Topic08_risk_ret[1]

Topic08_risk_ret[1] - Thomas Moeller FINA 30153: Financial...

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Thomas Moeller FINA 30153: Financial Management 1 Topic 8 Basic statistics; risk and return; portfolio theory Objectives 1. Review of basic statistical theory 2. Calculate the return and risk on a single security 3. Understand the concept of risk premia 4. Calculate the return and risk on a portfolio of securities 5. Explain effects of diversification
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Thomas Moeller FINA 30153: Financial Management 2 1. Basic statistical theory Random variable: A variable that takes different values with some probability. Example: Y 0 1 2 Probability 0.25 0.5 0.25 Probability distribution: A schedule of all possible payoffs and respective probabilities. Example: 0 0.1 0.2 0.3 0.4 0.5 012 Outcom e Probability
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Thomas Moeller FINA 30153: Financial Management 3 Expected value (mean): Expected payoff of a random variable: E(X) X i p i i1 n = = where X i = outcome in state i p i = probability of state i Example: Calculate the expected value of Y: Y 0 1 2 Probability 0.25 0.5 0.25
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Thomas Moeller FINA 30153: Financial Management 4 Variance: Expected value of squared distance from the expected payoff: × = = n 1 i i p 2 )] i E(X - i X [ 2 σ Example: Calculate the variance of Y: Y 0 1 2 Probability 0.25 0.5 0.25 Standard deviation: σσ = 2
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Thomas Moeller FINA 30153: Financial Management 5 Covariance: Measure of the co-movement of two random variables: × = = n 1 i i p )] i E(Y - i Y [ )] i E(X - i X [ Y) Cov(X, Correlation coefficient: Standardized measure of the co-movement of two random variables: Y X XY Y) Cov(X, σ ρ =
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Thomas Moeller FINA 30153: Financial Management 6 Example: Calculate the covariance and correlation between X and Y: State 1 2 3 X 2 1 0 Y 0 1 2 Probability 0.25 0.5 0.25
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Thomas Moeller FINA 30153: Financial Management 7 2. Single security return and risk Stock returns are made up of two components: 1) dividends, which tend to be stable and predictable, and 2) changes in the price of the stock, which may be highly volatile. The rate of return from holding a stock is the sum of these two components, expressed as a percentage of the price paid for the stock: price beginning price) beginning - price (ending + dividends = return
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Thomas Moeller FINA 30153: Financial Management 8 Example: A stock is selling today for $50.
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This note was uploaded on 04/21/2008 for the course FINA 30153 taught by Professor Moeller during the Spring '08 term at TCU.

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Topic08_risk_ret[1] - Thomas Moeller FINA 30153: Financial...

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