AEM324 - return, risk, portfolio theory_StudyGuide

AEM324 - return, risk, portfolio theory_StudyGuide -...

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Return, risk, and portfolio theory Return, where Pt is the stock price at time t, D1 is the dividend paid at time 1 Return = (Ending Value – Beginning Value)/Beginning Value Return = [(D1 + P1) – P0]/P0 Return = (Ending Value/Beginning Value) – 1 Return = [(D1 + P1)/P0] – 1 The expected return and variance of an asset or a portfolio of assets -to calculate the expected return or average return to an asset, multiply the asset return obtained for each economic scenario by the probability of that scenario, and add of the numbers -the variance is a measure of the spread or dispersion of the possible outcomes for an asset; multiply the probability of each return by the square of the difference between each possible return and the asset’s expected return -the standard deviation is the square root of the variance Ex: Probability Asset X Asset Y Boom economy .2 .30 .15 Slow Growth .7 .18 .09 Recession .1 -.20 -.10 E[r of asset x] = .2(.30) + .7(.18) + .1(-.20) = .166 σ^2 of asset x = .2(.30 – .166)^2 + .7(.18 – .166)^2 + .1(-.20 – .166)^2 = .017124 σ of asset x = (.017124)^.5 = .13086 *note The asset with the larger range of returns has the larger return variance and standard deviation Ibbotson and Sinquefield statistics on returns to various asset classes Investment Average Annual Return Standard Deviation Large-company stocks 12.3% 20.2% Small-company stocks 17.4% 32.9% Long-term corporate bonds 6.2% 8.5% Long-term government bonds 5.8% 9.2% Intermediate-term government bonds 5.5% 5.7% U.S. treasury bills 3.8% 3.1% Inflation 3.1% 4.3%
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Portfolio characteristics -the expected return of a portfolio of 3 securities (A, B, C), where Rp is return on the portfolio, E[] is the expectations operator, R of A is return on asset A, w of A is the fraction of the portfolio invested in asset A E[Rp] = (w of A)E[R of A] + (w of B)E[R of B] + (w of C)E[R of C] -the sum of portfolio weightings (w) is equal to 1 -the variance of the 3-security portfolio, where σ^2 is the variance of an asset, σ of A,B is the covariance between assets A and B σ^2 of p = (w of A)^2(σ of A)^2 + (w of B)^2(σ of B)^2 + (w of C)^2(σ of C)^2 + 2(w of A)(w of B)(σ of A,B) + 2(w of A)(w of C)(σ of A,C) + 2(w of B)(w of C)(σ of B,C) -the correlation coefficient between assets A and B p (A,B) = (σ of A,B)/(σ of A) )(σ of B) -the covariance and correlation coefficient between 2 assets both measure the extent to which the assets move in the same direction, independently, or in opposite directions (on average) -the covariance is unbound, while the correlation coefficient is between -1 and 1 inclusive -Harry Markowitz is credited with the recognition of the fact that a portfolio’s riskiness
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AEM324 - return, risk, portfolio theory_StudyGuide -...

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