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1. Describe what are the three types of efficiency and mention why they are important to understand modern finance?

2. Explain the principle of non-arbitrage, how is this applied in portfolio optimization?

3. An agent says the best strategy to diversify a portfolio is to invest in assets with positive correlation, given that in good times the investor will make big profits.

4. Compute the correlation between assets A and B if you know that the standard deviation of B is 50% of the standard deviation of A and the covariance between the two assets is 0.5 times the variance of asset A.

5. What is the risk (measured as the variance) of the portfolio created by investing 50% in asset A and 50% in asset B in the previous point? Assume that the variance of the asset A is 4/9.

6. Compute the expected return and risk on your portfolio using the following information, if you invest 20%, 40% and 40% in assets A, B and C: Expected returns on assets A, B and C, respectively, 10%, 5% and 2%. Standard deviations of A, B and C, respectively, 10%, 6% and 1%. The Covariances between the assets are all zero but the covariance between B and C which is 1.

7. If you have two assets with expected returns 10% and 5%, respectively, what is the percentage you have to invest in every asset in order to get an expected return of 8%? What would be the risk on that portfolio if the covariance between the two assets is zero?

8. Explain all the recipe you have to use in order to be able to maximize expected return given a predefined risk?

9. Explain all the recipe you have to use in order to be able to minimize expected return given a predefined risk?