Week 1 Notes
Week 1 Notes FIN 500
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This 2 page Class Notes was uploaded by D S on Wednesday October 7, 2015. The Class Notes belongs to FIN 500 at University of Illinois at Urbana-Champaign taught by Adam Clark-Joseph in Summer 2015. Since its upload, it has received 43 views. For similar materials see Introduction to Finance in Finance at University of Illinois at Urbana-Champaign.
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Date Created: 10/07/15
Introduction to Finance Week 1 Professor ClarkJoseph University of Illinois Urbana Champaign October 7 2015 1 Basic Statistics to Know Random Variable X is a measurable function X Q gt S that maps from the sample space Q to the state space S where S 6 IR look at Feng s notes for in depth discussion on Probability Space Q 73 If Looked at concrete example of coin ips Russian Roulette and Urbana Roulette all within the notes take away how you value the payoff in that state Meteorite Insurance Know Expectation and its properties X E 2211 IEiPz39 IEa bX CZ a blEX clEZ Quiz fair7 3 sided die once and rv X denotes score What is IEX 1 2 3 2 Quiz score on die doubled 10 IE2X 10 14 Variance and its properties and standard deviation Quiz variance of 3 sided die 2 12 12 g Bivariate and conditional distributions IEIEYX Covariance and Correlation again just review but highly encouraged to know these 012 covX1X2 IEX1 EX1X2 EX2 Correlation Coef cient is invariant to af ne transformations corra bX1d 0X2 2 corrX1 X2 2 Gaussian Normal Distributions return empirical stats properties of stock returns fwlu 02 1 62 7 a27r Know the main reasons of why the Gaussian is so special Return iiidt 1 also note for a small n the ordinary return and continuously compounded return are very similar multiperiod return is the sum of the returns Excess Return how much return exceeds a risk free rate short term government security a US Treasury Bill 7 Dividends payments made by a company to the shareholders in practice we ll usually ignore it for algebraic simplicity ex MSFT didn t pay dividends for many years Why do standard deviations grow approx with the square root of time prices make a so called random walk Brownian Motion Autocorrelations daily stock returns have low correlations with previous returns Correlations stock returns though tend to be highly correlated with each other and indexes which makes sense since indexes tend to hold the market trend Volatility standard deviation of the continuously compounded return a Note to extend T period volatility then multiply by VET Volatility Clustering high and low periods and high follows high low follows low Daily Returns are NOT Gaussian symmetric fat tails and high peak look at the kurtosis which is larger than normal Do daily returns have in nite variance No hurt CLT Failed proof times Lindenberg L vy Central Limit Theorem look up proof on Wikipedia if interested Why the independent and identically distributed assumptions are used and why nite variance matters 3 Side comments Talked about how much people in the class had to invest Talked about problem of being able to cut a sphere into two sphere of equal sie ie BanachTarski paradox Benoit B Mandelbrot and CLT Look at current events for the Chinese equities