1. If variance of asset A is 0.04 and variance of asset B is 0.02, what is the correlation between the two assets? Assume covariance between the 2 assets to be 0.015.
2. Suppose a portfolio has expected return of 15% and volatility of 30%. How can you combine this portfolio with the risk-free asset to create a portfolio with 10% expected return? Risk-free asset has expected return of 3%. Show how you found the values. Describe the steps.
3. There are 3 assets with variances of 0.03 (asset A), 0.04 (asset B) and 0.025 (asset C). Covariance between asset A and B is -0.01, covariance between asset B and C is 0.04 and covariance between asset C and A is 0.015. Assume risk-free rate to be 5%.
a. What is the variance of a portfolio with 30% invested in asset A, 30% invested in asset B and 40% invested in asset C? Show how you found the values.
b. What is the Sharpe Ratio of the assets if expected returns of asset A, B and C are 13%, 20% and 15%, respectively? Show how you found the values.
c. If you have the option to invest in just one of the assets out of assets A, B and C, which asset would you prefer? Why?