Using Implied Cost of Capital as a Sector ETF Valuation Tool

[Sunday 6.14.2015]


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 

# ================================================================== #
In [3]:
# datetime management

num_weeks = 3 # number of weeks since last update

date_today = dt.date.today()
d_mon, d_day = date_today.month, date_today.day
prev_date_today = date_today - num_weeks * Week(weekday=0) # weekday 0 = Monday
pre_d_mon, pre_d_day = prev_date_today.month, prev_date_today.day

last_month = date_today - 21 * BDay() # switch to 21

one_year_ago = date_today - 252 * BDay()
In [4]:
# ~~~ 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 [5]:
# ================================================================== #
# 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, one_year_ago, 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 [6]:
# ~~~~~ Additional risk and return computations ~~~~~ #

# ================================================================== #
# 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)

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

# ================================================================== #
# correlation matrix of composite ETF groups' risk adjusted returns
cor = risk_rets.corr()

Current ICC Estimates and Rankings

In [7]:
# ================================================================== #
# 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_{}.csv'.format(prev_date_today.date()), 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[7]:
Current ICC Est Rank Previous ICC Est Previous Rank Change in Rank
Category
Europe_Equity 0.234 1 0.220 2 1
Financials 0.228 2 0.234 1 -1
AsiaPac_Equity 0.202 3 0.204 3 0
Utilities 0.190 4 0.183 4 0
Energy 0.187 5 0.182 5 0
Global_Equity 0.183 6 0.179 6 0
Materials 0.177 7 0.171 7 0
Latam_MidEast_Africa 0.171 8 0.168 8 0
Industrial 0.140 9 0.140 9 0
Small_Cap 0.136 10 0.136 10 0
Telecom 0.135 11 0.136 10 -1
Real_Estate 0.135 11 0.132 12 1
Large_Cap 0.133 12 0.133 11 -1
Mid_Cap 0.132 13 0.133 11 -2
Consumer_Discretionary 0.131 14 0.130 13 -1
Broad_Market 0.130 15 0.130 13 -2
Technology 0.122 16 0.123 14 -2
Consumer_Staples 0.114 17 0.113 15 -2
Healthcare 0.109 18 0.109 16 -2

Z-Score of ICC Estimates by Category

In [8]:
def z_score(df):
    return ( df - df.mean() ) / df.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)

Cumulative Log Returns and Rankings - L/21 Days

In [9]:
# ================================================================== #
# construct dataframe and proper multi index
log_rets_recent = np.log( px.ix[prev_date_today.date():] / px.ix[prev_date_today.date():].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

# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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 [{pm}.{prd} - {m}.{d}]'.format(pm=pre_d_mon, prd=pre_d_day,m=d_mon,d=d_day), 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 [10]:
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 [{pm}.{prd} - {m}.{d}]'.format(pm=pre_d_mon, prd=pre_d_day,m=d_mon,d=d_day),'Rank']
sortd = br.sort('Rank',ascending=True)
sortd.columns = cols
sortd.index.name = 'Category'
sortd.to_csv(filepath + 'Cum Log Returns_ranks_{}.csv'.format(date_today))
sortd
Out[10]:
Cum. log returns [5.25 - 6.15] Rank
Category
Financials 0.0309 1
Small_Cap 0.0233 2
Healthcare 0.0158 3
Telecom 0.0098 4
Technology 0.0062 5
Broad_Market 0.0058 6
Mid_Cap 0.0056 7
Consumer_Discretionary 0.0055 8
Large_Cap -0.0026 9
Industrial -0.0048 10
Materials -0.0091 11
Consumer_Staples -0.0133 12
Energy -0.0152 13
Global_Equity -0.0195 14
AsiaPac_Equity -0.0227 15
Real_Estate -0.0245 16
Utilities -0.0275 17
Latam_MidEast_Africa -0.0282 18
Europe_Equity -0.0308 19

Z-Score Average Risk-Adjusted Returns - L/21 days

In [11]:
# last 21 days average category risk adjusted returns
date_mask = last_month
l_month = risk_rets.ix[date_mask:].mean().order(ascending=False) 
l_month

# z scored and plotted
z_l_21 = z_score(l_month)

plt.figure()
z_l_21.plot('barh', figsize=size, color='r', alpha=.5)
plt.axvline(0, color='k')
plt.title('Z-Score of Average Risk-Adjusted Returns [Last 21 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)

Z-Score Comparison [ICC Estimates vs. Risk-Adjusted Returns]

In [12]:
z_data = p.DataFrame()
z_data['Z_ICC estimates'] = z_grp
z_data['Z_risk adj returns'] = z_l_21

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[12]:
<matplotlib.legend.Legend at 0xa686588>

Interpretation


Potential Long Positions:


  • Financials: Recent economic data regarding inflation, employment, GDP etc continues to be mixed at best. However the belief is that there are enough positives to warrant the Federal Reserve following through and raising rates sometime in 2015. 10-Year Breakeven Inflation Rate closed at 1.85% (June 12, 2015) steadily rising towards the magic 2% mark. Clearly inflation expecatations are rising. If oil continues to climb in price we will certainly see inflation numbers pick up in the CPI as well. Should the economic data continue to support rising inflation expectations this is all bullish for the banking sector overall. The belief is that the increase in rates will give Banks the ability earn more via their Net Interest Margin (NIM). Clearly there is current momentum behind the trend as Financials were the strongest performers over the last 3 weeks.
  • Real-Estate and/or Utilities: This would be a tactical diversification/hedging trade. As a result of rising inflation expectations, interest rate sensitive sectors have been hammered. Should inflation fail to materialize or sentiment change there is likely to be tradeable reversal in both sectors.

Potential Short Positions:


  • Neutral bias:

Notes:


  • The Real-Estate and Utilities sectors could just as easily be tactical short positions. Long term the writing is on the wall. The Fed will and must raise rates eventually. To do otherwise is extremely risky and likely short-sighted. Consider what happens in an economic downturn if rates still remain at/near zero. That would effectively leave the Fed with only QE as a policy response. This would go against the Federal Reserve's stated position that QE is reserved for extraordinary economic situations.
In [13]:
# ~~~~~ 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

Additional Charts


Cumulative Log Returns - L/252 Days

In [14]:
# 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[14]:

60-Day Rolling Standard Deviation

In [15]:
# ~~~~~ plot code
title = '<b>60-Day Rolling 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[15]:

60-Day Rolling Average of Risk-Adjusted Returns

In [16]:
# ~~~~~ 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[16]:

Composite ETF Correlation Heat Map

In [17]:
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 0xa677240>

Composite ETF Correlation Matrix

In [18]:
# ================================================================== #
# correlation matrix of composite ETF groups' risk adjusted returns
# ~~ 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()

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. Please contact me to report any errors.

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 [19]:
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[19]:
The raw code for this IPython notebook is by default hidden for easier reading. To toggle on/off the raw code, click here.
In [20]:
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[20]:
In [ ]: