Open Yale Lecture 2

The Universal Principle of Risk Management: Pooling and the Hedging of Risks

LINK

http://www.youtube.com/watch?v=WMkD8HKJQCM&list=PL8F7E2591EE283A2E&index=2&feature=plpp_video

SUMMARY


It is interesting that the concept of probability and statistic were appeared relatively late in the history, after 17 century. Today's class reviewed all principals in mathematics aspect. 1) Independent theory 2) Multiplication theory 3) Sampling/Geometric average 4) variance/co-variance 5) Gaussian distribution 6) PV


NOTES

1.     Historical introduction

Probability

1600 <

17 century

Probable …  trust worthy ness , in Shakespeare

Probability theory / sampling theory - Nala M.

Life table – insurance – ancient Rome

In Renaissance Italy – insurance policy started

Slow start of insurance in history  – due to no lack of probability concept, no clear meaning

Luck / Risk – the theory is away from this.

2.    Principals

P: Prob  0<= P <= 1  (basic)

·         Independent Theory

Independence  (Independent Event) 

·         Multiplication rule

P(A & B) = P(A) * P(B)

i.e. Fire in London

No risk of whole city burn down for insurance company

·         Binominal Distributor

F(x) = P^x (1-P) ^(n-x) n!/(n-x) !

# of accidents

·         Expected Value, Mean, Average

x : Random Variable

Population  E(x) = Myu x = (Sum i= 1-infinit) P(x-xi)xi

Average Sum(i=1-n) xi/n  

·         Sampling Ave.

·         G(x) = Geometric average  : multiply  all and ^1/n  -- Finance use to expect returns

  - lower number then E(x)

Experiment

E(x) = Myu x = Integral –infinit to + infinit f(x)x dx

Variance Sigma S^2 Standard Deviation

·         Population Variance Var(x) = Sum P(x-xi_(xi-u)^2

S(x)^2 = Sum (x-xbar)^2/n – Sample variance

·         Covariance (2 random variables)

C(x,y) = Sum (xi -xbar)(yi -ybar)/n

Negative / positive

Move differently / move together

Correlation

Corr -1 ~ <= P <= +1

P=Cov(x,y)/SxSy

·         Regression – Gauss

Y=Return on A Inc.

X= Return on MKT

Regression line

Alpha (Y(X0))  & Beta (slope)

A’s Performance  in the market

·         Normal Distribution – Gaussian distribution

Bell Shape Curve

Fat Tailed distribution = lots of returns

(+) Right tail / (-) Left tail

·         Present Values PV

·         Console or Perpetuity

• Annuity
• Utility function