Anglo American (AAL) and Glencore (GLEN) are two of the most volatile stocks on the London Stock Exchange The annualized volatilities of their returns are 60 and 50 , respectively The correlation coefficient between the returns on AAL and GLEN is 0 85 a) 6 marks Consider an equally weighted portfolio with assets AAL, GLEN, and a Treasury security Calculate the standard deviation of the return on the portfolio b) 6 marks Consider an equally weighted portfolio that contains AAL and GLEN The portfolio is financed at a 25 margin That is, the in vestor puts up only 25 of the total amount invested and borrows the rest from his broker What is the standard deviation of this portfolio Suppose the Treasury security is no longer available and the agent can only trade in the shares of Deutsche Bank (DBK) and BNP Paribas (BNP) Fur ther assume that the returns on these two stocks are perfectly negatively correlated c) 8 marks What are the volatility minimizing portfolio weights Assume now that there are n risky assets in the market and one risk free asset d) 5 marks You are a fund manager who has m different clients Each of your clients has a different risk tolerance It would be very expensive for you to offer m different funds What is the smallest number of funds you can offer so that you can meet the needs of all your clients Describe in detail the characteristics of these funds

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Anglo American (AAL) and Glencore (GLEN) are two of the most volatile stocks on the London Stock Exchange. The annualized volatilities of their returns are

Anglo American (AAL) and Glencore (GLEN) are two of the most volatile stocks on the London Stock Exchange. The annualized volatilities of their returns are 60% and 50%, respectively. The correlation coefficient between the returns on AAL and GLEN is 0.85.

a) [6 marks] Consider an equally weighted portfolio with assets AAL, GLEN, and a Treasury security. Calculate the standard deviation of the return on the portfolio.
b) [6 marks] Consider an equally weighted portfolio that contains AAL and GLEN. The portfolio is financed at a 25% margin. That is, the in- vestor puts up only 25% of the total amount invested and borrows the rest from his broker. What is the standard deviation of this portfolio?

Suppose the Treasury security is no longer available and the agent can only trade in the shares of Deutsche Bank (DBK) and BNP Paribas (BNP). Fur- ther assume that the returns on these two stocks are perfectly negatively correlated.

c) [8 marks] What are the volatility minimizing portfolio weights?

Assume now that there are n risky assets in the market and one risk-free asset.

d) [5 marks] You are a fund manager who has m different clients. Each of your clients has a different risk tolerance. It would be very expensive for you to offer m different funds. What is the smallest number of funds you can offer so that you can meet the needs of all your clients? Describe in detail the characteristics of these funds.