L2_Models and Regression

# L2_Models and Regression - Topic 2 Basic Models in Finance...

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Topic 2 asic Models in Finance and Basic Models in Finance and Linear regression

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Key concepts from last topic Returns – focus of financial econometrics Stylized facts: 1. Linear nonpredictability of returns . Predictability of volatility (or squared returns) 2. Predictability of volatility (or squared returns) 3. Heavy tails (leptokurtosis) N lit 4. Non-normality (Geometric) Random Walk = (weakly) efficient market
Portfolio • Portfolio – collection of individual stocks • Combining stocks into portfolios can reduce standard eviation (risk of the portfolio) deviation (risk of the portfolio) • Example with 2 stocks: – Coca-Cola – lower exp (average) return, lower risk xxon Mobile – igher exp (average) return higher risk Exxon Mobile higher exp (average) return, higher risk •M a gic: portfolio can provide higher exp return with gp p g p lower risk

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Markowitz Portfolio Theory Expected Returns and Standard Deviations vary given ifferent weighted combinations of the ocks: Expected Return (%) different weighted combinations of the stocks: Exxon Mobil 0% in Coca Cola 40% in Coca Cola Coca Cola Standard Deviation
Power of Diversification •Twos to ck s :AandB ame xp turn = Same exp return 2 • Same risk, std. dev = 1 • No correlation! • Simple Portfolio: 0.5A+0.5B xp return of the portfolio 0.5 2 0.5 2 R  Exp return of the portfolio • What about risk of the portfolio? p 22 0.5 * 1 0.5 * 1 0.5 0.7 1! p 

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Market portfolio • Market portfolio - collection of many stocks on themarket E.g. Indices: Dow Jones Industrial Averages, Standard and Poors 500 e n duce dividual ock sk We can reduce individual stock risk • Still susceptible to market risk • Many stocks returns are correlated, why? usinesses e terrelated! Businesses are interrelated!
Capital asset pricing model • What would be a “fair” expected return on any stock? – Since there is risk involved it should be higher then risk-free rate Risk-free rate – interest on bank deposit, useful benchmark xcess turn turn n p f e sk ee te lled Excess return – return on top of the risk-free rate, so called risk premium • How are individual stock (or small portfolio) returns related to the market ortfolio returns? p ,, cov( , )  it ft mt RR R R var( )

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antas (beta=1 18) vs Qantas (beta=1.18) vs. AORD
Lihir Gold vs. AORD

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CAPM | ) ( ) R R R R R R ,, , , , , (| , )( it mt ft ER Expected return at time t is conditional on (determined by) sk free return at time t, t R risk free return at time t, • market return at time t, nsitivity to market movements , , R sensitivity to market movements,
CAPM | ) ( ) R R R R R R ,, , , , , (| , )( it mt ft ER What about actual return –its not known and depends on stochastic (random) factor u ) R R R u , , ()  f tm t f tt RR

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Testing for CAPM and computing beta ) R R R u )  R R R u ,, , , ()  it ft mt t RR   t • Estimate the model and test whether 0 
Simple example: CAPM • Suppose that we have the following data on the excess

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L2_Models and Regression - Topic 2 Basic Models in Finance...

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