課程名稱︰投資學 課程性質︰財金系必修 課程教師︰何憲章 開課學院：管理學院 開課系所︰財務金融學系 考試日期（年月日）︰100年6月15日 考試時限（分鐘）：180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. 1. Suppose our Central Government Construction Bonds 2011 are just issued, with 4% coupon rate, NT$100 face value, paying coupon semi-annually, and expiring in 2013 (i.e. 4 coupon payment periods) (1) If you purchased it at 6% asked yield (i.e. i=6%), then what's your buying price? (2) What's the bond's MaCaulay's Duration and Modified Duration (in years)? (3) What's the Convexity? (4) Using the dP/P= -Dm di + CV/2 (di)^2 formula, if the interest rate increases 1%, how many percentage points your bond price will decrease? 2. For the Dec 2011 expiration( T= 185/365), strike price $550, Google stock option, the annual standard deviation σ is 0.25, and the risk free interest rate is 0.5%. If Google stock's price is now $500, use the Black- Scholes formula to calculate the theoretical value of (1) call option, (2) put option. 3. If Google stock price is now $500, it's up factor u=1.2 and down factor d=0.9 by year-end. For Google stock option, if the strike price is $550, the time to expiration is 1 year, and the risk free interest is 1%. Use the Binomial Option Pricing method to calculate the one period theoretical value of (1) call option, and (2) put option. 4. (1) In the Chicago Board of Trade (CBT) Futures Settlement prices data, if one Oats Dec contract price is 450 cents per bushel and one Wheat Dec contract price is 850 cents per bushel, suppose you except the future spread of these two contracts to narrow to 300 cents per bushel, what's your inter-commodity spread investment strategy and what'll be your net profit for one Oats and one Wheat contract (5,000 bushels for each contract)? (2) If the Oct 2011 S&P 500 Index (CME) Futures price is 1500 and the Aug 2011 S&P 500 Index Futures price is 1480, suppose you except the future spread of these two contracts to widen to 40 points (1 index points is worth $250), what's your intra-commodity spread investment strategy and what'ss be your net profit for one contract each? 5. If Portfolio 1, r1=15%, σ1=0.5, β1=0.8; Portfolio 2, r2=25%, σ2=0.7, β2=1.2; Market Portfolio, rm=10%, σm=0.3, and risk free interest rate rf=5%. Calculate and compare Portfolio 1 and 2's (1) Sharpe Ratio (2) Treynor Ratio (3) Jensen's α (4) M^2 measure 試題卷背面附有常態分配表 --

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