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Unformatted text preview: BUS3026W Finance II 2009 - Tutorial 18 - Suggested Solutions Due: Monday 5 th October 09 QUESTION 1 Using our target duration formula: V B = V A x (D V * - D* A ) (D B * - D V *) a) V B = R145m x (9 - 13.1) (7 – 9) = 297.25m b) V B = R145m x (4 - 13.1) (7 – 4) = -R439.833m c) V B = R145m x (0 - 13.1) (7 – 0) = -R271.357m Alternatively, we could take the long route: Bond A is worth R145m, and has a modified duration of 13.1. If we call the value of this bond A V , then we know that: 13.1*145 * A V m y If we held B V worth of bond B, we would have 7* * B B V V y We would like to purchase a certain amount of the bond B so that we end up with a portfolio V with a value A B V V V . We would also like to end up with a modified duration of 9 so that 9* * 9*( ) A B V V y V V We know that A B V V V , so using the first two equations and the one above, we can find B V The same technique would then apply to the other two questions as well. QUESTION 2 For the ALSI TOP 40 Futures Index Level 7213 Mul 10 6-Month Jibar NACC 8.27% q_div 2% num 200 T 0.5 Therefore the ALSI Exposure is calculated as: 7213 x 10 x 200 x e (0.0827-0.02)0.5 = R 14 885 418.86 For the ALSI RESI Put Options Index Level 5120.3 Mul 10 Delta -0.54 Number of Contract 200 Therefore the RESI Exposure is calculated as: 5120.3 x 10 x 200 x -0.54 = -R 5 529 924.00 Notice that the price of the options is totally redundant for this question! From the information provided we can extract the following information: μ ALSI 4.33% μ RESI 6.24% σ ALSI 6.70% σ RESI 7.50% ρ ALSI,RESI 0.52 We then calculate our VaR calculations as normal: μ ΔV = R 299 471.38 σ ΔV = R 858 188.04 99% 1-month VaR is thus -R 1 696 674.00 QUESTION 3 The value of the manager’s investment in dollars is $19 736 842.11 invested in the S&P 500 index. This position is exposed to both risk of changes in the S&P500 and foreign exchange rate risk. The currency exposure As far as the exposure to the currency is concerned (i.e. holding the S&P 500 constant), the manager’s position behaves as if it were a cash deposit in the US of $19 736 842.11 This is plugged into the mean change in value calculation as 19 736 842.11 – we do not need to convert this to rands ....
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- Summer '09