# Application: Why do I care?

Suppose you were given a number of loans of grade B-2 to choose from. Since all of them are in the same sub-grade, they pay the same interest rate. Is random selection good enough, or it possible to beat the average return in a statistically reliable way?

Viewed as a black box, the model takes in loan features as input and returns the predicted rate of return. What we'll be doing here is to use our the predicted rate of return to rank the loans, and attempt to beat the average by choosing the top quartile. We'll then compare the average rate of return of the loans in the top quartile against the sub-grade average.

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In [13]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.ensemble import RandomForestRegressor
from transfers.fileio import load_from_pickle
from helpers.preprocessing import process_payment, process_features
from model.model import StatusModel
from model.validate import actual_IRR

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In [14]:

# Load data, then pre-process
df_raw = pd.concat((df_3c, df_3b), axis=0)

# Pre-process data
print "Pre-processing data..."
df_features = process_features(df_raw)

# Train models for every grade for every month
print "Training models..."
model = StatusModel(model=RandomForestRegressor, parameters={'n_estimators':100, 'max_depth':10})
model.train_model(df_features)

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Pre-processing data...
Training models...
A training completed...
B training completed...
C training completed...
D training completed...

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In [15]:

# Load data, then pre-process
df_raw = df_3a.copy()

# Pre-process data
print "Pre-processing data..."
df_features = process_features(df_raw, True, False)

# Calculating expected rate of return for loans already matured
print "Calculating rate of return..."
int_rate_dict = {'A1':0.0603, 'A2':0.0649, 'A3':0.0699, 'A4':0.0749, 'A5':0.0819,
'B1':0.0867, 'B2':0.0949, 'B3':0.1049, 'B4':0.1144, 'B5':0.1199,
'C1':0.1239, 'C2':0.1299, 'C3':0.1366, 'C4':0.1431, 'C5':0.1499,
'D1':0.1559, 'D2':0.1599, 'D3':0.1649, 'D4':0.1714, 'D5':0.1786}

rate_predict = model.expected_IRR(df_features, False, int_rate_dict)

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Pre-processing data...
Calculating rate of return...

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In [16]:

# Pre-process data
print "Pre-processing data..."
df_payment = process_payment(df_raw)

# Calculating actual rate of return for loans already matured with Dec 2014 int_rate
print "Calculating rate of return..."

# Replace int_rate with values set in Dec 2015 by sub_grade
int_rate_dict = {'A1':0.0603, 'A2':0.0649, 'A3':0.0699, 'A4':0.0749, 'A5':0.0819,
'B1':0.0867, 'B2':0.0949, 'B3':0.1049, 'B4':0.1144, 'B5':0.1199,
'C1':0.1239, 'C2':0.1299, 'C3':0.1366, 'C4':0.1431, 'C5':0.1499,
'D1':0.1559, 'D2':0.1599, 'D3':0.1649, 'D4':0.1714, 'D5':0.1786}

rate_true = actual_IRR(df_payment, False, int_rate_dict)

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Pre-processing data...
Calculating rate of return...

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In [17]:

df_select = df_features[['id', 'sub_grade']]

df_select['rate_true'] = rate_true
df_select['rate_predict'] = rate_predict

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Now that we have the predicted rate of return for each loan, we can rank the loans and identify which loans fall into the top quartile of each sub-grade band. We then compare the average actual return of the top quartile against the average actual return of the whole sub-grade band.

For the purpose of comparison, we do the same for the bottom quartile.

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In [18]:

sub_grade_range = ['A1', 'A2', 'A3', 'A4', 'A5',
'B1', 'B2', 'B3', 'B4', 'B5',
'C1', 'C2', 'C3', 'C4', 'C5',
'D1', 'D2', 'D3', 'D4', 'D5']

average_list = []
top_list = []
bottom_list = []

top_IRR = df_select[df_select['id'].isin(id_top)]['rate_true'].values.mean()
bottom_IRR = df_select[df_select['id'].isin(id_bottom)]['rate_true'].values.mean()

average_list.append(average_IRR)
top_list.append(top_IRR)
bottom_list.append(bottom_IRR)

print 'Average IRR of %s:                %f' % (sub_grade, average_IRR)
print 'Actual IRR of top quartile:      ', top_IRR
print 'Actual IRR of bottom 10 quartile:', bottom_IRR, '\n'

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Average IRR of A1:                0.054840
Actual IRR of top quartile:       0.0609649358862
Actual IRR of bottom 10 quartile: 0.0479582747645

Average IRR of A2:                0.054009
Actual IRR of top quartile:       0.0617128185805
Actual IRR of bottom 10 quartile: 0.0455468922785

Average IRR of A3:                0.058820
Actual IRR of top quartile:       0.0658823684175
Actual IRR of bottom 10 quartile: 0.0531802151515

Average IRR of A4:                0.063289
Actual IRR of top quartile:       0.0729703370975
Actual IRR of bottom 10 quartile: 0.0542778271452

Average IRR of A5:                0.066053
Actual IRR of top quartile:       0.076326752739
Actual IRR of bottom 10 quartile: 0.0495989199483

Average IRR of B1:                0.065036
Actual IRR of top quartile:       0.0782048952685
Actual IRR of bottom 10 quartile: 0.0598065915381

Average IRR of B2:                0.074596
Actual IRR of top quartile:       0.0861272389098
Actual IRR of bottom 10 quartile: 0.067878864993

Average IRR of B3:                0.082055
Actual IRR of top quartile:       0.0879444375318
Actual IRR of bottom 10 quartile: 0.0763224566661

Average IRR of B4:                0.089151
Actual IRR of top quartile:       0.107760897919
Actual IRR of bottom 10 quartile: 0.0674763278059

Average IRR of B5:                0.094420
Actual IRR of top quartile:       0.113305029251
Actual IRR of bottom 10 quartile: 0.0782373558138

Average IRR of C1:                0.094693
Actual IRR of top quartile:       0.111661636407
Actual IRR of bottom 10 quartile: 0.0713285488386

Average IRR of C2:                0.095258
Actual IRR of top quartile:       0.107181515047
Actual IRR of bottom 10 quartile: 0.0825596304619

Average IRR of C3:                0.093860
Actual IRR of top quartile:       0.0968144006752
Actual IRR of bottom 10 quartile: 0.0747091212339

Average IRR of C4:                0.106270
Actual IRR of top quartile:       0.123439262441
Actual IRR of bottom 10 quartile: 0.0829277686622

Average IRR of C5:                0.111463
Actual IRR of top quartile:       0.133481380903
Actual IRR of bottom 10 quartile: 0.0794123661788

Average IRR of D1:                0.114010
Actual IRR of top quartile:       0.129431513537
Actual IRR of bottom 10 quartile: 0.0869874716797

Average IRR of D2:                0.120886
Actual IRR of top quartile:       0.139640911826
Actual IRR of bottom 10 quartile: 0.0943985976305

Average IRR of D3:                0.121501
Actual IRR of top quartile:       0.135473825402
Actual IRR of bottom 10 quartile: 0.0974996755731

Average IRR of D4:                0.123292
Actual IRR of top quartile:       0.153563208667
Actual IRR of bottom 10 quartile: 0.0987375235712

Average IRR of D5:                0.137635
Actual IRR of top quartile:       0.157133471078
Actual IRR of bottom 10 quartile: 0.0903370979012

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Finally, we plot the average overall return, as well as the average return of the top and bottom quartiles. We are able to beat the average of 9.1% by 1.3%.

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In [19]:

plt.figure(figsize = (12, 6))
x = xrange(20)

plt.plot(x, average_list, label='Average IRR')
plt.plot(x, top_list, label='Top quartile IRR')
plt.plot(x, bottom_list, label='Bottom quartile IRR')
plt.ylabel('IRR')
plt.legend(loc='best')
plt.title("Performance of selective loan selection strategy")

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Out[19]:

<matplotlib.text.Text at 0x10ae63050>

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