The following questions relate to modern portfolio theory:
1. Assume the rates of return for shares A and B have a perfect, negative correlation (i.e. coefficient -1). If their respective expected rates of return are 10% and 12% for the relevant investment period, and standard deviation of rates of return estimated to be 15% and 25% respectively, calculate what proportions of your money should be invested into assets A and B (i.e. calculate the asset weightings) to achieve a portfolio that has an expected zero risk.
2. Your research has indicated a particular portfolio of shares has weekly returns that are normally distributed, with a mean rate of return of 0.25% (i.e. 0.25 of one percent) and standard deviation of 0.50%. What is the dollar value of the possible loss that we are 99% confident will not be exceeded over a given week, assuming the portfolio investment amount is $100,000.