Posted: September 16th, 2017
FINA 471 Problem Set 2 (problem from Chapters 4-5)
1. You enter into a five-to-eight-month forward rate agreement with a bank. The bank agrees to give you a 3-month loan of $5 million starting 5 months from now, with a quarterly compounded forward interest rate of 2.5% per annum. Currently, the continuously compounded 5-month and 8-month interest rates are 3% per annum and 3.5% per annum, respectively. What is the present value of this forward rate
agreement to you now? (Hint: note that the forward rate you calculate using the formula in Lecture 4 is continuously compounded, but the forward rate specified in the FRA is quarterly compounded.)
2. A stock is currently traded at $60 per share. For this stock, a dividend of $6 per share will be paid in 6 months. The 6-month interest rate is 4% per annum and the 10month interest rate is 5% per annum. These two interest rates are continuously compounded. We consider a 10-month forward contract (i.e. this contract matures in 10 months) on this stock.
1) What should be the no-arbitrage forward price for this 10-month forward contract? (Hint: this is an asset with a known income)
2) Suppose the forward price for this 10-month forward contract is $61, is there any arbitrage opportunity? If so, how would you take advantage of this opportunity?
Draw the cash flow table as we did in class. (Hint: now there are three dates we need to consider in the table: today, 6 months later, 10 months later).
2) Suppose the forward price for this 10-month forward contract is $61, is there any arbitrage opportunity? If so, how would you take advantage of this opportunity?
Draw the cash flow table as we did in class. (Hint: now there are three dates we need to consider in the table: today, 6 months later, 10 months later).
3. The spot price of gold now is $1200. The quoted 2-year forward price of gold is $1300. The 1-year interest rate is 5% per annum and the implied forward rate for the period between year 1 and year 2 is 7% per annum. These two interest rates are continuously compounded.
1) What is the 2-year interest rate?
2) What should be the no-arbitrage forward price for this 2-year forward contract?
3) Is there any arbitrage opportunity? If so, should you do “cash and carry” or “reverse cash and carry” strategy?
4. An asset is currently traded at $1000. It generates a yield of 10% per annum, which is quarterly compounded. The interest rate is 5% per annum and monthly compounded.
1) What is the 2-year interest rate?
2) What should be the no-arbitrage forward price for this 2-year forward contract?
3) Is there any arbitrage opportunity? If so, should you do “cash and carry” or “reverse cash and carry” strategy?
4. An asset is currently traded at $1000. It generates a yield of 10% per annum, which is quarterly compounded. The interest rate is 5% per annum and monthly compounded.
We consider a 9-month forward contract on this asset. Suppose holding this asset would incur a storage cost of $100 to be paid in 9 months.
1) What is the no-arbitrage forward price for this 9-month forward contract? (Hint: the yield and interest rate in the forward pricing formulas discussed in class are continuously compounded.)
2) Suppose the forward price for this 9-month forward contract is $500. Is there any arbitrage opportunity? If so, draw the cash flow table as we did in class to illustrate your arbitrage strategy.
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