# Find the optimal complete portfolio based on your client’s indifference curve. Hint: Plot an indifference curve on the same graph you just created…

1.   Find the optimal complete portfolio based on your client’s indifference curve. Hint: Plot an indifference curve on the same graph you just created using the utility function formula from Chapter 6. To make things easier, you can use the same portfolio risk numbers from the table above and then calculate the expected return based on U = 9% and a risk aversion coefficient A = 10. Plot the indifference curve AND the opportunity set of risky assets on the same graph.

Next determine the optimal complete portfolio. While this can be done graphically, you need to use the formula to determine a more precise allocation between the optimal risky portfolio and T-Bills.

2.   Use the capital asset pricing model (CAPM) to determine the beta and alpha of Portfolio A & Portfolio B. Show the CAPM relationship graphically for BOTH Portfolio A and Portfolio B (separate graphs). The market portfolio is represented by the S&P 500 and the risk free rate is represented by 90 day T-Bills. Determine the beta for portfolio A & B using the following methods:

i.     The slope function in Excel, and

ii.    The beta formula (co-variance divided by the market variance) This is explained in the Modules 6& 7 notes and pages 296 & 297 in the text. Recall the covariance between two assets is the volatility of asset A times the volatility of asset B times the correlation between them.

Then calculate the alpha for each portfolio A & B using the intercept function in Excel and the index model of CAPM formula (equation 9.9 on page 302 – note that the terms are in excess return form). Ignore the error term and you have all the information to solve for alpha based on the monthly returns. Note the two regressions you did are based on monthly returns so the y-intercept (or alpha) is a MONTHLY alpha.

If you plug the annualized returns of the respective portfolio (A or B); the S&P 500; and T-Bills into equation 9.9, the alpha you calculate will be an ANNUALIZED alpha.

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