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ACF524: Foundations of Financial Markets

1. Based on daily levels of FTSE All Share index and the stock prices of your assigned firm, generate 1-year time series of daily simple returns of the index and the stock.

2. Based on simple daily returns from the period between 15 November 2020 and 15 November 2021, calculate the annualised (sample) standard deviation of index returns. Subsequently, calculate the annualised standard deviation of daily stock returns and their correlation with the FTSE All Share index (the market). Finally, calculate your firm's stock beta and use the CAPM relationship to calculate the expected return on the stock, assuming that the equity market premium is 5% and the relevant riskless interest rate is equal to 2%.

3. Your initial wealth on 15 November 2021, Wi = £100, 000, is invested entirely in the stock of your analysed firm. Your investment horizon is 1-year and your wealth on 15 November 2022 is denoted by W2. Assume that the forward contract on the stock of your firm is available and that the discounted forward price for the 15 November 2022 contract equals the stock price on 15 November 2021. How many one-year forward contracts would you long/short to minimise the variance of W₂ assuming that 1 contract is for 10 shares?

4. Now, you want to include a speculative component in your hedging strategy. In other words, simply minimising the variance of your portfolio is not your objective anymore and you take into account the expected return on your portfolio as well. Assume therefore that your objective function is U = E[W2] — avar\W2], where a = 0.000001 * (10 + y) and y is the penultimate digit of your group number (so if your group number is 13, y = 1; if you are in group 4, y = 0). How many one-year forward contracts on the company's stock would you long/short to maximise the objective function U?

Compare the above risk management strategy with the strategy designed in the answer to Question 3 (focus on the expected returns and the standard deviation of terminal wealth).

5. How would the strategy derived in response to Question 4 change if there was a proportional (to the initial forward price) transaction cost k = 1% of entering a forward position (long or short)?

6. Assume that the riskless asset and the stock of your analysed firm are the only two elements of your investment opportunity set. Also assume that your objective function is given by U (see Question 4). Again, your initial wealth is Wi = £100, 000. What fraction x of initial wealth would you allocate in the stock (such that (1 — x)Wi will be allocated in the riskless asset) in order to maximise the objective function U with your investment horizon being 15 November 2022?

Compare the expected return and the standard deviation of terminal wealth associated with the above strategy with the corresponding values derived as an answer to Question

4.

7. Subsequently, assume that your entire wealth (Wi = £100, 000) is invested in the firm's stock. How can you minimise the risk of your stock holding over a one-year horizon using index futures contracts? Assume that one futures contract is for £10 times the value of the index. (Ignore any effects of the marking-to-market requirement.)

8. Finally, assume that both call and put at-the-money European option contracts on the stock of your firm that mature on 15 November 2022 are available. What (static) hedging strategy would you adopt to ensure that the value of your stock portfolio on 15 November 2022 is at least as high as it is on 15 November 2021? What is the cost of implementing such a strategy?

If your objective is to construct a hedge that makes the value of your stock portfolio insensitive to the fluctuations of the stock price, what possible option positions can you adopt? Will you need to adjust your position in option contracts over time? Interpret your findings.

Very Important Remarks

• Describe clearly each time which calculations and/or Excel operations you perform to obtain your solution. We need to be able to follow all your results and findings without making our own calculations.

• Providing mathematical results only is not sufficient. An important component of the grade awarded will be the critical interpretation of the obtained results. Moreover, you should always sufficiently motivate any answer you provide. (“Yes, it will.” or “By 15%.” are not complete answers.)

• Conclusions based on analytical results will be more highly evaluated than those based solely on numerical results.

• An appendix can be used for any illustrative material that supports your report but that is not essential for the understanding of the report itself (the appendix as such will not be marked).

• Any problems within groups, such as certain members not contributing their fair share (free riding), should be reported to me in advance of the deadline such that an appropriate action can be taken in time.