d&e plz
Today is March 1, 2014 (= Year O). A company is interested in purchasing 6-month zero-coupon Treasuries with the proceeds of a sale of equipment to take place in 6 months (= Year 0.5). The company is interested in locking in the price of the Treasuries today through a forward contract. The company calls up its bank to get a quote for a forward price, Pfwd. In fact, on March 1, 2014, the market price of 6-month T-bills is Po.s and the price of 1-year T-bills is P4. Denote the face value of the T-bills by F. To compute the no-arbitrage price, consider two alternative investment strategies for 1-year investment horizon as follows: (i) Buy $100 million worth of 1-year T-bills at price Pu. (ii) Buy $100 million worth of 6-month T-bills at price Pos today, and enter into a forward contract by which you will use the proceeds from the 6-month bill in Year 0.5 to buy new 6-month T-bills at Pfwd. a) How much would you earn at the end of Year 1 by strategy (i)? b) How much would you earn at the end of Year 1 by strategy (ii)? c) To prevent arbitrage opportunities between (i) and (ii), what should be the forward price Pfwd? Accordingly, what is the implied (semi-annually compounded) forward rate fo.s, 1 that you can lock in today for the period from Year 0.5 to 1? d) Now suppose that today's price of 6-month T-bills is $97.728, and the price of 1- year bills is $95.713. Assume that the face value of the T-bills is $100. Suppose a bank quoted a forward price (for the period from Year 0.5 to Year 1) of $97.80. Would there be an arbitrage opportunity? If so, give details (positions taken in different assets, cash flows at all times) of a strategy that would take advantage of the opportunity. e) Suppose today's 6-month T-bill prices are expected to increase to $99.326 and decrease to $96.550 with the equal probability over the next six months (= Year 0.5). What is the expected rate of return on investing in short-term (i.e., buy 6- month T-bills today and use the proceeds to buy 6-month T-bills at Year 0.5) vs. long-term (i.e., buy 1-year T- bills) over 1-year investment horizon (i.e. from Year 0 to Year 1)? Can you provide the economic intuition why these two are or are not the same in this case? Today is March 1, 2014 (= Year O). A company is interested in purchasing 6-month zero-coupon Treasuries with the proceeds of a sale of equipment to take place in 6 months (= Year 0.5). The company is interested in locking in the price of the Treasuries today through a forward contract. The company calls up its bank to get a quote for a forward price, Pfwd. In fact, on March 1, 2014, the market price of 6-month T-bills is Po.s and the price of 1-year T-bills is P4. Denote the face value of the T-bills by F. To compute the no-arbitrage price, consider two alternative investment strategies for 1-year investment horizon as follows: (i) Buy $100 million worth of 1-year T-bills at price Pu. (ii) Buy $100 million worth of 6-month T-bills at price Pos today, and enter into a forward contract by which you will use the proceeds from the 6-month bill in Year 0.5 to buy new 6-month T-bills at Pfwd. a) How much would you earn at the end of Year 1 by strategy (i)? b) How much would you earn at the end of Year 1 by strategy (ii)? c) To prevent arbitrage opportunities between (i) and (ii), what should be the forward price Pfwd? Accordingly, what is the implied (semi-annually compounded) forward rate fo.s, 1 that you can lock in today for the period from Year 0.5 to 1? d) Now suppose that today's price of 6-month T-bills is $97.728, and the price of 1- year bills is $95.713. Assume that the face value of the T-bills is $100. Suppose a bank quoted a forward price (for the period from Year 0.5 to Year 1) of $97.80. Would there be an arbitrage opportunity? If so, give details (positions taken in different assets, cash flows at all times) of a strategy that would take advantage of the opportunity. e) Suppose today's 6-month T-bill prices are expected to increase to $99.326 and decrease to $96.550 with the equal probability over the next six months (= Year 0.5). What is the expected rate of return on investing in short-term (i.e., buy 6- month T-bills today and use the proceeds to buy 6-month T-bills at Year 0.5) vs. long-term (i.e., buy 1-year T- bills) over 1-year investment horizon (i.e. from Year 0 to Year 1)? Can you provide the economic intuition why these two are or are not the same in this case
