CHAPTER 13 Most important chapter RISK, RETURN, and the SML Expected returns: - Looking forward - Predicting - If a trial is done many times, what is the average outcome (50% chance of tossing tails) - Expected returns are based on the probabilities of possible outcomes. - In this context, "expected" means average if the process is repeated many times. - The "expected" return does not even have to be a possible return: "Pi" = probability of outcome "Ri" = amount EX. *Probabilities must sum up to one (100%), The missing value "???" = 1-(0.3+0.5) = 0.2 *Probability = Pi * C and T = Ri (return) Step 1
Variance and Standard Deviation - SD = Square root of variance - Variance and standard deviation still measure the volatility of returns. - You can use unequal probabilities for the entire range of possibilities. - Weighted average of squared deviations: *E = Expected return EX. Step 2 (plug-in step 1 values for E) Portfolios — A collection of assets - An asset's risk and return are important in how it affects the risk and return of the portfolio - The risk-return trade-off for a portfolio is measured by the portfolio's expected return and standard deviation, just with individual assets - The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio: *wj = Weight
Portfolio variance - Compute the portfolio return for each state: RP = w1R1 + w2R2 + ... + wmRm - Compute the expected portfolio return using the same formula as for an individual asset. - Compute the portfolio variance and standard deviation using the same formulas as for an individual asset. Wa = 60%, Wb = 40% METHOD 1 Wa(Ra)+Wb(Rb) = 0.6(0.7) + 0.4(0.1) = 41% .....0% E[Rp] = 0.5(0.46) + 0.5(0) = 23% SD [Rp] = 0.5(46%-23%)^2 + 0.5(0%-23%)^2 OR Diversification - There are benefits to diversification whenever the correlation between two stocks is less than perfect (p < 1) - Put your money in more than one stock is correlation is not perfect - If two stocks are perfectly positively correlated, that there is simply a risk-return trade-off between the two securities
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