課程名稱︰投資學 課程性質︰必修 課程教師︰何憲章 開課學院：管理學院 開課系所︰財金系 考試日期（年月日）︰2011/4/20 考試時限（分鐘）： 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : ------------------------------------------------------------------------------ Note: Answer to the 4th decimal point, and list calculation process. You may answer the questions in either English, traditional or simplified Chinese. Each problem is worth 20 points. ------------------------------------------------------------------------------ 1.If the initial margin requirement is 60% and maintenance margin is 40% for both long and short accounts, then for initial stock price of $150, what are the "critical prices" for getting a margin call of your (1) long margin account? (2) short-sale margin account? 2.Given the following information: ┌───┬──────┬─────────┬────────┐ │Stock │Mean Return │Standard Deviation│Correlation │ │ │ Ri │ σi │Coefficient ρ12│ ├───┼──────┼─────────┼────────┤ │1 │ 10% │ 0.2 │ │ ├───┼──────┼─────────┤ 0.5 │ │2 │ 15% │ 0.3 │ │ └───┴──────┴─────────┴────────┘ (1) What are the optimal weights X1﹡ and X2﹡ of the "minimum-variance portfolio"? 2 (2) What are the mean return Rp and variance σp of the "minimum-variance portfolio"? (3) If the risk free interest rate rf=5% exists, then what are the "optimal 2 portfolio's" optimal weights X1﹡,X2﹡,mean return Rp, and variance σp? 3.Given the following information: ┌───┬──────┬─────────┬────────┐ │Stock │Mean Return │Standard Deviation│ Covariance │ │ │ │ │ 2 │ │ │ Ri,% │ σi,% │ ρij,(%) │ ├───┼──────┼─────────┼────────┤ │1 │ 10 │ 2 │ σ12=5 │ ├───┼──────┼─────────┤ │ │2 │ 12 │ 3 │ σ13=7 │ ├───┼──────┼─────────┤ │ │3 │ 15 │ 4 │ σ23=11 │ └───┴──────┴─────────┴────────┘ If the risk free interest rate rf=5% exists, then what are the "optimal portfolio's" (1) optimal weights X1﹡,X2﹡andX3﹡? 2 (2) mean return Rp and variance σp? 4.Given the following information: ┌───┬──────┬────┬─────┐ │Stock │Mean Return │ bi1 │ bi2 │ │ │ │ │ │ │ │ Ri,% │ │ │ ├───┼──────┼────┼─────┤ │1 │ 12 │ 1 │ 0.5 │ ├───┼──────┼────┼─────┤ │2 │ 13.4 │ 3 │ 0.2 │ ├───┼──────┼────┼─────┤ │3 │ 12 │ 3 │ -0.5 │ └───┴──────┴────┴─────┘ If 3 stocks are all on the APT(Arbitrage Pricing Theory) plane, then (1) What is the APT equilibrium equation: Ri=λ0+λ1bi1+λ2bi2, i.e., what is λ0,λ1 and λ2? (2) If stock 4 with bi1=2 and bi2=1is also on the APT plane, then what is its mean return R4? (3) If stock 5 also with bi1=2 and bi2=1, but has a mean return of 15%, then what should you do about it, i.e. long or short it? 5.State your understanding of and comments on CAPM(Capital Asset Pricing Model) , APT(Arbitrage Pricing Theory) and EMH(Efficient Market Hypothesis), elaborate as much as possible. p.s.可帶A4大抄 --

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