Task 4 A portfolio comprises three stocks, whose weightings are x, y and (1 X-y), so the total of the weightings is 1. The expected variance of the portfolio comprising these three stocks is given by: An investor requires a return of 6% from the portfolio, and given the expected returns from the three stocks of 4%, 5% and 8%respectively, this means the weights must satisfy the following constraint: 1. Use a Lagrangian multiplier to find the weightings of the three stocks which minimise the value of v subject to the constraint. 5 marks 2. Explain, using the analogy of a walker on a path or otherwise, how the method of Lagrangian multipliers works, and whether in this scenario, the multiplier has a meaning. (400 words) 20 marks Total: 25 marks Task 4 A portfolio comprises three stocks, whose weightings are x, y and (1 X-y), so the total of the weightings is 1. The expected variance of the portfolio comprising these three stocks is given by: An investor requires a return of 6% from the portfolio, and given the expected returns from the three stocks of 4%, 5% and 8%respectively, this means the weights must satisfy the following constraint: 1. Use a Lagrangian multiplier to find the weightings of the three stocks which minimise the value of v subject to the constraint. 5 marks 2. Explain, using the analogy of a walker on a path or otherwise, how the method of Lagrangian multipliers works, and whether in this scenario, the multiplier has a meaning. (400 words) 20 marks Total: 25 marks