This is an analysis of the stock prices of 300 high-tech companies based in China, using 16 financial indicators as independent variables. In order to reduce the dimensionality of the dataset, we will be performing Principal Component Analysis (PCA) on the data. After which, we will attempt to fit a regression to the data and conduct K-means clustering on the sample.
stock = read.csv('stkpc_analysis1.csv',header=T, sep=",", row.names=1)
stock2 = read.csv('stkpc_analysis1.csv')
pca <- prcomp(stock[2:17], center = TRUE, scale. =TRUE)
pca2 <- prcomp(stock2[3:18], center = TRUE, scale. =TRUE) #without scaling
summary(pca)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 2.1526 1.8636 1.2870 1.12791 1.07534 1.00220
## Proportion of Variance 0.2896 0.2171 0.1035 0.07951 0.07227 0.06277
## Cumulative Proportion 0.2896 0.5067 0.6102 0.68971 0.76198 0.82476
## PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.93517 0.83553 0.76182 0.58420 0.37911 0.25505
## Proportion of Variance 0.05466 0.04363 0.03627 0.02133 0.00898 0.00407
## Cumulative Proportion 0.87941 0.92305 0.95932 0.98065 0.98963 0.99370
## PC13 PC14 PC15 PC16
## Standard deviation 0.22086 0.17649 0.13389 0.05467
## Proportion of Variance 0.00305 0.00195 0.00112 0.00019
## Cumulative Proportion 0.99675 0.99869 0.99981 1.00000
print(pca$rotation)
## PC1 PC2 PC3
## rate.of.return.on.total.assets_ROA_A -0.44224402 0.073868053 -0.043174643
## net.assets.income.rateA -0.43565462 0.149695050 0.002659954
## operating.profit.ratio -0.41838654 0.011077526 0.035680902
## Sales.Margin.rate -0.42846830 -0.002899346 0.065164067
## turnover.of.account.receivableA -0.01160320 0.122693913 -0.418485716
## rate.of.stock.turnoverA -0.04008024 0.004083312 -0.050944985
## velocity.of.liquid.assetsA 0.01283187 0.358002946 -0.485599640
## turnover.of.total.capitalA -0.01206318 0.352915222 -0.493149821
## liquidity.ratio -0.09623227 -0.380577724 -0.257872626
## quick.ratio -0.09877442 -0.379858199 -0.251907833
## asset.liability.ratio 0.17587925 0.405077262 0.157893080
## equity.multiplier 0.15531869 0.372018976 0.122986624
## Total.Assets.Growth.RateA -0.07761889 0.275792499 0.282515485
## net.profit.growth.rateA -0.02705228 0.009669171 0.117144018
## increase.rate.of.business.revenue -0.13920350 0.044294057 0.265758804
## sustainable.growth.rate -0.39208811 0.185697955 0.041263870
## PC4 PC5
## rate.of.return.on.total.assets_ROA_A 0.068188737 -0.02905737
## net.assets.income.rateA -0.015013679 -0.00753518
## operating.profit.ratio -0.026999228 -0.20332443
## Sales.Margin.rate -0.044307740 -0.11687588
## turnover.of.account.receivableA -0.008441741 0.13114553
## rate.of.stock.turnoverA 0.031405405 -0.30150326
## velocity.of.liquid.assetsA 0.054997487 0.05790117
## turnover.of.total.capitalA 0.066551697 0.12887644
## liquidity.ratio -0.492223595 0.14240290
## quick.ratio -0.497250914 0.13982949
## asset.liability.ratio -0.364983656 -0.02307701
## equity.multiplier -0.448870363 -0.02581236
## Total.Assets.Growth.RateA -0.373312779 0.01610454
## net.profit.growth.rateA 0.117835361 0.72516808
## increase.rate.of.business.revenue 0.069246183 0.49018714
## sustainable.growth.rate -0.040478267 0.09269209
## PC6 PC7
## rate.of.return.on.total.assets_ROA_A 0.0611107801 -0.10640886
## net.assets.income.rateA 0.0568129272 -0.08008401
## operating.profit.ratio 0.0056663012 0.10788521
## Sales.Margin.rate -0.0054873697 0.04425377
## turnover.of.account.receivableA -0.3226459373 0.63177769
## rate.of.stock.turnoverA -0.8875467123 -0.23903170
## velocity.of.liquid.assetsA 0.0793331553 -0.11919148
## turnover.of.total.capitalA 0.1029154149 -0.12331533
## liquidity.ratio 0.0003684995 -0.05787465
## quick.ratio -0.0111023202 -0.05443203
## asset.liability.ratio -0.0209210029 -0.04543759
## equity.multiplier -0.0204698080 -0.06714192
## Total.Assets.Growth.RateA -0.0739224460 0.13490381
## net.profit.growth.rateA -0.2370678050 -0.44526908
## increase.rate.of.business.revenue -0.1428725728 0.48488875
## sustainable.growth.rate 0.0345297431 -0.13604402
## PC8 PC9
## rate.of.return.on.total.assets_ROA_A 0.013238171 -0.052477922
## net.assets.income.rateA -0.031542516 -0.003853726
## operating.profit.ratio 0.100447467 0.232266574
## Sales.Margin.rate 0.165662149 0.248373225
## turnover.of.account.receivableA 0.483158323 0.087846903
## rate.of.stock.turnoverA -0.237868521 -0.043571055
## velocity.of.liquid.assetsA -0.158895648 -0.148714308
## turnover.of.total.capitalA -0.246648374 -0.040999515
## liquidity.ratio -0.103321855 -0.016083346
## quick.ratio -0.099180688 -0.013374941
## asset.liability.ratio 0.009547949 0.277643401
## equity.multiplier -0.017170816 0.408139101
## Total.Assets.Growth.RateA 0.170105804 -0.766558077
## net.profit.growth.rateA 0.385782903 0.082741331
## increase.rate.of.business.revenue -0.619849608 0.085394502
## sustainable.growth.rate -0.048097287 -0.048282444
## PC10 PC11
## rate.of.return.on.total.assets_ROA_A 0.2154127359 -0.064677162
## net.assets.income.rateA 0.2101199381 -0.028769563
## operating.profit.ratio -0.4634231860 -0.090088410
## Sales.Margin.rate -0.3721107771 -0.006499780
## turnover.of.account.receivableA 0.2154488914 0.020711162
## rate.of.stock.turnoverA 0.0065277022 -0.014340430
## velocity.of.liquid.assetsA -0.3697622802 0.641373704
## turnover.of.total.capitalA -0.0506459839 -0.687144201
## liquidity.ratio -0.0029333815 0.027869909
## quick.ratio -0.0007036395 0.002570466
## asset.liability.ratio 0.0496292985 0.082148892
## equity.multiplier 0.0519176942 -0.051523858
## Total.Assets.Growth.RateA -0.1956097315 -0.123980927
## net.profit.growth.rateA -0.1688518388 -0.030812258
## increase.rate.of.business.revenue -0.1007815601 0.037626732
## sustainable.growth.rate 0.5370017154 0.273397334
## PC12 PC13
## rate.of.return.on.total.assets_ROA_A 0.635410276 0.120478457
## net.assets.income.rateA 0.217020490 0.247643935
## operating.profit.ratio -0.068268957 -0.030453768
## Sales.Margin.rate -0.270273199 -0.045871647
## turnover.of.account.receivableA 0.029578263 0.007699905
## rate.of.stock.turnoverA -0.006514900 0.004930651
## velocity.of.liquid.assetsA 0.107120965 -0.033758040
## turnover.of.total.capitalA -0.211078200 -0.009601974
## liquidity.ratio -0.009986703 0.031331071
## quick.ratio 0.003147158 0.060628996
## asset.liability.ratio -0.151678227 0.708043836
## equity.multiplier 0.303440000 -0.585460717
## Total.Assets.Growth.RateA -0.008829424 -0.064676701
## net.profit.growth.rateA 0.029325393 0.008604606
## increase.rate.of.business.revenue 0.049773504 0.009210710
## sustainable.growth.rate -0.543961685 -0.258303295
## PC14 PC15
## rate.of.return.on.total.assets_ROA_A -0.207862646 0.510440305
## net.assets.income.rateA 0.169975517 -0.770801081
## operating.profit.ratio 0.655401884 0.218117691
## Sales.Margin.rate -0.691637868 -0.114230198
## turnover.of.account.receivableA 0.009620330 -0.011022674
## rate.of.stock.turnoverA -0.011949509 -0.005774755
## velocity.of.liquid.assetsA -0.011551844 -0.023103146
## turnover.of.total.capitalA -0.038955691 0.042306806
## liquidity.ratio 0.033550027 -0.007995366
## quick.ratio -0.014141600 0.034330425
## asset.liability.ratio -0.013632798 0.180231281
## equity.multiplier -0.007302468 -0.089972506
## Total.Assets.Growth.RateA -0.017478632 0.007003499
## net.profit.growth.rateA 0.071800435 0.002769287
## increase.rate.of.business.revenue -0.032397847 0.026965094
## sustainable.growth.rate 0.100126657 0.199020981
## PC16
## rate.of.return.on.total.assets_ROA_A -0.0318725332
## net.assets.income.rateA 0.0206583244
## operating.profit.ratio 0.0136487505
## Sales.Margin.rate -0.0185291086
## turnover.of.account.receivableA -0.0036020410
## rate.of.stock.turnoverA -0.0066819873
## velocity.of.liquid.assetsA 0.0159607367
## turnover.of.total.capitalA -0.0083604099
## liquidity.ratio -0.7067524860
## quick.ratio 0.7053437446
## asset.liability.ratio -0.0202666990
## equity.multiplier 0.0079602403
## Total.Assets.Growth.RateA -0.0040199310
## net.profit.growth.rateA 0.0006675884
## increase.rate.of.business.revenue -0.0026678458
## sustainable.growth.rate 0.0117809962
We have created 2 PCA objects, one with scaling and the other without, as a backup.
Let us visualize this discovery using a scree plot below.
screeplot(pca, type = 'l',
main = 'PCA on Stock Price')
It may not be immediately clear which PCs we should select as the kink in the scree plot at PC3 may not be sufficient to explain the variability of the diagram.
We will take a look at their eigenvalues to decide which PCs should be selected.
ev <- pca$sdev^2
print(ev)
## [1] 4.63374849 3.47304513 1.65634120 1.27219009 1.15635905 1.00439849
## [7] 0.87453769 0.69810936 0.58036587 0.34128443 0.14372716 0.06504970
## [13] 0.04877853 0.03114990 0.01792618 0.00298872
The first 6 PCs have eigenvalues above 1, thus we will discard the rest. Cumulatively, the 6 PCs explain 82.5% of the variance in the data, which should be sufficient for our needs.
The first 4 PCs seem to be relatively strongly correlated (about -0.40) to various financial indicators tied to company assets, such as rate of return on total assets and liquidity ratio. These correlations are considered strong as compared to the other variables, which have correlations even lower than -/+ 0.40. This would suggest that these 4 PCs would increase with decreasing asset-based financial ratios.
PC5 is very highly correlated with net profit growth rate, which indicates that this PC is very likely to rise the quicker the company's net profit grows. The 6th and last PC is negatively correlated with the rate of stock turnover, which suggests that the slower that stock is sold or used the higher PC6 increases. However, this is not surprising in the high-tech industry as capital equipment is not frequently replaced or sold.
biplot(pca2, scale = TRUE, expand = 2)
We visualize the orthogonal variables for the first 2 PCs, using the above biplot.
pca$rotation[,1:2]
## PC1 PC2
## rate.of.return.on.total.assets_ROA_A -0.44224402 0.073868053
## net.assets.income.rateA -0.43565462 0.149695050
## operating.profit.ratio -0.41838654 0.011077526
## Sales.Margin.rate -0.42846830 -0.002899346
## turnover.of.account.receivableA -0.01160320 0.122693913
## rate.of.stock.turnoverA -0.04008024 0.004083312
## velocity.of.liquid.assetsA 0.01283187 0.358002946
## turnover.of.total.capitalA -0.01206318 0.352915222
## liquidity.ratio -0.09623227 -0.380577724
## quick.ratio -0.09877442 -0.379858199
## asset.liability.ratio 0.17587925 0.405077262
## equity.multiplier 0.15531869 0.372018976
## Total.Assets.Growth.RateA -0.07761889 0.275792499
## net.profit.growth.rateA -0.02705228 0.009669171
## increase.rate.of.business.revenue -0.13920350 0.044294057
## sustainable.growth.rate -0.39208811 0.185697955
Here, we can see for PC1, the Velocity of liquid Assets , Asset Liablity ratio and Equity multiplier is having negative correlation with everything else, i.e the more assets , likely to have stronger stock price. So, we can call PC1 as "Strong Equity Assets".
For PC2, its intresting as, sales margin , liquidity and quick ratio have neagive impact , comparing to everything else, but sales marin rate is almost negligible. So liquidity and quick ratio have inverse propostion on stock price. so we can call PC2 as "Lower Liquidity holding"
# install.packages('caTools')
stock.re <- data.frame(pca$x)
stock.re$stock_price = stock$stock.price
fit1<- lm(stock_price ~ stock.re$PC1 + stock.re$PC2 + stock.re$PC3 + stock.re$PC4 + stock.re$PC5 + stock.re$PC6, data=stock.re)
summary(fit1)
##
## Call:
## lm(formula = stock_price ~ stock.re$PC1 + stock.re$PC2 + stock.re$PC3 +
## stock.re$PC4 + stock.re$PC5 + stock.re$PC6, data = stock.re)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.839 -6.766 -2.134 4.499 49.698
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 17.4862 0.5298 33.005 < 2e-16 ***
## stock.re$PC1 -1.5872 0.2465 -6.439 4.57e-10 ***
## stock.re$PC2 0.3690 0.2847 1.296 0.19592
## stock.re$PC3 0.1370 0.4123 0.332 0.73983
## stock.re$PC4 -0.6799 0.4705 -1.445 0.14939
## stock.re$PC5 0.5311 0.4935 1.076 0.28268
## stock.re$PC6 -1.4644 0.5295 -2.766 0.00602 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.448 on 311 degrees of freedom
## Multiple R-squared: 0.1483, Adjusted R-squared: 0.1318
## F-statistic: 9.024 on 6 and 311 DF, p-value: 4.228e-09
From the summary of the regression fit, we can tell that PC1 and PC6 are significant in the fit. However, the overall model is not a good fit as told by the adjust R-squared indicator of 13.2%.
par(mfrow = c(2, 2))
plot(fit1)
From the
diagnostic plots, we can see that the model does not follow that of a
linear regression. There is a visible curve in the Normal Q-Q plots,
thus it does not adhere to the dotted straight line. In the
Scale-Location plot, we do not see a straight red line and points which
are very closely positioned together.
Thus a linear regression model is not strong enough to predict the results of this model. There are also a couple of outlier in the dataset, identified in the Residuals vs Leverage plot which can drastically affect the overall analysis when removed.
plot(stock.re[1:6], pch=16, col=rgb(0,0,0,0.5))
Here are twelve 2-D projections of data which are in a 6-D space. You can see there’s a clear outlier in all the dimensions, as well as some bunching together in the different projections.
Let us visualize in a 3-D space below.
# install.packages('rgl')
library(rgl)
# Multi 3D plot
comp <- stock.re[1:6]
plot3d(comp$PC1, comp$PC2, comp$PC3)
plot3d(comp$PC4, comp$PC5, comp$PC6)
plot3d(comp$PC1, comp$PC3, comp$PC4)
Comparing PC1, PC2, PC3
Comparing PC4, PC5, PC6
Comparing PC1, PC3 and PC4
# Reset Within-Cluster Sum of Squares
wcss = vector()
# Determine number of clusters
for (i in 1:10) wcss[i] = sum(kmeans(stock[2:17], i)$withinss)
plot(1:10, wcss, type = 'b',
main = paste('Clusters of Companies'),
xlab = 'Number of clusters',
ylab = 'WCSS')
So here we can see that the “elbow” in the scree plot is at k = 4, so we apply the k-means clustering function with k = 4 and plot.
# Apply k-means with k=4
comp = stock.re[1:6]
k <- kmeans(comp, 4, nstart=25, iter.max=1000)
library(RColorBrewer)
library(scales)
palette(alpha(brewer.pal(9,'Set1'), 0.5))
plot(comp[1:6], col=k$clust, pch=16)
Here, few outliers, with 2 and 3. Lets visualize with 3d plot
plot3d(comp$PC1, comp$PC2, comp$PC3, col=k$clust)
plot3d(comp$PC4, comp$PC5, comp$PC6, col=k$clust)
{ width:100px; }
Comparing PC1, PC2 and PC3 with K-mean clustering
Comparing PC4, PC5 and PC6 with K-mean clustering
#Sorting based on cluster sizes
table(k$clust)
##
## 1 2 3 4
## 1 138 83 96
clust <- names(sort(table(k$clust)))
clust
## [1] "1" "3" "4" "2"
head(k$clust)
## Beijing Ultrapower Software Co.,LTD
## 2
## Lepu Medical Technology (Beijing) Co., Ltd.
## 2
## Toread Holdings Group Co., Ltd.
## 3
## Henan Hanwei Electronics Co.,Ltd.
## 2
## Bestway Marine & Energy Technology Co., Ltd.
## 4
## Anhui Anke Biotechnology (Group) Co., Ltd
## 2
hist(k$clust)
We Can Categorize different Clusters as
- Enery Companies - 109 companies
- Techonology Companies - 128 companies
- PhotoElectric Companies - 1 Company
- Raw Material Companies - 80 Companies
Generate report rmarkdown::render( input="stock.Rmd", output_format="md_document", output_file="README.md" )