Solution Manual for Statistics and Data Analysis for Financial Engineering 2nd Edition by David Ru

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A Solution Manual for: Statistics and Data Analysis for Financial Engineering: 2nd Edition

by David Ruppert and David Matteson John L. Weatherwax∗ March 24, 2021

∗

wax@alum.mit.edu

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Introduction Here you’ll find some notes that I wrote up as I worked through this excellent book. For some of the problems I used R to perform any needed calculations. The code snippets for various exercises can be found at the following location: http://www.waxworksmath.com/Authors/N_Z/Ruppert/SNDAFFE_2nd_Edition/ruppert.html

I’ve worked hard to make these notes as good as I can, but I have no illusions that they are perfect. If you feel that that there is a better way to accomplish or explain an exercise or derivation presented in these notes; or that one or more of the explanations is unclear, incomplete, or misleading, please tell me. If you find an error of any kind – technical, grammatical, typographical, whatever – please tell me that, too. I’ll gladly add to the acknowledgments in later printings the name of the first person to bring each problem to my attention.

Acknowledgments Special thanks to (most recent comments are listed first): Chenguang Wang, Reina Shintaku, Ajay Julian, Som Sowmyan, Duc Truyen Dam, Martin Vedani, Patrick Ahearn, John Chung, and Xu Ren for helping improve these notes and solutions.

Contents 1 Chapter 2 (Returns)

6

2 Chapter 3 (Fixed Income Securities)

17

3 Chapter 4 (Exploratory Data Analysis)

31

4 Chapter 5 (Modeling Univariate Distributions)

45

5 Chapter 6 (Resampling)

64

6 Chapter 7 (Multivariate Statistical Models)

71

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7 Chapter 8 (Copulas)

79

8 Chapter 9 (Regression: Basics)

93

9 Chapter 10 (Regression: Troubleshooting)

102

10 Chapter 11 (Regression: Advanced Topics)

109

11 Chapter 12 (Time Series Models: Basics)

118

12 Chapter 13 (Time Series Models: Further Topics)

137

13 Chapter 14 (GARCH Models)

154

14 Chapter 15 (Cointegration)

171

15 Chapter 16 (Portfolio Theory)

176

16 Chapter 17 (The Capital Asset Pricing Model)

185

17 Chapter 18 (Factor Models and Principal Components)

195

18 Chapter 19 (Risk Management)

207

19 Chapter 20 (Bayesian Data Analysis and MCMC)

220

20 Chapter 21 (Nonparametric Regression and Splines)

228

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0.1

0.15 0.10

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MRK return

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FReturn

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−0.10 −0.15

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GMReturn

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MSFT return

Figure 1: Left: A scatter plot of the returns of Ford as a function of the returns of GM. Left: A scatter plot of the returns of Merck as a function of the returns of Microsoft.

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Chapter 2 (Returns)

R Lab See the R script Rlab.R where the problem for this chapter are worked.

Problem 1 (GM and Ford returns) In Figure 1 (left) we show the scatter plot of the returns of Ford as a function of the returns of GM. We notice that these returns do appear to be correlated (they are distributed somewhat symmetrically about a line) and the outliers of each stocks return do appear together.

Problem 2 In the accompanying R code we plot the two returns. The two sets of points lie almost exactly on the line y = x. They have a correlation (using the R function cor) given by 0.9995408.

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