financial maths

Consider two risky assets S1 and S2 with expected returns r1=0.2 and r2=0.3 and standard deviations of returns 1=0.1 and 2=0.25, respectively. The returns of the assets are correlated with the correlation coefficient =0.3. a) Write down the covariance matrix of the returns. b) Suppose that short sales are allowed. Show that the minimum-risk portfolio is then a portfolio with w1=0.8 holdings of asset S1 and w2=0.2 holdings of asset S2 and calculate the expected return and variance of this portfolio. Find the portfolio i) by using the method used in the specal case of the portfolio with two risky assets (i.e. by computing the point of minimum x ). ii) by using the general method discussed in Week 7. Make sure that the results are the same... c) Find the tangency portfolio, if the risk-free return is r0=0.05. You may assume that the inverse of the covariance matrix of the returns of the risky assets is given by C1=(109.890113.186813.186817.5824) Consider two risky assets S1 and S2 with expected returns r1=0.2 and r2=0.3 and standard deviations of returns 1=0.1 and 2=0.25, respectively. The returns of the assets are correlated with the correlation coefficient =0.3. a) Write down the covariance matrix of the returns. b) Suppose that short sales are allowed. Show that the minimum-risk portfolio is then a portfolio with w1=0.8 holdings of asset S1 and w2=0.2 holdings of asset S2 and calculate the expected return and variance of this portfolio. Find the portfolio i) by using the method used in the specal case of the portfolio with two risky assets (i.e. by computing the point of minimum x ). ii) by using the general method discussed in Week 7. Make sure that the results are the same... c) Find the tangency portfolio, if the risk-free return is r0=0.05. You may assume that the inverse of the covariance matrix of the returns of the risky assets is given by C1=(109.890113.186813.186817.5824)