Using Implied Cost of Capital as a Sector ETF Valuation Tool

[Sunday 5.10.2015]


This is a follow-up to these posts here and here where I detail the ICC methodology used. All the data and plots have been updated and reflects current information. Scroll to the bottom to see the results of our previous predictions.

The following IPython Notebook examines the Implied Cost of Capital (ICC) method of valuation for purposes of trade/portfolio positioning. The ICC model is a forward looking estimate that uses earnings forecasts to calculate an implied earnings growth rate. The goal of this analysis is to identify asymmetric investing opportunities due to incongruence between "recent" historical returns and forward looking expectations of earnings growth (as measured by the ICC).

Please note: there will be some category overlap as some of the groupings include international sector ETF's while other groupings contain regional and/or country ETF's.


In [1]:
%%javascript
IPython.load_extensions('IPython-notebook-extensions-3.x/usability/runtools/main')
In [2]:
# ================================================================== #
# composite returns; vol; risk adjusted returns; correlation matrix, ICC analysis

import pandas as p
import numpy as np
import pandas.io.data as web
from pandas.tseries.offsets import *
import datetime as dt
import math
import seaborn as sns
sns.set_style('white')

import matplotlib.pyplot as plt
%matplotlib inline
size=(10,8)
import plotly.plotly as py
from plotly.graph_objs import *
import plotly.tools as tls

import cufflinks 

# ================================================================== #

date_today = dt.date.today()
month = 'MAY-2015'

# ~~~ Market Cap ~~~ #
Broad_mkts = ['THRK','RSCO'] # Russell 3000, Russell Small Cap Completeness
Large_cap  = ['ONEK','SPY','SPYG','SPYV'] # Russell 1000, sp500 (growth, value)
Mid_cap    = ['MDY','MDYG', 'MDYV'] # sp400 mid (growth, value)
Small_cap  = ['TWOK','SLY','SLYG','SLYV'] # russ 2K, sp600, (growth, value)

# ~~~ International/Global Equities ~~~ #
Global = [
        'DGT', #  global dow
        'BIK', # sp BRIC 40 ETF
        'GMM', # sp emerging mkts 
        'EWX', # sp emerging mkts small caps
        'CWI', # msci acwi ex-US
        'GII', # global infrastructure
        'GNR', # global natural resources
        'DWX', # intl dividends
        'GWL', # sp developed world ex-US 
        'MDD', # intl mid cap (2B-5B USD)
        'GWX'  # intl small cap (<2B USD)
        ]

Asia   = ['JPP','JSC','GXC','GMF'] # japan, smallcap japan, china, emg asiapac
Europe = ['FEZ','GUR','RBL','FEU'] # euro stoxx 50, emg europe, russia, stoxx europe 50
Latam  = ['GML'] # emg latin america
Africa = ['GAF'] # emg mideast/africa

# ~~~ Real Assets ~~~ #
Real_assets = [ 'RWO', # global real estate
                'RWX', # intl real estate ex-US
                'RWR'  # US select REIT
                ]        

# ~~~ sectors and industries ETF's ~~~ #
Sector = [
          'XLY','XHB','IPD','XRT',                   # consumer discretionary
          'XLP','IPS',                               # consumer staples
          'XLE','IPW','XES','XOP',                   # energy
          'XLF','KBE','KCE','KIE','IPF','KRE',       # financials
          'XLV','XBI','XHE','XHS','IRY','XPH',       # healthcare
          'XLI','XAR','IPN','XTN',                   # industrial
          'XLB','IRV','XME',                         # materials
          'XLK','MTK','IPK','XSD','XSW',             # technology
          'IST','XTL',                               # telecom
          'IPU','XLU'                                # utilities
          ]
   
stock_list = [Broad_mkts, Large_cap, Mid_cap, Small_cap, Global, Asia, Europe, Latam, Africa, Real_assets, Sector]

# ~~~ Category structure ~~~ #
cat = {'Broad_Market'          :['THRK','RSCO'],
       'Large_Cap'             :['ONEK','SPY','SPYG','SPYV'],
       'Mid_Cap'               :['MDY','MDYG', 'MDYV'], 
       'Small_Cap'             :['TWOK','SLY','SLYG','SLYV'],
       'Global_Equity'         :['DGT','BIK','GMM','EWX','CWI','GII','GNR','DWX','GWL','MDD','GWX'],
       'AsiaPac_Equity'        :['JPP','JSC','GXC','GMF'],
       'Europe_Equity'         :['FEZ','GUR','RBL','FEU'],
       'Latam_MidEast_Africa'  :['GML','GAF'],
       'Real_Estate'           :['RWO','RWX','RWR'],
       'Consumer_Discretionary':['XLY','XHB','IPD','XRT'],
       'Consumer_Staples'      :['XLP','IPS'],                         
       'Energy'                :['XLE','IPW','XES','XOP'],                   
       'Financials'            :['XLF','KBE','KCE','KIE','IPF','KRE'],
       'Healthcare'            :['XLV','XBI','XHE','XHS','IRY','XPH'],
       'Industrial'            :['XLI','XAR','IPN','XTN'],
       'Materials'             :['XLB','IRV','XME'],
       'Technology'            :['XLK','MTK','IPK','XSD','XSW'],
       'Telecom'               :['IST','XTL'],                            
       'Utilities'             :['IPU','XLU']
        }    

filepath   = r'C:\Users\Owner\Documents\Visual_Studio_2013\Projects\iVC_Reporting_Engine\PythonApplication2\\'
In [3]:
# ================================================================== #
# get prices
def get_px(stock, start, end):
    '''
    Function to call Pandas' Yahoo Finance API to get daily stock prices.
    
    Parameters:
    ==========
    stock = type('str'); stock symbol 
    start = 3 business days before today; datetime date_today object offset by pandas.DateOffset method 
    end   = today; datetime date_today object

    Returns:
    ========
    time series = Pandas.Series object corresponding to stock symbol, and start/end dates
    **Note that if price column is not specified the function will return a Pandas.DataFrame object
    '''      
    try:
        return web.DataReader(stock, 'yahoo', start, end)['Adj Close']
    except Exception as e:
        print( 'something is fucking up' )

px = p.DataFrame()
for category in stock_list:
    for stock in category:
        px[stock] = get_px( stock, date_today - 252 * BDay(), date_today )
        
# ================================================================== #
# construct dataframe and proper multi index
log_rets = np.log( px / px.shift(1) ).dropna()

lrets = log_rets.T.copy()
lrets.index.name = 'ETF'
lrets['Category'] = p.Series()

for cat_key, etf_val in cat.items():
    for val in etf_val:
        if val in lrets.index:
            idx_loc = lrets.index.get_loc(val)
            lrets.ix[idx_loc,'Category'] = cat_key
        else:
            pass

lrets.set_index('Category', append=True, inplace=True)
lrets = lrets.swaplevel('ETF','Category').sortlevel('Category')
lrets.head()       

# ================================================================== #
# cumulative returns of ETF's
cum_rets = lrets.groupby(level='Category').cumsum(axis=1)
cum_rets.head()

# ================================================================== #
# composite groupings of cumulative ETF returns (equally weighted intra-category mean returns)
composite_rets = p.DataFrame()
for label in cat.keys():
    composite_rets[label] = cum_rets.ix[label].mean(axis=0) # equal weighted mean
    
comp_rets = np.round(composite_rets.copy(),4) # rounding
In [4]:
# ~~~~~ plot code ~~~~~ 
# function to create Plotly 'Layout' object

def create_layout( main_title, y_title ):
    '''
    Function to create custom Plotly layout object to pass to Cufflinks df.iplot() method
    
    Parameters:
    ==========
    
    main_title = type('str')
    y_title    = type('str')

    Returns:
    ========
    plotly_layout = Plotly Layout object basically constructed using a JSON or Dict structure    
    '''    
    plotly_layout = Layout(
        # ~~~~ construct main title
            title=main_title,
            font=Font(
                family='Open Sans, sans-serif',
                size=14,
                color='SteelBlue'
            ),
        # ~~~~ construct X axis
        xaxis=XAxis(
            title='$Date$',
            titlefont=Font(
                family='Open Sans, sans-serif',
                size=14,
                color='SteelBlue'
            ),
            showticklabels=True,
            tickangle=-30,
            tickfont=Font(
                family='Open Sans, sans-serif',
                size=11,
                color='black'
            ),
            exponentformat='e',
            showexponent='All'
        ),
        # ~~~~ construct Y axis
        yaxis=YAxis(
            title= y_title,
            titlefont=Font(
                family='Open Sans, sans-serif',
                size=14,
                color='SteelBlue'
            ),
            showticklabels=True,
            tickangle=0,
            tickfont=Font(
                family='Open Sans, sans-serif',
                size=11,
                color='black'
            ),
            exponentformat='e',
            showexponent='All'),
        # ~~~~ construct figure size
            autosize=False,
            width=850,
            height=500,
            margin=Margin(
            l=50,
            r=20,
            b=60,
            t=50,
            pad=2
            ),
        # ~~~~ construct legend      
            legend=Legend(
            y=0.5,
            #traceorder='reversed',
            font=Font(
                family='Open Sans, sans-serif',
                size=9,
                color='Black'
        ),            
        )
    )
    return plotly_layout
In [5]:
# test the function
title = '<b>Cumulative Log Returns of Composite ETF Sectors [1 Year]</b>'
y_label = '$Returns$'

custom_layout_1 = create_layout( title, y_label )
comp_rets.iplot(theme='white',filename='{}_{}'.format(title, date_today), layout=custom_layout_1, world_readable=True)
Out[5]:
In [6]:
# ================================================================== #
# composite rolling std

sigmas = lrets.groupby(level='Category').std() # equal weighted std

composite_sigs = p.DataFrame()
for label in cat.keys():
    composite_sigs[label] = sigmas.ix[label] 

rsigs = p.rolling_mean( composite_sigs, window=60 ).dropna()*math.sqrt(60)

# ~~~~~ plot code
title = '<b>60-Day Moving Average of Standard Deviation</b>'
#y_label = r'$return \ \sigma$'
y_label = r'$\sigma \ of \ returns$'

custom_layout_2 = create_layout( title, y_label )
rsigs.iplot(theme='white',filename='{}_{}'.format(title, date_today), layout=custom_layout_2, world_readable=True)
Out[6]:
In [7]:
# ================================================================== #
# composite rolling risk adjusted returns

mean_rets = lrets.groupby(level='Category').mean() # equal weighted mean
#risk_rets = (mean_rets-lrets.loc['Global_Equity','DGT'])/sigmas
#risk_rets = mean_rets/sigmas

composite_risk_rets = p.DataFrame()
for label in cat.keys():
    composite_risk_rets[label] = mean_rets.ix[label] 

rs = p.rolling_mean( composite_risk_rets, window=60 ).dropna() 
risk_rets = rs/rsigs

# ~~~~~ plot code
title = r'<b>60 day Moving Average of Composite Risk-Adjusted Returns</b>'
y_label = '$\mu/\sigma$$'

custom_layout_3 = create_layout( title, y_label )
risk_rets.iplot(theme='white', filename='{}_{}'.format(title, date_today), layout=custom_layout_3, world_readable=True)
Out[7]:
In [8]:
# ================================================================== #
# correlation matrix of composite ETF groups' risk adjusted returns
cor = risk_rets.corr()

# ~~ plot code
f, ax = plt.subplots(figsize=(12,12))

cmap = sns.diverging_palette(h_neg=12, h_pos=144, s=91, l=44, sep=29, n=12, center='light',as_cmap=True)
sns.corrplot(cor, annot=True, sig_stars=False, diag_names=False, cmap=cmap, ax=ax)
ax.set_title('Composite ETF Group Correlation Matrix', fontsize=18)

for label in (ax.get_xticklabels() + ax.get_yticklabels()):
    label.set_fontsize(13)

f.tight_layout()
In [9]:
f = plt.figure()
sns.clustermap(cor, figsize=(12,12))
plt.title('Composite ETF Group Correlation ClusterMap', fontsize=16, loc='left')
plt.tick_params(axis='both', labelsize=14)
<matplotlib.figure.Figure at 0xa4662e8>

Note the change in rankings below.

In [10]:
# ================================================================== #
# import ICC estimates
frame = p.read_csv( filepath+'Spdr_ICC_est_{}.csv'.format(date_today) , index_col=0 ).dropna()
pre_frame = p.read_csv( filepath+'Spdr_ICC_est_2015-04-26.csv', index_col=0 ).dropna()
# ================================================================== #
# group ICC data by category
f        = frame.copy()
pre_f    = pre_frame[['ETF_ICC_est','Category']]

grp      = f.groupby('Category')
grp_mean = grp.mean().sort('ETF_ICC_est', ascending=False)

pre_grp  = pre_f.groupby('Category')
pre_grp_mean = pre_grp.mean().sort('ETF_ICC_est', ascending=False) 
pre_grp_mean = np.round( pre_grp_mean, 3 )
p.set_option('colheader_justify', 'right')
gm_cols = ['Current ICC Est', 'Rank', 'Previous ICC Est', 'Previous Rank', 'Change in Rank']
grp_mean_rnd = grp_mean['ETF_ICC_est'].round(3)
grp_mean = p.DataFrame( grp_mean_rnd )
grp_mean['Rank'] = grp_mean.rank(ascending=False, method='dense')
grp_mean['Previous ICC est'] = pre_grp_mean
grp_mean['Previous Rank'] = pre_grp_mean.rank(ascending=False, method='dense')
grp_mean['Change in Ranking'] = grp_mean['Previous Rank'] - grp_mean['Rank']
grp_mean.columns = gm_cols
grp_mean
Out[10]:
Current ICC Est Rank Previous ICC Est Previous Rank Change in Rank
Category
Financials 0.242 1 0.239 1 0
Europe_Equity 0.222 2 0.215 2 0
AsiaPac_Equity 0.205 3 0.207 3 0
Utilities 0.191 4 0.189 5 1
Global_Equity 0.183 5 0.185 6 1
Energy 0.179 6 0.191 4 -2
Latam_MidEast_Africa 0.174 7 0.175 7 0
Materials 0.168 8 0.173 8 0
Industrial 0.142 9 0.139 9 0
Small_Cap 0.140 10 0.136 11 1
Telecom 0.138 11 0.137 10 -1
Mid_Cap 0.138 11 0.133 12 1
Consumer_Discretionary 0.136 12 0.132 13 1
Large_Cap 0.136 12 0.133 12 0
Real_Estate 0.134 13 0.128 15 2
Broad_Market 0.133 14 0.129 14 0
Technology 0.126 15 0.122 16 1
Consumer_Staples 0.115 16 0.113 17 1
Healthcare 0.112 17 0.108 18 1
In [11]:
def z_score(df):
    return ( df - df.mean() ) / df.std()

#z_grp = (grp_mean - grp_mean.mean()) / grp_mean.std()
z_grp = z_score(grp_mean['Current ICC Est'])

plt.figure()
size = (10, 8)
z_grp.plot('barh', figsize=size, alpha=.8)
plt.axvline(0, color='k')
plt.title('Z-Score of ICC Estimates by Category', fontsize=20, fontweight='demibold')
plt.xlabel('$\sigma$', fontsize=24)
plt.ylabel('Category', fontsize=16, fontweight='demibold')
plt.tick_params(axis='both', which='major', labelsize=14)
In [12]:
# last 30 days average category risk adjusted returns
date_mask = date_today - 30 * BDay()
l_30 = risk_rets.ix[date_mask:].mean().order(ascending=False) 
l_30

# z scored and plotted
z_l_30 = z_score(l_30)

plt.figure()
z_l_30.plot('barh', figsize=size, color='r', alpha=.5)
plt.axvline(0, color='k')
plt.title('Z-Score of Average Risk Adjusted Returns [Last 30 days]', fontsize=20, fontweight='demibold')
plt.xlabel('$\sigma$', fontsize=24)
plt.ylabel('Category', fontsize=16, fontweight='demibold')
plt.tick_params(axis='both', which='major', labelsize=14)

Looking at the Z-Scores Comparison below, on a relative basis over the last 30 days, Real Estate and Utilities lost a significant amount of value.

In [13]:
z_data = p.DataFrame()
z_data['Z_ICC estimates'] = z_grp
z_data['Z_risk adj returns'] = z_l_30
# z_data.head()

cadet_blue = '#4e7496'

fig = plt.figure()
with p.plot_params.use('x_compat', True):
    z_data['Z_ICC estimates'].plot('barh', figsize=size, color=cadet_blue)
    z_data['Z_risk adj returns'].plot('barh',figsize=size, color='r', alpha=.5)
plt.axvline(0, color='k')
plt.title('Z-Scores Comparison', fontsize=20, fontweight='demibold')
plt.xlabel('$\sigma$', fontsize=24, fontweight='demibold')
plt.ylabel('Category', fontsize=16)
plt.tick_params(axis='both', which='major', labelsize=14)
plt.legend(loc='best', prop={'weight':'demibold','size':12})
Out[13]:
<matplotlib.legend.Legend at 0xbdc40f0>

Over the last 2 weeks we see momementum picking up in Basic Materials, Energy, and Europe Equity. I'm more interested in European equity returns as that sector has been one I've highlighted in previous reports as presenting the best relative value.

In [14]:
# ================================================================== #
# construct dataframe and proper multi index
log_rets_recent = np.log( px.ix['4/26/2015':] / px.ix['4/26/2015':].shift(1) ).dropna()

lrets_recent = log_rets_recent.T.copy()
lrets_recent.index.name = 'ETF'
lrets_recent['Category'] = p.Series()

for cat_key, etf_val in cat.items():
    for val in etf_val:
        if val in lrets_recent.index:
            idx_loc = lrets_recent.index.get_loc(val)
            lrets_recent.ix[idx_loc,'Category'] = cat_key
        else:
            pass

lrets_recent.set_index('Category', append=True, inplace=True)
lrets_recent = lrets_recent.swaplevel('ETF','Category').sortlevel('Category')
lrets_recent.head()       

# ================================================================== #
# cumulative returns of ETF's
cum_rets_recent = lrets_recent.groupby(level='Category').cumsum(axis=1)
cum_rets_recent.head();

# ================================================================== #
# composite groupings of cumulative ETF returns (equally weighted intra-category mean returns)
composite_rets_recent = p.DataFrame()
for label in cat.keys():
    composite_rets_recent[label] = cum_rets_recent.ix[label].mean(axis=0) # equal weighted mean
    
crr = np.round(composite_rets_recent.copy(),4) # rounding
#fig = plt.figure()
#comp_rets_recent.ix[-1:].plot(kind='bar', figsize=size)
#comp_rets_recent
#crr = crr.reset_index()
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
import matplotlib
from matplotlib.ticker import FuncFormatter

def to_percent(y, position):
    # Ignore the passed in position. This has the effect of scaling the default
    # tick locations.
    s = str(100 * y)
    # The percent symbol needs escaping in latex
    if matplotlib.rcParams['text.usetex'] == True:
        return s + r'$\%$'
    else:
        return s + '%'

# Create the formatter using the function to_percent. This multiplies all the
# default labels by 100, making them all percentages
formatter = FuncFormatter(to_percent)

f = plt.figure(figsize=size)
# Set the formatter
plt.gca().yaxis.set_major_formatter(formatter)
bar_rets = crr.ix[-1:].T.sort( '{}'.format(date_today - 1 * BDay()) )
bar_rets = bar_rets.reset_index()
cols = ['index', 'log_rets_2wk']
bar_rets.columns = cols
#bar_rets.head()
plt.xticks(rotation=77)
plt.axhline(0, color='k')
plt.title('Cumulative Log Returns [Apr 26 - May 10]', fontsize=20, fontweight='demibold')
sns.barplot( x=bar_rets.index, y=bar_rets['log_rets_2wk'], data=bar_rets.sort('log_rets_2wk'), palette='RdBu')
plt.xticks(bar_rets.index, bar_rets['index'])
plt.xlabel('Category', fontsize=16, fontweight='demibold')
plt.ylabel('Log Returns', fontsize=16, fontweight='demibold')
plt.tick_params(axis='both', which='major', labelsize=14)
In [15]:
br = crr.ix[-1:].T.sort( '{}'.format(date_today - 1 * BDay()) )
br['Rank'] = crr.ix[-1:].T.sort( '{}'.format(date_today - 1 * BDay()) ).rank(method='dense',ascending=False)
cols = ['Cum. log returns [4.26-5.10]','Rank']
sortd = br.sort('Rank',ascending=True)
sortd.columns = cols
sortd.index.name = 'Category'
sortd
Out[15]:
Cum. log returns [4.26-5.10] Rank
Category
Europe_Equity 0.0168 1
Materials 0.0149 2
Energy 0.0071 3
Large_Cap 0.0034 4
Mid_Cap 0.0005 5
Consumer_Staples 0.0002 6
Consumer_Discretionary -0.0011 7
Industrial -0.0018 8
Utilities -0.0021 9
Technology -0.0030 10
Broad_Market -0.0045 11
Financials -0.0060 12
Latam_MidEast_Africa -0.0064 13
Global_Equity -0.0065 14
Telecom -0.0122 15
Small_Cap -0.0125 16
Healthcare -0.0127 17
Real_Estate -0.0155 18
AsiaPac_Equity -0.0239 19

Interpretation


Potential Long Positions:


  • Europe_Equity: As previously mentioned positive momentum seems to be building. Furthermore it is likely the ECB will remain committed to QE in the Eurozone, which we know from the US playbook means increasing liquidity and improvement in exports. The combination serves to juice the equity markets as the liquidity in the bond market finds its way to equities.
  • Utilities: Utilities are of interest for the following reasons: The recent weakness is likely tied to risk positioning in case of the FED raising rates sooner rather than later. However, a bad economic report, a surprise jump in Unemployment, or surprise decline in wage growth makes raising rates unlikely and could provide a nice trade opportunity.

Potential Short Positions:


  • Mid Caps, Small Caps: Style wise it's difficult to bet against Mid Caps due the diversity of businesses and the general stage of growth a Mid Cap firm is likely to find itself in. Historically Small Caps have shown more sensitivity to general market conditions. However, there may be a divergence from historical patterns because of USD strength. Logically, Small Cap firms are more likely to be domestic firms that primarily earn revenue denominated in USD, while Large Caps especially, are more exposed to currency fluctuations as large components of their operating revenue may be denominated in currencies that are weaknening against the USD.

I conclude this analysis with the disclaimer that these calculations are presented "as is" and the data was aggregated from several sources. I recommend doing your own due diligence before taking any investment action and to stay within your personal risk/return objectives.

I expect to refine this model as necessary to improve its utility as a macro valuation tool.

For comments, questions, and feedback contact me via:

email: [email protected]

twitter: @blackarbsCEO


Data Sources: Yahoo Finance, S&P SPDR ETFs
Acknowledgements: Ipython Notebook styling modded from Plotly and Cam Davidson-Pilon custom CSS

In [16]:
from IPython.core.display import HTML 

HTML('''<script>
code_show=true; 
function code_toggle() {
 if (code_show){
 $('div.input').hide();
 } else {
 $('div.input').show();
 }
 code_show = !code_show
} 
$( document ).ready(code_toggle);
</script>
The raw code for this IPython notebook is by default hidden for easier reading.
To toggle on/off the raw code, click <a href="javascript:code_toggle()">here</a>.''')
Out[16]:
The raw code for this IPython notebook is by default hidden for easier reading. To toggle on/off the raw code, click here.
In [17]:
from IPython.core.display import HTML 
import requests

styles = requests.get("https://raw.githubusercontent.com/BlackArbsCEO/BlackArbsCEO.github.io/Equity-Analysis/Equity%20Analysis/custom.css")
HTML(styles.text)
Out[17]:
In [ ]: