APT application on Apple, MSFT, INTC Stock

Dataset

import pandas as pd import matplotlib.pyplot as plt import datetime import seaborn as sns import warnings !warnings.filterwarnings('ignore')

/bin/bash: -c: line 0: syntax error near unexpected token `'ignore''
/bin/bash: -c: line 0: `warnings.filterwarnings('ignore')'

from pandas_datareader import data as pdr import yfinance as yf yf.pdr_override()

stocks = ['AAPL','MSFT','INTC'] start = datetime.datetime(2012,1,1) end = datetime.datetime(2020,1,1) stock_prices = yf.download(stocks,start=start,end = end, interval='3mo') stock_prices.head()

[*********************100%***********************]  3 of 3 completed

Adj Close AAPLfloat64

Adj Close INTCfloat64

2012-01-01 00:00:00

18.252399444580078

20.153919219970703

2012-04-01 00:00:00

17.779001235961914

19.252975463867188

2012-07-01 00:00:00

20.308860778808594

16.489116668701172

2012-10-01 00:00:00

16.270668029785156

15.136100769042969

2013-01-01 00:00:00

13.595793724060059

16.19683837890625

stock_prices=stock_prices['Close'] stock_prices.dropna(inplace=True) stock_prices.head(10)

AAPLfloat64

14.161786079406738 - 23.825000762939453

INTCfloat64

20.6200008392334 - 30.899999618530273

2012-01-01 00:00:00

21.412500381469727

28.1200008392334

2012-04-01 00:00:00

20.85714340209961

26.649999618530273

2012-07-01 00:00:00

23.825000762939453

22.65999984741211

2012-10-01 00:00:00

19.006071090698242

20.6200008392334

2013-01-01 00:00:00

15.809286117553711

21.84000015258789

2013-04-01 00:00:00

14.161786079406738

24.229999542236328

2013-07-01 00:00:00

17.02678680419922

22.920000076293945

2013-10-01 00:00:00

20.036428451538086

25.959999084472656

2014-01-01 00:00:00

19.169286727905273

25.809999465942383

2014-04-01 00:00:00

23.232500076293945

30.899999618530273

stock_prices.describe()

AAPLfloat64

INTCfloat64

count

32.0

mean

32.35193094611168

35.91500002145767

std

13.747597193055293

10.615415412821108

min

14.161786079406738

20.6200008392334

25%

22.77750015258789

27.752500534057617

50%

27.928750038146973

34.095001220703125

75%

40.062500953674316

46.35249996185303

max

73.4124984741211

59.849998474121094

fig = plt.figure() ax1 = fig.add_axes([0.1,0.1,0.8,0.8]) ax1.plot(stock_prices.AAPL,label='Apple') ax1.plot(stock_prices.INTC,label='Intel') ax1.plot(stock_prices.MSFT,label='Microsoft') ax1.set_xlabel('Date') ax1.set_ylabel('Stock Price') ax1.set_title('Stock Prices') plt.legend() plt.show()

returns=stock_prices.pct_change() returns.dropna(inplace=True) returns.head()

AAPLfloat64

INTCfloat64

2012-04-01 00:00:00

-0.0259361106585535

-0.05227600202102978

2012-07-01 00:00:00

0.1422945272812901

-0.14971856766346214

2012-10-01 00:00:00

-0.2022635684334252

-0.09002643521251785

2013-01-01 00:00:00

-0.16819809617091608

0.05916582268188941

2013-04-01 00:00:00

-0.10421090654546916

0.10943220572117252

The distribution of the stocks

k=1 for i in range(0, len(returns.columns)): plt.subplot(3, 1, k) plt.hist(returns[returns.columns[i]]) plt.title('{}'.format(returns.columns[i])) k+=1 plt.tight_layout() plt.show()

Correlation Analysis

heat_corr=returns.corr() sns.heatmap(heat_corr, annot=True) plt.title('Correlation Matrix') plt.show()

Collecting the Macroeconomic Variables

At this point, I start collecting macroeconomic variables to be used in APT. These are: Quarterly GDP per capita growth, quarterly inflation growth, and quarterly oil price growth. I use two main database which are: * FRED * QUANDL

from fredapi import Fred apikey = 'f9ed611c3fd3fcfc1a0ffb5e7cac7422' fred = Fred(api_key=apikey)

fred.search('risk free')

idobject

DGS102.9%

GS102.9%

33 others94.3%

realtime_startdatetime64[ns]

2023-01-08 00:00:00 - 2023-01-08 00:00:00

DGS10

2023-01-08 00:00:00

GS10

2023-01-08 00:00:00

WGS10YR

2023-01-08 00:00:00

DGS2

2023-01-08 00:00:00

DGS1

2023-01-08 00:00:00

GS2

2023-01-08 00:00:00

WGS2YR

2023-01-08 00:00:00

GS1

2023-01-08 00:00:00

WGS1YR

2023-01-08 00:00:00

DGS5

2023-01-08 00:00:00

risk_free=fred.get_series('GS3M') #risk_free risk_free=risk_free['2012-1-1':'2020-1-1'] risk_free rf=risk_free/100

rf.head(5)

rf=rf.resample('Q').mean()*3

plt.plot(risk_free) plt.xlabel('Date') plt.ylabel('%') plt.title('3-Month Treasury Constant Maturity Rate')

So, we have a risk-free rate. Let’s move on and gather GDP growth, inflation growth, and oil return data.

GDP

gdp=fred.get_series('GDP') gdp=gdp['2012-1-1':'2020-1-1'] gdp.tail()

gdp_growth=gdp.pct_change().dropna()

gdp_growth.head(5)

plt.plot(gdp_growth) plt.ylabel('GDP Growth Rate') plt.xlabel('Date') plt.title('GDP Growth Rate, 2012–2020')

Inflation

fred.search('potential inflation') inf=fred.get_series('CPIEALL') inf=inf['2012-1-1':'2020-1-1']

print(inf.head()) print(inf.tail())

2012-01-01    243.820
2012-02-01    244.783
2012-03-01    246.291
2012-04-01    246.995
2012-05-01    246.813
dtype: float64
2019-09-01    279.587
2019-10-01    280.303
2019-11-01    280.376
2019-12-01    280.315
2020-01-01    281.482
dtype: float64

inf_quarterly=inf.resample('Q').mean() inf_growth=inf_quarterly.pct_change().dropna() inf_growth.head()

plt.plot(inf_growth) plt.ylabel('Inflation Growth Rate') plt.xlabel('Date') plt.title('Inflation Growth Rate, 2012–2020')

Oil Price

import quandl oil=quandl.get('ODA/POILBRE_USD', authtoken='LshasBpoXsU_NdH1mkxq', start_date='2012-1-1', end_date='2020-1-1')

oil_quarterly=oil.resample('Q').mean()

oil_quarterly

Valuefloat64

35.19993098688751 - 118.42796536796538

2012-03-31 00:00:00

118.42796536796538

2012-06-30 00:00:00

109.0604071773637

2012-09-30 00:00:00

110.13382674571805

2012-12-31 00:00:00

110.42449149883934

2013-03-31 00:00:00

112.8671801242236

2013-06-30 00:00:00

103.09964492753623

2013-09-30 00:00:00

110.26686805947675

2013-12-31 00:00:00

109.61320879603488

2014-03-31 00:00:00

108.21101725327811

2014-06-30 00:00:00

110.02562049062048

oil_return=oil_quarterly.pct_change().dropna() oil_return.head()

Valuefloat64

2012-06-30 00:00:00

-0.07909920736623244

2012-09-30 00:00:00

0.009842431328985102

2012-12-31 00:00:00

0.002639195982832687

2013-03-31 00:00:00

0.022120895394025286

2013-06-30 00:00:00

-0.08654008353834164

plt.plot(oil_return) plt.ylabel('Oil Return') plt.xlabel('Date') plt.title('Oil Return, 2012–2020')

returns=returns.reset_index() returns.drop('Date',axis=1,inplace=True)

rf=pd.DataFrame(rf) rf=rf.reset_index() rf.drop('index',axis=1,inplace=True) rf.columns=['rf'] returns['rf']=pd.DataFrame(rf)

stocks=['AAPL','INTC','MSFT'] for i in stocks: returns['excess_return_'+str(i)]=returns[i]-returns.rf

returns.head(5)

AAPLfloat64

INTCfloat64

-0.0259361106585535

-0.05227600202102978

0.1422945272812901

-0.14971856766346214

-0.2022635684334252

-0.09002643521251785

-0.16819809617091608

0.05916582268188941

-0.10421090654546916

0.10943220572117252

oil_return

Valuefloat64

-0.28733670048231574 - 0.3346877391156644

2012-06-30 00:00:00

-0.07909920736623244

2012-09-30 00:00:00

0.009842431328985102

2012-12-31 00:00:00

0.002639195982832687

2013-03-31 00:00:00

0.022120895394025286

2013-06-30 00:00:00

-0.08654008353834164

2013-09-30 00:00:00

0.06951743759135165

2013-12-31 00:00:00

-0.005927975238122163

2014-03-31 00:00:00

-0.012792176765538565

2014-06-30 00:00:00

0.016769117261832278

2014-09-30 00:00:00

-0.06774064877456853

gdp_growth=gdp_growth.reset_index() inf_growth=inf_growth.reset_index() oil_return=oil_return.reset_index() gdp_growth.drop('index',axis=1,inplace=True) inf_growth.drop('index',axis=1,inplace=True) oil_return.drop('Date',axis=1,inplace=True) gdp_growth.columns=["gdp_growth"] inf_growth.columns=["inf_growth"] oil_return.columns=["oil_return"]

data1=pd.concat([gdp_growth, inf_growth,oil_return,returns.excess_return_AAPL], axis=1) data2=pd.concat([gdp_growth, inf_growth,oil_return,returns.excess_return_INTC], axis=1) data3=pd.concat([gdp_growth, inf_growth,oil_return,returns.excess_return_MSFT], axis=1)

data1.head()

gdp_growthfloat64

inf_growthfloat64

0.008607101552671192

0.007660968792778222

0.0069358362646565475

0.002695388670725052

0.006179463391737583

0.0006504875289554679

0.01270761844453605

0.0063647118517689005

0.004239628842297005

0.0053307869664531715

data1['excess_return']=returns.excess_return_AAPL data2['excess_return']=returns.excess_return_INTC data3['excess_return']=returns.excess_return_MSFT

data1

gdp_growthfloat64

-0.007762640296478551 - 0.01857307401809405

inf_growthfloat64

-0.005344174174330307 - 0.010933057637632526

0.008607101552671192

0.007660968792778222

0.0069358362646565475

0.002695388670725052

0.006179463391737583

0.0006504875289554679

0.01270761844453605

0.0063647118517689005

0.004239628842297005

0.0053307869664531715

0.012666029164496662

0.00389241710322219

0.013130217441027492

-0.001975766056577566

0.0006517787717981172

0.008666233819688784

0.01857307401809405

0.01091775484414459

0.016064179754989638

0.0019037102818584284

Arbitrage pricing model

# Load required packages import statsmodels.api as smfmodels models= [] for i in (data1,data2,data3): formula = "excess_return~ gdp_growth+inf_growth+oil_return" models.append(smfmodels.OLS.from_formula(formula, data = i).fit())

First model output shows the association between excess return of Apple and pre-defined macroeconomic variables. Accordingly, the estimated coefficient of the model is not statistically significant indicating that these macroeconomic variables do not account for the excess return of Apple. More specifically, by looking at p-values, I conclude that the estimated coefficients of gdp growth, inflation growth, and oil return is not statistically significant at conventional levels.

1. AAPL Stock

models[0].summary()

The R-squared value of 0.145 indicates that the model explains about 14.5% of the variance in the dependent variable. The adjusted R-squared value of 0.050 is a modified version that adjusts for the number of independent variables in the model and the sample size.

The F-statistic of 1.531 and the associated p-value of 0.229 indicate that the model as a whole is not a significant predictor of the dependent variable. This means that the independent variables in the model do not significantly improve the prediction of the dependent variable beyond the intercept.

The coefficients table shows the estimated values of the model parameters, along with the standard errors, t-values, and p-values. The t-values and p-values are used to assess the statistical significance of each independent variable. A t-value greater than 2 and a p-value less than 0.05 indicates that the corresponding independent variable is a significant predictor of the dependent variable. In this case, only the gdp_growth variable has a statistically significant t-value and p-value.

We can see the same thing for INTC and MSFT stocks

2. INTC Stock

models[1].summary()

3. MSFT Stock

models[2].summary()

Conclusion

The results of the models suggest that APT cannot be validated by using US macroeconomic variables except for the GDP growth in Intel's case. As a final note, the variance in the dependent variable explained by an independent variable is quite low. This also implies that the model has very weak explanatory power and this needs to be improved. There are some ways to do that but two main possible modifications may be:

Using additional variables which might be more related to excess stock return lke news (see this article )

Using a different model

Testing in a different time period and country

.css-ytumd6{-webkit-text-decoration:none;text-decoration:none;}APT application on Apple, MSFT, INTC Stock

Dataset

The distribution of the stocks

Correlation Analysis

Collecting the Macroeconomic Variables

GDP

Inflation

Oil Price

Arbitrage pricing model

1. AAPL Stock

2. INTC Stock

3. MSFT Stock

Conclusion

APT application on Apple, MSFT, INTC Stock