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\"cells\": ["," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"## Crude Oil :: Brent vs. West Texas Intermediate (WTI)\\n\","," \"\\n\","," \"We examine the history of crude oil prices, and their spreads.\\n\","," \"A Boltzmann portfolio is computed for *optimal* financial positions.\\n\","," \"\\n\","," \"Deflated prices give additional insight, along with some of the\\n\","," \"statistical tools useful in financial economics.\\n\","," \"\\n\","," \"***Although WTI is more desirable than Brent from a petrochemical\\n\","," \"perspective, that preference is reversed when the metrics\\n\","," \"are financial.***\\n\","," \"\\n\","," \"Unless otherwise noted, the price per barrel is in U.S. dollars.\\n\","," \"The source of the data is the U.S. Department of Energy via FRED.\\n\","," \"We will use Federal Reserve USD index units to compute oil prices in non-dollar terms.\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"## Petrochemical background\\n\","," \"\\n\","," \"Before exploring our financial metrics, let's get familiar\\n\","," \"with the physical aspects.\\n\","," \"\\n\","," \"> **Crude oil is arguably the most crucial commodity in the world today.**\\n\","," \"An important issue is the different benchmarks for crude oil prices. \\n\","," \"\\n\","," \"> The American Petroleum Institute ***API gravity*** is a measure that is\\n\","," \"used to compare a petroleum liquid's density to water.\\n\","," \"This scale generally falls between 10 and 70, with \\\"light\\\" crude oil\\n\","," \"typically having an API gravity on the higher side of the range, while\\n\","," \"\\\"heavy\\\" oil has a reading that falls on the lower end of the range.\\n\","," \"\\n\","," \"> The sulfur content of petroleum must also be considered.\\n\","," \"***Sulfur content of 0.50% is a key benchmark.***\\n\","," \"When oil has a total sulfur level greater than the benchmark, it is considered \\\"sour.\\\"\\n\","," \"Sulfur content less than the benchmark indicates that an oil is \\\"sweet.\\\"\\n\","," \"Sour crude oil is more prevalent than its sweet counterpart and comes from\\n\","," \"oil sands in Canada, the Gulf of Mexico, some South American nations,\\n\","," \"as well as most of the Middle East.\\n\","," \"Sweet crude is typically produced in the central United States,\\n\","," \"the North Sea region of Europe, and much of Africa and the Asia Pacific region.\\n\","," \"*End users generally prefer sweet crude as it requires less processing\\n\","," \"to remove impurities than its sour counterpart.*\\n\","," \"\\n\","," \"> [Edited source: Daniela Pylypczak-Wasylyszyn](http://commodityhq.com/education/crude-oil-guide-brent-vs-wti-whats-the-difference)\\n\","," \"\\n\","," \"Light and sweet forms of crude oil are generally valued higher while\\n\","," \"heavy and sour types often trade at a discount.\\n\","," \"These two key factors distinguish the two major benchmarks for\\n\","," \"world oil prices: West Texas Intermediate (WTI) and Brent crude oil.\\n\","," \"\\n\","," \"***WTI is generally lighter and sweeter than Brent, but the supply of each\\n\","," \"can differ considerably over time, thus their price difference will vary.***\\n\","," \"\\n\","," \"WTI is refined mostly in the Midwest and Gulf Coast regions of the United States,\\n\","," \"while Brent oil is typically refined in Northwest Europe.\\n\","," \"\\n\","," \"#### Approximate characteristics:\\n\","," \"- **Brent**: API gravity 38.06, sulfur 0.37%\\n\","," \"- **WTI**: API gravity 39.6, sulfur 0.24%\\n\","," \"\\n\","," \"---\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"*Dependencies:*\\n\","," \"\\n\","," \"- Repository: https://github.com/rsvp/fecon235\\n\","," \"\\n\","," \"*CHANGE LOG*\\n\","," \"\\n\","," \" 2017-08-08 Fix #2 and introduce Boltzmann portfolio of oils.\\n\","," \" 2015-05-26 Code review and revision.\\n\","," \" 2014-10-09 First version for oil, using 2014-09-28 Template.\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 1,"," \"metadata\": {"," \"collapsed\": true"," },"," \"outputs\": [],"," \"source\": ["," \"from fecon235.fecon235 import *\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 2,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": ["," {"," \"name\": \"stdout\","," \"output_type\": \"stream\","," \"text\": ["," \" :: Python 2.7.13\\n\","," \" :: IPython 5.1.0\\n\","," \" :: jupyter_core 4.2.1\\n\","," \" :: notebook 4.1.0\\n\","," \" :: matplotlib 1.5.1\\n\","," \" :: numpy 1.11.0\\n\","," \" :: scipy 0.17.0\\n\","," \" :: sympy 1.0\\n\","," \" :: pandas 0.19.2\\n\","," \" :: pandas_datareader 0.2.1\\n\","," \" :: Repository: fecon235 v5.17.0722 develop\\n\","," \" :: Timestamp: 2017-08-09T09:31:30Z\\n\","," \" :: $pwd: /media/yaya/virt15h/virt/dbx/Dropbox/ipy/fecon235/nb\\n\""," ]"," }"," ],"," \"source\": ["," \"# PREAMBLE-p6.15.1223d :: Settings and system details\\n\","," \"from __future__ import absolute_import, print_function, division\\n\","," \"system.specs()\\n\","," \"pwd = system.getpwd() # present working directory as variable.\\n\","," \"print(\\\" :: $pwd:\\\", pwd)\\n\","," \"# If a module is modified, automatically reload it:\\n\","," \"%load_ext autoreload\\n\","," \"%autoreload 2\\n\","," \"# Use 0 to disable this feature.\\n\","," \"\\n\","," \"# Notebook DISPLAY options:\\n\","," \"# Represent pandas DataFrames as text; not HTML representation:\\n\","," \"import pandas as pd\\n\","," \"pd.set_option( 'display.notebook_repr_html', False )\\n\","," \"from IPython.display import HTML # useful for snippets\\n\","," \"# e.g. HTML('')\\n\","," \"from IPython.display import Image \\n\","," \"# e.g. Image(filename='holt-winters-equations.png', embed=True) # url= also works\\n\","," \"from IPython.display import YouTubeVideo\\n\","," \"# e.g. YouTubeVideo('1j_HxD4iLn8', start='43', width=600, height=400)\\n\","," \"from IPython.core import page\\n\","," \"get_ipython().set_hook('show_in_pager', page.as_hook(page.display_page), 0)\\n\","," \"# Or equivalently in config file: \\\"InteractiveShell.display_page = True\\\", \\n\","," \"# which will display results in secondary notebook pager frame in a cell.\\n\","," \"\\n\","," \"# Generate PLOTS inside notebook, \\\"inline\\\" generates static png:\\n\","," \"%matplotlib inline \\n\","," \"# \\\"notebook\\\" argument allows interactive zoom and resize.\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 3,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": [],"," \"source\": ["," \"# Define dictionary for dataframe:\\n\","," \"oils4d = { 'Brent' : d4brent, 'WTI' : d4wti }\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 4,"," \"metadata\": {"," \"collapsed\": true"," },"," \"outputs\": [],"," \"source\": ["," \"# Retrieve data:\\n\","," \"oils = groupget( oils4d )\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"## BoW spread := Brent - WTI\\n\","," \"\\n\","," \"***Brent over WTI spread***\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 5,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": [],"," \"source\": ["," \"# Define price variables individually for convenience:\\n\","," \"brent = oils['Brent']\\n\","," \"wti = oils['WTI']\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 6,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": [],"," \"source\": ["," \"# Define BoW: Brent over WTI spread:\\n\","," \"bow = todf( brent - wti, 'BoW' )\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"#### The difference between Brent and WTI is not superficial in the 21st century. Brent over WTI, bow, can represent over 20% of the underlying oil price!\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 7,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": ["," {"," \"data\": {"," \"image/png\": 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mvB6NHR9Y4aBRts0Pz93G2sGMMwMok/vG7hi9CuXd26R4/8bo9xLL54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\\ni/H/AfTmiOUogeybAAAAAElFTkSuQmCC\\n\","," \"text/plain\": ["," \"\""," ]"," },"," \"metadata\": {},"," \"output_type\": \"display_data\""," }"," ],"," \"source\": ["," \"plot( bow )\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"## Define \\\"Oil\\\" as weighted average price\\n\","," \"\\n\","," \"When BoW is non-zero, the price of \\\"Oil\\\" is ambiguous,\\n\","," \"thus we define a weighted average price of oil\\n\","," \"between Brent and WTI.\\n\","," \"\\n\","," \"Note that the composition of Brent oil benchmark no longer\\n\","," \"really represents Brent as an location.\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 8,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": [],"," \"source\": ["," \"# Set wtbrent, the primary weight for Oil:\\n\","," \"wtbrent = 0.50\\n\","," \"# 0.50 represents the mean\\n\","," \"# ==================================\\n\","," \"wtwti = 1 - wtbrent\\n\","," \"\\n\","," \"# Weighted average:\\n\","," \"oil = todf( (wtbrent * brent) + (wtwti * wti), 'Oil' )\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 9,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": ["," {"," \"data\": {"," \"image/png\": 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9hjD1i2LG41RqnUwof+U+Cp7PpGwMxA3uxsWmS0F99YnJje6Ema5qYm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\\nYbQR/j8z0wHAcGc+GQAAAABJRU5ErkJggg==\\n\","," \"text/plain\": ["," \"\""," ]"," },"," \"metadata\": {},"," \"output_type\": \"display_data\""," }"," ],"," \"source\": ["," \"plot( oil )\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"**The Great Recession plunge from \\\\$140 to \\\\$40 is extraordinary.**\\n\","," \"*But so is the post-2014 crash which wiped out legendary traders.*\\n\","," \"The volatility is around 33% annualized, as we shall see later.\\n\","," \"\\n\","," \"[Using equal weights, we have created two synthetic series called `d4oil` and `m4oil`\\n\","," \"for future convenience.]\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 10,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": ["," {"," \"name\": \"stdout\","," \"output_type\": \"stream\","," \"text\": ["," \" Brent WTI Oil\\n\","," \"count 7879.000000 7879.000000 7879.000000\\n\","," \"mean 45.011701 44.248576 44.630138\\n\","," \"std 33.469778 30.000004 31.660557\\n\","," \"min 9.100000 10.820000 9.960000\\n\","," \"25% 18.500000 19.850000 19.177500\\n\","," \"50% 28.560000 30.080000 29.275000\\n\","," \"75% 64.985000 64.870000 64.987500\\n\","," \"max 143.950000 145.310000 144.630000\\n\","," \"\\n\","," \" :: Index on min:\\n\","," \"Brent 1998-12-10\\n\","," \"WTI 1998-12-10\\n\","," \"Oil 1998-12-10\\n\","," \"dtype: datetime64[ns]\\n\","," \"\\n\","," \" :: Index on max:\\n\","," \"Brent 2008-07-03\\n\","," \"WTI 2008-07-03\\n\","," \"Oil 2008-07-03\\n\","," \"dtype: datetime64[ns]\\n\","," \"\\n\","," \" :: Head:\\n\","," \" Brent WTI Oil\\n\","," \"T \\n\","," \"1987-05-20 18.63 19.75 19.190\\n\","," \"1987-05-21 18.45 19.95 19.200\\n\","," \"1987-05-22 18.55 19.68 19.115\\n\","," \" :: Tail:\\n\","," \" Brent WTI Oil\\n\","," \"T \\n\","," \"2017-07-27 50.67 49.05 49.86\\n\","," \"2017-07-28 52.00 49.72 50.86\\n\","," \"2017-07-31 51.99 50.21 51.10\\n\","," \"\\n\","," \" :: Correlation matrix:\\n\","," \" Brent WTI Oil\\n\","," \"Brent 1.000000 0.990614 0.997901\\n\","," \"WTI 0.990614 1.000000 0.997386\\n\","," \"Oil 0.997901 0.997386 1.000000\\n\""," ]"," }"," ],"," \"source\": ["," \"# Temporarily combine data for Brent, WTI, and weighted Oil:\\n\","," \"stats( paste([oils, oil]) )\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"The very tight correlation between Brent and WTI (> 99%)\\n\","," \"can mask the potential turbulence of the BoW spread. \\n\","," \"\\n\","," \"## BoW spread as a function of Oil price\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 11,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": ["," {"," \"name\": \"stdout\","," \"output_type\": \"stream\","," \"text\": ["," \" :: FIRST variable:\\n\","," \"count 7879.000000\\n\","," \"mean 0.763125\\n\","," \"std 5.557796\\n\","," \"min -22.180000\\n\","," \"25% -1.810000\\n\","," \"50% -1.160000\\n\","," \"75% 0.685000\\n\","," \"max 29.590000\\n\","," \"Name: BoW, dtype: float64\\n\","," \"\\n\","," \" :: SECOND variable:\\n\","," \"count 7879.000000\\n\","," \"mean 44.630138\\n\","," \"std 31.660557\\n\","," \"min 9.960000\\n\","," \"25% 19.177500\\n\","," \"50% 29.275000\\n\","," \"75% 64.987500\\n\","," \"max 144.630000\\n\","," \"Name: Oil, dtype: float64\\n\","," \"\\n\","," \" :: CORRELATION\\n\","," \"0.625773327194\\n\","," \" OLS Regression Results \\n\","," \"==============================================================================\\n\","," \"Dep. Variable: Y R-squared: 0.392\\n\","," \"Model: OLS Adj. R-squared: 0.392\\n\","," \"Method: Least Squares F-statistic: 5070.\\n\","," \"Date: Wed, 09 Aug 2017 Prob (F-statistic): 0.00\\n\","," \"Time: 02:31:49 Log-Likelihood: -22736.\\n\","," \"No. Observations: 7879 AIC: 4.548e+04\\n\","," \"Df Residuals: 7877 BIC: 4.549e+04\\n\","," \"Df Model: 1 \\n\","," \"Covariance Type: nonrobust \\n\","," \"==============================================================================\\n\","," \" coef std err t P>|t| [95.0% Conf. Int.]\\n\","," \"------------------------------------------------------------------------------\\n\","," \"Intercept -4.1395 0.084 -49.036 0.000 -4.305 -3.974\\n\","," \"X 0.1099 0.002 71.203 0.000 0.107 0.113\\n\","," \"==============================================================================\\n\","," \"Omnibus: 1718.842 Durbin-Watson: 0.053\\n\","," \"Prob(Omnibus): 0.000 Jarque-Bera (JB): 10202.633\\n\","," \"Skew: 0.913 Prob(JB): 0.00\\n\","," \"Kurtosis: 8.267 Cond. No. 94.6\\n\","," \"==============================================================================\\n\","," \"\\n\","," \"Warnings:\\n\","," \"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\\n\""," ]"," }"," ],"," \"source\": ["," \"# Do the regression:\\n\","," \"stat2( bow['BoW'], oil['Oil'] )\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"Does the price of Oil influence the BoW spread?\\n\","," \"Not much, the correlation is about 63%, and the linear regression is not robust.\\n\","," \"\\n\","," \"*To roughly estimate BoW*: take 11% of Oil price and subtract $4.\\n\","," \"So higher Oil prices imply greater Brent premium over WTI.\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"## Record LOW: Oil on 1998-12-10 at 9.96 USD\\n\","," \"\\n\","," \"We use that date to define the variable `tmin`.\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 12,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": [],"," \"source\": ["," \"tmin = '1998-12-10'\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"**What is the geometric mean rate since tmin?**\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 13,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": ["," {"," \"data\": {"," \"text/plain\": ["," \"[1.9017090903568512,\\n\","," \" 8.6098951245776831,\\n\","," \" 33.342833957643094,\\n\","," \" 7.4891318245988723,\\n\","," \" 256,\\n\","," \" 4862]\""," ]"," },"," \"execution_count\": 13,"," \"metadata\": {},"," \"output_type\": \"execute_result\""," }"," ],"," \"source\": ["," \"gemrat( oil[tmin:], yearly=256 )\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"May 2015: The geometric mean rate since tmin is around 11%\\n\","," \"with volatility of 33% -- both very high relative to traditional assets.\\n\","," \"\\n\","," \"Aug 2017: The geometric mean rate since tmin is down to around 2%\\n\","," \"with volatility still of 33%. The kurtosis of 7.5 is very high\\n\","," \"since it would be 3 for a Gaussian distribution:\\n\","," \"hence oil returns are leptokurtotic, i.e. have \\\"fat tails.\\\"\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"## Oil trend since tmin on 1998-12-10\\n\","," \"\\n\","," \"Given the high price volatility,\\n\","," \"what seems to be underlying trend?\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 14,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": ["," {"," \"name\": \"stdout\","," \"output_type\": \"stream\","," \"text\": ["," \" :: regresstime slope = 0.0131256573363\\n\""," ]"," },"," {"," \"data\": {"," \"image/png\": 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x66iGTShAnhAhMNDeGSb4cemu6DgppLPXQR6TCmToWBA8P48eOPhylT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\\nTkSuQmCC\\n\","," \"text/plain\": ["," \"\""," ]"," },"," \"metadata\": {},"," \"output_type\": \"display_data\""," }"," ],"," \"source\": ["," \"plot( trend(todf(oil[tmin:])) )\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"Oil prices can easily go +/- 40% off their statistical trend (about 1.2 std).\\n\","," \"So the trend is very deceptive.\\n\","," \"\\n\","," \"Aug 2017: the trend indicates \\\\$92 oil, but the\\n\","," \"current market average is in fact around \\\\$50.\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"## Boltzmann portfolio of oils\\n\","," \"\\n\","," \"Given the BoW spread, correlations, volatilities, and overall uptrend --\\n\","," \"what would be an *optimal* portfolio structure out-of-sample?\\n\","," \"\\n\","," \"We shall compute a **Boltzmann portfolio**\\n\","," \"(see https://git.io/boltz1 for details),\\n\","," \"consisting of Brent and WTI, which uses cross-entropy\\n\","," \"as its foundation for best geometric growth at minimized risk.\\n\","," \"\\n\","," \"The short-side shall be practically unrestricted (floor=level=-25)\\n\","," \"since we assume that crude oil derivatives will be used\\n\","," \"to implement the strategy.\\n\","," \"\\n\","," \"The history since *tmin* will be the base,\\n\","," \"but the user can modify the date interactively\\n\","," \"(see https://git.io/boltz2 for details on sequential decisions).\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 15,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": ["," {"," \"data\": {"," \"text/plain\": ["," \"[0.7845, [[0.9814, 0.8337, 'Brent'], [0.0186, -1.82, 'WTI']]]\""," ]"," },"," \"execution_count\": 15,"," \"metadata\": {},"," \"output_type\": \"execute_result\""," }"," ],"," \"source\": ["," \"prtf = boltzportfolio( oils[tmin:], temp=55, floor=-25, level=-25, n=4 )\\n\","," \"prtf\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"Brent has a higher geometric mean rate (0.83% vs. -1.82 for WTI),\\n\","," \"hence ***0.98 of the portfolio's notional principal is dedicated to Brent***,\\n\","," \"and 0.02 towards WTI.\\n\","," \"The expected geometric mean rate of this particular\\n\","," \"Boltzmann portfolio is a mere 0.78%,\\n\","," \"hardly better than a Treasury note.\\n\","," \"\\n\","," \"In a Boltzmann portfolio, the second and fourth centralized moments\\n\","," \"are taken into account to properly access risk,\\n\","," \"and to adjust the geometric mean rates.\\n\","," \"\\n\","," \"This component analysis is more accurate out-of-sample than a\\n\","," \"treatment of a single time-series such as the weighted average.\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"## Deflated oil prices\\n\","," \"\\n\","," \"We use our monthly deflator consisting of CPI and PCE,\\n\","," \"both core and headline versions for each,\\n\","," \"to compute ***real*** oil prices.\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 16,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": [],"," \"source\": ["," \"# First change the sampling frequency to match inflation data:\\n\","," \"oilmth = todf(monthly( oil ))\\n\","," \"defl = todf(get( m4defl ))\\n\","," \"oildefl = todf( oilmth * defl )\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 17,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": ["," {"," \"data\": {"," \"image/png\": 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T2fBBn66tWFPa/LlEVAj5xH0gVc0wvuaXZNL5SW5mjLpV272AE9n5qD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\\nmeADusfj8ZQJPqB7PB5PmfD/Af3lThpuITFaAAAAAElFTkSuQmCC\\n\","," \"text/plain\": ["," \"\""," ]"," },"," \"metadata\": {},"," \"output_type\": \"display_data\""," }"," ],"," \"source\": ["," \"# Deflated Oil price:\\n\","," \"plot( oildefl )\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"The supportive 1998 uptrend is broken by the post-2014 crash in prices.\\n\","," \"The level support from the 1990's is around \\\\$20 in current US dollars.\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"## Oil price ex-USD\\n\","," \"\\n\","," \"Here we are interested in how oil prices appear when priced in\\n\","," \"foreign currencies (outside the United States).\\n\","," \"A basket of trade-weighted currencies against USD helps\\n\","," \"our foreign exchange viewpoint.\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 18,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": [],"," \"source\": ["," \"# rtb is the real trade-weighted USD index,\\n\","," \"# computed monthly by the Federal Reserve.\\n\","," \"rtb = get( m4usdrtb )\\n\","," \"oilrtb = todf( oilmth / rtb )\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 19,"," \"metadata\": {"," \"collapsed\": false"," },"," \"outputs\": ["," {"," \"data\": {"," \"image/png\": 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xKDeIsWmQNk0Kxda98AzjvP9LRpkzyIx3ri2dgpDQFng7hrXpdresE9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\\nfWYHdwAAAABJRU5ErkJggg==\\n\","," \"text/plain\": ["," \"\""," ]"," },"," \"metadata\": {},"," \"output_type\": \"display_data\""," }"," ],"," \"source\": ["," \"# Oil priced in rtb index units:\\n\","," \"plot( oilrtb )\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"No big suprises here. Oil from world-ex-USD perspective looks very similar to the dollar-only perspective.\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"## Concluding remarks\\n\","," \"\\n\","," \"Although WTI has more desirable petrochemical properties than Brent oil,\\n\","," \"our analysis of their prices reveal that Brent is preferable over WTI\\n\","," \"in the context of a financial portfolio -- denominated in practically\\n\","," \"any currency.\\n\","," \"\\n\","," \"Before taking a position in oil, carefully evaluate the premium of Brent over WTI,\\n\","," \"i.e. the BoW spread.\\n\","," \"\\n\","," \"The post-2014 crash in oil prices portends a downward look at\\n\","," \"the \\\\$20 support level in current U.S. dollars especially in view\\n\","," \"of the caveats listed below.\\n\","," \"This would be a major concern for oil companies worldwide\\n\","," \"(for example, in August 2017 BP announced their break-even point\\n\","," \"was \\\\$47 with respect to the price of oil). \\n\","," \"\\n\","," \"\\n\","," \"### Caveats\\n\","," \"\\n\","," \"- A complete analysis would include the impact of shale oil and *alternate energy sources*.\\n\","," \"\\n\","," \"- As electric cars become more popular, the demand for petroleum will obviously diminish.\\n\","," \"\\n\","," \"- If ISIS becomes dominate over oil fields, expect some minor supply at half the market price.\\n\","," \"\\n\","," \"- Be attentive to offshore storage of crude oil, literally on non-active tanker ships with no destinations.\""," ]"," },"," {"," \"cell_type\": \"markdown\","," \"metadata\": {},"," \"source\": ["," \"---\\n\","," \"\\n\","," \"*Dedicated to recently retired Andrew Hall: the name of the game has changed.*\""," ]"," }"," ],"," \"metadata\": {"," \"kernelspec\": {"," \"display_name\": \"Python 2\","," \"language\": \"python\","," \"name\": \"python2\""," },"," \"language_info\": {"," \"codemirror_mode\": {"," \"name\": \"ipython\","," \"version\": 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