lecture 2: probability and insurance - open yale courses · 2018-08-14 · lecture 2: risk and...
TRANSCRIPT
![Page 1: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/1.jpg)
Lecture 2: Risk and Financial Crises
Economics 252, Spring 2011Prof. Robert Shiller, Yale University
![Page 2: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/2.jpg)
Return
![Page 3: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/3.jpg)
Expected Value, Mean, Average
∑ ∞
====
1)()(
iix xxxprobxE iµ
∫∞
∞−
== xdxxfxE x )()( µ
∑=
=n
ii nxx
1/
nn
iixx /1
1
)()G( ∏=
=
![Page 4: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/4.jpg)
Variance and Standard Deviation
nxxsn
iix /)( 2
1
2 −= ∑=
2
1))((prob)var( xi
n
ii xxxx µ−== ∑
=
![Page 5: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/5.jpg)
Covariance
nyyxxyxn
i/))((),cov(
1−−= ∑
=
![Page 6: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/6.jpg)
Correlation
• A scaled measure of how much two variables move together
• -1 ≤ ρ ≤ 1
)/(),cov( yxssyx=ρ
![Page 7: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/7.jpg)
Variance of Sum
![Page 8: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/8.jpg)
Stock Market Level, 2000-2010, 2000=100
![Page 9: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/9.jpg)
Apple, Inc. and S&P 500 Monthly Adjusted Price First Decade of 2000s, 2000=100
![Page 10: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/10.jpg)
Apple, Inc. and S&P 500 Monthly Returns, First Decade of 2000s
![Page 11: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/11.jpg)
Scatter, Apple vs S&P 500
![Page 12: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/12.jpg)
Same Scatter with Regression Line
![Page 13: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/13.jpg)
Norm al Distribution w ith Zero M ean
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
-15 -10 -5 0 5 10 15
Return (x)
f(x) Standard Dev. = 3
Standard Dev. = 1
![Page 14: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/14.jpg)
Norm al Versus Fat Tailed Distributions
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
-15 -10 -5 0 5 10 15
Return x
f(x) Normal Distribution
Cauchy Distribution
![Page 15: Lecture 2: Probability and Insurance - Open Yale Courses · 2018-08-14 · Lecture 2: Risk and Financial Crises Economics 252, Spring 2011 Prof. Robert Shiller, Yale University](https://reader033.vdocuments.site/reader033/viewer/2022042310/5ed835c50fa3e705ec0e0a5b/html5/thumbnails/15.jpg)