International Investment and Risk

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MACQUARIE UNIVERSITY Faculty of Business and Economics AFIN828 International Investment and Risk Assignment Semester 1 / 2013 1) Using the price series provided in the spreadsheet assignment_data.xls calculate the monthly returns for Westpac (WBK), Wesfarmers (WES) and Rio Tinto (RIO) for the considered time period from January 2nd, 2012 to January 1st, 2013. (25 Marks) a) Considering a possible investment in WBK and WES, calculate the mean (monthly) return, the standard deviation of return and the coefficient of correlation between the returns. Using Excel, produce a chart showing alternative risk-return combinations in terms of 5% (e.g. 0% in WBK and 100% in WES, 5% in WBK and 95% in WES, 10% in WBK and 90% in WES, etc.) from the two investments. Interpret your results, also in comparison to investing in either of the individual stocks. Meanwhile please also calculate the minimum standard deviation of the portfolio contains these two stocks via EXCEL SOLVER. b) Now assume that an investor is interested in combining all three stocks into an optimal portfolio. Using a spreadsheet and the Excel Solver Tool, calculate the optimal weights for each of the investments such that they maximize the expected portfolio return for a given standard deviation of portfolio return (assume that the individual weights have to be positive or zero, so no short-selling is allowed). Provide the expected returns and individual weights of the optimal portfolio with a standard deviation of 6% and 6.5%. c) Provide a plot that contains several alternative risk-return combinations for the optimal three asset portfolios. Also plot the efficient frontier. Interpret your results in comparison to the two asset case in a).

2) Assume that on 1/8/2012, when the WBK share price was S= AUD 22.5 a trader has sold 200,000 European WBK call options with strike price K=25 and expiration date 1/11/2012. Suppose that the amount received for the options was AUD 200,000. Further assume that the yearly standard deviation of WBK returns is 40%, the risk-free rate is 3% and that WBK doesn’t pay any dividend during the time-period from 1/8/ 2012 to 1/11/2012. (20 Marks) a) Using the DerivaGem software, apply the Black-Scholes formula to calculate the price of the option as well as the delta, gamma, vega, theta and rho of the option (we can use week as the time units with respect to time to exercise and we assume there are 52 weeks in each year). Interpret your results. Further, provide a graph showing (i) the relationship between the value of the option and the strike price, (ii) the Delta of the option as a function of the stock price, (iii) the relationship between the Gamma of the option and the volatility of the stock price, (iv) the relationship between Vega of the option and the stock price, (v) the relationship between Rho of the option and the stock price. For each graph, provide a brief explanation and interpretation. b) Explain how the trader can hedge the risk and make his option portfolio delta neutral. Further assume that every week (on 1/8, 8/8, 15/8, 22/8 etc.) until maturity of the option, the trader decides to rebalance his portfolio to preserve delta neutrality. Provide a Table that contains for each week, the share price, the current delta of the option, the number of shares purchased/sold, the cost of shares purchased/sold, the cumulative cost including interest and the interest cost. What is the overall profit or loss of the trader at maturity of the option? Interpret your results. c) Assume that on 1/8/2012 there is another WBK call option available in the market with strike price K=AUD 23 and expiration date 27/9/2012. Assume again that the yearly standard deviation of WBK returns is 40% and the risk-free rate is 3%. Illustrate how on 1/8/2012 this option can be used to create (i) a delta- and gamma neutral portfolio; (ii) a delta- and vega-neutral portfolio.

3) Assume that the risk-free rates (treasury rates) are 3% for 6 months and 3.5%...
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