Chapter trade-Off Between Risk & Return Chapter Risk, Return, and the capm



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Chapter 6 Trade-Off Between Risk & Return


Today’s Chapter 6 & 7 Topics



Risk and Return



Quick Review: Financial Return



Quick Review: Dollar and Percentage Returns



Percentage Returns on Bills, Bonds, and Stocks, 1900 - 2003



Variability of Stock Returns

  • Variance (2) - the expected value of squared deviations from the mean



Volatility of Asset Returns



Average Returns and St. Dev. for Asset Classes, 1900-2003



Probabilistic Expected Return

  • Expected Rate of Return given a probability distribution of possible returns (ri): E(r)

  • n

  • E(R) = Pi Ri

  • i=1



Probabilistic Standard Deviation

  • Relevant Risk Measure for single asset

  • Variance = 2 = pi( ri - E(r))2

  • Standard Deviation = Square Root of Variance



Example: Exp. Return and 



Example: Standard Deviation



Portfolio Risk and Return

  • E(rp) = wiE(ri) = weighted average of the expected return of each asset in the portfolio

  • In our example, MAD E(r) = 33.5% and CON E(r) = 7.5%

  • What is the expected return of a portfolio consisting of 70% MAD and 30% CON?



Risk and Diversification

  • E(rp) = wiE(ri) = .7(33.5%) + .3(7.5%) = 25.7%



Portfolio Risk

  • Looking at a 2-asset portfolio for simplicity, the riskiness of a portfolio is determined by the relationship between the returns of each asset over different scenarios or over time.

  • This relationship is measured by the correlation coefficient( ): -1<= < =+1

  • Lower = less portfolio risk compared to the weighted average of the standard deviations.



Example 70% MAD, 30% CON Portfolio 



Average Return and St. Dev. for Individual Securities, 1994-2003



Average Return and St. Dev. for Individual Securities, 1994-2003



Diversification



The Impact of Additional Assets on the Risk of a Portfolio



Systematic and Unsystematic Risk



Systematic and Unsystematic Risk



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