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tutorial7sol(1)

# tutorial7sol(1) - TUTORIAL 7 WEEK 8 ECON3107/ECON 5106...

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TUTORIAL 7– WEEK 8 ECON3107/ECON 5106 – Economics of Finance ANSWERS 1. (i) The return is obtained as r = ( c - p ) /p = c/p - 1. Since p is normalized to 1, r = c - 1. E ( r X ) = prob( B ) × r X ( B ) + prob( G ) × r X ( G ) = 0 . 4 × 0 . 10 + 0 . 6 × 0 = 0 . 04 The expected return on X is 4 %. E ( r Y ) = prob( B ) × r Y ( B ) + prob( G ) × r Y ( G ) = 0 . 4 × - 0 . 2 + 0 . 6 × 0 . 5 = 0 . 22 The expected return on Y is 22 %. (ii) The atomic prices are given by p atom = (1 1) 1 . 10 0 . 80 1 . 00 1 . 50 - 1 = (0 . 5882 0 . 3529) . (iii) The discount factor is df = p B + p G = 0 . 9412 . Risk-free rate of return is1 /df - 1 = 0 . 0625. This is because if you buy one good and bad atomic security you are guaranteed one dollar in the next period. A portfolio that pays one dollar in each state can be found as follows: n = Q - 1 c = 1 . 10 0 . 80 1 . 00 1 . 50 - 1 1 1 = 0 . 8235 0 . 1176 . That is, you should invest \$0.8235 in X and \$0.1176 in Y. To obtain \$K in each state you should invest K times these amounts in each security. (iv) Returns of the atomics securities in each state of the world are r B ( B ) = 1 - 0 . 5882 0 . 5882 = 0 . 7 , r B ( G ) = 0 - 0 . 5882 0 . 5882 = - 1 , r G ( B ) = 0 - 0 . 3529 0 . 3529 = - 1 , r G ( G ) = 1 - 0 . 3529 0 . 3529 = 1 . 8337 .

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tutorial7sol(1) - TUTORIAL 7 WEEK 8 ECON3107/ECON 5106...

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