4. Suppose you are an investment professional who is considering to invest in a portfolio of three risky assets, S1,S2 and S3. Suppose that the risk-free rate of return is 1%. It is known that the tangency portfolio contains 5% of S1, 30% of S2 and 65% of S3. It is also known that the expected return and the standard deviation of the return for the tangency portfolio are 10% and 5% respectively. (a) If you want the volatility (standard deviation) of the return on a portfolio to be 3%, what proportions of your funds should be in the risk-free asset, asset S1, asset S2 and asset S3? [7 marks] (b) If you want the expected return on your investment to be 13%, what proportions of your funds should be in the risk-free asset, asset Si, asset S2 and asset S3? [7 marks] 4. Suppose you are an investment professional who is considering to invest in a portfolio of three risky assets, S1,S2 and S3. Suppose that the risk-free rate of return is 1%. It is known that the tangency portfolio contains 5% of S1, 30% of S2 and 65% of S3. It is also known that the expected return and the standard deviation of the return for the tangency portfolio are 10% and 5% respectively. (a) If you want the volatility (standard deviation) of the return on a portfolio to be 3%, what proportions of your funds should be in the risk-free asset, asset S1, asset S2 and asset S3? [7 marks] (b) If you want the expected return on your investment to be 13%, what proportions of your funds should be in the risk-free asset, asset Si, asset S2 and asset S3? [7 marks]