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fecon235 :: Notebooks for financial economics

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Spin-off Notice: the modules and functions used by our research notebooks have been refactored into another repository, fecon236. The home for our Jupyter notebooks will remain here at fecon235 in the nb directory.

What is this repository for?

fecon235 provides an interface for financial economics to the Python ecosystem, especially packages for mathematics, statistics, science, engineering, and data analysis. Complex packages such as numpy, pandas, statsmodels, scipy, and matplotlib are seamlessly integrated at a high-level with APIs of various data hosts for:

To practically test theoretical ideas interactively, our code can employed with any Python IDE interactive development environment, IPython console, or with a Jupyter notebook. The code has been tested against both python27 and python3 since 2014, and works across major platforms: Linux, Mac, and Windows.

Database: the primary source is FRED, the U.S. Federal Reserve Economic Data bank which is accessed directly online using our interface. Other specialized data can be directly retrieved using our Quandl API module, for example, futures prices. Data for stocks, mutual funds, and ETFs is retrieved from the best available sources using pandas_datareader. Data is designed to be accessible free of charge, and interoperable in different time frequencies.

How does one get started?

Some basic commands like get() and plot() will do a lot of the heavy lifting to get you started immediately. The commands are very easy to customize, producing sophisticated results quickly without tweaking the underlying numerical packages.

The docs directory should be gradually adding tutorials. The source code, in the meantime, is thoroughly annotated.

Examples of code

The best way to see the code in action is to run the notebooks in the nb directory which are described further below. Note that GitHub can render Jupyter notebooks directly in the browser, however, they will not be executable.

Here is a rendering of a notebook at GitHub for Housing economy, home prices and affordibility https://git.io/housing If you had executed that notebook locally, it would have also retrieved the latest available data and recomputed the results.

How is worker's wage correlated with GDP output? See https://git.io/gdpwage How much Federal debt must each worker assume? And how fast is the US government debt increasing? https://git.io/debtpop

To score the Federal Reserve's performance under its dual mandate for inflation and unemployment, see https://git.io/fed (where tangentially the Phillips curve is discredited by constructing heat map scatter plots). Notebook https://git.io/infl gives an in-depth analysis of inflation, including a combined forecast using three orthogonal methods.

Elevated default risk across bond markets is indicative of a weak economy. But how can a policy maker calibrate credit spreads to assess changes in interest rates? We consider mortgage and corporate credit spreads to construct a robust Unified Credit Profile (a tutorial on MAD, Median Absolute Deviation, in rescaling non-Gaussian time-series), see https://git.io/creditprof

Please see https://git.io/fedfunds to forecast the Fed Funds rate using futures contracts on LIBOR.

The notebook https://git.io/cotr discerns how various asset classes are positioned in the market. In contrast, an overview of asset prices is given in https://git.io/georet using geometric mean returns.

In https://git.io/gold we make a conjecture that real gold prices is a stationary time-series bound by real interest rates. In https://git.io/xbt Bitcoin is statistically analyzed as a financial asset. We examine the crude oil markets, specifically the Brent over WTI spread, and construct an optimal portfolio, in https://git.io/oil .

SEC 13F filings can be easily parsed, see https://git.io/13F where we track asset managers Stanley Druckenmiller and John Paulson.

In https://git.io/equities we examine the separable components of total return for equities, especially due to enterprise earnings and market speculation, using S&P data assembled by Robert Shiller which goes back to the year 1871. In https://git.io/gdpspx we examine the close relationship between the real economy and the equities market, while demonstrating the Holt-Winters time-series model for predictions.

In https://git.io/gmix we analytically and visually show how a Gaussian Mixture model handles "fat tail" risk of leptokurtotic financial assets under small-sample conditions. Markowitz portfolios, designed in the arithmetic mean-variance framework for a static period, are notoriously fragile when markets change. In contrast, our Boltzmann portfolios are adaptive over multi-periods to geometrically maximize wealth using techniques from reinforcement learning. Part 1: https://git.io/boltz1 Part 2: https://git.io/boltz2

Bootstrapping has two benefits: small-sample statistics and simulation from controlled population. In https://git.io/bootspx we simulate alternate histories for leptokurtotic SPX equity returns: to visualize sample price paths, and for estimating probabilities of events such as investment loss.

Development and contacts

This project is a derivative from the seminar series held at the University of California at Berkeley, jointly sponsored by the Department of Economics and the Haas School of Business. We are also grateful to BIDS, Berkeley Institute for Data Science, and the Mathematical Sciences Group for their technical support.

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Partial contents of nb directory

gauss-mix-kurtosis.ipynb : Gaussian Mixture and Leptokurtotic Assets

Gaussian Mixture GM(n) can create distributions with leptokurtosis ("fat tails"). Our problem is the inverse: from observable statistics, deduce the model parameters analytically. We demonstrate how a GM(2) model can synthesize Gaussian risk-equivalence for leptokurtotic financial assets. A numerical solution provides accurate probabilities which can be used to experimentally understand how kurtosis itself is distributed under small-sample conditions. The non-Gaussian distributions are visualized through quantile-quantile probability plots. Shortcut: https://git.io/gmix

boots-eq-spx.ipynb : Bootstrap leptokurtotic SPX equity returns

Bootstrapping has two benefits: small-sample statistics and simulation from controlled population. We simulate alternate histories: to visualize sample price paths, and for estimating probabilities of events such as investment loss. Bootstrapping facilitates study of small-sample behaviour for which asymptotic statistical theory is unsuitable, or where closed-form mathematical analysis is intractable, for example, geovolatility which is the volatility of the geometric mean rate. Shortcut: https://git.io/bootspx

prtf-boltzmann-1.ipynb : Boltzmann portfolios

We develop an alternative to the Markowitz framework called Boltzmann portfolios which handle uncertainty from the standpoint of cross-entropy and optimal sequential decisions. The improved result is a faster online algorithm which is more robust. Markowitz portfolios are designed in the arithmetic mean-variance framework for a static period, and are fragile to changing market conditions. In contrast, Boltzmann portfolios are adaptive over multi-periods to geometrically maximize wealth using techniques from reinforcement learning. Part 1: https://git.io/boltz1 Part 2: https://git.io/boltz2

qdl-spx-earn-div.ipynb : Separable components of total return for equities

We specify a model for equity returns by decomposition into enterprise and speculative returns, plus dividend yield. That model is then tested using stock market data going back to the year 1871 (well-known database assembled by Robert Shiller). An understanding of their respective contributions helps us to form better informed expectations of total return for equities. We demonstrate that the (arithmetic) percentage reasoning is prone is large errors, whereas a logarithmic (geometric) version is exact. Shortcut: https://git.io/equities or https://git.io/spx

qdl-libor-fed-funds.ipynb : Use pandas to analyze short-term rates

We examine the spread between two interest rates: LIBOR and Fed Funds. The former has a much greater depth in the futures market in terms of volume and maturity horizon, implying richer information content. Modeling their relationship, we construct a synthetic forward Fed Funds rate, useful in gauging market sentiment regarding Fed policy. Estimate is given for the change in Fed Funds rate over the next 12 months. Shortcut: https://git.io/fedfunds

qdl-xau-contango.ipynb : Use pandas to analyze gold contango

The London Bullion Market Association ceased publishing daily data on their Gold Forward Offered Rate (GOFO), as of 30 January 2015 -- so we develop an observable proxy called tango using gold futures and LIBOR. This supply/demand indicator is then compared against change in spot prices. Observed strong correlations appear to be artificial. Shortcut: https://git.io/xau-contango

qdl-xbt-bitcoin.ipynb : Statistical analysis of Bitcoin as financial asset

We first examine time-series data for price, mining, and capitalization of Bitcoin, then optimize a robust model for the extremely volatile USD price series. Taking the viewpoint of a Chinese user we perform a comparative valuation in Chinese yuan, and also cross-check with the perennial store of value: gold. The astonishing volatility and geometric return makes Bitcoin a speculative financial asset which may hinder it as a payment system. Shortcut: https://git.io/xbt

qdl-COTR-positions.ipynb : Use pandas to read CFTC COTR

Commitment of Traders Report (COTR) is useful to extract market positions in precious metals, US dollar, interest rates, and equities markets. We develop our own scale-free measures to gauge market sentiment across time which can diverge from price directionality at interesting points. Shortcut: https://git.io/cotr

SEC-13F-parse.ipynb : Use pandas to read 13F filings from SEC

Sort percentage allocation to long equities. Caveats are noted for portfolio management. Module yi_secform easily sums up 13F filings by one function. For illustration, we follow asset managers with significant positions in GLD, a gold ETF; see Stanley Druckenmiller's sudden accumulation, and John Paulson's dramatic liquidation. Shortcut: https://git.io/13F

fred-credit-spreads.ipynb : Robust profiles of credit spreads

Serves as a tutorial on MAD, Median Absolute Deviation, for robustly rescaling non-Gaussian time-series. We consider mortgage and corporate credit spreads to construct a robust Unified Credit Profile to calibrate credit default risk in the context of monetary policy. Shortcut: https://git.io/creditprof

fred-debt-pop.ipynb : Growth of Federal debt, its burden on the US population

We examine US government debt in real terms, and the current Federal debt per capita. Shortcut: https://git.io/debtpop

fred-employ-nfp.ipynb : US employment data, Nonfarm Payroll

We focus on forecasting the monthly change in NFP using a variety of optics: baseline expectation since 1939, Holt-Winters method, visual selection of local range, regression against economic activity (SPX) -- but the standard errors are inherently very large due to survey measurement error.

fred-eur-fx.ipynb : Euro currency qua Foreign Exchange

We examine euro FX data from the Fed Reserve FRED database. Our synthetic time-series, which takes us far back as 1971, give additional perspective to observe the cross-rates against U.S. dollar and Japanese yen.

fred-eurozone.ipynb : Eurozone economics

We examine the usual suspects: unemployment, inflation, real interest rate, foreign exchange rate, comparative GDP. Appendix 1 concisely explains the euro crisis in a video.

fred-gdp-spx.ipynb : US real GDP vs. SPX: Holt-Winters time series forecasting

We examine the US gross domestic product's relationship to the US equity market (S&P 500), in real terms. Forecasts for both are demonstrated using the Holt-Winters time-series model. We derive the most likely range for real GDP growth, and identify extreme equity valuations aside from inflationary pressures. Shortcut: https://git.io/gdpspx

fred-gdp-wage.ipynb : U.S. GDP vs. Wage Income

How is wage correlated with GDP output? In answering this question, we derive a model for GDP growth based on observations from wage growth. Shortcut: https://git.io/gdpwage

fred-georeturns.ipynb : Comparative geometric mean returns

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. The focus is on geometric mean returns because they optimally express mean-variance under logarithmic utility. Shortcut: https://git.io/georet

fred-housing.ipynb : Housing economy, home prices and affordibility

Alan Greenspan in 2014 pointed out that there was never a recovery from recession without improvements in housing construction. Here we examine some relevant data, including the Case-Shiller series, and derive an insightful measure of the housing economy, hscore, which takes affordibility into account. Shortcut: https://git.io/housing

fred-inflation.ipynb : Inflation data from FRED using pandas

We examine inflation data: CPI and PCE, including the core versions, along with the 10-year BEI rate (break-even inflation) from the bond market. A unified inflation statistic m4infl is introduced, which leads to the estimation of the geometric mean rate. A robust optimized Holt-Winters model is used for forecasting. Shortcut: https://git.io/infl

fred-infl-unem-fed.ipynb : Score for the Fed's dual mandate

We examine unemployment and inflation data to construct a time-series which gives a numerical score to the Fed's performance on its dual mandate. The key is to find comparable units to measure performance and a suitable scalar measure to show deviation from the dual mandate. The visualization includes sequential scatter plots using color heat map, which can be extended to studies of the Phillips curve. Shortcut: https://git.io/phillips

fred-infl-velocity.ipynb : Inflation, money velocity, and interest rates

We examine and attempt to replicate the results of two interesting articles by Yi Wen and Maria Arias -- along the way, we take a detour and explore the connection between money velocity and bond rates. This will tie together their relationship with GDP and the money supply in a fitted equation.

fred-oil-brent-wti.ipynb : Oil: Brent vs. West Texas Intermediate (WTI)

We examine the history of crude oil prices, and their spreads. A Boltzmann portfolio is computed for optimal financial positions. Deflated prices give additional insight, along with some of the statistical tools useful in financial economics. Although WTI is more desirable than Brent from a petrochemical perspective, that preference is reversed when the metrics are financial. Shortcut: https://git.io/oil

fred-usd-RTB-xau.ipynb : Real trade-weighted indexes for USD, gold, and SPX

We examine the value of USD against a basket of 26 foreign currencies using real trade numbers. Trade statistics are released annually, however, the Fed uses international inflation data to adjust the weights monthly.

fred-wage-capital.ipynb : Real capital equivalence to wage-income

We determine how much real capital has been necessary for risk-free interest to match annual wage.

fred-xau-spx.ipynb : Gold vs. SP500 returns, XAU vs. SPX

Long-term comparison of two asset classes: we boxplot their return distribution and also compute geometric mean returns. Correlation between the two is shown to be nil. We then look at the history of projected returns using Holt-Winters method, which also gives the latest forecasts. To conclude, we closely examine the relative value of the two assets in terms of gold troy ounces per equity share. Analytically short equities vs. long gold is favorable for an investor with log utility, but hardly profitable over the long haul.

fred-xau-tips.ipynb : Gold and Treasury TIPS, their daily relationship

Using monthly data we previously found that there is strong correlation between gold and real rates, so we investigate this relationship on a daily frequency. We then use this correlation to help make forecasts using the Holt-Winters time-series method. Lastly, we show the history of gold prices in real terms which leads to our conjecture that real gold is a stationary time-series bound by real interest rates. Shortcut: https://git.io/gold

BSD License and TOS / This page, last update : 2018-12-03