{
"metadata": {
"name": "",
"signature": "sha256:99159f50a56b9d50b0e82032368b63351365330ee92a1dab740c272b8f0e6af5"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Geometric mean returns on FRED series"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We examine economic and financial time series where Holt-Winters is used to forecast one-year ahead. Daily data for bonds, equity, and gold is then analyzed.\n",
"\n",
"The focus is on geometric mean returns because they optimally express mean-variance under logarithmic utility."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Dependencies:*\n",
"\n",
" - Linux, bash\n",
" - Python: matplotlib, pandas\n",
" - Modules: yi_1tool, yi_plot, yi_timeseries, yi_fred\n",
" \n",
"*CHANGE LOG*\n",
"\n",
" 2015-05-26 Code revision using template v14.12.21.\n",
" 2014-10-11 Code review. Template 2014-09-28.\n",
" 2014-09-01 First version."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# NOTEBOOK settings and system details: [00-tpl v14.12.21]\n",
"\n",
"# Assume that the backend is LINUX (our particular distro is Ubuntu, running bash shell):\n",
"print '\\n :: TIMESTAMP of last notebook execution:'\n",
"!date\n",
"print '\\n :: IPython version:'\n",
"!ipython --version\n",
"\n",
"# Automatically reload modified modules:\n",
"%load_ext autoreload\n",
"%autoreload 2\n",
"# 0 disables autoreload.\n",
"# Generate plots inside notebook:\n",
"%matplotlib inline\n",
"\n",
"# DISPLAY options\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.display import HTML # useful for snippets\n",
"# e.g. HTML('')\n",
"\n",
"import pandas as pd\n",
"print '\\n :: pandas version:'\n",
"print pd.__version__\n",
"# pandas DataFrames are represented as text by default; enable HTML representation:\n",
"# [Deprecated: pd.core.format.set_printoptions( notebook_repr_html=True ) ]\n",
"pd.set_option( 'display.notebook_repr_html', False )\n",
"\n",
"# MATH display, use %%latex, rather than the following:\n",
"# from IPython.display import Math\n",
"# from IPython.display import Latex\n",
"\n",
"print '\\n :: Working directory (set as $workd):'\n",
"workd, = !pwd\n",
"print workd + '\\n'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" :: TIMESTAMP of last notebook execution:\n",
"Thu Jun 25 20:35:28 PDT 2015\r\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" :: IPython version:\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2.3.0\r\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" :: pandas version:\n",
"0.15.0\n",
"\n",
" :: Working directory (set as $workd):\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"/home/yaya/Dropbox/share/git/nous/fecon235/nb\n",
"\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from yi_1tools import *\n",
"from yi_plot import *\n",
"from yi_timeseries import *\n",
"from yi_fred import *"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Download data and construct a dataframe"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We shall retrieve the following data of monthly frequency: **(aggregated) inflation, bonds (zero coupon equivalent of 10-y Treasury), equities (S&P 500), and gold (London PM fix) -- all denominated in US dollars -- then lastly, the real trade-weighted USD index (Federal Reserve) and US home prices (per Case-Shiller).** The details for each series is given in their respective notebooks.\n",
"\n",
"*Home prices will create a 3-month lag, due to their release cycle.*"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Specify monthly series of interest as ms list:\n",
"ms = [ m4infl, m4zero10, m4spx, m4xau, m4usdrtb, m4homepx ]\n",
"names = ['Infl', 'Zero10', 'SPX', 'XAU', 'USD', 'Homes']\n",
"\n",
"# Download into a dictionary:\n",
"msd = {}\n",
"for i in ms:\n",
" msd[i] = getfred(i)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" :: S&P 500 prepend successfully goes back to 1957.\n",
" :: Case-Shiller prepend successfully goes back to 1987."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"After downloading the level series, we compute the YoY percentage change for each series. *This will be the a trailing 12-month statistic, thus it's overlapping.*"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Compute the YoY percentage change:\n",
"msdc = {}\n",
"for i in ms:\n",
" msdc[i] = pcent( msd[i], 12 )"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Construct the mega YoY dataframe:\n",
"mega = paste( [ msdc[i] for i in ms ] )\n",
"# Give names to the columns for mega:\n",
"mega.columns = names"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Define start time and get stats"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Start time given by t0\n",
"t0 = '1988'"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"stats( mega[t0:] )"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Infl Zero10 SPX XAU USD Homes\n",
"count 327.000000 327.000000 327.000000 327.000000 327.000000 327.000000\n",
"mean 2.424121 2.229173 8.753083 4.949457 -0.286063 3.882495\n",
"std 1.005295 7.463804 16.416248 15.524655 4.982369 8.088091\n",
"min -0.180575 -18.521264 -42.349361 -27.752361 -10.577564 -18.906156\n",
"25% 1.690927 -3.217100 2.288186 -6.463883 -3.809645 -1.218646\n",
"50% 2.366964 2.912582 10.726925 1.898076 -0.357301 4.293769\n",
"75% 2.887417 7.752083 19.981864 14.325670 2.682498 10.684985\n",
"max 5.242059 20.492399 52.051354 60.357143 14.508997 17.077118\n",
"\n",
" :: Index on min:\n",
"Infl 2009-07-01\n",
"Zero10 1994-10-01\n",
"SPX 2009-03-01\n",
"XAU 2013-12-01\n",
"USD 2008-03-01\n",
"Homes 2009-01-01\n",
"dtype: datetime64[ns]\n",
"\n",
" :: Index on max:\n",
"Infl 1990-10-01\n",
"Zero10 1996-01-01\n",
"SPX 2010-03-01\n",
"XAU 2006-05-01\n",
"USD 2009-03-01\n",
"Homes 2004-07-01\n",
"dtype: datetime64[ns]\n",
"\n",
" :: Head:\n",
" Infl Zero10 SPX XAU USD Homes\n",
"T \n",
"1988-01-01 3.984315 -12.661625 -6.207571 17.042392 -9.836868 12.139461\n",
"1988-02-01 3.876021 -8.068941 -8.186030 9.982617 -8.633477 11.661442\n",
"1988-03-01 3.924380 -9.248410 -8.156954 8.841782 -9.393214 11.345646\n",
"1988-04-01 3.992870 -5.477528 -8.960111 2.878355 -8.283502 10.974485\n",
"1988-05-01 4.017727 -4.487925 -11.871026 -1.578661 -7.507266 10.543908\n",
"1988-06-01 4.129092 -4.738070 -10.689462 0.022137 -7.401580 10.559567\n",
"1988-07-01 4.276206 -5.671538 -12.487441 -3.115990 -6.469468 10.756853\n",
"\n",
" :: Tail:\n",
" Infl Zero10 SPX XAU USD Homes\n",
"T \n",
"2014-09-01 1.573155 2.870055 18.259104 -8.035048 1.924209 4.982426\n",
"2014-10-01 1.590927 2.873362 13.047620 -6.736243 4.278896 4.557101\n",
"2014-11-01 1.397419 3.603244 14.134137 -8.234146 4.984866 4.353347\n",
"2014-12-01 1.098285 6.108084 14.380677 -2.298029 6.786695 4.482448\n",
"2015-01-01 0.731306 9.213133 10.175566 1.235684 7.608924 4.485425\n",
"2015-02-01 0.806330 6.585098 14.399577 -7.207207 8.760392 4.996752\n",
"2015-03-01 0.849246 6.019017 11.453936 -11.421092 10.734463 4.990347"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" :: Correlation matrix:\n",
" Infl Zero10 SPX XAU USD Homes\n",
"Infl 1.000000 -0.059018 -0.016182 -0.072354 -0.308788 0.005064\n",
"Zero10 -0.059018 1.000000 -0.137220 -0.000802 0.214137 -0.295339\n",
"SPX -0.016182 -0.137220 1.000000 -0.212138 -0.049899 0.248055\n",
"XAU -0.072354 -0.000802 -0.212138 1.000000 -0.513692 -0.244964\n",
"USD -0.308788 0.214137 -0.049899 -0.513692 1.000000 0.039124\n",
"Homes 0.005064 -0.295339 0.248055 -0.244964 0.039124 1.000000"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is not much correlation among our assets, except a mild negative between gold XAU and USD. Next, the boxplot gives us an idea of the range of returns, and their persistence. It's a visual aid to the geometric mean returns which is most significant as investment metric."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Overlapping YoY percentage change, recently:\n",
"boxplot(mega[t0:], 'Assets YoYm')\n",
"# where the red dot represents the latest point."
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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"text": [
""
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" :: Finished: boxplot-Assets_YoYm.png\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Geometric mean returns on non-overlapping periods"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Geometric mean returns, non-overlapping, annualized:\n",
"for i in range(len(ms)):\n",
" print names[i], georet(msd[ms[i]][t0:], 12)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Infl "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[2.33, 2.33, 0.5, 12]\n",
"Zero10 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[2.0, 2.25, 7.19, 12]\n",
"SPX "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[7.82, 8.57, 12.23, 12]\n",
"XAU "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[3.28, 4.14, 13.09, 12]\n",
"USD "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[0.03, 0.12, 4.12, 12]\n",
"Homes "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[3.43, 3.46, 2.55, 12]\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Note: the geometric returns do not include interest and dividend payouts for bonds and equities. Some observations in chronological order:\n",
"\n",
"- 2014-09-01, georet since 2010\n",
" - Inflation at 1.7% which is below Fed target of 2%.\n",
" - Total return on bonds, approx 2.52 + 2.33 = 4.85%\n",
" - Total return on equity, approx. 11.9 + 2 = 13.9% -- very heated.\n",
" - Gold indecisive about breaking 1260 LTS.\n",
" - USD though at -0.69%, will strengthen given Draghi wanting weak EUR.\n",
" \n",
" \n",
" - 2014-10-11, georet since 2004\n",
" - Inflation over ten years is running 2% annually.\n",
" - Gold dominates over ten years.\n",
" - Gold recently holds at 1180 triple local bottom.\n",
"\n",
"\n",
" - 2014-10-12, georet since 1988\n",
" - Inflation in the long-run about 3% annually.\n",
" - Bond price alone increases 2% annually (excludes interest income).\n",
" - Gold at 1.73% does not keep up with inflation.\n",
" - USD at break-even over the long-run.\n",
" - Home prices have georet of 3.6%.\n",
"\n",
"- 2015-05-27, georet since 1988\n",
" - Inflation in the long-run drops 70 bp to about 2.3% annually.\n",
" - Bond price continues its increase at 2% annually.\n",
" - Gold at 3.4% reacting more to stronger USD (cf. correlation).\n",
" - Home prices also have georet of 3.4% (but low 2.6% volatility)."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Forecasts using Holt-Winters method"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We forecast one-year ahead using the monthly data. Note that current infl is rebased to 1, thus 1.02 would signify 2% increase."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# 12-periods ahead forecasts use default alpha and beta values (robust update):\n",
"for i in range(len(ms)):\n",
" print names[i] \n",
" print holtfred(msd[ ms[i]], h=12 )\n",
" # ^we use all available data to forecast\n",
" print '------------------------------------'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Infl\n",
" Forecast\n",
"0 1.000000\n",
"1 0.998873\n",
"2 0.999353\n",
"3 0.999834\n",
"4 1.000314\n",
"5 1.000794\n",
"6 1.001274\n",
"7 1.001755\n",
"8 1.002235\n",
"9 1.002715\n",
"10 1.003195\n",
"11 1.003675\n",
"12 1.004156"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"------------------------------------\n",
"Zero10\n",
" Forecast\n",
"0 80.929358\n",
"1 83.871671\n",
"2 84.151155\n",
"3 84.430640\n",
"4 84.710124\n",
"5 84.989608\n",
"6 85.269093\n",
"7 85.548577\n",
"8 85.828062\n",
"9 86.107546\n",
"10 86.387030\n",
"11 86.666515\n",
"12 86.945999"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"------------------------------------\n",
"SPX\n",
" Forecast\n",
"0 2105.200000\n",
"1 2146.564284\n",
"2 2161.256033\n",
"3 2175.947782\n",
"4 2190.639532\n",
"5 2205.331281\n",
"6 2220.023030\n",
"7 2234.714780\n",
"8 2249.406529\n",
"9 2264.098278\n",
"10 2278.790028\n",
"11 2293.481777\n",
"12 2308.173527"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"------------------------------------\n",
"XAU\n",
" Forecast\n",
"0 1178.500000\n",
"1 1178.805087\n",
"2 1172.707278\n",
"3 1166.609470\n",
"4 1160.511661\n",
"5 1154.413853\n",
"6 1148.316045\n",
"7 1142.218236\n",
"8 1136.120428\n",
"9 1130.022619\n",
"10 1123.924811\n",
"11 1117.827002\n",
"12 1111.729194"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"------------------------------------\n",
"USD\n",
" Forecast\n",
"0 93.018000\n",
"1 95.042219\n",
"2 95.923105\n",
"3 96.803990\n",
"4 97.684876\n",
"5 98.565762\n",
"6 99.446648\n",
"7 100.327534\n",
"8 101.208420\n",
"9 102.089306\n",
"10 102.970192\n",
"11 103.851077\n",
"12 104.731963"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"------------------------------------\n",
"Homes\n",
" Forecast\n",
"0 214289.270829\n",
"1 212418.051023\n",
"2 213348.196411\n",
"3 214278.341799\n",
"4 215208.487187\n",
"5 216138.632575\n",
"6 217068.777963\n",
"7 217998.923351\n",
"8 218929.068739\n",
"9 219859.214127\n",
"10 220789.359515\n",
"11 221719.504904\n",
"12 222649.650292"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"------------------------------------\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Forecast log for monthly data\n",
"\n",
"Changing Holt-Winters *alpha* from 0.20 to 0.10 varies the forecast only slightly. The important parameter is *beta* to capture trend effects. Currently we shall rely on default Holt-Winters settings for robustness.\n",
"\n",
"\n",
"- 2014-09-01, Twelve-month Forecasts given data through 2014-07-01:\n",
" - Inflation at 1.44%.\n",
" - 10-y Bonds price -6.7%, thus rate +75 bp given zero10dur. \n",
" - SPX +16.6% to 2280.\n",
" - Gold tanks from 1286 to 1067. \n",
" - USD +1.4% broadly.\n",
"\n",
"\n",
"- 2014-10-11, Twelve-month Forecasts given ten-year data, robust HW:\n",
" - Inflation at 1.9%\n",
" - Zero10 indicates slight downward pressure on interest rates.\n",
" - SPX to 2239, but market seems skeptical.\n",
" - Gold tanks to 1184 (region which we have seen just recently).\n",
" - USD definitely has an upward bias against all FX, even NZD and AUD.\n",
" - Home prices looking to increase from \\$203K to \\$220K \n",
"\n",
"\n",
"- 2015-05-28, Twelve-month Forecasts given data through 2015-03-01, robust HW:\n",
" - Inflation at 0.5% (which seems dramatic).\n",
" - Zero10 price increases by 8.92%, thus 10-year rate decreases by 100 bp.\n",
" - SPX to 2322, but no metric says it's fair valued.\n",
" - Gold to 1130, which would break support.\n",
" - USD very strong, up 12% globally (QE-EU started, and possible Grexit).\n",
" - Home prices looking to increase from \\$214K to \\$223K"
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"DAILY DATA"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We examine bonds (zero coupon equivalent of 10-y Treasury), equities (SPX), gold (XAU), EURUSD, and USDJPY at higher frequency (daily) for the most recent developments. \n",
"\n",
"[Inflation, real trade-weighted USD, and US home price data have a slow release schedule (monthly).] "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Specify daily series of interest:\n",
"ds = [ d4zero10, d4spx, d4xau, d4eurusd, d4usdjpy ]\n",
"names = [ 'Zero10', 'SPX', 'XAU', 'EURUSD', 'USDJPY' ]\n",
"\n",
"# Download into a dictionary:\n",
"dsd = {}\n",
"for i in ds:\n",
" dsd[i] = getfred(i)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" :: S&P 500 prepend successfully goes back to 1957.\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Compute the YoY percentage change (overlaping):\n",
"dsdc = {}\n",
"for i in ds:\n",
" dsdc[i] = pcent( dsd[i], 256 )"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Construct the YoY dataframe:\n",
"dega = paste( [ dsdc[i] for i in ds ] )\n",
"# Give names to the columns for mega:\n",
"dega.columns = names"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Start from the recent:\n",
"u0 = '2010-01-01'"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Overlapping YoY percentage change, recently:\n",
"boxplot( dega[u0:], 'Assets YoYd' )"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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0pegQkuG5yKT+GvEG3bk6hoeLjiAdnove4TV0rw8653pIqWvokpreoPnysVyh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\n5/qEN+jOOdcnvEF3zrk+8f8BS/pVNP686GMAAAAASUVORK5CYII=\n",
"text": [
""
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" :: Finished: boxplot-Assets_YoYd.png\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Geometric mean returns, non-overlapping, annualized:\n",
"for i in range(len(ds)):\n",
" print names[i], georet( dsd[ds[i]][u0:] )"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Zero10 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[2.33, 2.61, 7.52, 256]\n",
"SPX "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[11.36, 12.57, 15.53, 256]\n",
"XAU "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[1.36, 2.89, 17.49, 256]\n",
"EURUSD "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[-4.21, -3.77, 9.43, 256]\n",
"USDJPY "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[4.96, 5.4, 9.33, 256]\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Forecast log for daily data\n",
"\n",
"- 2014-10-11, Really near-term picture is too bright for SPX while XAU looks dark. Sell stocks, and start to accumulate gold.\n",
"\n",
"\n",
"- 2015-05-28, XAU georet changed from 2.6% to 1.6%. Zero10 monthly forecast is basically unchanged. Real rate is what matters for gold. USD stronger by 4.8% against both the EUR and JPY."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Show esp. correlations:\n",
"stats( dega[u0:] )"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Zero10 SPX XAU EURUSD USDJPY\n",
"count 1426.000000 1426.000000 1426.000000 1426.000000 1426.000000\n",
"mean 1.902672 15.245862 5.972715 -2.194030 4.307208\n",
"std 6.762567 9.818755 18.978442 8.842339 12.024459\n",
"min -13.248728 -5.657641 -29.210332 -23.984762 -14.310589\n",
"25% -3.402214 9.723296 -8.516970 -8.651129 -6.838512\n",
"50% 2.684079 14.060072 2.285300 -0.706405 1.967362\n",
"75% 6.184020 20.287348 24.319358 4.492467 15.174316\n",
"max 18.075299 65.300874 52.361809 21.056554 30.357599\n",
"\n",
" :: Index on min:\n",
"Zero10 2010-01-07\n",
"SPX 2011-10-03\n",
"XAU 2013-12-26\n",
"EURUSD 2015-03-11\n",
"USDJPY 2011-03-17\n",
"dtype: datetime64[ns]\n",
"\n",
" :: Index on max:\n",
"Zero10 2012-02-01\n",
"SPX 2010-03-02\n",
"XAU 2011-09-06\n",
"EURUSD 2011-06-06\n",
"USDJPY 2013-05-28\n",
"dtype: datetime64[ns]\n",
"\n",
" :: Head:\n",
" Zero10 SPX XAU EURUSD USDJPY\n",
"T \n",
"2010-01-01 -11.463243 22.574830 27.081507 4.506344 2.117389\n",
"2010-01-04 -11.776234 27.252204 32.369431 6.846980 2.548476\n",
"2010-01-05 -11.858700 30.595454 35.822249 7.904398 2.878992\n",
"2010-01-06 -12.554147 30.437376 36.721113 9.137748 3.212493\n",
"2010-01-07 -13.248728 35.492867 37.583688 8.653408 4.513889\n",
"2010-01-08 -13.173018 35.702942 39.104938 9.645639 3.471370\n",
"2010-01-11 -12.321456 34.919776 38.290855 9.755361 1.783143\n",
"\n",
" :: Tail:\n",
" Zero10 SPX XAU EURUSD USDJPY\n",
"T \n",
"2015-06-11 1.966382 7.760938 -7.186454 -17.181396 21.006265\n",
"2015-06-12 2.237337 6.870700 -8.522815 -17.195301 21.003535\n",
"2015-06-15 2.418714 6.192973 -9.988571 -17.076402 20.794987\n",
"2015-06-16 2.782262 6.811338 -10.334983 -17.325094 21.089303\n",
"2015-06-17 2.419197 7.715977 -10.656049 -17.250515 21.658670\n",
"2015-06-18 1.966775 8.252489 -8.726030 -16.380701 20.756757\n",
"2015-06-19 2.419923 7.805459 -8.259958 -16.715650 20.696439"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" :: Correlation matrix:\n",
" Zero10 SPX XAU EURUSD USDJPY\n",
"Zero10 1.000000 -0.750870 0.418415 -0.575325 -0.417933\n",
"SPX -0.750870 1.000000 -0.152196 0.404478 0.159153\n",
"XAU 0.418415 -0.152196 1.000000 0.074339 -0.866292\n",
"EURUSD -0.575325 0.404478 0.074339 1.000000 -0.093702\n",
"USDJPY -0.417933 0.159153 -0.866292 -0.093702 1.000000"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 2015-05-29, Suprisingly, very little correlation between EURUSD and USDJPY: -6%. Gold appears more correlated with USDJPY at -87% than EURUSD at +6%"
]
}
],
"metadata": {}
}
]
}