Calculate the skewness and kurtosis statistics for your assignment portfolio. How do these reconcile with the assumptions behind Modern Portfolio Theory?

Demonstrate analytically the proportion of your portfolio that you should hold in each of these four sub-indices in order to achieve an expected volatility of 20% per annum with maximum returns. Assume that you have $100; 000 to invest, according to these weights. Use the prices of these indices at 31 December 2006, to determine the dollar amount to invest in each sub-index.

Determine, using either MATLAB or Excel, the optimal weights and expected return if you can include a risk-free asset in your portfolio, returning 3% per annum. Determine a linear approximation for δwi / δrf where wi is the optimal weight in risky asset i.

If the risk-free rate of return suddenly changes to 4% per annum, what trades would you make in order to adjust your portfolio so that you continue to maximise your expected return subject to vol=20% per annum?

Determine the ex-post returns that your portfolio (of the original four assets) earned over the period 31 December 2006 - 31 January 2007. How does the risk- adjusted performance of your portfolio compare with the expected risk adjusted performance?

Suggest techniques to improve the risk-adjusted performance of your portfolio.