]
## Month 0.0191938
## [,1]
## Month 0.06377205
## [,1]
## Month 0.1280347
## [,1]
## Month 0.1906817
## [1] "Week_of_Month"
## [,1]
## Week_of_Month 0.02611121
## [,1]
## Week_of_Month -0.1348287
## [,1]
## Week_of_Month -0.0927099
## [,1]
## Week_of_Month 0.1344051
## [,1]
## Week_of_Month 0.005314537
## [,1]
## Week_of_Month -0.1352763
## [1] "stock_return"
## [,1]
## stock_return -0.02449959
## [,1]
## stock_return -0.02169831
## [,1]
## stock_return 0.005759634
## [,1]
## stock_return -0.06419919
## [,1]
## stock_return -0.1801155
## [,1]
## stock_return -0.02338938
## [1] "Percent_change_high_open"
## [,1]
## Percent_change_high_open 0.02898728
## [,1]
## Percent_change_high_open -0.03102705
## [,1]
## Percent_change_high_open 0.003481966
## [,1]
## Percent_change_high_open -0.1167935
## [,1]
## Percent_change_high_open -0.1050529
## [,1]
## Percent_change_high_open -0.03822145
## [1] "Percent_change_high_close"
## [,1]
## Percent_change_high_close 0.09857129
## [,1]
## Percent_change_high_close 0.01037067
## [,1]
## Percent_change_high_close 0.003572362
## [,1]
## Percent_change_high_close -0.09904599
## [,1]
## Percent_change_high_close 0.1065697
## [,1]
## Percent_change_high_close 0.01962257
## [1] "Percent_change_low_open"
## [,1]
## Percent_change_low_open -0.03373898
## [,1]
## Percent_change_low_open 0.01918971
## [,1]
## Percent_change_low_open 0.0008948175
## [,1]
## Percent_change_low_open 0.02310064
## [,1]
## Percent_change_low_open -0.08458079
## [,1]
## Percent_change_low_open 0.08101041
## [1] "Percent_change_low_close"
## [,1]
## Percent_change_low_close 0.04307057
## [,1]
## Percent_change_low_close 0.06641558
## [,1]
## Percent_change_low_close 0.002290362
## [,1]
## Percent_change_low_close 0.03926138
## [,1]
## Percent_change_low_close 0.1260682
## [,1]
## Percent_change_low_close 0.1557103Selected all that had cor > .05. Then removed ones with high correlation with other features. The following are the ones with correlation greater than .05 with the target variable, but less than .8 with other predictors.
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(percent_change_price.lag1 = dplyr::lag(percent_change_price, n=1))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(percent_change_price.lag5 = dplyr::lag(percent_change_price, n=5))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Month.lag2 = dplyr::lag(Month, n=2))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Month.lag4 = dplyr::lag(Month, n=4))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Month.lag5 = dplyr::lag(Month, n=5))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Month.lag6 = dplyr::lag(Month, n=6))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Percent_change_high_open.lag4 = dplyr::lag(Percent_change_high_open, n=4))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Percent_change_high_open.lag5 = dplyr::lag(Percent_change_high_open, n=5))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Percent_change_high_close.lag1 = dplyr::lag(Percent_change_high_close, n=1))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Percent_change_high_close.lag4 = dplyr::lag(Percent_change_high_close, n=4))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Percent_change_high_close.lag5 = dplyr::lag(Percent_change_high_close, n=5))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Percent_change_low_open.lag5 = dplyr::lag(Percent_change_low_open, n=5))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Percent_change_low_open.lag6 = dplyr::lag(Percent_change_low_open, n=6))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Percent_change_low_close.lag2 = dplyr::lag(Percent_change_low_close, n=2))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Percent_change_low_close.lag5 = dplyr::lag(Percent_change_low_close, n=5))
Dow_Jones <- Dow_Jones %>% group_by(stock) %>% mutate(Percent_change_low_close.lag6 = dplyr::lag(Percent_change_low_close, n=6))
cor(na.omit(Dow_Jones[4:ncol(Dow_Jones)]))## open high low
## open 1.000000000 0.9996551948 0.999282777
## high 0.999655195 1.0000000000 0.999374878
## low 0.999282777 0.9993748781 1.000000000
## close 0.999081049 0.9995475204 0.999537919
## volume -0.536699474 -0.5358789274 -0.537979581
## percent_change_price 0.060078688 0.0762492470 0.082516420
## percent_change_volume_over_last_wk -0.015222782 -0.0138332344 -0.024552839
## previous_weeks_volume -0.527222675 -0.5271536813 -0.526966539
## next_weeks_open 0.998963452 0.9994551240 0.999400829
## next_weeks_close 0.997840304 0.9984479773 0.998241649
## percent_change_next_weeks_price 0.048059006 0.0504209806 0.047537239
## days_to_next_dividend -0.040419876 -0.0415630470 -0.041270920
## percent_return_next_dividend -0.146973592 -0.1479640573 -0.143373774
## Month 0.005537335 0.0056369388 0.004516251
## Week_of_Month -0.009668378 -0.0034031662 -0.002703892
## stock_return 0.067124788 0.0826187263 0.088437226
## Percent_change_high_open -0.079520279 -0.0585847682 -0.068447546
## Percent_change_high_close -0.142531837 -0.1418332137 -0.158531371
## Percent_change_low_open 0.047434599 0.0569855950 0.079887441
## Percent_change_low_close -0.021810514 -0.0306237746 -0.012045019
## percent_change_price.lag1 0.109665948 0.1085655918 0.110489319
## percent_change_price.lag5 0.117544904 0.1164564623 0.115052098
## Month.lag2 0.001256881 0.0032000349 0.002101804
## Month.lag4 0.006533527 0.0076609548 0.006297042
## Month.lag5 0.005078403 0.0057669829 0.004961831
## Month.lag6 0.003013023 0.0051078705 0.004112009
## Percent_change_high_open.lag4 -0.005189752 -0.0038321765 -0.005481479
## Percent_change_high_open.lag5 0.001080476 -0.0009463028 -0.005367655
## Percent_change_high_close.lag1 -0.168810668 -0.1669177946 -0.169262910
## Percent_change_high_close.lag4 -0.156647792 -0.1586178413 -0.159536397
## Percent_change_high_close.lag5 -0.171376680 -0.1716806024 -0.173766196
## Percent_change_low_open.lag5 0.112414252 0.1110342529 0.113540930
## Percent_change_low_open.lag6 0.112321796 0.1081386894 0.109964423
## Percent_change_low_close.lag2 -0.033392421 -0.0313900375 -0.029430635
## Percent_change_low_close.lag5 -0.060010234 -0.0599543517 -0.054639303
## Percent_change_low_close.lag6 -0.027607664 -0.0273641143 -0.021780761
## close volume
## open 0.999081049 -0.536699474
## high 0.999547520 -0.535878927
## low 0.999537919 -0.537979581
## close 1.000000000 -0.538055871
## volume -0.538055871 1.000000000
## percent_change_price 0.096144543 -0.151365645
## percent_change_volume_over_last_wk -0.022846150 0.151993071
## previous_weeks_volume -0.527385783 0.903357808
## next_weeks_open 0.999905069 -0.537876615
## next_weeks_close 0.998790457 -0.537565502
## percent_change_next_weeks_price 0.048249439 -0.083490856
## days_to_next_dividend -0.041704819 -0.041552907
## percent_return_next_dividend -0.145163535 -0.269686818
## Month -0.001151985 0.003048129
## Week_of_Month 0.002524306 -0.001467390
## stock_return 0.101270099 -0.153327773
## Percent_change_high_open -0.059406934 0.102728414
## Percent_change_high_close -0.165769965 0.271177729
## Percent_change_low_open 0.071592291 -0.139885684
## Percent_change_low_close -0.038486497 0.029295488
## percent_change_price.lag1 0.110254796 -0.138786050
## percent_change_price.lag5 0.117362548 -0.145290025
## Month.lag2 -0.001207195 0.001656298
## Month.lag4 0.001666759 0.006279090
## Month.lag5 -0.000249611 0.007628334
## Month.lag6 0.000456997 0.003043100
## Percent_change_high_open.lag4 -0.001383803 -0.009037382
## Percent_change_high_open.lag5 -0.002975585 0.028161549
## Percent_change_high_close.lag1 -0.168659808 0.234026735
## Percent_change_high_close.lag4 -0.162097137 0.212064929
## Percent_change_high_close.lag5 -0.174872933 0.240051427
## Percent_change_low_open.lag5 0.112433814 -0.134008490
## Percent_change_low_open.lag6 0.105864141 -0.103613285
## Percent_change_low_close.lag2 -0.029879084 0.032850221
## Percent_change_low_close.lag5 -0.059786070 0.079310024
## Percent_change_low_close.lag6 -0.021701602 0.009708224
## percent_change_price
## open 0.060078688
## high 0.076249247
## low 0.082516420
## close 0.096144543
## volume -0.151365645
## percent_change_price 1.000000000
## percent_change_volume_over_last_wk -0.187044140
## previous_weeks_volume -0.108461316
## next_weeks_open 0.096672203
## next_weeks_close 0.096750746
## percent_change_next_weeks_price 0.017503689
## days_to_next_dividend -0.031576921
## percent_return_next_dividend 0.110792071
## Month -0.162333945
## Week_of_Month 0.294296516
## stock_return 0.949151582
## Percent_change_high_open 0.563181730
## Percent_change_high_close -0.642084431
## Percent_change_low_open 0.653084066
## Percent_change_low_close -0.481416185
## percent_change_price.lag1 0.024756878
## percent_change_price.lag5 0.004790606
## Month.lag2 -0.064854492
## Month.lag4 -0.115928548
## Month.lag5 -0.122456770
## Month.lag6 -0.066958776
## Percent_change_high_open.lag4 0.077585659
## Percent_change_high_open.lag5 -0.136904756
## Percent_change_high_close.lag1 -0.009393049
## Percent_change_high_close.lag4 -0.152327364
## Percent_change_high_close.lag5 -0.135415688
## Percent_change_low_open.lag5 0.033206590
## Percent_change_low_open.lag6 -0.161102543
## Percent_change_low_close.lag2 0.024783282
## Percent_change_low_close.lag5 0.029280527
## Percent_change_low_close.lag6 0.145233063
## percent_change_volume_over_last_wk
## open -0.015222782
## high -0.013833234
## low -0.024552839
## close -0.022846150
## volume 0.151993071
## percent_change_price -0.187044140
## percent_change_volume_over_last_wk 1.000000000
## previous_weeks_volume -0.130786965
## next_weeks_open -0.021645818
## next_weeks_close -0.021569107
## percent_change_next_weeks_price 0.020135989
## days_to_next_dividend -0.053476799
## percent_return_next_dividend -0.008354095
## Month 0.010705337
## Week_of_Month 0.080722138
## stock_return -0.190882595
## Percent_change_high_open 0.100830008
## Percent_change_high_close 0.323030463
## Percent_change_low_open -0.267689920
## Percent_change_low_close -0.072184320
## percent_change_price.lag1 0.071406352
## percent_change_price.lag5 0.014115582
## Month.lag2 0.016993876
## Month.lag4 0.069455376
## Month.lag5 0.001508881
## Month.lag6 0.003764949
## Percent_change_high_open.lag4 -0.026248633
## Percent_change_high_open.lag5 0.078108881
## Percent_change_high_close.lag1 -0.113726462
## Percent_change_high_close.lag4 0.066886275
## Percent_change_high_close.lag5 0.049923926
## Percent_change_low_open.lag5 0.071419041
## Percent_change_low_open.lag6 0.004950184
## Percent_change_low_close.lag2 0.012930790
## Percent_change_low_close.lag5 0.062454926
## Percent_change_low_close.lag6 -0.111414362
## previous_weeks_volume next_weeks_open
## open -0.527222675 0.9989634522
## high -0.527153681 0.9994551240
## low -0.526966539 0.9994008293
## close -0.527385783 0.9999050691
## volume 0.903357808 -0.5378766153
## percent_change_price -0.108461316 0.0966722033
## percent_change_volume_over_last_wk -0.130786965 -0.0216458179
## previous_weeks_volume 1.000000000 -0.5274277208
## next_weeks_open -0.527427721 1.0000000000
## next_weeks_close -0.527351717 0.9988205935
## percent_change_next_weeks_price -0.086044568 0.0472775653
## days_to_next_dividend -0.027366431 -0.0418904069
## percent_return_next_dividend -0.274336231 -0.1449792929
## Month -0.023587032 -0.0019283891
## Week_of_Month 0.013396402 0.0042963108
## stock_return -0.101267747 0.1012709598
## Percent_change_high_open 0.040578045 -0.0589231212
## Percent_change_high_close 0.161464960 -0.1659190903
## Percent_change_low_open -0.067597422 0.0710721618
## Percent_change_low_close 0.057716642 -0.0397304364
## percent_change_price.lag1 -0.207848578 0.1097272306
## percent_change_price.lag5 -0.125191428 0.1191631127
## Month.lag2 -0.013709090 -0.0020043467
## Month.lag4 -0.031494085 0.0012823320
## Month.lag5 -0.012530632 -0.0011654563
## Month.lag6 -0.010277222 -0.0005103252
## Percent_change_high_open.lag4 0.007787721 -0.0008862094
## Percent_change_high_open.lag5 0.006530527 -0.0014552057
## Percent_change_high_close.lag1 0.324745562 -0.1684635707
## Percent_change_high_close.lag4 0.192827069 -0.1627943174
## Percent_change_high_close.lag5 0.190324568 -0.1760741932
## Percent_change_low_open.lag5 -0.129894999 0.1135024666
## Percent_change_low_open.lag6 -0.109935809 0.1055224699
## Percent_change_low_close.lag2 0.004761604 -0.0299502782
## Percent_change_low_close.lag5 0.052679857 -0.0613880447
## Percent_change_low_close.lag6 0.045592301 -0.0239867010
## next_weeks_close
## open 0.997840304
## high 0.998447977
## low 0.998241649
## close 0.998790457
## volume -0.537565502
## percent_change_price 0.096750746
## percent_change_volume_over_last_wk -0.021569107
## previous_weeks_volume -0.527351717
## next_weeks_open 0.998820594
## next_weeks_close 1.000000000
## percent_change_next_weeks_price 0.087931435
## days_to_next_dividend -0.043867982
## percent_return_next_dividend -0.141680255
## Month 0.001934146
## Week_of_Month 0.009913664
## stock_return 0.101619085
## Percent_change_high_open -0.055569755
## Percent_change_high_close -0.162944027
## Percent_change_low_open 0.070316761
## Percent_change_low_close -0.040620500
## percent_change_price.lag1 0.103799058
## percent_change_price.lag5 0.109624243
## Month.lag2 0.005662235
## Month.lag4 0.003748265
## Month.lag5 0.004588252
## Month.lag6 0.006676320
## Percent_change_high_open.lag4 -0.006523658
## Percent_change_high_open.lag5 -0.009369582
## Percent_change_high_close.lag1 -0.164201579
## Percent_change_high_close.lag4 -0.167961468
## Percent_change_high_close.lag5 -0.169460144
## Percent_change_low_open.lag5 0.106450715
## Percent_change_low_open.lag6 0.108670801
## Percent_change_low_close.lag2 -0.023999854
## Percent_change_low_close.lag5 -0.054470125
## Percent_change_low_close.lag6 -0.016959819
## percent_change_next_weeks_price
## open 0.04805901
## high 0.05042098
## low 0.04753724
## close 0.04824944
## volume -0.08349086
## percent_change_price 0.01750369
## percent_change_volume_over_last_wk 0.02013599
## previous_weeks_volume -0.08604457
## next_weeks_open 0.04727757
## next_weeks_close 0.08793144
## percent_change_next_weeks_price 1.00000000
## days_to_next_dividend -0.04091792
## percent_return_next_dividend 0.12931951
## Month 0.09478831
## Week_of_Month 0.14887743
## stock_return 0.01994535
## Percent_change_high_open 0.08082352
## Percent_change_high_close 0.05490579
## Percent_change_low_open -0.00272999
## Percent_change_low_close -0.02185903
## percent_change_price.lag1 -0.06769337
## percent_change_price.lag5 -0.22190869
## Month.lag2 0.18575938
## Month.lag4 0.07294216
## Month.lag5 0.13480890
## Month.lag6 0.17134313
## Percent_change_high_open.lag4 -0.15658820
## Percent_change_high_open.lag5 -0.20593317
## Percent_change_high_close.lag1 0.10563616
## Percent_change_high_close.lag4 -0.16870163
## Percent_change_high_close.lag5 0.13635776
## Percent_change_low_open.lag5 -0.15420734
## Percent_change_low_open.lag6 0.11024501
## Percent_change_low_close.lag2 0.09183729
## Percent_change_low_close.lag5 0.17327983
## Percent_change_low_close.lag6 0.17142345
## days_to_next_dividend
## open -0.040419876
## high -0.041563047
## low -0.041270920
## close -0.041704819
## volume -0.041552907
## percent_change_price -0.031576921
## percent_change_volume_over_last_wk -0.053476799
## previous_weeks_volume -0.027366431
## next_weeks_open -0.041890407
## next_weeks_close -0.043867982
## percent_change_next_weeks_price -0.040917922
## days_to_next_dividend 1.000000000
## percent_return_next_dividend 0.113043872
## Month -0.044733095
## Week_of_Month -0.009088683
## stock_return -0.041323674
## Percent_change_high_open -0.039507086
## Percent_change_high_close -0.001861694
## Percent_change_low_open -0.023431017
## Percent_change_low_close 0.010180437
## percent_change_price.lag1 -0.019464515
## percent_change_price.lag5 0.040577308
## Month.lag2 -0.041094397
## Month.lag4 -0.054141934
## Month.lag5 -0.047499751
## Month.lag6 -0.040579762
## Percent_change_high_open.lag4 0.069959295
## Percent_change_high_open.lag5 0.043858784
## Percent_change_high_close.lag1 0.014494592
## Percent_change_high_close.lag4 -0.021508148
## Percent_change_high_close.lag5 -0.020660253
## Percent_change_low_open.lag5 0.008919554
## Percent_change_low_open.lag6 0.049041908
## Percent_change_low_close.lag2 -0.008543475
## Percent_change_low_close.lag5 -0.054002215
## Percent_change_low_close.lag6 -0.034517158
## percent_return_next_dividend Month
## open -0.146973592 0.005537335
## high -0.147964057 0.005636939
## low -0.143373774 0.004516251
## close -0.145163535 -0.001151985
## volume -0.269686818 0.003048129
## percent_change_price 0.110792071 -0.162333945
## percent_change_volume_over_last_wk -0.008354095 0.010705337
## previous_weeks_volume -0.274336231 -0.023587032
## next_weeks_open -0.144979293 -0.001928389
## next_weeks_close -0.141680255 0.001934146
## percent_change_next_weeks_price 0.129319509 0.094788306
## days_to_next_dividend 0.113043872 -0.044733095
## percent_return_next_dividend 1.000000000 0.011523535
## Month 0.011523535 1.000000000
## Week_of_Month -0.002931702 -0.166088980
## stock_return 0.113525503 -0.142404624
## Percent_change_high_open -0.023267619 0.064513907
## Percent_change_high_close -0.154214597 0.245492080
## Percent_change_low_open 0.159398002 -0.034551529
## Percent_change_low_close 0.045602050 0.162930320
## percent_change_price.lag1 0.115586279 -0.126778576
## percent_change_price.lag5 0.059819945 -0.079595746
## Month.lag2 0.011618684 0.925675676
## Month.lag4 0.007803315 0.984959168
## Month.lag5 0.010328252 0.960965611
## Month.lag6 0.009210527 0.930793419
## Percent_change_high_open.lag4 -0.098077054 -0.061014700
## Percent_change_high_open.lag5 -0.105116492 -0.019930551
## Percent_change_high_close.lag1 -0.160433111 0.164036457
## Percent_change_high_close.lag4 -0.209981868 -0.008826586
## Percent_change_high_close.lag5 -0.187577283 0.094359040
## Percent_change_low_open.lag5 0.151346647 -0.054088855
## Percent_change_low_open.lag6 0.119785402 -0.026240254
## Percent_change_low_close.lag2 0.052679371 0.105415748
## Percent_change_low_close.lag5 0.084953107 0.065024271
## Percent_change_low_close.lag6 0.093045709 -0.022511719
## Week_of_Month stock_return
## open -0.009668378 0.06712479
## high -0.003403166 0.08261873
## low -0.002703892 0.08843723
## close 0.002524306 0.10127010
## volume -0.001467390 -0.15332777
## percent_change_price 0.294296516 0.94915158
## percent_change_volume_over_last_wk 0.080722138 -0.19088259
## previous_weeks_volume 0.013396402 -0.10126775
## next_weeks_open 0.004296311 0.10127096
## next_weeks_close 0.009913664 0.10161908
## percent_change_next_weeks_price 0.148877433 0.01994535
## days_to_next_dividend -0.009088683 -0.04132367
## percent_return_next_dividend -0.002931702 0.11352550
## Month -0.166088980 -0.14240462
## Week_of_Month 1.000000000 0.18280654
## stock_return 0.182806544 1.00000000
## Percent_change_high_open 0.197322450 0.54216802
## Percent_change_high_close -0.155120545 -0.60315754
## Percent_change_low_open 0.179274059 0.62666509
## Percent_change_low_close -0.155041043 -0.44906563
## percent_change_price.lag1 -0.004419102 0.03765925
## percent_change_price.lag5 0.063287079 0.02447270
## Month.lag2 0.166088980 -0.08831894
## Month.lag4 -0.084181905 -0.09631607
## Month.lag5 0.010767707 -0.12889280
## Month.lag6 0.139077107 -0.09051514
## Percent_change_high_open.lag4 0.072620541 0.01689478
## Percent_change_high_open.lag5 -0.047239146 -0.12426223
## Percent_change_high_close.lag1 0.038144743 -0.01866114
## Percent_change_high_close.lag4 -0.040317421 -0.11879827
## Percent_change_high_close.lag5 -0.130579663 -0.15377414
## Percent_change_low_open.lag5 0.042290942 0.07806288
## Percent_change_low_open.lag6 -0.187714094 -0.14073114
## Percent_change_low_close.lag2 0.138702120 0.01323064
## Percent_change_low_close.lag5 -0.051895109 0.05098686
## Percent_change_low_close.lag6 0.057298360 0.10223609
## Percent_change_high_open
## open -0.07952028
## high -0.05858477
## low -0.06844755
## close -0.05940693
## volume 0.10272841
## percent_change_price 0.56318173
## percent_change_volume_over_last_wk 0.10083001
## previous_weeks_volume 0.04057805
## next_weeks_open -0.05892312
## next_weeks_close -0.05556975
## percent_change_next_weeks_price 0.08082352
## days_to_next_dividend -0.03950709
## percent_return_next_dividend -0.02326762
## Month 0.06451391
## Week_of_Month 0.19732245
## stock_return 0.54216802
## Percent_change_high_open 1.00000000
## Percent_change_high_close 0.27117495
## Percent_change_low_open 0.34164013
## Percent_change_low_close -0.29526448
## percent_change_price.lag1 -0.04102493
## percent_change_price.lag5 -0.06217511
## Month.lag2 0.12632824
## Month.lag4 0.09655509
## Month.lag5 0.08653063
## Month.lag6 0.12808780
## Percent_change_high_open.lag4 0.05029264
## Percent_change_high_open.lag5 -0.07235023
## Percent_change_high_close.lag1 0.08691865
## Percent_change_high_close.lag4 -0.03281206
## Percent_change_high_close.lag5 0.02153499
## Percent_change_low_open.lag5 -0.04981317
## Percent_change_low_open.lag6 -0.15064392
## Percent_change_low_close.lag2 0.06231824
## Percent_change_low_close.lag5 0.03957412
## Percent_change_low_close.lag6 0.02564765
## Percent_change_high_close
## open -0.1425318369
## high -0.1418332137
## low -0.1585313708
## close -0.1657699649
## volume 0.2711777286
## percent_change_price -0.6420844306
## percent_change_volume_over_last_wk 0.3230304628
## previous_weeks_volume 0.1614649599
## next_weeks_open -0.1659190903
## next_weeks_close -0.1629440274
## percent_change_next_weeks_price 0.0549057877
## days_to_next_dividend -0.0018616943
## percent_return_next_dividend -0.1542145974
## Month 0.2454920796
## Week_of_Month -0.1551205446
## stock_return -0.6031575423
## Percent_change_high_open 0.2711749478
## Percent_change_high_close 1.0000000000
## Percent_change_low_open -0.4501688393
## Percent_change_low_close 0.2795831545
## percent_change_price.lag1 -0.0645542067
## percent_change_price.lag5 -0.0604960288
## Month.lag2 0.1910809740
## Month.lag4 0.2219030835
## Month.lag5 0.2198003268
## Month.lag6 0.1952292364
## Percent_change_high_open.lag4 -0.0424956040
## Percent_change_high_open.lag5 0.0938383508
## Percent_change_high_close.lag1 0.0900778292
## Percent_change_high_close.lag4 0.1469462247
## Percent_change_high_close.lag5 0.1750579219
## Percent_change_low_open.lag5 -0.0840266144
## Percent_change_low_open.lag6 0.0462934561
## Percent_change_low_close.lag2 0.0274059958
## Percent_change_low_close.lag5 -0.0009337616
## Percent_change_low_close.lag6 -0.1466192078
## Percent_change_low_open
## open 0.047434599
## high 0.056985595
## low 0.079887441
## close 0.071592291
## volume -0.139885684
## percent_change_price 0.653084066
## percent_change_volume_over_last_wk -0.267689920
## previous_weeks_volume -0.067597422
## next_weeks_open 0.071072162
## next_weeks_close 0.070316761
## percent_change_next_weeks_price -0.002729990
## days_to_next_dividend -0.023431017
## percent_return_next_dividend 0.159398002
## Month -0.034551529
## Week_of_Month 0.179274059
## stock_return 0.626665087
## Percent_change_high_open 0.341640134
## Percent_change_high_close -0.450168839
## Percent_change_low_open 1.000000000
## Percent_change_low_close 0.349009231
## percent_change_price.lag1 0.040361633
## percent_change_price.lag5 -0.043825055
## Month.lag2 0.015753293
## Month.lag4 -0.012345966
## Month.lag5 -0.008152146
## Month.lag6 0.022014683
## Percent_change_high_open.lag4 -0.017830367
## Percent_change_high_open.lag5 -0.181021201
## Percent_change_high_close.lag1 -0.013410285
## Percent_change_high_close.lag4 -0.104122584
## Percent_change_high_close.lag5 -0.106731221
## Percent_change_low_open.lag5 0.053909040
## Percent_change_low_open.lag6 -0.072238698
## Percent_change_low_close.lag2 0.059184455
## Percent_change_low_close.lag5 0.135430720
## Percent_change_low_close.lag6 0.148317156
## Percent_change_low_close
## open -0.021810514
## high -0.030623775
## low -0.012045019
## close -0.038486497
## volume 0.029295488
## percent_change_price -0.481416185
## percent_change_volume_over_last_wk -0.072184320
## previous_weeks_volume 0.057716642
## next_weeks_open -0.039730436
## next_weeks_close -0.040620500
## percent_change_next_weeks_price -0.021859028
## days_to_next_dividend 0.010180437
## percent_return_next_dividend 0.045602050
## Month 0.162930320
## Week_of_Month -0.155041043
## stock_return -0.449065635
## Percent_change_high_open -0.295264483
## Percent_change_high_close 0.279583154
## Percent_change_low_open 0.349009231
## Percent_change_low_close 1.000000000
## percent_change_price.lag1 0.016448202
## percent_change_price.lag5 -0.056125428
## Month.lag2 0.101133968
## Month.lag4 0.131833341
## Month.lag5 0.144022479
## Month.lag6 0.110859005
## Percent_change_high_open.lag4 -0.116898147
## Percent_change_high_open.lag5 -0.038931468
## Percent_change_high_close.lag1 -0.003618337
## Percent_change_high_close.lag4 0.069426749
## Percent_change_high_close.lag5 0.044285095
## Percent_change_low_open.lag5 0.020266865
## Percent_change_low_open.lag6 0.112166484
## Percent_change_low_close.lag2 0.038222398
## Percent_change_low_close.lag5 0.118416607
## Percent_change_low_close.lag6 -0.011446679
## percent_change_price.lag1
## open 0.109665948
## high 0.108565592
## low 0.110489319
## close 0.110254796
## volume -0.138786050
## percent_change_price 0.024756878
## percent_change_volume_over_last_wk 0.071406352
## previous_weeks_volume -0.207848578
## next_weeks_open 0.109727231
## next_weeks_close 0.103799058
## percent_change_next_weeks_price -0.067693372
## days_to_next_dividend -0.019464515
## percent_return_next_dividend 0.115586279
## Month -0.126778576
## Week_of_Month -0.004419102
## stock_return 0.037659247
## Percent_change_high_open -0.041024935
## Percent_change_high_close -0.064554207
## Percent_change_low_open 0.040361633
## Percent_change_low_close 0.016448202
## percent_change_price.lag1 1.000000000
## percent_change_price.lag5 0.159637931
## Month.lag2 -0.132416404
## Month.lag4 -0.091627546
## Month.lag5 -0.143526553
## Month.lag6 -0.149099432
## Percent_change_high_open.lag4 0.002570047
## Percent_change_high_open.lag5 0.088060282
## Percent_change_high_close.lag1 -0.672772710
## Percent_change_high_close.lag4 -0.043841015
## Percent_change_high_close.lag5 -0.152978542
## Percent_change_low_open.lag5 0.152129703
## Percent_change_low_open.lag6 0.033408528
## Percent_change_low_close.lag2 -0.062898663
## Percent_change_low_close.lag5 -0.077609605
## Percent_change_low_close.lag6 0.032357754
## percent_change_price.lag5 Month.lag2
## open 0.117544904 0.001256881
## high 0.116456462 0.003200035
## low 0.115052098 0.002101804
## close 0.117362548 -0.001207195
## volume -0.145290025 0.001656298
## percent_change_price 0.004790606 -0.064854492
## percent_change_volume_over_last_wk 0.014115582 0.016993876
## previous_weeks_volume -0.125191428 -0.013709090
## next_weeks_open 0.119163113 -0.002004347
## next_weeks_close 0.109624243 0.005662235
## percent_change_next_weeks_price -0.221908695 0.185759382
## days_to_next_dividend 0.040577308 -0.041094397
## percent_return_next_dividend 0.059819945 0.011618684
## Month -0.079595746 0.925675676
## Week_of_Month 0.063287079 0.166088980
## stock_return 0.024472704 -0.088318935
## Percent_change_high_open -0.062175114 0.126328240
## Percent_change_high_close -0.060496029 0.191080974
## Percent_change_low_open -0.043825055 0.015753293
## Percent_change_low_close -0.056125428 0.101133968
## percent_change_price.lag1 0.159637931 -0.132416404
## percent_change_price.lag5 1.000000000 -0.079998508
## Month.lag2 -0.079998508 1.000000000
## Month.lag4 -0.059137058 0.924655546
## Month.lag5 -0.073201577 0.942896172
## Month.lag6 -0.079771573 0.985351470
## Percent_change_high_open.lag4 -0.010693717 -0.039329348
## Percent_change_high_open.lag5 0.758417368 -0.044959615
## Percent_change_high_close.lag1 -0.134218824 0.180499027
## Percent_change_high_close.lag4 0.008283891 -0.045981479
## Percent_change_high_close.lag5 -0.787993333 0.074511808
## Percent_change_low_open.lag5 0.788823127 -0.071329232
## Percent_change_low_open.lag6 -0.000814507 -0.068726394
## Percent_change_low_close.lag2 -0.046251659 0.167373276
## Percent_change_low_close.lag5 -0.672716658 0.044937247
## Percent_change_low_close.lag6 -0.012851885 0.015141181
## Month.lag4 Month.lag5 Month.lag6
## open 0.006533527 0.005078403 0.0030130231
## high 0.007660955 0.005766983 0.0051078705
## low 0.006297042 0.004961831 0.0041120090
## close 0.001666759 -0.000249611 0.0004569970
## volume 0.006279090 0.007628334 0.0030430995
## percent_change_price -0.115928548 -0.122456770 -0.0669587760
## percent_change_volume_over_last_wk 0.069455376 0.001508881 0.0037649490
## previous_weeks_volume -0.031494085 -0.012530632 -0.0102772224
## next_weeks_open 0.001282332 -0.001165456 -0.0005103252
## next_weeks_close 0.003748265 0.004588252 0.0066763197
## percent_change_next_weeks_price 0.072942159 0.134808904 0.1713431305
## days_to_next_dividend -0.054141934 -0.047499751 -0.0405797616
## percent_return_next_dividend 0.007803315 0.010328252 0.0092105265
## Month 0.984959168 0.960965611 0.9307934188
## Week_of_Month -0.084181905 0.010767707 0.1390771074
## stock_return -0.096316074 -0.128892799 -0.0905151360
## Percent_change_high_open 0.096555086 0.086530626 0.1280878040
## Percent_change_high_close 0.221903084 0.219800327 0.1952292364
## Percent_change_low_open -0.012345966 -0.008152146 0.0220146834
## Percent_change_low_close 0.131833341 0.144022479 0.1108590046
## percent_change_price.lag1 -0.091627546 -0.143526553 -0.1490994324
## percent_change_price.lag5 -0.059137058 -0.073201577 -0.0797715732
## Month.lag2 0.924655546 0.942896172 0.9853514700
## Month.lag4 1.000000000 0.951321769 0.9279486580
## Month.lag5 0.951321769 1.000000000 0.9517881701
## Month.lag6 0.927948658 0.951788170 1.0000000000
## Percent_change_high_open.lag4 -0.056374389 -0.056974481 -0.0522802698
## Percent_change_high_open.lag5 -0.007671817 -0.053334177 -0.0511371852
## Percent_change_high_close.lag1 0.143413855 0.188406080 0.1861496292
## Percent_change_high_close.lag4 -0.019362126 -0.008015744 -0.0349500287
## Percent_change_high_close.lag5 0.075915828 0.055548424 0.0680141158
## Percent_change_low_open.lag5 -0.036582849 -0.045173279 -0.0548870136
## Percent_change_low_open.lag6 -0.072459812 -0.049657865 -0.0573793716
## Percent_change_low_close.lag2 0.109491097 0.102211891 0.1378936984
## Percent_change_low_close.lag5 0.052608050 0.064753306 0.0643380480
## Percent_change_low_close.lag6 -0.039164023 0.003768467 0.0130907922
## Percent_change_high_open.lag4
## open -0.0051897523
## high -0.0038321765
## low -0.0054814788
## close -0.0013838026
## volume -0.0090373823
## percent_change_price 0.0775856592
## percent_change_volume_over_last_wk -0.0262486334
## previous_weeks_volume 0.0077877214
## next_weeks_open -0.0008862094
## next_weeks_close -0.0065236583
## percent_change_next_weeks_price -0.1565881953
## days_to_next_dividend 0.0699592946
## percent_return_next_dividend -0.0980770543
## Month -0.0610147004
## Week_of_Month 0.0726205406
## stock_return 0.0168947849
## Percent_change_high_open 0.0502926406
## Percent_change_high_close -0.0424956040
## Percent_change_low_open -0.0178303667
## Percent_change_low_close -0.1168981470
## percent_change_price.lag1 0.0025700465
## percent_change_price.lag5 -0.0106937165
## Month.lag2 -0.0393293483
## Month.lag4 -0.0563743889
## Month.lag5 -0.0569744812
## Month.lag6 -0.0522802698
## Percent_change_high_open.lag4 1.0000000000
## Percent_change_high_open.lag5 0.0418021546
## Percent_change_high_close.lag1 0.0075440114
## Percent_change_high_close.lag4 -0.1744304125
## Percent_change_high_close.lag5 0.0525825613
## Percent_change_low_open.lag5 -0.0590841201
## Percent_change_low_open.lag6 -0.1042899650
## Percent_change_low_close.lag2 0.0242689083
## Percent_change_low_close.lag5 -0.0503607025
## Percent_change_low_close.lag6 -0.0038055881
## Percent_change_high_open.lag5
## open 0.0010804758
## high -0.0009463028
## low -0.0053676553
## close -0.0029755849
## volume 0.0281615490
## percent_change_price -0.1369047564
## percent_change_volume_over_last_wk 0.0781088814
## previous_weeks_volume 0.0065305267
## next_weeks_open -0.0014552057
## next_weeks_close -0.0093695818
## percent_change_next_weeks_price -0.2059331699
## days_to_next_dividend 0.0438587841
## percent_return_next_dividend -0.1051164915
## Month -0.0199305509
## Week_of_Month -0.0472391463
## stock_return -0.1242622275
## Percent_change_high_open -0.0723502272
## Percent_change_high_close 0.0938383508
## Percent_change_low_open -0.1810212008
## Percent_change_low_close -0.0389314678
## percent_change_price.lag1 0.0880602817
## percent_change_price.lag5 0.7584173677
## Month.lag2 -0.0449596153
## Month.lag4 -0.0076718166
## Month.lag5 -0.0533341775
## Month.lag6 -0.0511371852
## Percent_change_high_open.lag4 0.0418021546
## Percent_change_high_open.lag5 1.0000000000
## Percent_change_high_close.lag1 -0.0477078461
## Percent_change_high_close.lag4 0.0492694846
## Percent_change_high_close.lag5 -0.1982995474
## Percent_change_low_open.lag5 0.4814084317
## Percent_change_low_open.lag6 -0.0337411420
## Percent_change_low_close.lag2 -0.0271081495
## Percent_change_low_close.lag5 -0.6408729889
## Percent_change_low_close.lag6 -0.0419031887
## Percent_change_high_close.lag1
## open -0.168810668
## high -0.166917795
## low -0.169262910
## close -0.168659808
## volume 0.234026735
## percent_change_price -0.009393049
## percent_change_volume_over_last_wk -0.113726462
## previous_weeks_volume 0.324745562
## next_weeks_open -0.168463571
## next_weeks_close -0.164201579
## percent_change_next_weeks_price 0.105636155
## days_to_next_dividend 0.014494592
## percent_return_next_dividend -0.160433111
## Month 0.164036457
## Week_of_Month 0.038144743
## stock_return -0.018661140
## Percent_change_high_open 0.086918653
## Percent_change_high_close 0.090077829
## Percent_change_low_open -0.013410285
## Percent_change_low_close -0.003618337
## percent_change_price.lag1 -0.672772710
## percent_change_price.lag5 -0.134218824
## Month.lag2 0.180499027
## Month.lag4 0.143413855
## Month.lag5 0.188406080
## Month.lag6 0.186149629
## Percent_change_high_open.lag4 0.007544011
## Percent_change_high_open.lag5 -0.047707846
## Percent_change_high_close.lag1 1.000000000
## Percent_change_high_close.lag4 0.051242714
## Percent_change_high_close.lag5 0.150771127
## Percent_change_low_open.lag5 -0.127158439
## Percent_change_low_open.lag6 -0.069633161
## Percent_change_low_close.lag2 0.049529186
## Percent_change_low_close.lag5 0.066435459
## Percent_change_low_close.lag6 -0.026270652
## Percent_change_high_close.lag4
## open -0.156647792
## high -0.158617841
## low -0.159536397
## close -0.162097137
## volume 0.212064929
## percent_change_price -0.152327364
## percent_change_volume_over_last_wk 0.066886275
## previous_weeks_volume 0.192827069
## next_weeks_open -0.162794317
## next_weeks_close -0.167961468
## percent_change_next_weeks_price -0.168701632
## days_to_next_dividend -0.021508148
## percent_return_next_dividend -0.209981868
## Month -0.008826586
## Week_of_Month -0.040317421
## stock_return -0.118798266
## Percent_change_high_open -0.032812062
## Percent_change_high_close 0.146946225
## Percent_change_low_open -0.104122584
## Percent_change_low_close 0.069426749
## percent_change_price.lag1 -0.043841015
## percent_change_price.lag5 0.008283891
## Month.lag2 -0.045981479
## Month.lag4 -0.019362126
## Month.lag5 -0.008015744
## Month.lag6 -0.034950029
## Percent_change_high_open.lag4 -0.174430413
## Percent_change_high_open.lag5 0.049269485
## Percent_change_high_close.lag1 0.051242714
## Percent_change_high_close.lag4 1.000000000
## Percent_change_high_close.lag5 0.029392036
## Percent_change_low_open.lag5 -0.010506405
## Percent_change_low_open.lag6 0.004112172
## Percent_change_low_close.lag2 -0.041521602
## Percent_change_low_close.lag5 -0.025779210
## Percent_change_low_close.lag6 -0.116364884
## Percent_change_high_close.lag5
## open -0.17137668
## high -0.17168060
## low -0.17376620
## close -0.17487293
## volume 0.24005143
## percent_change_price -0.13541569
## percent_change_volume_over_last_wk 0.04992393
## previous_weeks_volume 0.19032457
## next_weeks_open -0.17607419
## next_weeks_close -0.16946014
## percent_change_next_weeks_price 0.13635776
## days_to_next_dividend -0.02066025
## percent_return_next_dividend -0.18757728
## Month 0.09435904
## Week_of_Month -0.13057966
## stock_return -0.15377414
## Percent_change_high_open 0.02153499
## Percent_change_high_close 0.17505792
## Percent_change_low_open -0.10673122
## Percent_change_low_close 0.04428509
## percent_change_price.lag1 -0.15297854
## percent_change_price.lag5 -0.78799333
## Month.lag2 0.07451181
## Month.lag4 0.07591583
## Month.lag5 0.05554842
## Month.lag6 0.06801412
## Percent_change_high_open.lag4 0.05258256
## Percent_change_high_open.lag5 -0.19829955
## Percent_change_high_close.lag1 0.15077113
## Percent_change_high_close.lag4 0.02939204
## Percent_change_high_close.lag5 1.00000000
## Percent_change_low_open.lag5 -0.74272368
## Percent_change_low_open.lag6 -0.02652184
## Percent_change_low_close.lag2 0.04469970
## Percent_change_low_close.lag5 0.39412584
## Percent_change_low_close.lag6 -0.02728584
## Percent_change_low_open.lag5
## open 0.112414252
## high 0.111034253
## low 0.113540930
## close 0.112433814
## volume -0.134008490
## percent_change_price 0.033206590
## percent_change_volume_over_last_wk 0.071419041
## previous_weeks_volume -0.129894999
## next_weeks_open 0.113502467
## next_weeks_close 0.106450715
## percent_change_next_weeks_price -0.154207339
## days_to_next_dividend 0.008919554
## percent_return_next_dividend 0.151346647
## Month -0.054088855
## Week_of_Month 0.042290942
## stock_return 0.078062875
## Percent_change_high_open -0.049813174
## Percent_change_high_close -0.084026614
## Percent_change_low_open 0.053909040
## Percent_change_low_close 0.020266865
## percent_change_price.lag1 0.152129703
## percent_change_price.lag5 0.788823127
## Month.lag2 -0.071329232
## Month.lag4 -0.036582849
## Month.lag5 -0.045173279
## Month.lag6 -0.054887014
## Percent_change_high_open.lag4 -0.059084120
## Percent_change_high_open.lag5 0.481408432
## Percent_change_high_close.lag1 -0.127158439
## Percent_change_high_close.lag4 -0.010506405
## Percent_change_high_close.lag5 -0.742723681
## Percent_change_low_open.lag5 1.000000000
## Percent_change_low_open.lag6 0.078281417
## Percent_change_low_close.lag2 -0.013968342
## Percent_change_low_close.lag5 -0.076378686
## Percent_change_low_close.lag6 0.079529459
## Percent_change_low_open.lag6
## open 0.112321796
## high 0.108138689
## low 0.109964423
## close 0.105864141
## volume -0.103613285
## percent_change_price -0.161102543
## percent_change_volume_over_last_wk 0.004950184
## previous_weeks_volume -0.109935809
## next_weeks_open 0.105522470
## next_weeks_close 0.108670801
## percent_change_next_weeks_price 0.110245012
## days_to_next_dividend 0.049041908
## percent_return_next_dividend 0.119785402
## Month -0.026240254
## Week_of_Month -0.187714094
## stock_return -0.140731143
## Percent_change_high_open -0.150643917
## Percent_change_high_close 0.046293456
## Percent_change_low_open -0.072238698
## Percent_change_low_close 0.112166484
## percent_change_price.lag1 0.033408528
## percent_change_price.lag5 -0.000814507
## Month.lag2 -0.068726394
## Month.lag4 -0.072459812
## Month.lag5 -0.049657865
## Month.lag6 -0.057379372
## Percent_change_high_open.lag4 -0.104289965
## Percent_change_high_open.lag5 -0.033741142
## Percent_change_high_close.lag1 -0.069633161
## Percent_change_high_close.lag4 0.004112172
## Percent_change_high_close.lag5 -0.026521840
## Percent_change_low_open.lag5 0.078281417
## Percent_change_low_open.lag6 1.000000000
## Percent_change_low_close.lag2 -0.127377536
## Percent_change_low_close.lag5 0.097271794
## Percent_change_low_close.lag6 -0.088610884
## Percent_change_low_close.lag2
## open -0.033392421
## high -0.031390037
## low -0.029430635
## close -0.029879084
## volume 0.032850221
## percent_change_price 0.024783282
## percent_change_volume_over_last_wk 0.012930790
## previous_weeks_volume 0.004761604
## next_weeks_open -0.029950278
## next_weeks_close -0.023999854
## percent_change_next_weeks_price 0.091837286
## days_to_next_dividend -0.008543475
## percent_return_next_dividend 0.052679371
## Month 0.105415748
## Week_of_Month 0.138702120
## stock_return 0.013230640
## Percent_change_high_open 0.062318244
## Percent_change_high_close 0.027405996
## Percent_change_low_open 0.059184455
## Percent_change_low_close 0.038222398
## percent_change_price.lag1 -0.062898663
## percent_change_price.lag5 -0.046251659
## Month.lag2 0.167373276
## Month.lag4 0.109491097
## Month.lag5 0.102211891
## Month.lag6 0.137893698
## Percent_change_high_open.lag4 0.024268908
## Percent_change_high_open.lag5 -0.027108150
## Percent_change_high_close.lag1 0.049529186
## Percent_change_high_close.lag4 -0.041521602
## Percent_change_high_close.lag5 0.044699697
## Percent_change_low_open.lag5 -0.013968342
## Percent_change_low_open.lag6 -0.127377536
## Percent_change_low_close.lag2 1.000000000
## Percent_change_low_close.lag5 0.060891556
## Percent_change_low_close.lag6 0.105476801
## Percent_change_low_close.lag5
## open -0.0600102344
## high -0.0599543517
## low -0.0546393029
## close -0.0597860702
## volume 0.0793100245
## percent_change_price 0.0292805266
## percent_change_volume_over_last_wk 0.0624549259
## previous_weeks_volume 0.0526798575
## next_weeks_open -0.0613880447
## next_weeks_close -0.0544701248
## percent_change_next_weeks_price 0.1732798299
## days_to_next_dividend -0.0540022146
## percent_return_next_dividend 0.0849531068
## Month 0.0650242711
## Week_of_Month -0.0518951091
## stock_return 0.0509868619
## Percent_change_high_open 0.0395741153
## Percent_change_high_close -0.0009337616
## Percent_change_low_open 0.1354307201
## Percent_change_low_close 0.1184166069
## percent_change_price.lag1 -0.0776096047
## percent_change_price.lag5 -0.6727166578
## Month.lag2 0.0449372468
## Month.lag4 0.0526080499
## Month.lag5 0.0647533061
## Month.lag6 0.0643380480
## Percent_change_high_open.lag4 -0.0503607025
## Percent_change_high_open.lag5 -0.6408729889
## Percent_change_high_close.lag1 0.0664354592
## Percent_change_high_close.lag4 -0.0257792103
## Percent_change_high_close.lag5 0.3941258429
## Percent_change_low_open.lag5 -0.0763786858
## Percent_change_low_open.lag6 0.0972717936
## Percent_change_low_close.lag2 0.0608915562
## Percent_change_low_close.lag5 1.0000000000
## Percent_change_low_close.lag6 0.1157798261
## Percent_change_low_close.lag6
## open -0.027607664
## high -0.027364114
## low -0.021780761
## close -0.021701602
## volume 0.009708224
## percent_change_price 0.145233063
## percent_change_volume_over_last_wk -0.111414362
## previous_weeks_volume 0.045592301
## next_weeks_open -0.023986701
## next_weeks_close -0.016959819
## percent_change_next_weeks_price 0.171423451
## days_to_next_dividend -0.034517158
## percent_return_next_dividend 0.093045709
## Month -0.022511719
## Week_of_Month 0.057298360
## stock_return 0.102236095
## Percent_change_high_open 0.025647648
## Percent_change_high_close -0.146619208
## Percent_change_low_open 0.148317156
## Percent_change_low_close -0.011446679
## percent_change_price.lag1 0.032357754
## percent_change_price.lag5 -0.012851885
## Month.lag2 0.015141181
## Month.lag4 -0.039164023
## Month.lag5 0.003768467
## Month.lag6 0.013090792
## Percent_change_high_open.lag4 -0.003805588
## Percent_change_high_open.lag5 -0.041903189
## Percent_change_high_close.lag1 -0.026270652
## Percent_change_high_close.lag4 -0.116364884
## Percent_change_high_close.lag5 -0.027285841
## Percent_change_low_open.lag5 0.079529459
## Percent_change_low_open.lag6 -0.088610884
## Percent_change_low_close.lag2 0.105476801
## Percent_change_low_close.lag5 0.115779826
## Percent_change_low_close.lag6 1.000000000Examining the data for missing values. There are 30 rows where the variables percent_change_volume_over_last_wk and previous_weeks_volume both have NA values but this is because all 30 of the observations come from the date “2020-01-07” and so data for the prior week is nonexistent. No imputation is necessary. These will only be removed if there is an issue with them later.
md.pattern(Dow_Jones)
## quarter stock date open high low close volume percent_change_price
## 570 1 1 1 1 1 1 1 1 1
## 30 1 1 1 1 1 1 1 1 1
## 30 1 1 1 1 1 1 1 1 1
## 60 1 1 1 1 1 1 1 1 1
## 30 1 1 1 1 1 1 1 1 1
## 30 1 1 1 1 1 1 1 1 1
## 0 0 0 0 0 0 0 0 0
## next_weeks_open next_weeks_close percent_change_next_weeks_price
## 570 1 1 1
## 30 1 1 1
## 30 1 1 1
## 60 1 1 1
## 30 1 1 1
## 30 1 1 1
## 0 0 0
## days_to_next_dividend percent_return_next_dividend Month Week_of_Month
## 570 1 1 1 1
## 30 1 1 1 1
## 30 1 1 1 1
## 60 1 1 1 1
## 30 1 1 1 1
## 30 1 1 1 1
## 0 0 0 0
## Percent_change_high_open Percent_change_high_close Percent_change_low_open
## 570 1 1 1
## 30 1 1 1
## 30 1 1 1
## 60 1 1 1
## 30 1 1 1
## 30 1 1 1
## 0 0 0
## Percent_change_low_close percent_change_volume_over_last_wk
## 570 1 1
## 30 1 1
## 30 1 1
## 60 1 1
## 30 1 1
## 30 1 0
## 0 30
## previous_weeks_volume stock_return percent_change_price.lag1
## 570 1 1 1
## 30 1 1 1
## 30 1 1 1
## 60 1 1 1
## 30 1 1 1
## 30 0 0 0
## 30 30 30
## Percent_change_high_close.lag1 Month.lag2 Percent_change_low_close.lag2
## 570 1 1 1
## 30 1 1 1
## 30 1 1 1
## 60 1 1 1
## 30 1 0 0
## 30 0 0 0
## 30 60 60
## Month.lag4 Percent_change_high_open.lag4 Percent_change_high_close.lag4
## 570 1 1 1
## 30 1 1 1
## 30 1 1 1
## 60 0 0 0
## 30 0 0 0
## 30 0 0 0
## 120 120 120
## percent_change_price.lag5 Month.lag5 Percent_change_high_open.lag5
## 570 1 1 1
## 30 1 1 1
## 30 0 0 0
## 60 0 0 0
## 30 0 0 0
## 30 0 0 0
## 150 150 150
## Percent_change_high_close.lag5 Percent_change_low_open.lag5
## 570 1 1
## 30 1 1
## 30 0 0
## 60 0 0
## 30 0 0
## 30 0 0
## 150 150
## Percent_change_low_close.lag5 Month.lag6 Percent_change_low_open.lag6
## 570 1 1 1
## 30 1 0 0
## 30 0 0 0
## 60 0 0 0
## 30 0 0 0
## 30 0 0 0
## 150 180 180
## Percent_change_low_close.lag6
## 570 1 0
## 30 0 3
## 30 0 9
## 60 0 12
## 30 0 14
## 30 0 19
## 180 2070Analysis
BEGINNING CAPM EVALUATION. THIS CAN BE CUT INTO A SEPARATE RMD FILE IF NECESSARY!
Dr. Roy didn’t provide us with any S&P500 data, so I’m using getSymbols to get it during the date range we’re interested in.
#this is a vector of all the stocks we have in the given dow jones data file with the SP500 included for our CAPM evaluation
stocks = unique(Dow_Jones$stock)
symbols = c("^GSPC", stocks)
#we need to remove KRFT and UTX since Yahoo finance does not have this info
symbols = symbols[-c(19,28)]
#empty matrix that we will populate with week returns for each stock from 2011-01-07 to 2011-06-25
Returns = matrix(ncol=length(symbols), nrow=116)
#counter for populating the empty matrix
count = 0
for(i in symbols){
count = count + 1
temp_stock_info = getSymbols(i, auto.assign=FALSE, from = "2011-01-07", to = "2011-06-25", env = NULL, return.class = 'data.frame')
colnames(temp_stock_info) <- c("OPEN","HIGH","LOW","CLOSE","VOLUME","ADJUSTEDCLOSE")
temp_returns <- na.omit(Delt(temp_stock_info$CLOSE))
Returns[,count] = temp_returns
}## 'getSymbols' currently uses auto.assign=TRUE by default, but will
## use auto.assign=FALSE in 0.5-0. You will still be able to use
## 'loadSymbols' to automatically load data. getOption("getSymbols.env")
## and getOption("getSymbols.auto.assign") will still be checked for
## alternate defaults.
##
## This message is shown once per session and may be disabled by setting
## options("getSymbols.warning4.0"=FALSE). See ?getSymbols for details.#convert matrix to data frame
Returns = data.frame(Returns)
#rename the columns
colnames(Returns) = c("SP500", symbols[2:length(symbols)])
Returns## SP500 AA AXP BA BAC
## 1 -1.376327e-03 0.0042630684 0.0022542380 -0.0041798935 0.0105263158
## 2 3.725127e-03 -0.0097028252 0.0130454794 -0.0018815604 0.0201388889
## 3 9.007580e-03 -0.0055113543 -0.0008881216 0.0172564243 0.0204220558
## 4 -1.710746e-03 -0.0301723377 0.0013333556 -0.0045616535 -0.0146764510
## 5 7.384542e-03 0.0139682532 0.0264092094 0.0034368895 0.0324983074
## 6 1.376411e-03 0.0187851431 0.0025945730 0.0342514771 -0.0163934426
## 7 -1.011566e-02 -0.0129072171 -0.0243691401 -0.0102110941 -0.0420000000
## 8 -1.294959e-03 -0.0049812685 0.0006630857 -0.0085041123 0.0118302018
## 9 2.413546e-03 -0.0118898363 0.0161254694 0.0078739732 -0.0199449794
## 10 5.836280e-03 0.0405319285 -0.0045651957 0.0146484794 -0.0231578947
## 11 2.634626e-04 -0.0115642121 -0.0216204843 -0.0067373158 -0.0208333333
## 12 4.220907e-03 0.0221675395 -0.0075892859 -0.0307309117 -0.0058694057
## 13 2.244306e-03 -0.0078313000 0.0017994152 0.0077120969 0.0088560886
## 14 -1.785253e-02 -0.0206436186 -0.0152671752 -0.0188491360 -0.0051207023
## 15 7.662558e-03 0.0272783626 -0.0109439122 0.0036111511 0.0095588235
## 16 1.669360e-02 0.0452625215 0.0050713922 0.0116580018 0.0422432629
## 17 -2.722518e-03 -0.0063510872 0.0027523625 0.0101009957 -0.0048916841
## 18 2.354200e-03 0.0000000000 -0.0043458828 -0.0002816479 0.0133426966
## 19 2.884262e-03 -0.0040673786 0.0066620953 0.0056353055 -0.0097020097
## 20 6.240172e-03 0.0105017746 0.0228206298 0.0077052819 0.0265920224
## 21 4.184752e-03 0.0046188895 0.0236501785 0.0108438621 -0.0040899796
## 22 -2.785765e-03 -0.0137930559 -0.0034873583 -0.0011002888 0.0020533881
## 23 7.494928e-04 -0.0023310508 0.0185914038 0.0004131489 -0.0102459016
## 24 5.507371e-03 0.0146027798 0.0038651492 -0.0071566883 0.0193236715
## 25 2.384924e-03 0.0126655159 -0.0049197861 0.0016634738 0.0081245768
## 26 -3.234911e-03 -0.0108015687 -0.0070937446 -0.0119014666 -0.0080591001
## 27 6.257435e-03 0.0109195166 0.0145053478 0.0151260640 0.0047393365
## 28 3.075692e-03 -0.0039795104 -0.0230474173 -0.0033113271 -0.0020215633
## 29 1.924723e-03 -0.0136985592 -0.0054609001 0.0110742390 -0.0040513167
## 30 -2.052857e-02 -0.0428240961 -0.0272347469 -0.0288882937 -0.0386440678
## 31 -6.111961e-03 -0.0060459239 -0.0191917359 -0.0098688425 -0.0007052186
## 32 -9.943766e-04 0.0066909466 0.0027624770 0.0075466179 -0.0141143260
## 33 1.055052e-02 0.0078549597 -0.0006887511 0.0217637218 0.0164638511
## 34 5.561086e-03 0.0101918967 0.0009189295 -0.0040110787 0.0063380282
## 35 -1.573968e-02 -0.0367952760 -0.0096396144 -0.0262463401 -0.0251924423
## 36 1.615201e-03 -0.0030807404 -0.0030127924 -0.0078437390 -0.0071787509
## 37 1.721900e-02 0.0278121659 0.0297535797 0.0307603708 0.0318148952
## 38 -7.378038e-03 -0.0030066395 -0.0130925059 0.0012551109 -0.0105115627
## 39 -8.341232e-03 -0.0199034480 -0.0002287740 -0.0128134535 -0.0063739377
## 40 8.922734e-03 0.0147691532 0.0350035011 0.0163657456 0.0470420527
## 41 -1.361703e-03 -0.0115221097 -0.0041998893 0.0006939894 -0.0068073519
## 42 -1.887095e-02 -0.0306748466 -0.0228634633 -0.0110971708 -0.0226182317
## 43 7.080514e-03 0.0145569093 0.0059063835 0.0049094964 0.0084151473
## 44 -6.049325e-03 0.0056144991 -0.0083558945 -0.0125628282 -0.0104311544
## 45 -1.120035e-02 -0.0049627277 -0.0061489638 -0.0148430312 -0.0189739986
## 46 -1.949495e-02 -0.0236907725 -0.0293308439 -0.0286985212 -0.0193409742
## 47 1.339823e-02 0.0223499355 0.0250235358 0.0090116854 0.0211833455
## 48 4.310202e-03 0.0062460700 0.0172731468 0.0117129570 0.0042918455
## 49 1.498585e-02 0.0273122284 0.0033960155 0.0303907245 0.0007122507
## 50 -3.550567e-03 -0.0060422961 0.0097021661 0.0091292279 -0.0120996441
## 51 2.913979e-03 0.0303951368 0.0060335196 0.0121086016 -0.0165706052
## 52 9.340748e-03 0.0094395280 0.0126610395 0.0005500687 -0.0124542125
## 53 3.161137e-03 -0.0011689557 0.0000000000 0.0079713302 -0.0103857567
## 54 -2.747837e-03 0.0087770874 0.0028515245 -0.0005453095 0.0022488756
## 55 7.060045e-03 0.0145011604 -0.0015310367 0.0043656206 -0.0014958863
## 56 6.684707e-03 0.0085763533 0.0056954652 0.0024449877 0.0074906367
## 57 -1.829502e-03 0.0011338104 -0.0154650185 0.0017614769 -0.0089219331
## 58 4.962988e-03 -0.0107587531 0.0035398229 0.0010821317 0.0030007502
## 59 3.452098e-04 0.0051515931 0.0013226852 -0.0008107688 0.0052356021
## 60 -1.800551e-04 0.0279043530 0.0000000000 -0.0097362276 0.0022321429
## 61 2.183677e-03 0.0044321792 0.0189344130 0.0066912192 0.0185597624
## 62 -1.520006e-03 -0.0005516408 -0.0025928912 0.0077319587 -0.0080174927
## 63 -4.004444e-03 -0.0110374822 0.0025996317 -0.0110378246 -0.0095518001
## 64 -2.793380e-03 -0.0083705589 0.0021608038 0.0039472029 0.0007418398
## 65 -7.776699e-03 -0.0602138215 -0.0077619878 -0.0092190887 -0.0014825797
## 66 1.902356e-04 -0.0089820359 0.0017383312 -0.0129995207 -0.0148478099
## 67 8.367708e-05 0.0000000000 -0.0047721694 0.0023569390 -0.0105501130
## 68 3.925413e-03 -0.0018127140 0.0080644942 0.0041493083 -0.0236100533
## 69 -1.101785e-02 -0.0236076984 -0.0041080865 0.0026171213 -0.0312012480
## 70 5.731171e-03 0.0192188722 0.0125922273 0.0049457480 -0.0064412238
## 71 1.351495e-02 0.0121653989 0.0077187180 0.0262474087 -0.0056726094
## 72 5.276782e-03 0.0198317808 0.0023404468 0.0049287598 0.0032599837
## 73 -1.592670e-03 -0.0047142503 -0.0012736574 -0.0071580062 0.0105605199
## 74 8.979584e-03 0.0082889776 0.0010626780 0.0086782508 -0.0168810289
## 75 6.249847e-03 0.0088079122 0.0110403614 0.0075446721 0.0081766149
## 76 3.555424e-03 -0.0052386739 0.0188996434 0.0319232778 0.0072992701
## 77 2.300662e-03 -0.0052661404 0.0115416735 0.0156587645 -0.0112721417
## 78 -1.752711e-03 0.0129411758 0.0116136915 -0.0031336175 0.0048859935
## 79 -3.379304e-03 0.0261323546 0.0050352465 -0.0002514397 0.0210696921
## 80 -6.855309e-03 -0.0113185720 -0.0040080359 -0.0084266883 -0.0087301587
## 81 -9.069835e-03 -0.0263308755 -0.0036217504 -0.0049467151 -0.0152121697
## 82 3.819920e-03 0.0082304035 0.0137318457 0.0109624096 0.0008130081
## 83 4.544164e-03 0.0221575077 -0.0001992430 0.0041609004 -0.0105605199
## 84 8.074037e-03 -0.0005705218 -0.0003985057 0.0038924913 0.0082101806
## 85 -1.111150e-02 -0.0268264847 -0.0067768789 -0.0108817390 -0.0024429967
## 86 4.895437e-03 0.0058651028 -0.0058198071 0.0041730146 -0.0040816327
## 87 -8.067329e-03 -0.0029154034 -0.0010092652 -0.0047853542 -0.0221311475
## 88 -6.204392e-03 -0.0105263399 0.0117194984 -0.0159433382 -0.0058675608
## 89 -3.685612e-04 -0.0277777778 0.0137806671 -0.0140156492 0.0033726813
## 90 8.803800e-03 0.0145896910 0.0059102248 0.0059989437 -0.0092436975
## 91 2.177941e-03 -0.0011983473 0.0148844298 0.0114078041 -0.0084817642
## 92 -7.688267e-03 -0.0245950560 -0.0121574875 -0.0064086134 -0.0094097519
## 93 -1.192559e-02 -0.0172201974 -0.0013674546 -0.0159958469 -0.0138169257
## 94 -8.273803e-04 0.0081351690 -0.0109545777 -0.0093078003 0.0035026270
## 95 3.183169e-03 0.0136561142 -0.0029667919 0.0099245732 -0.0069808028
## 96 3.953115e-03 0.0024494540 0.0053560801 0.0044549790 0.0070298770
## 97 4.080920e-03 0.0067196346 0.0088792620 0.0043046437 0.0200698080
## 98 1.059272e-02 0.0200242213 0.0091921962 0.0135082612 0.0051325920
## 99 -2.278464e-02 -0.0428316499 -0.0327519005 -0.0343457777 -0.0434042553
## 100 -1.224836e-03 0.0068365965 0.0036064917 0.0045123293 0.0044483986
## 101 -9.733809e-03 -0.0172839506 -0.0161709124 -0.0112300961 -0.0008857396
## 102 -1.076021e-02 -0.0194723618 -0.0101461041 -0.0034739980 -0.0398936170
## 103 -9.564078e-04 0.0051249732 0.0022550226 -0.0053633949 -0.0166204986
## 104 -4.186874e-03 -0.0178457872 -0.0161587444 -0.0044486654 -0.0103286385
## 105 7.377490e-03 0.0058402822 0.0047817881 0.0044685445 0.0104364326
## 106 -1.397984e-02 -0.0141935491 -0.0122077380 -0.0200862497 0.0140845070
## 107 6.687564e-04 -0.0117800236 0.0104733971 0.0034392625 0.0157407407
## 108 1.261178e-02 0.0205298008 -0.0018656716 0.0233067858 -0.0154968095
## 109 -1.743185e-02 -0.0292018702 -0.0180685974 -0.0105841507 -0.0277777778
## 110 1.754335e-03 -0.0113635810 0.0239001909 0.0021666080 0.0095238095
## 111 3.045017e-03 -0.0047328994 0.0018591200 0.0020267801 0.0075471698
## 112 5.395191e-03 0.0040759736 0.0078350722 0.0048542743 -0.0074906367
## 113 1.342348e-02 0.0399188396 0.0137069964 -0.0072462966 0.0216981132
## 114 -6.468449e-03 -0.0052048907 0.0060544704 -0.0251419292 -0.0036934441
## 115 -2.827987e-03 -0.0006541039 -0.0128384960 -0.0120632690 -0.0074142725
## 116 -1.172579e-02 -0.0032721698 -0.0176793135 0.0001403789 -0.0177404295
## CAT CSCO CVX DD DIS
## 1 -0.0036274831 -0.0085835960 -0.0085535474 0.0163183557 0.0012674017
## 2 0.0059963380 0.0043289079 0.0157062044 -0.0002816763 -0.0025315949
## 3 -0.0048962109 0.0114943492 0.0067515516 0.0101436604 -0.0058376647
## 4 0.0069526261 -0.0018939867 -0.0029204652 -0.0055787820 0.0022976769
## 5 -0.0013808902 0.0061669355 0.0070514428 0.0078541072 0.0007642130
## 6 0.0236145192 0.0004714757 0.0056015942 0.0016698906 0.0025451259
## 7 -0.0071703417 -0.0188500951 -0.0040706696 -0.0227840844 -0.0076161210
## 8 -0.0202009627 -0.0024015370 -0.0027966225 -0.0250212780 0.0020465081
## 9 -0.0091870632 -0.0019258546 0.0115413657 0.0058325641 0.0145520559
## 10 0.0196226415 0.0212252774 0.0034122308 0.0144969788 0.0050326369
## 11 -0.0019033626 0.0174776098 -0.0002124973 0.0082880375 -0.0020029545
## 12 0.0144083167 -0.0055710768 0.0059523489 0.0008503383 -0.0105369290
## 13 0.0091905692 0.0009337535 0.0011623098 0.0073634104 0.0005070994
## 14 -0.0098312846 -0.0237873590 -0.0145646121 -0.0143379531 -0.0154587181
## 15 0.0139005226 0.0105112279 0.0167076893 0.0119794980 0.0005148263
## 16 0.0103082154 0.0151299764 0.0135889708 0.0248026778 0.0259841015
## 17 0.0110192223 0.0069865863 0.0027021617 0.0077007985 0.0152959124
## 18 -0.0016146534 0.0134134591 0.0086027671 0.0027292581 0.0002469252
## 19 0.0066713434 0.0063897307 -0.0020552564 0.0073489032 0.0051851605
## 20 0.0088362791 -0.0009069388 0.0056637112 0.0164820216 0.0056497177
## 21 0.0013934508 -0.0018157512 0.0008191071 0.0085061640 0.0058622620
## 22 -0.0081502832 0.0022738063 -0.0153468389 -0.0126515828 0.0529383439
## 23 0.0081170157 -0.1415608375 0.0047797071 0.0178857498 -0.0011531365
## 24 0.0292246825 -0.0116278541 -0.0025853155 0.0065564906 0.0023089124
## 25 -0.0027042592 0.0058822457 0.0051840333 0.0028661187 -0.0039161023
## 26 -0.0025179353 -0.0074427968 -0.0062919136 -0.0137698106 -0.0034690563
## 27 0.0053398350 -0.0048205678 0.0033216526 0.0089567462 0.0141564400
## 28 -0.0018348816 0.0053821313 0.0052761637 0.0120104793 0.0000000000
## 29 0.0241873063 0.0091006424 0.0159514565 -0.0056759302 -0.0032036613
## 30 -0.0363687792 -0.0137931034 0.0162074451 -0.0358070209 -0.0208907020
## 31 -0.0195079400 -0.0102205487 0.0194377691 -0.0306781588 -0.0121922855
## 32 0.0054989304 -0.0021738587 -0.0023467098 -0.0147139710 0.0068833846
## 33 0.0142189520 0.0152504349 0.0006860629 0.0233868313 0.0124941779
## 34 0.0091176471 -0.0042918457 0.0161606467 0.0231277227 0.0183935036
## 35 -0.0298260857 0.0000000000 -0.0081927518 -0.0274488113 -0.0171467756
## 36 0.0111155617 -0.0032327049 0.0055393488 0.0132816144 0.0069783435
## 37 0.0324848863 0.0016216757 0.0069585483 0.0346805695 0.0180179945
## 38 -0.0116067050 -0.0070157039 -0.0042230732 -0.0097651314 -0.0117994327
## 39 -0.0088315605 -0.0108695109 -0.0071325108 -0.0069295975 -0.0121698969
## 40 0.0195828851 0.0010987911 0.0073778758 0.0279119021 0.0041841237
## 41 -0.0169979454 -0.0054883647 -0.0157077965 -0.0101827091 -0.0018518981
## 42 -0.0387847007 -0.0110375822 -0.0299588509 -0.0287523252 -0.0150741655
## 43 0.0165667041 0.0016741629 0.0085789058 -0.0008147728 0.0108311511
## 44 0.0207958515 -0.0055710860 0.0087061243 -0.0048926232 -0.0160726299
## 45 -0.0132223117 -0.0257703641 0.0042658729 -0.0177547624 -0.0146781006
## 46 -0.0034739256 -0.0195514675 -0.0169910199 -0.0222469259 -0.0245074730
## 47 0.0270916429 -0.0029324928 0.0274343880 0.0156427887 0.0039408869
## 48 0.0188129843 0.0082352353 0.0054773573 0.0039204554 0.0115309623
## 49 0.0240814587 0.0145857651 0.0232490168 0.0312412811 0.0143099685
## 50 -0.0074355891 0.0034503740 0.0003802738 -0.0064917171 -0.0090865854
## 51 -0.0002809158 0.0074497990 0.0023757483 -0.0008167692 0.0193050922
## 52 0.0150805636 -0.0125141638 -0.0009481039 0.0016348738 0.0146780059
## 53 0.0066438404 -0.0046082947 0.0132852727 0.0106093157 0.0025664955
## 54 0.0028417455 -0.0052083330 -0.0069301181 -0.0029609564 -0.0104724456
## 55 0.0104204660 0.0145433383 0.0125424556 0.0053995311 0.0098776811
## 56 0.0089560158 -0.0063073964 0.0059606872 0.0008056592 0.0095481837
## 57 -0.0016139245 -0.0103866128 -0.0048144060 0.0128789440 -0.0059976473
## 58 0.0158958692 -0.0064139359 0.0077216673 0.0042384635 -0.0055697842
## 59 0.0022983910 0.0011735915 -0.0008308438 0.0063307510 -0.0051341193
## 60 -0.0094372820 0.0093786641 0.0101635311 0.0133682910 -0.0046915551
## 61 -0.0116641263 0.0493612688 -0.0061282172 -0.0043972943 -0.0037709168
## 62 -0.0103603784 -0.0088544549 0.0025768267 -0.0041569756 -0.0054411876
## 63 -0.0002730815 -0.0145170296 0.0066091609 0.0049570033 -0.0066603947
## 64 -0.0068293571 -0.0101983569 -0.0171439443 -0.0197300645 0.0031130509
## 65 -0.0229210599 -0.0017171152 -0.0334013642 -0.0211864079 -0.0062066843
## 66 0.0099464859 -0.0108945521 -0.0035515646 -0.0070346105 0.0016814797
## 67 -0.0004645080 -0.0046376812 0.0103072827 0.0062670099 -0.0163069780
## 68 -0.0034393288 -0.0081536983 0.0129672105 0.0230164932 0.0121891760
## 69 -0.0308739579 -0.0176160295 -0.0163779935 -0.0203811413 -0.0077071050
## 70 0.0211741671 -0.0071726838 0.0086124593 0.0186436076 0.0036407038
## 71 0.0205466639 0.0192654413 0.0228652368 0.0140583562 0.0166868932
## 72 0.0105282509 0.0005907265 0.0029681755 0.0326968318 0.0054709561
## 73 -0.0052092854 0.0094450408 -0.0065661613 -0.0032927875 -0.0080435297
## 74 0.0283877268 0.0245614035 0.0123813259 0.0157560311 0.0095397567
## 75 0.0059853403 -0.0188355594 0.0020229977 -0.0012509296 0.0059059766
## 76 0.0002663884 0.0058173353 -0.0014683215 0.0197895596 0.0103334424
## 77 0.0245916639 0.0133024284 0.0057899459 0.0068779424 0.0018595537
## 78 -0.0090113592 0.0034246575 -0.0115131760 0.0085386436 0.0039443621
## 79 -0.0096179590 -0.0096700796 -0.0185801627 -0.0200773919 -0.0046221401
## 80 -0.0220711580 0.0034462378 -0.0140340777 -0.0214762188 -0.0104481309
## 81 -0.0124582291 0.0005724671 -0.0196789931 -0.0103430421 0.0016424214
## 82 0.0086844959 0.0045766018 0.0025335606 0.0124903839 0.0086671822
## 83 0.0119630963 0.0022779614 0.0117612659 0.0032729624 0.0009288667
## 84 0.0108364585 0.0107955114 0.0025939573 0.0223337324 0.0187935508
## 85 -0.0256046773 -0.0005621135 -0.0201226426 -0.0427098789 -0.0544295149
## 86 -0.0122750133 -0.0478065777 0.0048894973 -0.0017948740 0.0014451349
## 87 -0.0211727429 -0.0029533963 -0.0036006519 -0.0143847925 -0.0014430495
## 88 -0.0022571804 -0.0165876195 -0.0072272391 -0.0172009380 -0.0142100193
## 89 -0.0377980408 0.0024095783 -0.0121987012 -0.0312914297 0.0019545077
## 90 0.0310540550 0.0006010217 0.0243999293 0.0120449008 0.0099975621
## 91 0.0004750879 0.0006006006 0.0098191910 -0.0032458490 -0.0009656447
## 92 -0.0092117851 -0.0078030612 -0.0125156731 -0.0227951038 0.0028999274
## 93 -0.0233873570 -0.0108893520 -0.0116992980 -0.0111080467 -0.0081927711
## 94 -0.0033368928 -0.0048929664 0.0088783069 -0.0039314648 -0.0017006803
## 95 0.0167404919 -0.0049169637 0.0095825074 0.0202988393 0.0009734972
## 96 0.0091041356 0.0037059294 0.0010653850 -0.0135396676 -0.0034038171
## 97 0.0039350801 0.0129230154 -0.0014512577 -0.0028011013 0.0129299335
## 98 0.0114723234 0.0206561373 0.0164713208 0.0148876408 0.0026493497
## 99 -0.0431002351 -0.0250000015 -0.0230674474 -0.0285081870 -0.0295459757
## 100 0.0093836825 -0.0079364474 -0.0133671092 0.0188034182 -0.0084158659
## 101 -0.0106664446 -0.0147692308 -0.0011867385 -0.0156599738 -0.0169745378
## 102 -0.0122650546 -0.0012492192 -0.0130693069 -0.0039772576 0.0005078974
## 103 0.0002002403 -0.0300187617 -0.0021067315 0.0034226966 -0.0012691370
## 104 -0.0184220670 -0.0135396518 0.0048255353 -0.0088117926 -0.0030495046
## 105 0.0124439105 0.0006535948 0.0128064636 0.0086033451 0.0035686719
## 106 -0.0248841522 -0.0124101894 -0.0154105004 -0.0028433130 -0.0220980194
## 107 -0.0139477114 -0.0039682540 -0.0074244809 -0.0031365705 -0.0033766494
## 108 0.0253562338 0.0013280212 0.0168806024 0.0177345487 0.0057336723
## 109 -0.0225832718 -0.0159151194 -0.0217693245 -0.0269814706 -0.0051827157
## 110 -0.0019864401 0.0141509434 0.0103647593 -0.0054881318 -0.0098984374
## 111 0.0051330191 -0.0053156146 -0.0026149251 0.0046470864 0.0007893450
## 112 0.0232413035 0.0113560454 0.0074619947 0.0106967575 0.0049947160
## 113 0.0326950397 0.0244385733 0.0168150529 0.0320366306 0.0143865812
## 114 -0.0122299735 -0.0096711799 -0.0051185749 -0.0027715996 -0.0121195980
## 115 0.0039940189 0.0071614583 -0.0169189572 -0.0100055951 -0.0127904199
## 116 -0.0053704722 -0.0349062702 -0.0146940317 -0.0109489405 -0.0063457959
## GE HD HPQ IBM INTC
## 1 0.0043408011 0.0002908086 -0.0051008850 -1.960346e-03 0.0014521297
## 2 0.0064830038 0.0136668221 0.0127062172 -2.438364e-03 0.0173996125
## 3 0.0021470445 -0.0008605565 0.0046224549 1.235746e-02 0.0118764851
## 4 -0.0037493476 0.0126327297 0.0002190903 -1.877927e-03 -0.0004693897
## 5 0.0118279314 0.0175786504 0.0131435044 7.928994e-03 -0.0098638323
## 6 -0.0116896669 0.0036222068 0.0019459015 4.333293e-03 0.0000000000
## 7 -0.0145161078 -0.0108272904 -0.0004316091 3.345508e-02 -0.0033206831
## 8 0.0054554894 0.0241369906 0.0099310111 7.065386e-04 -0.0028557354
## 9 0.0710797429 0.0005479857 0.0096194635 -1.925565e-03 -0.0062052980
## 10 0.0151976991 0.0038346756 0.0067753810 2.655952e-02 0.0201729107
## 11 -0.0029940996 0.0139153608 -0.0098843170 1.133870e-02 0.0145950565
## 12 -0.0030029350 0.0069967169 -0.0042480638 -2.477756e-03 0.0092807893
## 13 0.0180722442 0.0149653135 -0.0029864153 1.863761e-04 0.0000000000
## 14 -0.0039447692 -0.0337019221 -0.0263157374 -1.154777e-02 -0.0133333793
## 15 -0.0029702812 0.0019073296 0.0039551324 1.752398e-02 0.0000000000
## 16 0.0327705852 0.0059831928 0.0181658974 9.629617e-03 0.0009320131
## 17 -0.0043269000 -0.0116247899 0.0079535179 -1.589600e-03 0.0037243482
## 18 0.0019314070 0.0038293216 0.0091704452 1.408426e-03 0.0004638683
## 19 -0.0091565610 0.0027247411 0.0023246642 2.874097e-03 0.0050996755
## 20 0.0150777734 -0.0054348099 0.0149693742 5.000043e-03 0.0004613007
## 21 0.0196453854 0.0153006019 0.0000000000 7.462662e-03 -0.0023053019
## 22 0.0014098158 0.0002690527 0.0166181928 -8.431249e-03 -0.0083179301
## 23 -0.0018770755 0.0037665593 -0.0081733164 -3.401142e-03 0.0158434304
## 24 0.0028208594 0.0045563923 0.0020601902 -1.462551e-03 -0.0018348166
## 25 0.0079700180 0.0026681430 -0.0067845503 -3.845011e-03 -0.0087316176
## 26 -0.0018604874 0.0029270089 -0.0066239133 -2.328177e-03 -0.0055632360
## 27 -0.0009319292 0.0045105334 0.0208376474 3.438946e-03 0.0139859667
## 28 0.0037313395 0.0084521657 -0.0075525144 5.140826e-03 0.0101148966
## 29 -0.0037174683 0.0078575170 0.0010284001 3.653136e-03 0.0077378247
## 30 -0.0289178689 -0.0101351351 -0.0090404157 -1.753215e-02 -0.0149051497
## 31 -0.0216139161 -0.0207403781 -0.0962057072 -1.092932e-02 -0.0302613035
## 32 0.0103093257 -0.0042895444 -0.0325763131 3.683425e-03 0.0066194326
## 33 0.0116618462 -0.0016154282 0.0120939250 9.392268e-03 0.0267731317
## 34 0.0048030314 0.0105177718 0.0222587216 -2.464839e-03 -0.0178408958
## 35 -0.0320268292 -0.0189485717 -0.0165024823 -1.179889e-02 -0.0037261297
## 36 0.0034568574 -0.0027202939 0.0076905274 1.187741e-03 0.0046751288
## 37 0.0211613893 0.0242771140 -0.0009251048 2.072922e-02 0.0139600279
## 38 -0.0183132724 -0.0087882293 -0.0136573957 -1.009294e-02 -0.0105553919
## 39 0.0004908984 -0.0094036000 -0.0147852339 -1.174077e-02 -0.0162337670
## 40 0.0122669485 0.0046108491 0.0100047276 1.469397e-02 -0.0037718059
## 41 0.0000000000 0.0170085579 -0.0082547477 2.206065e-02 0.0033129202
## 42 -0.0256907228 -0.0159277418 -0.0135552091 -2.315204e-02 -0.0193396217
## 43 0.0129353234 0.0018882924 0.0060269928 2.530484e-03 0.0038480037
## 44 -0.0216109549 -0.0123855415 -0.0057512144 -6.402721e-03 -0.0014375179
## 45 -0.0155623567 -0.0106324700 -0.0134972667 -1.468489e-02 -0.0316698656
## 46 -0.0336562796 -0.0168090654 -0.0193012048 -3.785690e-02 -0.0183350347
## 47 0.0142480007 0.0022420964 0.0321374583 7.712373e-03 0.0045432107
## 48 0.0015609200 0.0067114657 -0.0026551028 1.109097e-02 0.0015075377
## 49 0.0244155808 0.0119444444 0.0108905742 1.148242e-02 0.0130457100
## 50 -0.0116632417 -0.0038429591 -0.0007181146 2.029471e-03 -0.0019812282
## 51 0.0020523591 0.0090933588 0.0079059920 9.683538e-03 0.0069479404
## 52 0.0128008392 0.0202075920 0.0244829749 3.196853e-03 0.0044355838
## 53 -0.0015167279 0.0016059154 -0.0132249779 1.337166e-02 -0.0004905790
## 54 0.0000000000 -0.0205771256 -0.0091700122 -4.994438e-03 -0.0014728031
## 55 0.0055695553 0.0286493572 -0.0244423046 9.357440e-03 -0.0029498033
## 56 0.0125881375 -0.0034483023 0.0046216824 4.420438e-03 0.0088756406
## 57 -0.0029835227 -0.0135746340 -0.0079903278 -3.239603e-03 -0.0136851913
## 58 0.0144637799 0.0134916348 0.0002440635 7.358784e-03 -0.0227948959
## 59 0.0093412352 -0.0023961661 -0.0156172750 -1.217751e-04 -0.0116632359
## 60 -0.0097418566 0.0034693621 -0.0012394847 -1.582922e-03 0.0112877886
## 61 0.0108214225 -0.0026595214 0.0220898472 3.048235e-04 0.0121766622
## 62 -0.0097323253 0.0088000533 -0.0024284028 2.072738e-03 0.0040100249
## 63 -0.0078623999 -0.0097806762 -0.0092502763 -2.007556e-03 -0.0004993010
## 64 -0.0004952749 0.0037372932 0.0085995409 -6.096068e-04 0.0049950549
## 65 -0.0084242058 0.0042553194 0.0007308173 -4.269576e-03 -0.0178926929
## 66 -0.0034982668 -0.0023834747 0.0012171571 4.287884e-03 0.0010121964
## 67 0.0030089589 0.0045129283 -0.0187210690 6.221433e-03 -0.0101112735
## 68 0.0020001281 0.0087208774 -0.0024777409 7.516554e-03 0.0086823289
## 69 -0.0029940996 -0.0107414205 -0.0126676803 -1.624481e-03 -0.0065822278
## 70 0.0145145589 0.0002648835 0.0060377455 -3.254236e-03 0.0122324153
## 71 0.0064134187 0.0045009002 0.0225056623 -3.929831e-03 0.0780462700
## 72 -0.0220588584 -0.0036900370 0.0024456254 2.142640e-02 0.0023353106
## 73 -0.0030075028 -0.0063491536 -0.0112223559 -3.624917e-03 0.0223672890
## 74 0.0105580654 -0.0093184769 0.0039477901 4.890601e-03 0.0246125331
## 75 0.0273631245 0.0029562215 0.0086015450 1.115787e-02 0.0066725534
## 76 -0.0024212612 0.0040193194 -0.0124269206 2.406551e-03 0.0075121523
## 77 -0.0072815147 -0.0085401385 -0.0039477357 -1.171080e-03 0.0153509217
## 78 0.0014669848 0.0053834721 -0.0071834732 9.203846e-03 -0.0103671706
## 79 0.0078124413 0.0000000000 0.0062375166 4.182405e-03 0.0139676997
## 80 -0.0179262953 -0.0042837753 0.0151252776 -1.301556e-02 0.0116229014
## 81 -0.0182536158 -0.0048400378 -0.0034197155 -1.265964e-02 0.0046808936
## 82 0.0055276785 -0.0005402864 0.0002451344 2.552487e-03 -0.0152478181
## 83 0.0029984847 -0.0008111111 0.0051457518 1.243454e-03 -0.0210752688
## 84 0.0114599501 0.0083874732 0.0134080976 7.569479e-03 0.0118629613
## 85 -0.0103448742 -0.0010732493 -0.0122684298 -5.164955e-03 0.0165001730
## 86 0.0024888043 0.0016116304 -0.0043838355 1.616522e-02 0.0128149936
## 87 -0.0124131279 -0.0075087957 -0.0114969932 -1.346962e-02 -0.0126528474
## 88 -0.0065359477 -0.0008105377 -0.0150953328 -6.238212e-03 0.0098248185
## 89 -0.0086032632 0.0113575446 -0.0726130514 9.712182e-03 -0.0038071068
## 90 0.0086779216 0.0016041978 -0.0113790479 -3.518944e-04 0.0140127394
## 91 0.0101214737 -0.0018686600 -0.0098657927 8.800399e-04 -0.0142377728
## 92 -0.0170340639 -0.0090933407 -0.0041516205 -2.520617e-03 -0.0135939671
## 93 -0.0117226868 -0.0062078004 -0.0047248140 -1.116601e-02 -0.0155037905
## 94 -0.0149562074 -0.0073329984 0.0044680122 -1.604600e-03 -0.0109361325
## 95 0.0062826344 0.0021888373 0.0011120192 -1.428686e-03 0.0030959309
## 96 0.0104058987 -0.0120120663 0.0149958586 -3.397955e-03 -0.0079365079
## 97 0.0010298785 -0.0052500416 0.0112174276 1.914147e-03 -0.0128889333
## 98 0.0102880286 0.0077777500 0.0113637149 8.537272e-03 0.0135074747
## 99 -0.0259673284 -0.0242557063 -0.0200642963 -1.402945e-02 -0.0226565971
## 100 -0.0020910903 -0.0087571181 -0.0054599746 -2.821818e-03 0.0040909091
## 101 -0.0141435106 -0.0131091194 -0.0087840039 -6.261623e-03 -0.0162969670
## 102 -0.0191285407 -0.0098180765 -0.0041539200 -1.817649e-03 0.0046019328
## 103 0.0010834930 0.0011665500 -0.0108452790 -6.433979e-03 0.0105359139
## 104 0.0016233116 -0.0066997957 -0.0059039844 3.970884e-03 -0.0108793749
## 105 0.0037817569 0.0067449857 0.0028281005 3.042473e-03 -0.0027497709
## 106 -0.0139935411 -0.0250510035 -0.0059221133 -1.007039e-02 -0.0174632812
## 107 0.0038209213 0.0011950104 -0.0170213032 -6.125138e-05 0.0004677269
## 108 0.0114192454 0.0370039413 0.0023087636 5.822130e-03 0.0201028995
## 109 -0.0112903185 -0.0250359424 -0.0135329484 -1.090661e-02 -0.0183318057
## 110 0.0027188168 0.0182998519 0.0207238667 2.094474e-03 0.0000000000
## 111 0.0027116141 0.0008695362 0.0008578796 1.088095e-02 -0.0107375817
## 112 -0.0005408112 0.0069505070 -0.0002856938 3.527134e-03 0.0066068425
## 113 0.0178570464 0.0189818809 0.0088597303 7.271827e-03 0.0150023441
## 114 -0.0132908244 -0.0141123342 -0.0050992204 -3.248755e-03 -0.0115473441
## 115 -0.0096982246 0.0206127111 0.0031321444 2.655734e-03 0.0144859346
## 116 -0.0223068117 -0.0159887789 -0.0093670316 -6.320660e-03 -0.0234913875
## JNJ JPM KO MCD MMM
## 1 -0.0070287223 -0.0054994731 0.0022251113 -0.0108915553 0.0106691287
## 2 0.0017696268 0.0046082026 -0.0058674911 0.0046221317 0.0067698908
## 3 0.0036935924 0.0254587397 0.0055830597 -0.0040595939 0.0104855940
## 4 0.0065600000 -0.0058152093 0.0057106916 -0.0126358699 -0.0069930405
## 5 -0.0057224766 0.0103486837 -0.0042586749 0.0191275635 0.0006814743
## 6 -0.0071942607 -0.0035626809 0.0055440835 0.0083716178 0.0004540409
## 7 0.0074074560 -0.0232402458 -0.0009452111 0.0089715854 -0.0020422056
## 8 0.0047953963 0.0237932058 -0.0077262380 -0.0025214865 0.0009095271
## 9 -0.0031816894 0.0120670615 -0.0025425075 -0.0019957689 0.0141980916
## 10 -0.0070220077 -0.0059616029 0.0076469651 0.0049326089 0.0115354350
## 11 -0.0183220666 -0.0033318747 -0.0045849802 0.0013266915 -0.0201505757
## 12 -0.0078586114 0.0024515490 0.0000000000 -0.0041071143 0.0120903955
## 13 0.0013201651 0.0026678079 -0.0041296061 -0.0109086074 -0.0042424696
## 14 -0.0110415623 -0.0124167855 -0.0078149920 -0.0143913790 -0.0196210333
## 15 -0.0039993002 0.0089806464 0.0102877029 0.0053220388 0.0054894326
## 16 0.0143885059 0.0220293952 0.0031822117 -0.0027147686 -0.0014785828
## 17 -0.0001649678 -0.0104506641 -0.0030134814 0.0023138424 -0.0004556441
## 18 0.0029693171 0.0002199780 -0.0046134267 0.0025801603 0.0022791681
## 19 0.0006579112 -0.0191376819 -0.0001597890 0.0029798320 0.0038658785
## 20 0.0004930802 0.0204081633 -0.0006394181 -0.0081027141 0.0056631554
## 21 0.0011499918 0.0052747692 0.0055981766 0.0260041399 0.0076585200
## 22 -0.0009845422 -0.0137735237 0.0044536982 0.0075636809 0.0146417568
## 23 0.0008212713 0.0093105296 0.0061757401 -0.0022388779 -0.0035250055
## 24 -0.0037748072 0.0228421046 0.0004721435 0.0050157998 0.0148132215
## 25 0.0000000000 -0.0006441701 -0.0067641969 0.0013133570 0.0010893137
## 26 -0.0013179901 0.0060163084 0.0007918594 -0.0011804303 0.0010881175
## 27 -0.0016496041 0.0239213798 0.0033233741 -0.0017072225 0.0035869783
## 28 0.0044613516 -0.0025031081 0.0181388322 -0.0005260984 0.0043322971
## 29 0.0052640236 0.0037641154 0.0000000000 0.0019741247 0.0024802760
## 30 -0.0075273931 -0.0414583750 -0.0122386669 -0.0056482335 -0.0103270117
## 31 -0.0042869413 -0.0010866986 0.0023526036 -0.0067370544 -0.0189130217
## 32 -0.0023182481 -0.0010878808 -0.0004693788 0.0002659529 -0.0025482273
## 33 -0.0101244979 0.0167719451 0.0067313085 -0.0102379605 0.0024436410
## 34 0.0301810870 0.0002142031 -0.0060643759 0.0166576836 0.0219390914
## 35 -0.0120442385 -0.0233454920 0.0154882045 -0.0104387024 -0.0191911953
## 36 0.0018121911 -0.0085526100 -0.0073949156 -0.0026705435 0.0095069756
## 37 0.0039466863 0.0192435970 0.0176936210 0.0207523893 0.0163162286
## 38 0.0001638329 -0.0121528207 -0.0054903157 -0.0027544466 -0.0066802717
## 39 -0.0108090237 -0.0072495826 0.0001533814 0.0034197291 0.0022779043
## 40 0.0051324005 0.0267759023 0.0064397115 -0.0098309082 0.0146103676
## 41 -0.0051061935 0.0034482542 -0.0003046618 0.0031770982 -0.0061866880
## 42 -0.0130794863 -0.0221220356 -0.0050289849 0.0118764979 -0.0339164545
## 43 0.0013420231 0.0046124095 -0.0073518456 0.0006520996 0.0177757912
## 44 -0.0093817726 -0.0096196541 -0.0134238548 -0.0138147395 -0.0064403885
## 45 -0.0109927446 -0.0152317443 -0.0142320930 -0.0072683364 -0.0166995940
## 46 -0.0140218878 -0.0179331984 -0.0226876098 -0.0231630182 -0.0217876760
## 47 0.0081512487 0.0171193787 0.0110389614 0.0002726220 0.0130211189
## 48 0.0075692240 0.0264811709 0.0067437703 -0.0055858854 0.0032698274
## 49 0.0044391668 -0.0024049190 0.0138755981 0.0105494454 0.0221397385
## 50 -0.0006799422 -0.0035064650 -0.0009438729 0.0014913367 -0.0027487631
## 51 -0.0011906787 0.0028589619 0.0119665883 0.0089345604 0.0158765386
## 52 0.0052792574 0.0028509212 0.0065350245 0.0053669798 0.0047753745
## 53 -0.0008470100 0.0028427947 0.0081929198 0.0042706526 -0.0033485093
## 54 0.0044083079 0.0021805058 -0.0029132780 -0.0033222591 -0.0016255988
## 55 -0.0003376266 0.0013055048 0.0106105493 0.0049333733 0.0078158161
## 56 0.0027017899 0.0093437853 0.0048691112 0.0058378000 -0.0039852975
## 57 -0.0021893061 -0.0075350483 0.0045426408 0.0036934179 0.0111387368
## 58 0.0040506667 0.0054229937 0.0132650897 -0.0013142069 -0.0039572513
## 59 0.0110943012 -0.0002157066 0.0065457005 0.0052638638 0.0054762377
## 60 -0.0058188360 0.0051791541 -0.0028081878 0.0027490379 -0.0026697993
## 61 -0.0023411204 0.0227564825 0.0023713650 0.0015666188 0.0046043581
## 62 -0.0030170969 -0.0050377205 -0.0028093450 -0.0092544185 -0.0067149648
## 63 -0.0003362643 -0.0118143877 -0.0025208481 0.0003946717 0.0003219122
## 64 0.0067272453 0.0004270068 0.0019326001 0.0027616912 0.0062218622
## 65 0.0013364183 -0.0046948783 -0.0074183974 0.0053771016 -0.0152452021
## 66 -0.0056723558 -0.0083618998 0.0056800596 0.0030001955 0.0053047308
## 67 0.0070470137 -0.0276756541 0.0153091562 0.0023410197 0.0008615227
## 68 0.0089970177 -0.0017790082 -0.0043916851 0.0040222784 -0.0012911771
## 69 -0.0016512880 -0.0207173094 -0.0102926625 -0.0049107911 -0.0147597824
## 70 0.0368838908 0.0156961560 -0.0032684892 -0.0051948312 0.0044833681
## 71 0.0271175630 -0.0020156998 0.0113280973 0.0234987473 0.0206836597
## 72 -0.0049697003 0.0026929757 0.0004421518 -0.0190050760 0.0017064419
## 73 0.0006243328 -0.0015666741 -0.0020624632 0.0028603951 0.0021295252
## 74 0.0131024175 0.0114323692 -0.0119574553 -0.0024633088 0.0193370053
## 75 0.0095458511 0.0084220082 0.0010458688 0.0120873535 0.0055242755
## 76 -0.0028977124 0.0076922637 0.0061194627 0.0020546551 0.0078781175
## 77 0.0052004285 -0.0047981900 0.0007416703 0.0035883507 -0.0002057390
## 78 0.0074558429 -0.0098619546 0.0038541654 0.0042140341 -0.0029832425
## 79 0.0007552183 0.0163788845 0.0023626107 0.0038148907 -0.0009285597
## 80 -0.0089043764 -0.0091462983 -0.0061873602 0.0016467950 -0.0065062996
## 81 -0.0100501907 -0.0072527912 -0.0112659947 -0.0059441255 -0.0133056033
## 82 0.0039993077 -0.0028779501 0.0029985909 0.0012722519 0.0071639277
## 83 0.0055155510 -0.0017762433 0.0007472944 0.0077509660 0.0040794980
## 84 0.0019808777 0.0044484209 0.0058252431 0.0050435129 -0.0029169602
## 85 0.0123174875 -0.0205934455 -0.0002969409 -0.0025090579 -0.0019851844
## 86 0.0093135346 -0.0031652724 0.0147058526 0.0144636143 0.0118300360
## 87 -0.0084833901 -0.0213199819 -0.0019030596 0.0009917431 -0.0066218312
## 88 -0.0037526267 -0.0062572651 -0.0051334409 0.0049541864 -0.0057286011
## 89 0.0004519964 0.0216884323 0.0023587792 -0.0025881070 -0.0167609262
## 90 0.0015059939 0.0061629992 0.0045595824 0.0070431237 0.0008523439
## 91 -0.0016541504 -0.0018149273 0.0023425474 0.0123926626 0.0081966892
## 92 -0.0105437116 -0.0197727045 -0.0023370727 -0.0021815537 -0.0121423399
## 93 -0.0019790531 -0.0134477623 -0.0118595308 0.0020648366 -0.0114365116
## 94 0.0033557201 -0.0049353468 -0.0002962809 0.0016969576 -0.0056221971
## 95 0.0077531470 -0.0016532829 -0.0082999553 0.0009680784 0.0078286506
## 96 -0.0117664654 0.0042583629 -0.0031386637 -0.0035058148 0.0014025029
## 97 0.0192336279 0.0080094227 -0.0028484859 -0.0098264831 0.0070028119
## 98 0.0077879890 0.0105164989 0.0045105396 -0.0009801764 0.0097357012
## 99 -0.0120374199 -0.0342276580 -0.0007483311 -0.0068677703 -0.0311506155
## 100 0.0000000000 -0.0035918824 -0.0107849308 -0.0028402444 0.0002186898
## 101 -0.0058665310 -0.0009613314 -0.0077226227 -0.0026006068 -0.0083096655
## 102 -0.0006051294 -0.0250180659 -0.0016786205 0.0019865408 -0.0008819625
## 103 -0.0083270700 0.0046879350 -0.0033629166 0.0054523174 0.0025380158
## 104 0.0097709771 -0.0081041747 0.0030675769 0.0001232808 0.0006604953
## 105 0.0096764441 0.0146076013 0.0074923239 0.0013555144 0.0115498290
## 106 -0.0103324799 0.0017081259 -0.0075884049 -0.0110755720 -0.0133753372
## 107 0.0075654415 0.0151035083 -0.0041290411 0.0046043056 0.0062823761
## 108 0.0076588381 -0.0014398129 0.0075245391 0.0091663319 0.0141291671
## 109 -0.0140088529 -0.0223504200 -0.0097545801 -0.0028231619 -0.0168484401
## 110 0.0024183191 -0.0078662488 0.0080036322 0.0070162483 0.0060419972
## 111 -0.0004523372 0.0109018332 0.0019850970 0.0086786336 0.0021838501
## 112 0.0033187660 -0.0078431129 0.0032002437 0.0020601673 0.0084985728
## 113 -0.0003007668 0.0106225296 0.0065319761 0.0013302817 0.0093993304
## 114 -0.0063167095 -0.0053776827 0.0021128886 -0.0018116062 -0.0067429841
## 115 -0.0060542152 -0.0152371348 -0.0213855114 -0.0043557289 -0.0049569718
## 116 -0.0092888689 -0.0144746194 -0.0007695290 -0.0054685259 -0.0157028055
## MRK MSFT PFE PG T
## 1 -0.0040159842 -0.0132867483 -0.0043620314 -0.0021705271 -0.0176776430
## 2 -0.0067204299 -0.0038978740 -0.0021905422 -0.0049720322 -0.0151729005
## 3 0.0054127468 0.0156527209 0.0082327116 0.0145221734 0.0046578646
## 4 -0.0662181122 -0.0126093875 -0.0081654875 0.0078498075 0.0014264978
## 5 -0.0132602771 0.0039020219 0.0065861115 0.0007635308 0.0124643875
## 6 -0.0105171195 0.0127208838 0.0021810444 -0.0004577903 -0.0035174112
## 7 0.0011810157 -0.0066294836 -0.0032643608 -0.0022901069 0.0000000000
## 8 0.0041285462 -0.0042149281 -0.0043667931 0.0068860752 -0.0035298270
## 9 -0.0044051984 -0.0116402116 0.0065788896 0.0016717476 0.0035423309
## 10 -0.0029499408 0.0128479300 0.0049019611 0.0101653461 0.0052947406
## 11 -0.0130176927 0.0024665963 0.0010840490 0.0018022679 0.0098314607
## 12 -0.0047961629 0.0115992966 -0.0059556418 -0.0088455176 -0.0010431154
## 13 0.0015059939 0.0031271715 0.0065359481 -0.0291937826 -0.0208841281
## 14 -0.0054135338 -0.0387946298 -0.0178571439 0.0003115768 -0.0227514761
## 15 0.0030238282 -0.0007207207 0.0038567689 -0.0166666051 0.0010913059
## 16 0.0250226726 0.0093761269 0.0548847056 -0.0033265167 0.0127180596
## 17 -0.0052941176 -0.0017863165 -0.0135275582 -0.0020660681 -0.0071762107
## 18 -0.0272027794 -0.0103794198 0.0110760056 0.0017518872 0.0115648717
## 19 -0.0003040425 0.0043399638 0.0067813377 0.0112877421 -0.0007145766
## 20 0.0033445121 0.0154843716 -0.0134714856 0.0147775819 -0.0003575259
## 21 0.0081818182 0.0028368793 0.0063025215 0.0013942060 -0.0017882333
## 22 -0.0054102795 -0.0109618808 -0.0057411644 -0.0038675743 0.0021497313
## 23 -0.0015110003 -0.0168036831 -0.0010497951 0.0029508154 0.0096532360
## 24 0.0009079600 -0.0090909091 -0.0105098142 0.0023227159 0.0081444405
## 25 -0.0075597218 -0.0007339450 0.0116835040 -0.0029353003 -0.0003512469
## 26 -0.0009140463 -0.0099155711 0.0000000000 -0.0096064919 -0.0077301127
## 27 0.0051844463 0.0022255565 0.0120734737 -0.0025031290 0.0021246105
## 28 0.0042475426 0.0070317913 0.0046681051 0.0037641469 0.0070671734
## 29 -0.0075528705 -0.0055126794 -0.0092927214 0.0046875469 0.0024561404
## 30 -0.0155250542 -0.0173687737 -0.0156331434 -0.0035770294 -0.0129506125
## 31 -0.0077303649 0.0000000000 -0.0068819672 0.0012486655 -0.0060283686
## 32 -0.0018697725 0.0067694622 0.0074626685 -0.0171473572 -0.0039244023
## 33 0.0049953170 -0.0082181920 -0.0021163652 -0.0033306741 0.0075214542
## 34 0.0118049398 0.0011299812 0.0201484452 0.0033418046 0.0088873092
## 35 -0.0033773718 -0.0158013544 -0.0051974692 -0.0049166852 -0.0105707897
## 36 0.0036969502 -0.0030581040 0.0026123120 -0.0052598341 0.0032051282
## 37 0.0159605883 0.0046012653 0.0302240956 0.0022432142 -0.0014199858
## 38 -0.0012083687 -0.0095419844 -0.0055639684 -0.0083133495 -0.0074653042
## 39 -0.0069570173 -0.0088632752 -0.0025433244 -0.0051587942 -0.0007163324
## 40 0.0045689306 0.0073872864 0.0035696257 0.0055096420 0.0197132975
## 41 0.0093996665 -0.0007719413 -0.0010161889 -0.0008057857 0.0119507904
## 42 -0.0117151994 -0.0185399389 -0.0152595177 -0.0082257742 -0.0062521707
## 43 -0.0051672337 0.0106257379 0.0056819097 0.0000000000 -0.0052429918
## 44 -0.0106935228 0.0003894470 0.0174627822 -0.0022768580 -0.0094869294
## 45 -0.0160592954 -0.0116777730 -0.0025240666 -0.0112469115 -0.0134800279
## 46 -0.0244821398 -0.0236312731 -0.0232793196 -0.0153313551 -0.0172599431
## 47 0.0115830438 -0.0004033884 0.0300518890 0.0117194040 0.0150018295
## 48 0.0149490771 0.0008070218 0.0150905435 0.0028131392 0.0072098414
## 49 0.0150422751 0.0213710089 -0.0099108900 0.0115511720 0.0114530776
## 50 0.0043223218 -0.0011844058 -0.0020019670 -0.0060358729 -0.0056617127
## 51 0.0030741470 0.0094862454 -0.0010029915 -0.0003282455 0.0014234520
## 52 0.0027581979 0.0105715736 0.0190762886 0.0037760466 0.0142147127
## 53 -0.0045843825 -0.0073614106 0.0024630371 -0.0042525025 0.0108619127
## 54 -0.0036843414 -0.0081967600 -0.0039311870 -0.0036136826 0.0176776776
## 55 0.0101694296 0.0031483668 0.0054267221 0.0102208869 0.0235012935
## 56 0.0158633318 0.0047077678 -0.0019626742 0.0112598239 0.0219633951
## 57 -0.0087087390 -0.0085904721 -0.0014749781 -0.0059706793 -0.0032562033
## 58 0.0018176917 0.0035447422 0.0034465957 0.0077922730 0.0003266906
## 59 0.0060477774 0.0027472135 0.0078508003 0.0028994200 0.0048987262
## 60 -0.0033062819 0.0090020356 -0.0043816435 -0.0094763896 -0.0022749106
## 61 0.0057297346 0.0143521717 -0.0078239271 0.0014593806 -0.0074919216
## 62 -0.0005995802 0.0019120841 0.0019713799 0.0059909814 0.0022974074
## 63 0.0102008995 -0.0049618700 0.0063944568 -0.0037018992 0.0055664045
## 64 -0.0023759431 -0.0034522440 0.0102639822 0.0046849272 -0.0016281016
## 65 -0.0008930932 -0.0130870285 -0.0101597032 0.0112558291 -0.0061970320
## 66 -0.0026817639 -0.0003900156 0.0000000000 0.0015901256 -0.0095175257
## 67 0.0116522255 -0.0081934845 0.0014663273 0.0049213683 0.0036448310
## 68 0.0191966031 -0.0019669158 0.0019521376 0.0139020697 0.0118850772
## 69 -0.0168066657 -0.0114308628 -0.0063321631 -0.0028046120 -0.0110930179
## 70 -0.0053050398 0.0027910686 0.0063725149 -0.0021874844 0.0000000000
## 71 0.0085926222 0.0242544732 -0.0068193237 -0.0021922956 -0.0059386343
## 72 0.0000000000 -0.0093167702 -0.0294261412 -0.0070621625 0.0182542655
## 73 0.0085194181 0.0035266850 0.0176856301 0.0015805121 -0.0042373207
## 74 0.0212641700 0.0226474025 0.0024827092 0.0072590028 0.0127660233
## 75 0.0162578432 0.0072546007 0.0217929506 0.0029765783 0.0155138650
## 76 0.0039292449 0.0125094774 0.0096946031 0.0074977042 -0.0015913113
## 77 0.0050321778 -0.0295769011 0.0067211097 0.0062015814 -0.0079693973
## 78 0.0100139079 -0.0100308642 0.0023842917 0.0043142988 0.0028919665
## 79 0.0027540346 0.0058456352 -0.0275926884 0.0081313133 0.0208267229
## 80 0.0041197748 0.0096861685 0.0097846674 0.0115660023 -0.0021971123
## 81 -0.0084792394 -0.0103606297 -0.0121124214 -0.0088762448 -0.0179302291
## 82 0.0038620414 0.0031019774 0.0078470537 -0.0092592597 0.0012812621
## 83 0.0024732345 -0.0015462311 0.0024330731 -0.0019916961 0.0028790787
## 84 0.0079495614 -0.0061943477 0.0126213430 0.0090574763 0.0108453270
## 85 -0.0038074245 -0.0120763148 -0.0119846775 0.0028905369 -0.0097823285
## 86 0.0155610151 -0.0015773264 0.0135857076 0.0139562808 0.0082855325
## 87 -0.0032257795 -0.0114533570 0.0014360939 0.0002992968 -0.0072692480
## 88 0.0059330364 -0.0183779857 0.0028680185 0.0011965450 -0.0111429799
## 89 -0.0008042628 -0.0020350020 0.0076263784 0.0071705406 0.0019318095
## 90 0.0083177354 0.0069331566 0.0018921144 -0.0005933106 0.0025706940
## 91 -0.0053220061 0.0012149858 -0.0070821533 0.0011873257 0.0064102242
## 92 -0.0085607274 -0.0093041670 -0.0161674476 -0.0014823303 -0.0025477707
## 93 -0.0043172962 -0.0130665578 -0.0048331684 -0.0046021080 -0.0076628352
## 94 -0.0008130894 -0.0008274721 -0.0033997258 -0.0005965846 0.0025740026
## 95 -0.0048820180 0.0016563561 0.0126705488 -0.0094016562 -0.0051347882
## 96 -0.0084491144 0.0198428681 0.0057747838 -0.0028622327 0.0035484194
## 97 -0.0046729520 0.0036481557 0.0014354068 0.0001510047 0.0057859207
## 98 0.0149130355 0.0100969305 0.0248447390 0.0120846380 0.0086288907
## 99 -0.0136054422 -0.0231907237 -0.0186480359 -0.0089551940 -0.0123573832
## 100 -0.0027585655 -0.0085960295 -0.0023752804 -0.0058734938 -0.0064164581
## 101 -0.0091286855 -0.0127992986 -0.0076190145 -0.0087865775 -0.0103325480
## 102 -0.0072584869 0.0041823505 -0.0047984814 0.0010698456 -0.0094616313
## 103 0.0002811867 0.0020824240 0.0000000000 -0.0067175878 -0.0016469696
## 104 0.0061850155 -0.0049874483 -0.0028930114 -0.0032277898 0.0009898054
## 105 0.0058675327 0.0008353383 0.0033849302 0.0024672938 -0.0003295979
## 106 -0.0152777500 -0.0104340572 -0.0308433417 -0.0047685739 0.0003297066
## 107 -0.0033850211 0.0139182629 0.0174042072 0.0010819166 0.0069215227
## 108 0.0087743273 0.0074874373 0.0058652063 -0.0001543153 0.0078560395
## 109 -0.0131874583 -0.0198182915 -0.0189504885 -0.0154416919 -0.0142903860
## 110 0.0002843901 0.0109519798 0.0024764040 0.0078419701 0.0026359143
## 111 0.0059692723 0.0108333333 0.0009882292 0.0066915653 0.0111731844
## 112 0.0113026847 0.0086561830 0.0004935488 0.0061832430 0.0061748131
## 113 -0.0002794635 0.0118512878 0.0078935085 -0.0133660325 0.0048450260
## 114 -0.0086640025 -0.0044426494 -0.0073421439 -0.0024914824 -0.0073931852
## 115 -0.0140964191 -0.0008113996 0.0182444893 -0.0093662039 -0.0051813473
## 116 -0.0120103514 -0.0133982953 -0.0276029079 -0.0137094077 -0.0091145185
## TRV VZ WMT XOM
## 1 0.0097505340 -0.0002783746 -0.0064719302 -0.0060854481
## 2 0.0009285794 -0.0155901178 0.0104225014 0.0074538137
## 3 0.0128014466 0.0031108596 0.0103149197 0.0117584883
## 4 0.0014654332 0.0093035802 -0.0010938378 0.0016975319
## 5 -0.0007316079 -0.0094972070 0.0003650301 0.0147307654
## 6 0.0007321435 -0.0310208131 0.0060207625 0.0111768120
## 7 -0.0040240901 0.0069847786 -0.0019949221 -0.0059712998
## 8 0.0078971532 0.0002891041 0.0174450848 -0.0062627558
## 9 0.0021865707 0.0098237501 -0.0046437219 0.0158199743
## 10 0.0112727091 0.0082975963 0.0057419523 -0.0049380474
## 11 0.0109672961 0.0156072352 0.0215878505 0.0011452348
## 12 -0.0005335052 0.0170438945 0.0010478869 0.0124555669
## 13 0.0076512454 0.0024725273 0.0043614794 0.0027616494
## 14 -0.0144799574 -0.0235681270 -0.0151120201 -0.0111417005
## 15 0.0080630172 -0.0002807185 -0.0111111286 0.0213951392
## 16 0.0097760935 0.0182482038 0.0046370965 0.0400347546
## 17 -0.0017602887 -0.0030328095 -0.0083437064 -0.0059587651
## 18 0.0095221479 0.0060840985 0.0010740601 0.0003596451
## 19 0.0027947598 -0.0019241341 0.0019671138 -0.0019175814
## 20 -0.0040062707 -0.0079868078 0.0007139211 0.0078050073
## 21 0.0122420602 0.0088839534 0.0055288211 -0.0113189205
## 22 0.0160677261 0.0093560815 0.0062078573 -0.0051819714
## 23 -0.0059514027 -0.0070883860 -0.0200951877 0.0078739428
## 24 0.0090660795 -0.0008236958 0.0017988667 -0.0045672718
## 25 -0.0025428377 -0.0134651556 -0.0159813255 0.0252354987
## 26 0.0086675391 0.0155988014 0.0027372628 -0.0228477554
## 27 0.0018534289 -0.0079539498 -0.0072793811 0.0086778473
## 28 0.0053817693 0.0055294722 0.0036663795 0.0022702234
## 29 0.0190699066 0.0068737973 0.0115068676 0.0073915477
## 30 -0.0064018223 -0.0169306121 -0.0308776267 0.0111242840
## 31 -0.0018172972 -0.0052777500 -0.0119247070 0.0190776915
## 32 -0.0180403184 -0.0064227588 -0.0177257971 -0.0126335018
## 33 0.0045507499 0.0109611854 -0.0065271645 -0.0073281958
## 34 0.0055369465 0.0264108138 0.0044444444 0.0022264238
## 35 -0.0118471383 -0.0243769786 0.0017314352 -0.0085349703
## 36 -0.0069233366 0.0088839534 -0.0019204724 0.0033018749
## 37 0.0040809045 0.0005503853 0.0007696171 0.0086976726
## 38 0.0022015411 -0.0077007424 0.0011536628 -0.0086226754
## 39 -0.0037174890 -0.0019402438 -0.0009602458 -0.0042313234
## 40 0.0016960991 0.0130519863 0.0080737985 -0.0014164660
## 41 0.0057568743 0.0046601425 0.0043859459 -0.0026004847
## 42 -0.0148148480 -0.0068212820 -0.0003796469 -0.0355534499
## 43 0.0061517601 -0.0151099992 -0.0011396391 0.0090932173
## 44 -0.0003396739 -0.0186889271 -0.0051340559 0.0031660252
## 45 -0.0057764355 -0.0088118533 -0.0049693998 -0.0120174561
## 46 -0.0080314593 -0.0163464301 -0.0130618515 -0.0255559777
## 47 0.0108527306 0.0300292429 -0.0001946672 0.0233262646
## 48 -0.0105657635 0.0144352667 0.0029200117 -0.0038196893
## 49 0.0153289698 0.0172990792 0.0077639363 0.0246134576
## 50 -0.0113655978 0.0134394409 0.0015408706 -0.0033799857
## 51 0.0025737989 0.0008118809 -0.0069230962 0.0004844961
## 52 0.0068458326 0.0054083288 0.0183966115 0.0015739104
## 53 0.0025496854 0.0029586068 -0.0045636433 0.0107578867
## 54 -0.0011868430 0.0123357197 -0.0030563325 -0.0017938531
## 55 0.0059412324 0.0143046623 0.0013412340 -0.0026356894
## 56 0.0021937395 0.0044397492 0.0019135669 0.0148948709
## 57 0.0015154235 0.0020801353 -0.0059205881 -0.0042608712
## 58 0.0038668292 -0.0018162947 0.0015370221 0.0065375374
## 59 -0.0013397756 0.0036391993 0.0099750813 0.0022437766
## 60 -0.0083850409 -0.0059570058 0.0017094016 0.0064804404
## 61 0.0136985961 -0.0138093535 0.0045505876 -0.0028096231
## 62 -0.0025024692 -0.0023778073 0.0003775009 0.0068091336
## 63 -0.0035122762 -0.0010592426 -0.0086792264 0.0022154267
## 64 0.0140986232 0.0034463679 0.0053292538 -0.0091913092
## 65 -0.0120820759 -0.0055481905 0.0132525559 -0.0232503982
## 66 0.0040207908 0.0013283741 0.0020553251 -0.0002403943
## 67 -0.0050058235 0.0005306447 -0.0024240350 0.0033669792
## 68 0.0028508804 0.0037125167 0.0009345607 0.0101869485
## 69 -0.0132107193 -0.0142667643 -0.0044817555 -0.0141179616
## 70 -0.0140653792 -0.0018761458 0.0007502720 0.0084236464
## 71 0.0163286525 0.0147690379 0.0063730274 0.0220763596
## 72 0.0370370195 -0.0232866096 -0.0020487428 0.0082895386
## 73 0.0075016145 0.0021674885 -0.0039194287 -0.0016211209
## 74 -0.0063127227 0.0173019455 0.0101180628 0.0139178495
## 75 0.0140088127 0.0164761888 0.0094601744 0.0041180623
## 76 0.0130120643 0.0005228758 0.0049614298 -0.0050125656
## 77 0.0034887091 -0.0128037889 0.0053026331 0.0073277654
## 78 0.0037926834 -0.0058231341 0.0010913241 -0.0114799041
## 79 0.0083438759 0.0063897229 0.0076307775 -0.0155225708
## 80 -0.0079625601 -0.0034391800 -0.0016227912 -0.0094604645
## 81 -0.0084985992 -0.0146004521 -0.0054180785 -0.0258223683
## 82 0.0068253968 0.0043103449 -0.0009079354 0.0008472403
## 83 -0.0006306322 -0.0010728809 0.0014539804 0.0059257224
## 84 0.0074144503 0.0088613851 0.0078040112 0.0019234912
## 85 -0.0095521608 -0.0082513175 -0.0064830003 -0.0266377863
## 86 0.0094861344 0.0045625875 0.0099692409 -0.0008629191
## 87 -0.0238057329 -0.0045418648 0.0000000000 -0.0022208512
## 88 0.0097865712 -0.0077830654 0.0061019382 -0.0077903422
## 89 -0.0058785988 0.0037868541 -0.0092757758 0.0021187189
## 90 0.0068723030 -0.0005389652 -0.0064818328 0.0165401559
## 91 -0.0030158571 0.0062011324 0.0054367524 0.0072180574
## 92 -0.0089157935 -0.0045551447 -0.0034246395 -0.0092311670
## 93 -0.0130120643 -0.0080754774 -0.0012660517 -0.0110334927
## 94 -0.0068359213 0.0013569607 -0.0079681636 0.0076856702
## 95 0.0072107342 -0.0135501348 -0.0040160278 0.0082420715
## 96 -0.0040676864 0.0057692030 0.0010996701 0.0052464618
## 97 0.0050645484 0.0016388145 0.0014647016 0.0029129506
## 98 0.0091027633 0.0070903194 0.0095063984 0.0101658481
## 99 -0.0141752734 -0.0178716491 -0.0166606661 -0.0172517310
## 100 -0.0003268137 -0.0027571547 -0.0138121550 -0.0085334269
## 101 0.0000000000 -0.0149294175 0.0020541737 -0.0018443624
## 102 -0.0019614090 -0.0117878751 0.0018635483 -0.0109632791
## 103 0.0027841303 0.0048282308 0.0013021578 -0.0036119192
## 104 -0.0088192226 0.0146975971 -0.0026008359 0.0095000250
## 105 0.0064261494 -0.0064067963 -0.0013037810 0.0052005695
## 106 -0.0306156342 -0.0134566590 -0.0167847448 -0.0172456393
## 107 -0.0076000846 0.0125036093 -0.0018968513 -0.0068939083
## 108 -0.0018719538 -0.0014032837 0.0055112316 0.0145146277
## 109 -0.0189258476 -0.0129286952 -0.0111510112 -0.0213982715
## 110 0.0038233750 0.0034169420 0.0097477446 0.0071192089
## 111 0.0027700832 0.0076616341 -0.0001893242 -0.0025246655
## 112 -0.0060427834 0.0039426643 0.0041651079 0.0087319922
## 113 0.0088588154 0.0095371664 0.0047134237 0.0107891232
## 114 -0.0130854334 -0.0013893581 -0.0052543253 -0.0093086757
## 115 -0.0027913468 0.0030606567 0.0052820791 -0.0172888750
## 116 -0.0083974808 -0.0013869349 -0.0165134356 -0.0211627098#empty vector that we will populate with the betas
Betas = c()
#counter for populating the empty vector
count = 0
for(i in symbols[2:length(symbols)]){
count = count + 1
temp_lm = lm(as.formula(paste(i, "~ SP500", sep = " ")), data = Returns)
temp_beta = summary(temp_lm)$coefficient[2,1]
Betas[count] = temp_beta
}
#convert the values in the Betas vector to be named numbers
names(Betas) = c(symbols[2:length(symbols)])
print(Betas)## AA AXP BA BAC CAT CSCO CVX DD
## 1.6696576 1.0007034 1.1328828 1.1576051 1.5705195 0.8248017 1.0018358 1.5539673
## DIS GE HD HPQ IBM INTC JNJ JPM
## 1.0157583 1.2701668 0.9626960 0.9041199 0.7916701 0.9328237 0.5473714 1.1666383
## KO MCD MMM MRK MSFT PFE PG T
## 0.4868550 0.3643799 1.0151111 0.7303533 0.9262416 0.9081653 0.3390901 0.7187690
## TRV VZ WMT XOM
## 0.7097738 0.7148044 0.4648297 1.0507018Making the mean and standard deviation:
DataMean <- apply(Returns, 2, mean)
DataSD <- apply(Returns, 2, sd)
cbind(DataMean, DataSD)## DataMean DataSD
## SP500 1.196352e-05 0.008105651
## AA -4.896440e-04 0.017858349
## AXP 8.189464e-04 0.012541301
## BA 3.111256e-04 0.012750645
## BAC -2.484728e-03 0.016065682
## CAT 6.924660e-04 0.016370897
## CSCO -2.749163e-03 0.018315796
## CVX 6.814994e-04 0.011805157
## DD 2.013403e-04 0.016025300
## DIS -3.427346e-04 0.012356505
## GE -1.181788e-04 0.014231713
## HD 2.409852e-04 0.011647408
## HPQ -2.075570e-03 0.015989342
## IBM 9.924957e-04 0.009733620
## INTC 3.220759e-04 0.014252143
## JNJ 3.690760e-04 0.008636530
## JPM -7.727595e-04 0.013330436
## KO 2.992041e-04 0.007524679
## MCD 8.556321e-04 0.007809415
## MMM 5.099839e-04 0.010624304
## MRK -6.090392e-04 0.011152684
## MSFT -1.344127e-03 0.010931823
## PFE 8.578013e-04 0.012419157
## PG -2.301348e-04 0.007634249
## T 5.066423e-04 0.009431203
## TRV 5.719429e-04 0.009697733
## VZ 7.577811e-05 0.010903261
## WMT -2.372820e-04 0.008155824
## XOM 2.081733e-04 0.012173666Model Set Up
Let’s split the data into train and test sets. According to the case study instructions we should “use quarter 1 (Jan-Mar) data for training and quarter 2 (Apr-Jun) data for testing.” There are 360 observations in the train set and 390 observations in the test set.
Dow_Jones$stock = Dow_Jones$stock %>% as.factor()
train = Dow_Jones %>% dplyr::filter(quarter == 1)
test = Dow_Jones %>% dplyr::filter(quarter == 2)
# remove observations with NAs. SVR throws warnings if this isn't done before tuning
clean_train = na.omit(train)
clean_test = na.omit(test)
#set formula, remove unnecessary variables
formula = percent_change_next_weeks_price ~ . - quarter - date - next_weeks_open - next_weeks_close - previous_weeks_volume - open - high - low - stock_returnSVR
#set how many folds for k-fold cross validation, set seed, and divide up train set into folds
k = 10
set.seed(1)
folds = sample(1:k, nrow(clean_train), replace = TRUE)
#set parameter and accuracy metrics
gamma = c()
cost = c()
MSE = c()
#loop through all folds to determine best gammas and costs. Record MSE for validation folds.
for (j in 1:k){
#tune svr
tuned_svr = tune.svm(formula, data = clean_train[folds != j, ], kernel = 'radial', gamma = c(.0001, .001, .01, .1, 1, 10, 100), cost = seq(.1, 1, by = .1))
#save best parameters
gamma[j] = tuned_svr$best.parameters$gamma
cost[j] = tuned_svr$best.parameters$cost
#predictions for validation set
mysvr = svm(formula, data = clean_train[folds != j, ], gamma = gamma[j], cost = cost[j])
svr_pred = predict(mysvr, clean_train[folds == j, ],)
#MSE for validation
MSE[j] = mean((svr_pred - clean_train[folds == j, ]$percent_change_next_weeks_price) ^ 2)
}
#select best gamma and cost for best model. Median is used as the mean would not be a usable number. Like .012 for gamma when the gamma needs to be .01, .02, .03...
best_gamma = median(gamma)
best_cost = median(cost)
#record MSE to compare against other SVR models
svr_val_MSE = mean(MSE)
svr_val_MSE## [1] 3.816869#Now that the SVR hyperparamters and predictors are finalized. Calculate test score using full training data set.
#create best svr model and calculate performance on test set
svr = svm(formula, data = clean_train, kernel = 'radial', gamma = best_gamma, cost = best_cost)
svr_test_pred = predict(svr, clean_test)
svr_test_MSE = mean((svr_test_pred - clean_test$percent_change_next_weeks_price) ^ 2)
print(svr_test_MSE)## [1] 8.514477plot(clean_test$percent_change_next_weeks_price, svr_test_pred, ylab = 'SVR Prediction', xlab = 'True', main = 'Next Week\'s Percent Change in Price')
Regression Tree
tree.dowjones = tree(formula, data = clean_train)
summary(tree.dowjones)##
## Regression tree:
## tree(formula = formula, data = clean_train)
## Variables actually used in tree construction:
## [1] "Month.lag2" "stock"
## [3] "percent_change_volume_over_last_wk" "percent_change_price.lag1"
## [5] "Percent_change_low_close.lag6" "Percent_change_low_open.lag5"
## [7] "Percent_change_high_close.lag1" "Percent_change_low_close.lag5"
## [9] "Percent_change_low_close.lag2"
## Number of terminal nodes: 17
## Residual mean deviance: 1.763 = 287.3 / 163
## Distribution of residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -5.3330 -0.7015 0.1023 0.0000 0.7540 3.5420plot(tree.dowjones)
text(tree.dowjones, pretty = 0, cex = 0.6)
Below we perform cost complexity pruning by cv and find that a the best tree size includes 15 nodes
cv.dowjones = cv.tree(tree.dowjones)
cv.dowjones## $size
## [1] 17 16 15 14 13 12 11 10 9 8 6 4 3 2 1
##
## $dev
## [1] 1241.1035 1222.7985 1227.0946 1171.5431 1173.9730 1173.9730 1113.3936
## [8] 1131.3742 1125.1374 1087.3100 1029.4845 1029.4845 873.8302 789.5843
## [15] 894.5641
##
## $k
## [1] -Inf 8.710636 9.499872 13.505835 14.202140 14.222533
## [7] 18.949603 20.328154 21.495834 25.522829 32.328793 32.807989
## [13] 55.581310 70.228121 177.824952
##
## $method
## [1] "deviance"
##
## attr(,"class")
## [1] "prune" "tree.sequence"which.min(cv.dowjones$size)## [1] 15Prune down to 15 nodes
prune.dowjones = prune.tree(tree.dowjones, best = 15)
plot(prune.dowjones)
text(prune.dowjones, pretty = 0, cex = 0.6)
Here is a plot of the predictions of decision tree model on test set vs. the actual values of percent_change_next_weeks_price.
prune.preds = predict(prune.dowjones, clean_test)
plot(prune.preds, clean_test$percent_change_next_weeks_price)
The mean square error of our predictions on the test data is about 9.77.
mean((clean_test$percent_change_next_weeks_price - prune.preds)^2)## [1] 10.71859Linear Regression
OLS Regression
#had to remove Month.lag4 because both Month.lag2 and Month.lag4 could not both be used in the model
ols.full.fit = lm(percent_change_next_weeks_price ~ . - quarter - date - next_weeks_open - next_weeks_close - previous_weeks_volume - open - high - low - stock_return - Month.lag4,data=clean_train)
ols.null.fit = lm(percent_change_next_weeks_price ~ 1, data = clean_train)
#ld.vars = attributes(alias(fit)$Complete)$dimnames[[1]]
#ld.vars
ols_coll_diag(ols.full.fit)$vif_t## Warning in summary.lm(lm(fm, data = data)): essentially perfect fit: summary may
## be unreliable
## Warning in summary.lm(lm(fm, data = data)): essentially perfect fit: summary may
## be unreliable## Variables Tolerance VIF
## 1 stockAXP 0.0140908548 70.968015
## 2 stockBA 0.0038732759 258.179386
## 3 stockBAC 0.0429163880 23.301122
## 4 stockCAT 0.0020778851 481.258556
## 5 stockCSCO 0.0984583115 10.156583
## 6 stockCVX 0.0017607050 567.954306
## 7 stockDD 0.0050231184 199.079522
## 8 stockDIS 0.0055246044 181.008434
## 9 stockGE 0.0181884989 54.979798
## 10 stockHD 0.0100815149 99.191442
## 11 stockHPQ 0.0225410963 44.363415
## 12 stockIBM 0.0008034707 1244.600388
## 13 stockINTC 0.0101781605 98.249581
## 14 stockJNJ 0.0033313503 300.178577
## 15 stockJPM 0.0097020807 103.070675
## 16 stockKO 0.0039136624 255.515140
## 17 stockKRFT 0.0065430395 152.834168
## 18 stockMCD 0.0027567346 362.748015
## 19 stockMMM 0.0023848916 419.306268
## 20 stockMRK 0.0040863064 244.719780
## 21 stockMSFT 0.0190834185 52.401513
## 22 stockPFE 0.0069338918 144.219154
## 23 stockPG 0.0035542849 281.350545
## 24 stockT 0.0025219109 396.524714
## 25 stockTRV 0.0051190788 195.347646
## 26 stockUTX 0.0029627470 337.524604
## 27 stockVZ 0.0028530498 350.502120
## 28 stockWMT 0.0056827793 175.970233
## 29 stockXOM 0.0030042199 332.865112
## 30 close 0.0005761701 1735.598504
## 31 volume 0.0331755829 30.142651
## 32 percent_change_price 0.0001009335 9907.515400
## 33 percent_change_volume_over_last_wk 0.2429720291 4.115700
## 34 days_to_next_dividend 0.1265562945 7.901622
## 35 percent_return_next_dividend 0.0016921803 590.953579
## 36 Month 0.0541961179 18.451506
## 37 Week_of_Month 0.0851417339 11.745121
## 38 Percent_change_high_open 0.0016073531 622.140851
## 39 Percent_change_high_close 0.0011501683 869.438012
## 40 Percent_change_low_open 0.0001316920 7593.477608
## 41 Percent_change_low_close 0.0002843605 3516.662905
## 42 percent_change_price.lag1 0.1700164891 5.881782
## 43 percent_change_price.lag5 0.0001175771 8505.059513
## 44 Month.lag2 0.0000000000 Inf
## 45 Month.lag5 0.1142766779 8.750692
## 46 Month.lag6 0.0000000000 Inf
## 47 Percent_change_high_open.lag4 0.5552081056 1.801126
## 48 Percent_change_high_open.lag5 0.0028185553 354.791690
## 49 Percent_change_high_close.lag1 0.1786842166 5.596465
## 50 Percent_change_high_close.lag4 0.5069569064 1.972554
## 51 Percent_change_high_close.lag5 0.0022905967 436.567470
## 52 Percent_change_low_open.lag5 0.0002639190 3789.041370
## 53 Percent_change_low_open.lag6 0.5921541646 1.688749
## 54 Percent_change_low_close.lag2 0.5076311459 1.969934
## 55 Percent_change_low_close.lag5 0.0003185070 3139.648368
## 56 Percent_change_low_close.lag6 0.4383403261 2.281332step.AIC.fit = step(ols.null.fit, scope = list(upper = ols.full.fit),
direction = "both", trace = F)
summary(step.AIC.fit)##
## Call:
## lm(formula = percent_change_next_weeks_price ~ Month.lag2 + percent_return_next_dividend +
## Percent_change_low_open + close + Percent_change_high_open.lag4,
## data = clean_train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.1849 -1.1417 0.1842 0.9915 4.6652
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.566882 0.939891 -6.987 5.74e-11 ***
## Month.lag2 1.882652 0.310220 6.069 7.85e-09 ***
## percent_return_next_dividend 1.693732 0.462570 3.662 0.000332 ***
## Percent_change_low_open -0.204186 0.077388 -2.638 0.009083 **
## close 0.010613 0.004357 2.436 0.015862 *
## Percent_change_high_open.lag4 -0.145050 0.087105 -1.665 0.097665 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.867 on 174 degrees of freedom
## Multiple R-squared: 0.301, Adjusted R-squared: 0.2809
## F-statistic: 14.98 on 5 and 174 DF, p-value: 3.168e-12#ols_step_both_aic(ols.full.fit)
#step.AIC.fit = lm(percent_change_next_weeks_price ~ close + stock + Month + percent_change_price.lag1 + volume + Week_of_Month+ days_to_next_dividend + percent_change_volume_over_last_wk, data = clean_train)
summary(step.AIC.fit)##
## Call:
## lm(formula = percent_change_next_weeks_price ~ Month.lag2 + percent_return_next_dividend +
## Percent_change_low_open + close + Percent_change_high_open.lag4,
## data = clean_train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.1849 -1.1417 0.1842 0.9915 4.6652
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.566882 0.939891 -6.987 5.74e-11 ***
## Month.lag2 1.882652 0.310220 6.069 7.85e-09 ***
## percent_return_next_dividend 1.693732 0.462570 3.662 0.000332 ***
## Percent_change_low_open -0.204186 0.077388 -2.638 0.009083 **
## close 0.010613 0.004357 2.436 0.015862 *
## Percent_change_high_open.lag4 -0.145050 0.087105 -1.665 0.097665 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.867 on 174 degrees of freedom
## Multiple R-squared: 0.301, Adjusted R-squared: 0.2809
## F-statistic: 14.98 on 5 and 174 DF, p-value: 3.168e-12ols_coll_diag(step.AIC.fit)$vif_t## Variables Tolerance VIF
## 1 Month.lag2 0.9055371 1.104317
## 2 percent_return_next_dividend 0.9065425 1.103092
## 3 Percent_change_low_open 0.9326674 1.072194
## 4 close 0.9667980 1.034342
## 5 Percent_change_high_open.lag4 0.8718510 1.146985#MSE for train set
(val_MSE = mean(step.AIC.fit$residuals^2))## [1] 3.36964ols.pred=predict(step.AIC.fit,newdata=clean_test)
#MSE for test set
mean((ols.pred - clean_test$percent_change_next_weeks_price)^2)## [1] 22.14086There is some serious overfitting happening here…
Ridge Regression
set.seed(1)
grid=10^seq(10,-2,length=100)
k = 10
set.seed(1)
folds = sample(1:k, nrow(clean_train), replace = TRUE)
#set parameter and accuracy metrics
lambda = c()
MSE = c()
#loop through all folds to determine best gammas and costs. Record MSE for validation folds.
for (j in 1:k){
xtrain = model.matrix(formula,clean_train[folds != j, ])[,-1]
ytrain = clean_train[folds != j, ]$percent_change_next_weeks_price
xtest = model.matrix(formula,clean_train[folds == j, ])[,-1]
ytest = clean_train[folds == j, ]$percent_change_next_weeks_price
ridge.mod=glmnet(xtrain,ytrain,alpha=0,lambda=grid)
cv.out=cv.glmnet(xtrain,ytrain,alpha=0)
bestlam = cv.out$lambda.min
ridge.pred=predict(ridge.mod ,s=bestlam ,newx=xtest)
lambda[j] = bestlam
MSE[j] = mean((ridge.pred - ytest)^2)
}
best_lambda = median(lambda)
ridge_val_MSE = mean(MSE)xtrain = model.matrix(formula,clean_train)[,-1]
ytrain = clean_train$percent_change_next_weeks_price
xtest = model.matrix(formula,clean_test)[,-1]
ytest = clean_test$percent_change_next_weeks_price
final_ridge=glmnet(xtrain,ytrain,alpha=0,lambda=best_lambda)
ridge.pred=predict(final_ridge, s=best_lambda,newx=xtest)
mean((ridge.pred - ytest)^2)## [1] 13.12915ridge.coef=predict(ridge.mod,type="coefficients", s=best_lambda) [1:48,]
ridge.coef## (Intercept) stockAXP
## -3.130443e+00 2.681397e-01
## stockBA stockBAC
## 2.327225e-01 -1.828070e-01
## stockCAT stockCSCO
## 6.542908e-02 -5.896745e-01
## stockCVX stockDD
## 7.708722e-01 -6.592602e-02
## stockDIS stockGE
## 9.764723e-02 -1.006400e-01
## stockHD stockHPQ
## -2.689236e-01 -1.053394e+00
## stockIBM stockINTC
## 1.202409e-01 -6.259491e-01
## stockJNJ stockJPM
## -1.364769e-01 -2.061538e-01
## stockKO stockKRFT
## 4.408056e-01 3.567876e-01
## stockMCD stockMMM
## -1.787873e-03 -1.496573e-01
## stockMRK stockMSFT
## 6.844053e-02 -3.752796e-01
## stockPFE stockPG
## 1.100177e+00 -1.806673e-01
## stockT stockTRV
## -2.578628e-02 4.211096e-02
## stockUTX stockVZ
## -7.398829e-04 2.233288e-01
## stockWMT stockXOM
## -1.748938e-01 -1.311379e-01
## close volume
## 1.209413e-03 -8.251780e-10
## percent_change_price percent_change_volume_over_last_wk
## -3.184517e-02 2.135924e-03
## days_to_next_dividend percent_return_next_dividend
## 1.612460e-04 3.942278e-01
## Month Week_of_Month
## 3.098381e-02 1.694810e-01
## Percent_change_high_open Percent_change_high_close
## -1.865030e-02 4.675315e-02
## Percent_change_low_open Percent_change_low_close
## -5.446074e-02 -3.350960e-02
## percent_change_price.lag1 percent_change_price.lag5
## -5.458053e-02 -8.441761e-03
## Month.lag2 Month.lag4
## 4.971541e-01 3.091601e-02
## Month.lag5 Month.lag6
## 1.516941e-01 4.974607e-01ridge.coef[ridge.coef!=0]## (Intercept) stockAXP
## -3.130443e+00 2.681397e-01
## stockBA stockBAC
## 2.327225e-01 -1.828070e-01
## stockCAT stockCSCO
## 6.542908e-02 -5.896745e-01
## stockCVX stockDD
## 7.708722e-01 -6.592602e-02
## stockDIS stockGE
## 9.764723e-02 -1.006400e-01
## stockHD stockHPQ
## -2.689236e-01 -1.053394e+00
## stockIBM stockINTC
## 1.202409e-01 -6.259491e-01
## stockJNJ stockJPM
## -1.364769e-01 -2.061538e-01
## stockKO stockKRFT
## 4.408056e-01 3.567876e-01
## stockMCD stockMMM
## -1.787873e-03 -1.496573e-01
## stockMRK stockMSFT
## 6.844053e-02 -3.752796e-01
## stockPFE stockPG
## 1.100177e+00 -1.806673e-01
## stockT stockTRV
## -2.578628e-02 4.211096e-02
## stockUTX stockVZ
## -7.398829e-04 2.233288e-01
## stockWMT stockXOM
## -1.748938e-01 -1.311379e-01
## close volume
## 1.209413e-03 -8.251780e-10
## percent_change_price percent_change_volume_over_last_wk
## -3.184517e-02 2.135924e-03
## days_to_next_dividend percent_return_next_dividend
## 1.612460e-04 3.942278e-01
## Month Week_of_Month
## 3.098381e-02 1.694810e-01
## Percent_change_high_open Percent_change_high_close
## -1.865030e-02 4.675315e-02
## Percent_change_low_open Percent_change_low_close
## -5.446074e-02 -3.350960e-02
## percent_change_price.lag1 percent_change_price.lag5
## -5.458053e-02 -8.441761e-03
## Month.lag2 Month.lag4
## 4.971541e-01 3.091601e-02
## Month.lag5 Month.lag6
## 1.516941e-01 4.974607e-01Final Model Predictions for Last Month using SVR
for (i in c('2011-06-03', '2011-06-10', '2011-06-17', '2011-06-24')){
train1 = Dow_Jones[Dow_Jones$date < i,]
test1 = Dow_Jones[Dow_Jones$date == i,]
#train svr model and predict test set
best_svr = svm(formula, data = train1, kernel = 'radial', gamma = best_gamma, cost = best_cost)
print(summary(best_svr))
best_svr_pred = predict(best_svr, test1)
names(best_svr_pred) = unique(Dow_Jones$stock)
best_svr_MSE = mean((best_svr_pred - test1$percent_change_next_weeks_price) ^ 2)
print(best_svr_MSE)
plot(test1$percent_change_next_weeks_price, best_svr_pred, ylab = 'SVR Prediction', xlab = 'True', main = 'Next Week\'s Percent Change in Price')
print(i)
print(sort(best_svr_pred, decreasing = TRUE))
}##
## Call:
## svm(formula = formula, data = train1, kernel = "radial", gamma = best_gamma,
## cost = best_cost)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: radial
## cost: 0.75
## gamma: 0.01
## epsilon: 0.1
##
##
## Number of Support Vectors: 398
##
##
##
##
##
## [1] 2.61584
## [1] "2011-06-03"
## HD KO VZ KRFT WMT PG MCD
## 0.7207491 0.6748416 0.1118799 -0.1230569 -0.2010948 -0.2588820 -0.3019928
## JPM T GE DIS HPQ MMM DD
## -0.3183506 -0.3240435 -0.3681167 -0.5677919 -0.6513704 -0.8204993 -0.9274146
## MSFT AXP UTX IBM BA MRK PFE
## -0.9474690 -0.9900058 -1.0046203 -1.1076522 -1.1511398 -1.2477376 -1.2659930
## CSCO TRV CVX JNJ BAC XOM AA
## -1.3009295 -1.3750335 -1.5425999 -1.5867484 -1.6943738 -1.7318169 -1.8428461
## CAT INTC
## -1.9899958 -2.1881468
##
## Call:
## svm(formula = formula, data = train1, kernel = "radial", gamma = best_gamma,
## cost = best_cost)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: radial
## cost: 0.75
## gamma: 0.01
## epsilon: 0.1
##
##
## Number of Support Vectors: 419
##
##
##
##
##
## [1] 3.825189
## [1] "2011-06-10"
## CVX XOM VZ HD PFE GE
## 0.74648783 0.33105441 -0.09294774 -0.22756724 -0.27187563 -0.50484587
## IBM WMT UTX MMM CAT T
## -0.51197228 -0.62163579 -0.65041949 -0.69560203 -0.74860099 -0.76677639
## MCD TRV KO AA JNJ BA
## -0.86830486 -0.88672801 -1.00908559 -1.01407981 -1.04503081 -1.06706335
## AXP JPM DD DIS MRK MSFT
## -1.09767673 -1.15896264 -1.34188032 -1.51737679 -1.52725814 -1.69726675
## HPQ PG CSCO INTC BAC KRFT
## -1.70353452 -1.74029036 -1.74642218 -1.90317083 -1.96173207 -2.31464782
##
## Call:
## svm(formula = formula, data = train1, kernel = "radial", gamma = best_gamma,
## cost = best_cost)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: radial
## cost: 0.75
## gamma: 0.01
## epsilon: 0.1
##
##
## Number of Support Vectors: 449
##
##
##
##
##
## [1] 5.187631
## [1] "2011-06-17"
## DIS TRV JPM BA CSCO DD
## 0.04449807 -0.06822346 -0.21477775 -0.36018008 -0.36532138 -0.39492017
## AXP VZ CAT T HD IBM
## -0.60870194 -0.62302997 -0.68546864 -0.81368739 -0.85080291 -0.98721631
## XOM KO MCD JNJ MMM MRK
## -0.99371543 -1.09670019 -1.12522349 -1.20106568 -1.39442926 -1.40790728
## CVX PG KRFT AA UTX GE
## -1.47347496 -1.48344693 -1.51232621 -1.56271736 -1.58774630 -1.59438412
## WMT BAC MSFT INTC PFE HPQ
## -1.72081089 -1.86932777 -1.89323429 -2.12548666 -2.17742217 -2.74554789
##
## Call:
## svm(formula = formula, data = train1, kernel = "radial", gamma = best_gamma,
## cost = best_cost)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: radial
## cost: 0.75
## gamma: 0.01
## epsilon: 0.1
##
##
## Number of Support Vectors: 479
##
##
##
##
##
## [1] 37.37889
## [1] "2011-06-24"
## BA AA CAT HPQ MMM VZ
## 0.98344970 0.56263922 0.31579483 0.28828545 0.25694219 -0.08417645
## UTX TRV T JNJ GE DD
## -0.11011767 -0.20027520 -0.24548189 -0.25834588 -0.26845689 -0.27657610
## MRK IBM PG KO CVX WMT
## -0.42192259 -0.44822939 -0.45215933 -0.48372979 -0.49715490 -0.61228031
## PFE JPM CSCO DIS MSFT XOM
## -0.71298582 -0.83492305 -0.86258539 -0.97748107 -1.07987398 -1.29956496
## BAC INTC HD MCD AXP KRFT
## -1.43109457 -1.63340580 -1.63690112 -1.67981865 -1.77057285 -2.12430403print(formula)## percent_change_next_weeks_price ~ . - quarter - date - next_weeks_open -
## next_weeks_close - previous_weeks_volume - open - high -
## low - stock_return