Solutions_wk8 - Solutions Tutorial Week 9 Chapter 23 2. The...

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Solutions – Tutorial Week 9 Chapter 23 2. The key here is to find a combination of these two bonds (i.e., a portfolio of bonds) that has a cash flow only at t = 6. Then, knowing the price of the portfolio and the cash flow at t = 6, we can calculate the 6-year spot rate. We begin by specifying the cash flows of each bond and using these and their yields to calculate their current prices: Investment Yield C 1 . . . C 5 C 6 Price 6% bond 12% 60 . . . 60 1,060 $753.32 10% bond 8% 100 . . . 100 1,100 $1,092.46 From the cash flows in years one through five, it is clear that the required portfolio consists of one 6% bond minus 60% of one 10% bond, i.e., we should buy the equivalent of one 6% bond and sell the equivalent of 60% of one 10% bond. This portfolio costs: $753.32 – (0.6 × $1,092.46) = $97.84 The cash flow for this portfolio is equal to zero for years one through five and, for year 6, is equal to: $1,060 – (0.6 × 1,100) = $400 Thus: $97.84 × (1 + r 6 ) 6 = 400 r 6 = 0.2645 = 26.45%
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Solutions_wk8 - Solutions Tutorial Week 9 Chapter 23 2. The...

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