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EQ_readme.txt
# stard R Console on MacOS # get a working directory getwd() # change the working directory setwd("/Users/yoshi/Downloads/") dat <- read.csv('EQ_z.csv') head(dat) # SR InstAUMNetFlow Views PassedScreens #1 0.168106 -0.07055196 -0.33920655 -1.70145662 #2 0.155648 -0.09568507 -0.56343473 -1.66043722 #3 -0.335729 -0.13467625 1.28164263 -0.01438553 #4 1.249691 -0.14978894 -0.05731972 -0.77510918 #5 0.502996 -0.13648457 -0.49296294 0.27428721 #6 0.451817 -0.04294418 0.11565621 -0.21678547 # All the data are expressed in z-score. ########## 1.1 Regression Analysis (SR ~ InstAUMNetFlow) reg_InstAUMNetFlow <- lm(SR~InstAUMNetFlow,data=dat) summary(reg_InstAUMNetFlow) #Call: #lm(formula = SR ~ InstAUMNetFlow, data = dat) # #Residuals: # Min 1Q Median 3Q Max #-3.2166 -0.6249 -0.0146 0.6306 2.9913 # #Coefficients: # Estimate Std. Error t value Pr(>|t|) #(Intercept) 0.02248 0.04290 0.524 0.6006 #InstAUMNetFlow 0.51079 0.22452 2.275 0.0233 * #--- #Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # #Residual standard error: 0.9966 on 564 degrees of freedom #Multiple R-squared: 0.009094, Adjusted R-squared: 0.007337 #F-statistic: 5.176 on 1 and 564 DF, p-value: 0.02328 #Multiple R-squared: 0.009094 # InstAUMNetFlow does not explain SR (Sharpe Ratio) very much. plot(dat$InstAUMNetFlow,dat$SR,xlab='Inst AUM Net Flow 1Y (%)',ylab='Sharpe Ratio (USD, 1Y)') abline(reg_InstAUMNetFlow) ########## 1.2 Regression Analysis (SR ~ Views) reg_Views <- lm(SR~Views,data=dat) summary(reg_Views) #Call: #lm(formula = SR ~ Views, data = dat) # #Residuals: # Min 1Q Median 3Q Max #-3.2360 -0.5970 -0.0080 0.6647 2.9892 # #Coefficients: # Estimate Std. Error t value Pr(>|t|) #(Intercept) 0.001304 0.041664 0.031 0.975047 #Views 0.140832 0.041670 3.380 0.000776 *** #--- #Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # #Residual standard error: 0.9912 on 564 degrees of freedom #Multiple R-squared: 0.01985, Adjusted R-squared: 0.01811 #F-statistic: 11.42 on 1 and 564 DF, p-value: 0.0007759 #Multiple R-squared: 0.01985 # Views do not explain SR (Sharpe Ratio) very much. plot(dat$Views,dat$SR,xlab='Views 1Y (%)',ylab='Sharpe Ratio (USD, 1Y)') abline(reg_Views) ########## 1.3 Regression Analysis (SR ~ PassedScreens) reg_PassedScreens <- lm(SR~PassedScreens,data=dat) summary(reg_PassedScreens) #Call: #lm(formula = SR ~ PassedScreens, data = dat) # #Residuals: # Min 1Q Median 3Q Max #-3.2178 -0.5859 -0.0177 0.6604 2.9539 # #Coefficients: # Estimate Std. Error t value Pr(>|t|) #(Intercept) 0.001163 0.041945 0.028 0.9779 #PassedScreens 0.081500 0.042048 1.938 0.0531 . #--- #Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # #Residual standard error: 0.9979 on 564 degrees of freedom #Multiple R-squared: 0.006617, Adjusted R-squared: 0.004856 #F-statistic: 3.757 on 1 and 564 DF, p-value: 0.05309 #Multiple R-squared: 0.006617 # Passed Screens do not explain SR (Sharpe Ratio) very much. plot(dat$PassedScreens,dat$SR,xlab='PassedScreens 1Y (%)',ylab='Sharpe Ratio (USD, 1Y)') abline(reg_PassedScreens) ########## 2 Multiple Regression Analysis (SR ~ InstAUMNetFlow + Views + PassedScreens) ##### multiple regression (with all explanatory variables) reg_multiple <- lm(SR~InstAUMNetFlow+Views+PassedScreens,data=dat) summary(reg_multiple) #Call: #lm(formula = SR ~ InstAUMNetFlow + Views + PassedScreens, data = dat) # #Residuals: # Min 1Q Median 3Q Max #-3.1985 -0.5797 -0.0276 0.6324 3.0271 # # #Coefficients: # Estimate Std. Error t value Pr(>|t|) #(Intercept) 0.02399 0.04253 0.564 0.57288 #InstAUMNetFlow 0.55353 0.22643 2.445 0.01481 * #Views 0.11937 0.04466 2.673 0.00773 ** #PassedScreens 0.05587 0.04542 1.230 0.21916 #--- #Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # #Residual standard error: 0.9872 on 562 degrees of freedom #Multiple R-squared: 0.03122, Adjusted R-squared: 0.02605 #F-statistic: 6.036 on 3 and 562 DF, p-value: 0.0004748 #Multiple R-squared: 0.03122 # R2 is still very small. ##### stepwise regression reg0 <- lm(SR~1,dat) step(reg0,direction='both', scope=list(upper=~InstAUMNetFlow+Views+PassedScreens)) #Start: AIC=1.37 #SR ~ 1 # # Df Sum of Sq RSS AIC #+ Views 1 11.2227 554.15 -7.9799 #+ InstAUMNetFlow 1 5.1412 560.23 -1.8022 #+ PassedScreens 1 3.7411 561.63 -0.3894 #<none> 565.37 1.3683 # #Step: AIC=-7.98 #SR ~ Views # # Df Sum of Sq RSS AIC #+ InstAUMNetFlow 1 4.9513 549.19 -11.0598 #<none> 554.15 -7.9799 #+ PassedScreens 1 0.6017 553.54 -6.5948 #- Views 1 11.2227 565.37 1.3683 # #Step: AIC=-11.06 #SR ~ Views + InstAUMNetFlow # # Df Sum of Sq RSS AIC #<none> 549.19 -11.0598 #+ PassedScreens 1 1.4748 547.72 -10.5818 #- InstAUMNetFlow 1 4.9513 554.15 -7.9799 #- Views 1 11.0328 560.23 -1.8022 # #Call: #lm(formula = SR ~ Views + InstAUMNetFlow, data = dat) # #Coefficients: # (Intercept) Views InstAUMNetFlow # 0.02199 0.13965 0.50131 #As a result of stepwise regression, Views is selected first, InstAUMNetFlow is selected second, and then PassedScreens is rejected. #If you look at a correlation matrix of data, PassedScreens is highly correlated to Views. # cor(dat) # SR InstAUMNetFlow Views PassedScreens #SR 1.00000000 0.09536016 0.14089073 0.08134542 #InstAUMNetFlow 0.09536016 1.00000000 0.01267051 -0.17021810 #Views 0.14089073 0.01267051 1.00000000 0.36147622 #PassedScreens 0.08134542 -0.17021810 0.36147622 1.00000000 ##### multiple regression (after removing PassedScreens) reg_multiple2 <- lm(SR~InstAUMNetFlow+Views,data=dat) summary(reg_multiple2) #Call: #lm(formula = SR ~ InstAUMNetFlow + Views, data = dat) # #Residuals: # Min 1Q Median 3Q Max #-3.1469 -0.6066 0.0004 0.6293 3.0273 # #Coefficients: # Estimate Std. Error t value Pr(>|t|) #(Intercept) 0.02199 0.04252 0.517 0.605257 #InstAUMNetFlow 0.50131 0.22251 2.253 0.024646 * #Views 0.13965 0.04152 3.363 0.000823 *** #--- #Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # #Residual standard error: 0.9877 on 563 degrees of freedom #Multiple R-squared: 0.02861, Adjusted R-squared: 0.02516 #F-statistic: 8.29 on 2 and 563 DF, p-value: 0.0002829 ########## stepwise regression (explained variable: InstAUMNetFlow) reg0 <- lm(InstAUMNetFlow~1,dat) step(reg0,direction='both', scope=list(upper=~SR+Views+PassedScreens)) #Start: AIC=-382.15 #InstAUMNetFlow ~ 1 # # Df Sum of Sq RSS AIC #+ SR 1 1.30504 61.456 -385.74 #<none> 62.761 -382.15 #+ Views 1 0.10122 62.659 -380.58 #+ PassedScreens 1 0.00000 62.761 -380.15 # #Step: AIC=-385.74 #InstAUMNetFlow ~ SR # # Df Sum of Sq RSS AIC #<none> 61.456 -385.74 #+ Views 1 0.09613 61.359 -384.15 #+ PassedScreens 1 0.00373 61.452 -383.75 #- SR 1 1.30504 62.761 -382.15 # #Call: #lm(formula = InstAUMNetFlow ~ SR, data = dat) # #Coefficients: #(Intercept) SR # -0.05398 0.07050 reg_multiple3 <- lm(InstAUMNetFlow~SR,data=dat) summary(reg_multiple3) #Call: #lm(formula = InstAUMNetFlow ~ SR, data = dat) # #Residuals: # Min 1Q Median 3Q Max #-0.7203 -0.1332 -0.0501 0.0531 5.9795 # #Coefficients: # Estimate Std. Error t value Pr(>|t|) #(Intercept) -0.05398 0.02958 -1.825 0.0692 . #SR 0.07050 0.02977 2.368 0.0186 * #--- #Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # #Residual standard error: 0.4825 on 264 degrees of freedom #Multiple R-squared: 0.02079, Adjusted R-squared: 0.01708 #F-statistic: 5.606 on 1 and 264 DF, p-value: 0.01862 plot(dat$SR,dat$InstAUMNetFlow,xlab='Sharpe Ratio (USD, 1Y)',ylab='Inst AUM Net Flow 1Y (%)') abline(reg_multiple3) |
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