1.Calculate the average monthly returns, the standard deviations of monthly returns, and the correlation between the monthly returns of the S&P 500 and Gold. Report all the results in percentages with 2 decimal places.

2. Assume that the average returns, the standard deviations of returns, and the correlation between monthly returns that you calculated above provide reasonable forecasts of the expected returns and risks of these assets. Based on these forecasts, plot the two risky securities on an expected return - standard deviation graph. Also, plot the risk-free security.Be sure to label all three securities on the graph.Draw the Capital Allocation Line for each of the two risky securities (S&P 500 and Gold).

3.Calculate the expected returns and the standard deviations of portfolios that combine the two risky securities (S&P 500 and Gold). Assume that short-selling and margin trading are not allowed (not possible to have weights smaller than 0% or larger than 100%). Vary weights from 0% to 100% in increments of 5% (note: this should result in 21 Portfolios). Plot the risk-free security and the 21 portfolios on an expected return - standard deviation graph.Be sure to clearly label the S&P 500, the Gold, and the risk-free security. Identify analytically (formula on the book), graphically, and numerically with excel the Minimum Variance Portfolio and the Optimal Risky Portfolio. Clearly label these portfolios on the graph. Draw also the Capital Allocation Line (CAL) for this portfolio.

[Insert graph here]

What are the portfolio weights in the Optimal Risky Portfolio?

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What is the standard deviation of the Minimum Variance Portfolio?

4. Assume your target monthly return is 0.5%. Using the risk-free security and the Optimal Risky Portfolio you found in question 3 calculate the portfolio weights (on the risky asset and the risk-free asset) that would be required to achieve this target monthly return. Calculate also the standard deviation of this portfolio.

5. Repeat questions 1 to 3 using the period from January 2000 through July 2013 (short period). Repeat all the calculations, report all the tables and graphs and elaborate on the findings. As before, assume that the annual risk-free rate is 3%, and you can divide this by 12 to get the monthly risk-free rate. Ignore dividends.

Return Calculations: Calculate the average monthly returns, the standard deviations of monthly returns, and the correlation between the monthly returns of the S&P 500 and Gold. Report all the results in percentages with 2 decimal places.

Capital Allocation Lines:Assume that the average monthly returns, the standard deviations of monthly returns, and the correlation between monthly returns that you calculated above provide reasonable forecasts of the expected returns and risks of these assets. Based on these forecasts, plot the two risky securities on an expected return - standard deviation graph. Also, plot the risk-free security.Be sure to label all three securities on the graph.Draw the Capital Allocation Line for each of the two risky securities (S&P 500 and Gold).

.[Insert graph here]

The Opportunity Set and the Optimal Risky Portfolio:Calculate the expected returns and the standard deviations of portfolios that combine the two risky securities (S&P 500 and Gold). Assume that short-selling is not allowed (not possible to have weights smaller than 0% or larger than 100%). Vary weights from 0% to 100% in increments of 5% (note: this should result in 21 Portfolios). Plot the risk-free security and the 21 portfolios on an expected return - standard deviation graph.Be sure to clearly label the S&P 500, the Gold, and the risk-free security. Identify and label the Minimum Variance Portfolio and the Optimal Risky Portfolio on the graph. Draw also the Capital Allocation Line (CAL) for this portfolio.

[Insert graph here]

What is the standard deviation of the Minimum Variance Portfolio?

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What are the portfolio weights in the Optimal Risky Portfolio?

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What would be the weights in the Optimal Risky Portfolio if short-selling were allowed (hint: create portfolios with weights varying from -500% to 500%)?

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Realized Returns as a Proxy for Expected Returns: Above we used realized returns as a proxy for expected returns. The period from January 2000 through July 2013, however, is characterized by two crises. Comment on whether such period is suitable for predictions about the future. Comment also on the return on the risk-free rate in comparison to the return on the S&P 500. Is this situation sustainable in the equilibrium?