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1. If the correlation between two risky assets A and B is positive, can the variance of a portfolio that comprises A and B be zero, when short positions can be taken? Explain.

2. If the correlation between two risky assets A and B is zero, can the variance of a portfolio that comprises A and B be zero, when short positions can be taken? Explain.

3. Suppose you are going on a skiing holiday and are considering buying insurance. Your assessment of the likelihood of incidents that need insuring is 5%. Such incidents cause a loss of 500 to your belongings and if there is no such incident, the loss is 0. Assume that you are an expected utility maximiser with a utility function u(x) = ln x where x is the monetary value of your belongings (this reflects the insurance premium and payment if you purchase the travel insurance). You plan to take belongings worth 3000 on your trip. Suppose there is only one insurance policy available. The policy pays you back the loss (i.e. 500) in full, and its premium is 25. Should you buy this policy? Explain.