Descriptive Statistics - Analytical Questions

Questions

Assume all returns are Normally distributed.

1. The risk-free rate is 5%. Apple’s risk premium is 3% and Sharpe ratio is 0.5. What is the probability Apple has a return between 10% and 15%?

2. Apple and Google’s Sharpe ratios are 0.5 and 0.7. They have a correlation of 0.8. Apple and Google’s risk premiums are 6% and 8%. What is the covariance between Apple and Google?

3. A portfolio is invested in Apple and Google. Apple and the portfolio have expected returns of 5% and 6.2%. The investment weight in Apple is 60%. What is the expected return of Google?

4. Apple and Google have expected returns of 5% and 6%, variances of 0.0144 and 0.0100, and correlation of -0.05. You create a portfolio holding Apple and Google with investment weights 20% and 80%. What is the probability the portfolio has a returns between -5% and 6%? There is a 80% probability that the portfolio will have a return less than x. What is x?

5. A portfolio is invested in Apple and Google. The portfolio has a standard deviation of 7.11% and there is a 50% probability the portfolio has a return less than 5.8%. Apple’s expected return and risk premium are 5% and 4%. What is the Sharpe ratio of the portfolio?