a) An investor is given the following information: Payoff State 1 State 2 Security (s=1) (s=2)...

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a) An investor is given the following information: Payoff State 1 State 2 Security (s=1) (s=2) Market prices X 15 20 PJ = 19 Y 25 10 PK = 25 Explaining the method(s) and the underlining concept(s), how could the investor use Arrow- Debreu pure securities to replicate the payoff of security X and security Y? What are the prices of pure security 1 and pure security 2? b) Explaining the method, compute the capital weights on portfolios of X and Y assets that replicate the payoffs of pure securities 1 and 2. Further consider that an investor has an initial wealth of 1000 - he can short-sell securities; however, he must be able to meet all claims under the occurrence of either state. Explaining the method, what is the maximum number of security Y he could sell (short selling) to buy security X? (investor may buy fractions of shares). c) Suppose that you have estimated the expected returns and betas of the following five stocks using annual data available for the last 10 years: Stock Market Capitalisation ($m) Beta Expected Return (%) A 40 0.5 14.0 B 250 1.3 16.7 C 20 1.6 17.0 D 22 0.6 13.0 E 45 1.4 17.6 The risk-free rate of interest and the expected return on the market are 5% and 14% per annum, respectively. Explain the extent to which data is consistent with the Capital Asset Pricing Model (CAPM) and whether there is any arbitrage opportunity; what advice would you give to an investor who would like to hold a portfolio with a beta equal to 1? Discuss whether any arbitrage opportunity exists. a) An investor is given the following information: Payoff State 1 State 2 Security (s=1) (s=2) Market prices X 15 20 PJ = 19 Y 25 10 PK = 25 Explaining the method(s) and the underlining concept(s), how could the investor use Arrow- Debreu pure securities to replicate the payoff of security X and security Y? What are the prices of pure security 1 and pure security 2? b) Explaining the method, compute the capital weights on portfolios of X and Y assets that replicate the payoffs of pure securities 1 and 2. Further consider that an investor has an initial wealth of 1000 - he can short-sell securities; however, he must be able to meet all claims under the occurrence of either state. Explaining the method, what is the maximum number of security Y he could sell (short selling) to buy security X? (investor may buy fractions of shares). c) Suppose that you have estimated the expected returns and betas of the following five stocks using annual data available for the last 10 years: Stock Market Capitalisation ($m) Beta Expected Return (%) A 40 0.5 14.0 B 250 1.3 16.7 C 20 1.6 17.0 D 22 0.6 13.0 E 45 1.4 17.6 The risk-free rate of interest and the expected return on the market are 5% and 14% per annum, respectively. Explain the extent to which data is consistent with the Capital Asset Pricing Model (CAPM) and whether there is any arbitrage opportunity; what advice would you give to an investor who would like to hold a portfolio with a beta equal to 1? Discuss whether any arbitrage opportunity exists.