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Lecture2_StockPricing

# T rst ers rbt erb cov 1t correlation coefficient

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Unformatted text preview: T Covariance observations): observations): Cov (rs, rB) = 1/T ∑tt=1,..,T [ rSt – E(rs) ] [ rBt – E(rB) ] Cov =1,..,T Correlation Coefficient: Correlation ρ SB Cov(rS , rB ) = σ Sσ B Range of values for ρ: -1.0 < ρ < 1.0 Range ρ: 5-35 Covariance and Correlation Coefficient – probability-based Covariance (with probabilities of K scenarios): Cov (rs, rB) = ∑k=1,..,K pk [ rSk – E(rs) ] [ rBk – E(rB) ] Cov k=1,..,K Correlation Coefficient: Correlation ρ SB Cov(rS , rB ) = σ Sσ B Range of values for ρ: -1.0 < ρ < 1.0 Range ρ: 5-36 Example: Bond and Stock Returns (1) Expected returns Bond = 6% Stock = 10% Standard deviation Standard Bond = 12% Stock = 25% Bond Initial weights Bond = 50% Stock = 50% Correlation coefficient (Bonds and Stock) Correlation = 0, as a simplistic setting (will be changed later) later) 5-37 Example: Bond and Stock Returns (2) Expected return = 8% .5(0.06) + .5 (0.10) =8% Standard deviation = 13.87% [(.5)2 (.12)2 + (.5)2 (.25)2 + 2 (.5) (.12) (.5) (.25) (0)] ½ =13.87% Now, let the weight and correlation Now, change: “2 risky assets line” in “Lecture2_StockPricing” “Lecture2_StockPricing” 5-38 Figure: The risk-return trade-off of the portfolio of 2 risky assets 5-39 Exercise 3 1. Plot the risk-return relation for the 1. following two assets: following • Expected returns Bond = 5% Stock = 7% • Standard deviation Standard Bond = 8% Stock = 12% Bond • Correlation coefficient = -0.5 2. What’s the minimum volatility we can 2. reach using these two assets? Ans: 4.77% reach 5-40 More than 2 assets – we will discuss when we use Matlab 5-41 CAPM model and market risk 5-42 Specification of CAPM Model So, the relation between individual stock r i and the market portfolio rm can now be stated as: market can E(ri) - rf = α + β [E(rm) - rf ] or rit - rft = α + β [ rmt - rft ] + εit or – Note that, we need to consider the risk-free rate Note – β measures “market risk exposure” (“market beta”) of (“market stock i stock – α measures “abnormal returns”...
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