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pf_sol

# pf_sol - 2 Therefore we can always have positive payoﬀ it...

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E120 Practice Final Solution Summer, 2007 Question 1 Let r m denote the monthly interest rate and r q denote the quarterly interest rate. Since EAR = 12%, from (1 + r m ) 12 - 1 = EAR, we have r m = 0 . 0095; from (1 + r q ) 4 - 1 = EAR, we have r q = 0 . 0287. Thus, the current price of the stock is P 0 = 1 1 + r m ( D 0 + D 0 (1 + g ) r q - g ) = 108 . 78 , where D 0 = 2 is the first dividend. Question 2 Consider the following strategy: t = 0: Buy the call option with strike price K 2 and sell the call option with strike price K 1 . Total payoff= C ( K 1 ) - C ( K 2 ) > 0 t = T : If S T K 2 , none of the options will be exercised, payoff=0; If K 2 < S T < K 1 , when the call option with strike price K 2 will be exercised, we will buy the underlying stock at price K and sell it at S T , with payoff= S T - K 2 ; If K 1 S T , both of the call options will be exercised, we buy the underlying stock at price K 2 and sell it at price K 1 , with payoff=

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Unformatted text preview: 2 . Therefore, we can always have positive payoﬀ, it is a arbitrage strategy. Question 3 (a) w A = σ 2 B-σ AB σ 2 A-2 σ AB + σ 2 B = 0 . 62 , w B = 1-w A = 0 . 38 . 1 (b) w A = r-r B r A-r B = 1 . 67 , w B = 1-w A =-. 67 . (c) β A = σ AM σ 2 M = 0 . 2 , β B = σ BM σ 2 M = 0 . 5 . Then from CAPM, we have r A-r f = β A ( r M-r f ) r B-r f = β B ( r M-r f ) Therefore, r f = 0 . 1, r m = 0 . 2. Question 3 (a) FALSE. The security with beta of 0 is the risk-free asset, which still has pos-itive return. (b) TRUE. Since F = S (1 + r f ) T , and r f > 0. (c) TRUE. If put-call parity is not satisﬁed, we can construct arbitrage strategy (need to explain in more details). 2...
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