tutorial2sol-1 - TUTORIAL 2– WEEK 3 ECON3107/ECON5106 –...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: TUTORIAL 2– WEEK 3 ECON3107/ECON5106 – Economics of Finance ANSWERS 1. Consider the following trades. First, trade 1PA for GA for BA. These trades can be summarized as 1P A −→ 1 0.3 GA. Then, trade the obtained amount of 1 1 GA −→ 0.6BA = 2BA. 0.3 0.3 Hence 1BA costs 0.5PA. 2. One way to determine whether there are arbitrage opportunities is the following. Consider the impact of trading in a clockwise and anticlockwise direction: Clockwise : 1P A −→ 1 GA −→ 2BA −→ 1.2P A 0.3 This trading sequence generates a profit of 0.2PA. Hence, there are arbitrage opportunities if you trade in the clockwise direction. Anticlockwise : 1P A −→ 1 1 0. 3 5 BA −→ 2 GA −→ 2 PA = 6PA 0. 6 (0.6) (0.6) If you trade in the anticlockwise direction, you will make a loss. Also, note that if you trade in one direction followed by the other direction you must break even, i.e., 1.2 × 5/6 = 1 (when there are no transaction costs). 3. In the previous question it would have been sufficient to check the trades in one direction only. If you ended up with anything other than 1PA, then arbitrage opportunities must exist. In this question, if you end up with an answer less than 1PA in one direction, this tells you nothing about what will happen if you trade in the other direction. In such cases, you must check in both directions. Clockwise : 1P A −→ 2GA −→ 1.5BA −→ 0.75P A This trading sequence generates a loss of 0.25PA. Hence there are no arbitrage opportunities if you trade in the clockwise direction. Anticlockwise : 1P A −→ 1.5BA −→ 1.5GA −→ 0.6P A Hence if you trade in the anticlockwise direction, you also make a loss. There are no arbitrage opportunities. 1 4. (i) Let Q {states*securities} be the payment matrix of the two securities: Q: Good Weather Bad Weather Bond 20 20 Stock 50 25 Let pS {1*securities} be a vector of security prices: ps: Bond 18 Stock 30 Then, the vector of the atomic prices patom can be found as patom = pS · Q −1 ￿ ￿ ￿ 20 50 −1 ￿ ￿ = 18 30 = 0. 3 0 . 6 . 20 25 ￿ (ii) Let q {states*1} be a vector of payments for the apple tree: q: Good Weather Bad Weather Tree 70 45 Then, the price of the tree can be calculated as follows: ptree ￿￿ ￿ 70 = patom · q = 0.3 0.6 = 48. 45 ￿ (iii) Buy an apple tree and sell one bond and one stock. You make money now while at the same time being perfectly hedged. (iv) The discount factor is 0.9 (i.e., the sum of the atomic security prices). It tells us the value of an apple in the next period in terms of present apples. (v) Let c {states*1} be a vector of state-contingent payments: c: Good Weather Bad Weather Security 80 100 The portfolio n that provides the desired set of state contingent payments will be given by n=Q −1 ·c= ￿ 20 50 20 25 ￿− 1 ￿ 80 100 ￿ = ￿ ￿ 6 . −0.8 In other words, the investor should buy 6 bonds and sell (short) 0.8 stocks. The price of this payment combination is calculated as follows: ￿ ￿ ￿ ￿ 6 p = pS · n = 18 30 = 84. − 0. 8 2 ...
View Full Document

This note was uploaded on 07/13/2011 for the course ECON 3107 at University of New South Wales.

Ask a homework question - tutors are online