23 6 15 the investor can buy x amount of pesos at the

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15. The investor can buy X amount of pesos at the (indirect) spot exchange rate, and invest the pesos in the Mexican bond market. Then, in one year, the investor will have: X × (1 + r MEX ) pesos These pesos can then be converted back into dollars using the (indirect) forward exchange rate. Interest rate parity asserts that the two holding period returns must be equal, which can be represented by the formula: (1 + r US ) = E 0 × (1 + r MEX ) × (1/ F 0 ) The left side of the equation represents the holding period return for a U.S. dollar- denominated bond. If interest rate parity holds, then this term also corresponds to the U.S. dollar holding period return for the currency-hedged Mexican one-year bond. The right side of the equation is the holding period return, in dollar terms, for a currency-hedged peso-denominated bond. Solving for r US : (1 + r US ) = 9.5000 × (1 + 0.065) × (1/9.8707) (1 + r US ) = 1.0250 r US = 2.50% Thus r US = 2.50%, which is the as the yield for the one-year U.S. bond. 16. a. From parity: 06453 . 122 0380 . 1 0010 . 1 30 . 124 r 1 r 1 E F 5 . 0 5 . 0 Japan US 0 0 = × = + + × = b. Action Now CF in $ Action at period-end CF in ¥ Borrow $1,000,000 in U.S. $1,000,000 Repay loan ($1,000,000 × 1.035 0.25 ) = $1,008,637.45 Convert borrowed dollars to yen; lend ¥124,300,000 in Japan –$1,000,000 Collect repayment in yen ¥124,300,000 × 1.005 0.25 = ¥124,455,084.52 Sell forward $1,008,637.45 at F 0 = ¥123.2605 0 Unwind forward (1,008,637.45 × ¥123.2605) = ¥124,325,156.40 Total 0 Total ¥129,928.12 The arbitrage profit is: ¥129,928.12 17. The farmer must sell forward: 100,000 × (1/0.90) = 111,111 bushels of yellow corn This requires selling: 111,111/5,000 = 22.2 contracts 23-7
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18. Municipal bond yields, which are below T-bond yields because of their tax-exempt status, are expected to close in on Treasury yields. Because yields and prices are inversely related, this means that municipal bond prices will perform poorly compared to Treasuries. Therefore you should establish a spread position, buying Treasury-bond futures and selling municipal bond futures. The net bet on the general level of interest rates is approximately zero. You have simply made a bet on relative performances in the two sectors. 19. The closing futures price will be: 100 5.20 = 94.80 The initial futures price was 94.9825, so the loss to the long side is 18.25 basis points or: 18.25 basis points × $25 per basis point = $456.25 The loss can also be computed as: 0.001825 × ¼ × $1,000,000 = $456.25 20. Suppose the yield on your portfolio increases by 1.5 basis points. Then the yield on the T-bond contract is likely to increase by 1 basis point. The loss on your portfolio will be: $1 million × Δ y × D* = $1,000,000 × 0.00015 × 4 = $600 The change in the futures price (per $100 par value) will be: $95 × 0.0001 × 9 = $0.0855 This is a change of $85.50 on a $100,000 par value contract. Therefore you should sell: $600/$85.50 = 7 contracts 21. She must sell: 8 . 0 $ 10 8 million 1 $ = × million of T-bonds 22. If yield changes on the bond and the contracts are each 1 basis point, then the bond value will change by: $10,000,000 × 0.0001 × 8 = $8,000 The contract will result in a cash flow of: $100,000 × 0.0001 × 6 = $60 Therefore, the firm should sell: 8,000/60 = 133 contracts The firm sells the contracts because you need profits on the contract to offset losses as a bond issuer if interest rates increase.
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