STATISTICAL FINANCE R PROGRAMMING AND EXAMPLES

R Code and examples

for David Ruppert 's book: Statistics and Finance: An Introduction

Shortcut I: Chapter 2, 3 (Returns), 4 (Times Series), 5 (Portfolio Theory), 7 (CAPM), 8 (Option Pricing), 9 (Fixed Income), 10 (Resampling), 12 (Garch); Useful Resources, Link of the book , About this Homepage

Note: Some programming might require additional R packages, please install required packages before running them. Please click Useful Resources for package information .

Chapter 1: Introduction

Chapter 2: Probability and Statistical Models

Fig 2.2 & R Code : Binomial Probability distribution with n=10 and p=0.6

Fig 2.3 & R Code: Example of Normal Probability densities

Fig 2.4 & R Code: Example of lognormal Probability densities

Fig 2.5 & R Code: CDF & Empirical CDF

Fig 2.6&2.7 & R Code: Normal Probability Plot, normal data vs lognormal data

Fig 2.8 & R Code: Several binomial probability distributions with n=10 and their skew ness

Fig 2.9 & R Code: Comparison of a normal density and a t-density with 5 degrees of freedom. Both densities have mean 0 and standard deviation 1.

Fig 2.10 & R Code: Normal Plot of a sample of 999 N(0,1) data plus a contaminant.

Fig 2.11 & R Code: Comparison on normal and heavy-tailed distributions.

Fig 2.12 & R Code: Survival function of a Pareto distribution with c=0.25 and a=1.1 and of normal and exp distribution on being greater than 0.25.

Fig 2.13 & R Code: Sample correlation coefficients for eight random samples.

Fig 2.14 & R Code: Prior and posterior densities in Examples 2.17.

Fig 2.15 & R Code: Posterior CDF in Examples 2.17.

Chapter 3: Returns

Required packages: fSeries nortest

Fig 3.1 & R Code: Comparison of functions log(1+x) and x

Fig 3.2 & R Code: Means and bounds on a random walk with S0=0, mean = 0.5 and standard deviation=1.

Fig 3.3 & R Code: Two independent simulations of a geometric random walk (GRW) with u=0.1 and sigma=0.2

Fig 3.4 & R Code : GE Daily return. The first plot is the prices. The second and third are the net returns and log returns. The fourth plot is a normal probability plot of log returns. The final plot is of the absolute value of log returns.

Fig 3.5 & R Code: Five independent simulations of a geometric random walk( GRW) and GE Daily daily log returns.

Fig 3.6 & R Code: Three independent simulations of Price series. On Left: log prices. On right: prices.

Basic Statistic (including skewness and kurtosis) and Normality Tests for univariate statistics, using GE Daily return data.

An example for downloading Finance data from YAHOO.

Chapter 4: Time Series

Required packages: fSeries tseries

Fig4.1 & R Code: Autocorrelation functions of AR(1) processes with r equal to 0.95 , 0.75,0.2 and -0.9

Fig4.2 & R Code: Simulations of 200 Observations from AR(1) processes with various parameters. The white noise process is the same for all four AR(1) Processes.

Fig4.3 & R Code: Simulations of 30 Observations from AR(1) processes with various parameters. The white noise process is the same for all four AR(1) Processes.

Fig4.4 & R Code: Simulations of 1000 Observations from AR(1) processes with various parameters. The white noise process is the same for all four AR(1) Processes.

Fig4.6 & R Code: AR(1) Process with mu=0.4 and a=0.4, the integral of this AR(1) and second integral of this AR(1).

Fig4.7 & R Code: Time series plot of the 3 month Treasury bill rates, plot of first differences, and ACFs. The data set contains monthly values of the 3 month rates from Jan 1950 until Mar 1996.

Model fit and diagnostics:

Model Fit Examples R Codes: Fit GE Daily log return using AR(1),AR(6), MA(2), ARMA(2,1) and log price using ARIMA(2,1,0) Model

Results: AR(1), AR(6), MA(2), ARMA(2,1), ARIMA(2,1,0)

Residual Plots: AR(1), AR(6), MA(2), ARMA(2,1), ARIMA(2,1,0)

Model Selection:

AIC BIC

Forecasting:

Fig4.8 & R Code & Predicts: Time series plot of the daily GE log returns with forecasts from an AR(1).

Fig4.9 & R Code: Time series plot of the daily GE log Prices with forecasts from an ARIMA(1,1,0) Model.

Chapter 5: Portfolio Theory

Required packages: quadprog

Fig5.1 & R Code: Expected Return for a portfolio with allocation w to the risky asset and risk free return.

Fig5.2 & R Code: Expected Return Versus risk for Example 5.4.

Fig5.3 & R Code: Expected frontier and tangency portfolio with different r.

Tangency portfolio without the constraints R code

Fig5.4 : Efficient frontier (solid) plotted for N=3 assets.

Fig5.5 : Weights for assets 1,2 and 3 as functions of return.

Fig5.7 : Weights for assets 1,2, and 3 as function of return. The weights for all three assets are constrained to be nonnegative

Fig5.8 : Efficient frontier and line of optimal combination of N=3 risky assets with risk free asset.

Tangency portfolio with the constraints R Code:

Fig5.6 : Efficient frontier for N=3 with and without constraint of no negative weights.

Fig5.9 : Efficient frontier and tangency portfolio with the constraints that the weights are nonnegative.

Chapter 7: The Capital Asset Pricing Model

Required packages: pspline

Example 7.3: R Code, Data & Output, Page 239

An interesting Question: R Code & Data, Page 247-250

Output: 1. Linear regression with an intercept,

2. Broken Line Model: output

3. Linear regression with no intercept: output

Figure 7.4: Monthly excess log return from 03-1996 to 02-2001 for Ford plotted against those for the S&P 500 index. The curve is a a penalized spline.

Figure 7.5: Excess log returns of Ford plotted against those of the S&P 500 with three fits, a penalized spline, broken line model and line with no intercept.

Figure 7.6: Gross k period return of S&P 500 and Ford since 03-1996 plotted against k.

Is Beta Constant? Example 7.4: R Code ,Data & Output, Page 251

Chapter 8: Option Pricing

R Code Volatility smiles and polynomial regressionpage 283-284

Fig8.9 : A plot of hatV vs K when T=mean(T) for GE options.

Fig8.10: A plot of hatV vs T when K=mean(K) for GE options.

R Code: Page285

Fig8.11: A plot of hatV vs K and T for GE call options.

Fig8.12: A plot of standard error of Hat(V) vs K and T for GE call options.

R Code

Fig 8.14 : Evolution of option prices. Stock prices is a Geometric Brownian motion. Page 289.

Fig 8.15: Ratio of Log Return on a call to log return on the underlying stock. Page 291.

Fig 8.16: Ratio of Log Return on a put to log return on the underlying stock. Page 291.

Fig 8.17: Delta and Theta for the call option and simulated data (stock 2). Page 294.

Chapter 9 Fixed Income Securities

Fig 9.1 & R Code : Bond price versus the interest rate r. Page 308

R Code for Fig 9.3 : Prices of the U.S. STRIPS plotted as a function of maturity. Page 322

Fig 9.4 : Polynomial and spline estimates of forward rates of U.S. Treasury bonds.

output: Anova for nonlinear regression.

Chapter 10 Resampling

Resampling and Efficient Portfolios:

R Code

Fig 10.2 : Time series plots of returns for the 10 equity markets. Page 333

Fig 10.3: Autocorrelation plots of returns for the 10 equity markets. Page 334

Fig 10.4 : Normal probability plots of returns for the 10 equity markets. Page 335

Fig 10.5 : Actual efficient frontier for the sample (optimal) and bootstrap efficient frontier (achieved) for each of six bootstrap resamples.

Fig 10.6: Results from 400 bootstrap resamples. For each resample, the efficient portfolio with a mean return of 0.012 is estimated. In the upper subplot, the actual mean return and standard deviation of the return are plotted as a small dot. The large dot is the point on the efficient frontier with mean return of 0.012.

Fig 10.7 : Results from 400 bootstrap resamples assuming that the vector of mean returns is known. For each resample, the efficient portfolio with a mean return of 0.012 is estimated using the mean returns from the sample and the covariance matrix of return from the resample.

Chapter 12: GARCH Models

Required packages: fSeries

Data Simulation:

Fig12.2 & R Code: Simulations of 60 observations from an ARCH (1) process and an AR(1)/ARCH(1) process. Page 368

Fig12.3 & R Code: Simulations of 600 observations from an ARCH (1) process and an AR(1)/ARCH(1) process. Page 369

Fig12.4 & R Code: Simulations of 600 observations from an GARCH (1,1) process and an AR(1)/GARCH(1,1) process. Page 371.

Model Fit:

** R Code: GARCH Model Fit, Page 373.

USEFUL LINKS:

R General: R Project R Package Index standard library Contributed Packages

The R Manuals: An Introduction to R [browse HTML | download PDF ]

The R language definition [browse HTML | download PDF ]

R for Beginners (PDF) R reference card (PDF)

Finance: CRAN Task View: Empirical Finance

Finance Package Rmetrics :

Overall: Overview Fact Sheet Reference Card