Fidelity Mini Exercise Using R
Jason Chan
October 31, 2016
Libraries Used
library(Quandl) #to get VIX and Oil Price data
library(randomForest) # to predict net sales
library(plotly) #better visualization
library(rpart) # Recursive Partitioning and Regression Trees (RPART)
library(rattle) #fancy R plot
library(caret) #Classification and Regression Training (CARET)
library(caretEnsemble) #package of machine learning models Business Objective
Show how the net sales of Hong Kong Equity Fund and Global Bond Fund will change if the Oil Price and VIX increases and decreases by 5%.
Data Exploration
Target Variables:
These historical target variables data were obtained from the Hong Kong Investment Funds Association (HKIFA)
- Hong Kong Equity Fund (HKEF)
- Global Bond Fund (GBF)
Features:
Data for features were convenient obtained using the Quandl package (getsymbols) from R.
- Oil Price
- Volatility Index (VIX)
Time Frame & Frequency
- Past 5 years
- Exclude too old data, not reflective of present changes
- Monthly
- Daily data not available for target variable and annually have too little data points
- Daily data not available for target variable and annually have too little data points
Change Instead of Absolute
- The dataset has been manipulated into its percentage change as the business objective specifies the change instead of the absolute value.
head(RawData)## Date HKEF GBF VIX Oil_Price
## 1 2010-12-31 60.56 -39.39 17.15 93.23
## 2 2011-01-31 128.34 -112.56 19.53 98.97
## 3 2011-02-28 100.69 -47.83 18.35 112.27
## 4 2011-03-31 66.58 12.43 17.74 116.94
## 5 2011-04-29 -33.78 17.25 14.75 126.59
## 6 2011-05-31 61.66 72.28 15.45 117.18head(Data)## Date HKEF GBF VIX Oil_Price
## 1 2011-01-31 1.11922061 1.8575781 0.13877551 0.06156817
## 2 2011-02-28 -0.21544335 -0.5750711 -0.06041987 0.13438416
## 3 2011-03-31 -0.33876254 -1.2598787 -0.03324251 0.04159615
## 4 2011-04-29 -1.50735957 0.3877715 -0.16854566 0.08252095
## 5 2011-05-31 -2.82534044 3.1901449 0.04745763 -0.07433447
## 6 2011-06-30 -0.02854363 1.9673492 0.06925566 -0.04668032Visualization
Preliminary visualization helps us understand the data better before coming out with an estimation model.
HKEF
Price of the HKEF is plotted against the Oil Price and VIX to have an idea of it’s movements.
GBF
Price of the GBF is plotted against the Oil Price and VIX to have an idea of it’s movements.
Insights
From visualizing our data, we have an idea that:
- Variables are not linear
- So that we dont use linear models to estimate our data
- Generalized Linear Model (GLM), etc
\(\qquad \qquad \qquad \qquad y\quad =\quad { \beta }_{ 0 }\quad +\quad { \beta }_{ 1 }{ X }_{ 1 }\quad +\quad { \beta }_{ 2 }{ X }_{ 2 }\)
- Movement of target variables
- HKEF and GBF moves in opposite direction with the features
- Stronger validation and provides an intuition to our estimated answer
Predicting the Change
Based on our findings from the preliminary visualization, we can see that our data is not linear. Hence, it is best we avoid using linear regression models which are invalid.
Tree Based Regression
Tree based models does not assume linearity in data. In fact, a tree based model maps observations about an item (branches) to conclusions about the item’s target value (leaves). Think of it as the motherload of nested if-else statements.
Example of estimating employment with tree depth of 3:
How Does it Compare ?
The diagrams shows an attempt using linear regression and tree based regression. 
Random Forest
- Grows multiple trees as far as possible
- Randomness to prevent building the same tree
- Helps prevent overfitting by using multiple trees and emsembling
HKEF & GBF
Code preview and predicted change:
fit <- randomForest(HKEF ~ VIX + Oil_Price, data = Data, ntree=2000, importance = TRUE)
VIX <- c(0.05, -0.05)
Oil_Price <- c(0.05, -0.05)
change <- data.frame("Change in VIX" = VIX, "Change in Oil_Price" = Oil_Price )
predictions <- predict(fit, change)
change$Change.in.HKEF <- predictions
fit2 <- randomForest(GBF ~ VIX + Oil_Price, data = Data, ntree=2000)
change2 <- data.frame("Change in VIX" = VIX, "Change in Oil_Price" = Oil_Price )
predictions2 <- predict(fit2, change2)
change$Change.in.GBF <- predictions2Prediction
## Change.in.VIX Change.in.Oil_Price Change.in.HKEF Change.in.GBF
## 1 0.05 0.05 0.22 -0.10
## 2 -0.05 -0.05 0.73 0.47Evaluation
Calculating the Mean Absolute Error (MAE) for predicting HKEF & GBF
#HKEF
mae <- mean(abs(Data$HKEF - predict(fit, Data[, 4:5])))
mae## [1] 2.672729#GBF
mae <- mean(abs(Data$GBF - predict(fit2, Data[ , 4:5])))
mae## [1] 0.886063What Now ?
Despite the errors being large due to volatility of the target variables:
- feature engineering using VIX and Oil Price. i.e, lags, VIX_2monthslag, OilPrice2monthslag
- predict using other models(non linear) -
Updated Dataset
## Date HKEF GBF VIX VIX_last2 VIX_last3
## 1 5/31/11 -2.82534044 3.19014493 0.04745763 -0.16854566 -0.03324251
## 2 6/30/11 -0.02854363 1.96734920 0.06925566 0.04745763 -0.16854566
## 3 7/29/11 -0.09899833 0.08373741 0.52845036 0.06925566 0.04745763
## 4 8/31/11 0.20511395 -0.48958871 0.25227723 0.52845036 0.06925566
## 5 9/30/11 -0.92220172 -0.14430209 0.35863378 0.25227723 0.52845036
## 6 10/31/11 -5.39328063 0.56648936 -0.30260708 0.35863378 0.25227723
## VIX_last4 VIX_last5 VIX_3months_average VIX_5months_average
## 1 -0.06041987 0.13877551 -0.05144351 -0.01519498
## 2 -0.03324251 -0.06041987 -0.01727746 -0.02909895
## 3 -0.16854566 -0.03324251 0.21505455 0.08867510
## 4 0.04745763 -0.16854566 0.28332775 0.14577904
## 5 0.06925566 0.04745763 0.37978712 0.25121493
## 6 0.52845036 0.06925566 0.10276798 0.18120199
## Oil_Price Oil_Price_last2 Oil_Price_last3 Oil_Price_last4
## 1 -0.074334466 0.082520951 0.041596152 0.13438416
## 2 -0.046680321 -0.074334466 0.082520951 0.04159615
## 3 0.037776385 -0.046680321 -0.074334466 0.08252095
## 4 0.004744242 0.037776385 -0.046680321 -0.07433447
## 5 -0.094951923 0.004744242 0.037776385 -0.04668032
## 6 0.028552457 -0.094951923 0.004744242 0.03777639
## Oil_Price_last5 Oil_Price_3months_average Oil_Price_5months_average
## 1 0.06156817 0.016594212 0.049146992
## 2 0.13438416 -0.012831279 0.027497295
## 3 0.04159615 -0.027746134 0.008175740
## 4 0.08252095 -0.001386565 0.000805358
## 5 -0.07433447 -0.017477099 -0.034689217
## 6 -0.04668032 -0.020551741 -0.014111832Using CARET
Stands for Classification and Regression Training (CARET).
- consist of many famous machine learning packages
- call different machine learning models such as xgbtree, knn, random forest, extraTrees
- Choose the weightage that gives the lowest Mean Absolute Error (MAE)
HKEF
## rf rf.1 xgbLinear xgbTree kknn extraTrees
## rf 1.00 0.43 0.58 0.57 -0.08 0.35
## rf.1 0.43 1.00 0.25 0.44 0.29 0.72
## xgbLinear 0.58 0.25 1.00 0.34 -0.23 0.35
## xgbTree 0.57 0.44 0.34 1.00 -0.27 0.71
## kknn -0.08 0.29 -0.23 -0.27 1.00 -0.02
## extraTrees 0.35 0.72 0.35 0.71 -0.02 1.00## A glmnet ensemble of 2 base models: rf, rf, xgbLinear, xgbTree, kknn, extraTrees
##
## Ensemble results:
## glmnet
##
## 46 samples
## 6 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 42, 41, 41, 41, 42, 42, ...
## Resampling results across tuning parameters:
##
## alpha lambda MAE
## 0.10 0.0009849867 0.4325490
## 0.10 0.0098498665 0.4325490
## 0.10 0.0984986654 0.4437686
## 0.55 0.0009849867 0.5798329
## 0.55 0.0098498665 0.5798329
## 0.55 0.0984986654 0.5754898
## 1.00 0.0009849867 0.5794388
## 1.00 0.0098498665 0.5807361
## 1.00 0.0984986654 0.5276956
##
## MAE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 0.1 and lambda
## = 0.009849867.HKEF Prediction
## Change.in.VIX Change.in.Oil_Price Change.in.HKEF
## 1 0.05 0.05 -0.41790984
## 2 -0.05 -0.05 0.01335041GBF
## rf rf.1 xgbLinear xgbTree kknn extraTrees
## rf 1.00 0.89 -0.16 0.74 0.37 0.60
## rf.1 0.89 1.00 0.07 0.56 0.58 0.79
## xgbLinear -0.16 0.07 1.00 0.11 0.09 0.12
## xgbTree 0.74 0.56 0.11 1.00 0.23 0.16
## kknn 0.37 0.58 0.09 0.23 1.00 0.73
## extraTrees 0.60 0.79 0.12 0.16 0.73 1.00## A glmnet ensemble of 2 base models: rf, rf, xgbLinear, xgbTree, kknn, extraTrees
##
## Ensemble results:
## glmnet
##
## 46 samples
## 6 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 40, 42, 41, 41, 41, 42, ...
## Resampling results across tuning parameters:
##
## alpha lambda MAE
## 0.10 0.0007280638 0.3244459
## 0.10 0.0072806380 0.3244459
## 0.10 0.0728063801 0.3244459
## 0.55 0.0007280638 0.3177243
## 0.55 0.0072806380 0.3177243
## 0.55 0.0728063801 0.3092113
## 1.00 0.0007280638 0.3304099
## 1.00 0.0072806380 0.3292084
## 1.00 0.0728063801 0.2999794
##
## MAE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.07280638.GBF Prediction
## Change.in.VIX Change.in.Oil_Price Change.in.GBF
## 1 0.05 0.05 -0.04026385
## 2 -0.05 -0.05 0.12993277Conclusion
Though we managed to answer the business objective:
- HKEF and GBF data are very volatile
- VIX and Oil Price are not really good predictors
- By feature engineering and using CARET, we reduced the errors of our prediction model
- Outside of question scope, try other features such as HSI and interest rate, which might be better predictors