Q1 (Essential to cover) The risk free rate is 4% and the following data is given...

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Q1 (Essential to cover) The risk free rate is 4% and the following data is given about assets X and Z: Asset X Z E(r) 8% 16% 20% 30% (a) What are the Sharpe ratios of the two risky assets? (b) Show how you can dominate asset X using a portfolio that combines asset Z and the risk free asset. (c) Show how you can dominate a portfolio with equal weights in asset X and the risk-free asset using a portfolio that combines asset Z and the risk-free asset. (d) Show (in general) how you can dominate any portfolio combining asset X and the risk-free asset using a portfolio that combines asset Z and the risk-free asset. Hint: by general, I mean you assume any general fraction (like yx) of wealth in asset X. And then show how to design a portfolio combining asset Z (with the fraction y of wealth in asset Z) and the risk-free asset which will dominate the portfolio of asset X and the risk-free rate. So essentially you will need to show the relationship between y of the DOMINATING portfolio and yx of the DOMINATED portfolio. Q1 (Essential to cover) The risk free rate is 4% and the following data is given about assets X and Z: Asset X Z E(r) 8% 16% 20% 30% (a) What are the Sharpe ratios of the two risky assets? (b) Show how you can dominate asset X using a portfolio that combines asset Z and the risk free asset. (c) Show how you can dominate a portfolio with equal weights in asset X and the risk-free asset using a portfolio that combines asset Z and the risk-free asset. (d) Show (in general) how you can dominate any portfolio combining asset X and the risk-free asset using a portfolio that combines asset Z and the risk-free asset. Hint: by general, I mean you assume any general fraction (like yx) of wealth in asset X. And then show how to design a portfolio combining asset Z (with the fraction y of wealth in asset Z) and the risk-free asset which will dominate the portfolio of asset X and the risk-free rate. So essentially you will need to show the relationship between y of the DOMINATING portfolio and yx of the DOMINATED portfolio.