ACT245H1 W07 Final Privacy ID A with sols for web v12

# ACT245H1 W07 Final Privacy ID A with sols for web v12 -...

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UNIVERSITY OF TORONTO : ACT245H1S WINTER 2007 FINAL ACT245H1 W07 Final Privacy ID A with sols for web v12 Page 2 out of 20 1. (Assignment Mar 29, 2007) A stock index is currently trading at S 0 =100. A one-year forward contract is available for long or short position on the index with forward price \$104.40. The continuously compounded rate of interest is 6%. Suppose that the index pays continuous dividends at rate 2%. Determine the implied repo rate expressed as a continuous rate. (A) Less than 6.400% (B) 6.400% but less than 6.500% (C) 6.500% but less than 6.600% (D) 6.600% but less than 6.700% (E) 6.700% or more (A) Solution Implied repo rate r is that risk- free rate at which the forward price is ‘correct’. 104.40 = 100*exp(r - 0.02) r= 0.063059
UNIVERSITY OF TORONTO : ACT245H1S WINTER 2007 FINAL ACT245H1 W07 Final Privacy ID A with sols for web v12 Page 3 out of 20 2. (Assignment Jan 18, 2007) According to the current term structure of interest rates, the effective annual interest rates for 1, 2 and 3 year maturity zero-coupon bonds are: 1-year : 0.08 2-year: 0.10 3-year: 0.13 Find the two year forward effective rate of interest, i 2,3 (A) Less than 17.000% (B) 17.000% but less than 18.000% (C) 18.000% but less than 19.000% (D) 19.000% but less than 20.000% (E) 20.000% or more ( D) Solution 1.13 3 /(1.10 2 ) 1 = 19.248% 3. You are given: s 1 =i 0,1 =0.083 s 2 =i 0,2 =0.090 i 2,4 =0.115 Calculate s 4 (A) Less than 0.10000 (B) 0.10000 but less than 0.10050 (C) 0.10050 but less than 0.10100 (D) 0.10100 but less than 0.10150 (E) 0.10150 or more ( E) Solution (1+s 4 ) 4 =(1+s 2 ) 2 (1+ i 2,4 ) 2 = (1+0.09) 2 (1+0.115) 2 Hence s 4 = 0.102429

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UNIVERSITY OF TORONTO : ACT245H1S WINTER 2007 FINAL ACT245H1 W07 Final Privacy ID A with sols for web v12 Page 4 out of 20 4. Steve sells a stock short at a price of P, and buys it back one year later for 1275. The required
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## This note was uploaded on 04/24/2011 for the course ACT 245 taught by Professor Sharp during the Spring '07 term at University of Toronto- Toronto.

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ACT245H1 W07 Final Privacy ID A with sols for web v12 -...

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