12. You expect equities to have a real (after inflation) return of 5% with a standard...

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12. You expect equities to have a real (after inflation) return of 5% with a standard deviation of 20%, and you expect fixed income securities to have a real return of 2% with a standard deviation of 5%. Assume the correlation of equities and fixed income is 25%. a. What is the expected return and risk (standard deviation) of a portfolio that is 60% equity and 40% fixed income? b. Suppose that you can tolerate a maximum risk of 10%. What portfolio will provide that level of risk? What is its expected return? Hints: The expected return of the portfolio is just the weighted average of the expected returns of the various assets. The variance of the portfolio is just: 0 = w 1+W202 + 2 W1W201020 where Wi weight on asset i = i = standard deviation of the expected return of asset i = correction between assets 1 and 2 If you have more than two risky assets, the variance of the portfolio is: = wwT where w = the vector of weights on the individual assets in the portfolio, is the covariance matrix, and w is the transpose of the weights on the individual assets. In order to do this in Excel, you should use the MMULT function for matrix multiplication. Another hint: Use Solver in Excel. Solver can be found on the Data tab in the Excel ribbon. However, it is not normally loaded in the default installation. You may have to go to File then Options then Add-Ins to load Solver, which comes with Excel. 12. You expect equities to have a real (after inflation) return of 5% with a standard deviation of 20%, and you expect fixed income securities to have a real return of 2% with a standard deviation of 5%. Assume the correlation of equities and fixed income is 25%. a. What is the expected return and risk (standard deviation) of a portfolio that is 60% equity and 40% fixed income? b. Suppose that you can tolerate a maximum risk of 10%. What portfolio will provide that level of risk? What is its expected return? Hints: The expected return of the portfolio is just the weighted average of the expected returns of the various assets. The variance of the portfolio is just: 0 = w 1+W202 + 2 W1W201020 where Wi weight on asset i = i = standard deviation of the expected return of asset i = correction between assets 1 and 2 If you have more than two risky assets, the variance of the portfolio is: = wwT where w = the vector of weights on the individual assets in the portfolio, is the covariance matrix, and w is the transpose of the weights on the individual assets. In order to do this in Excel, you should use the MMULT function for matrix multiplication. Another hint: Use Solver in Excel. Solver can be found on the Data tab in the Excel ribbon. However, it is not normally loaded in the default installation. You may have to go to File then Options then Add-Ins to load Solver, which comes with Excel.