PRINCIPLES OF FINANCIAL ENGINEERING Answers to Exercises PDF
Preview PRINCIPLES OF FINANCIAL ENGINEERING Answers to Exercises
PRINCIPLES OF FINANCIAL ENGINEERING Answers to Exercises S. Neftci Center for Financial Engineering, Kent State University, Kent, Ohio and Global Finance Program, New School for Social Research, New York, New York and ICMA Centre, University of Reading, Reading, UK and University of Lausanne, Switzerland B. Ozcan First Draft November 2004 This first draft will be revised and the answers will be extended as comments are received. 1 Chapter 1 Introduction Case Study: Japanese Loans and Forwards 1. Follow Figures 1-1 and 1-2 from the text. 2. Japanese banks borrow in yen, and buy spot dollars from their Western counterparties. So, the Western banks are left holding the yen for the time of the loan (three months, in this case). The main point is here. In an FX transaction, in this case buying Yen, the purchased currency may have to be kept overnight in a Yen denominated account. The FX is by definition not euroYen, so these accounts have to be in a bank Japan. some of these will be Japanese banks. 3. A nostro account is one that a bank holds with a “foreign bank”. (In this case London banks hold Nostro accounts with Japanese Banks in Tokyo, for example.) Nostro accounts are usually in the currency of the foreign country. Suppose an American bank called Bank A buys Euros from an European bank Bank B. These Euros cannot “leave” Europe. They will be sent to a European bank, say Bank of Europe, to be kept in a Deposit account for the use of Bank A. This would be a nostro account of Bank A. Bank Awill have similar nostro accounts in Japan, Australia, etc... to trade Dollar against Yen or Australian dollar. This allows for easy cash management because the currency doesn’t need to be converted. Incidentally, nostro is derived from the Latin term “ours”. The Western banks may not be willing to hold the Yen in their nostro accounts because this requires them to hold capital against the yen for regulatory purposes. Japanese banks being more risky, risk managers may also be against holding “too much” in a Nostro account in Japan. Note that banks operate in an environment where others have credit lines against each other. The “Headquarters” may not want a currency desk to have 2 exposure to Japanese Banks beyond a certain limit. This may force Western banks to dump the excess Yens at a negative interest rate. 4. By not holding the yen, the Western banks could potentially lose sig- nificant sums if the bank where the Nostro account is held defaults. For this reason they may prefer to dump the yen deposits and earn negative yield because they can be more than compensated with their earnings from the spot-forward trade. 3 Chapter 2 A Review of Markets, Players and Conventions Exercises Question 1 Going by swap market conventions, the fixed payments for fixed payer swaps are: • 100×.0506×1 = USD 5.06 million per year • 100×.0506×1 = Euro 5.06 million per year Fixed payments for the fixed receiver swaps are: • 100×.0510×0.5 = JPY 2.55 million per 6 months • 100×.0510×0.5 = GBP 2.55 million per 6 months Question 2 (a) One could take a market arbitrage position as follows: buy Honeywell shares and sell General Electric shares. If the merger takes place, the Honeywell shares will convert to GE shares - that is, these shares will become similar and now one can sell the expensive shares and make a profit. (b) You do not need to deposit funds to take this position. (c) You could borrow funds for this position. You would need to if you do not have any GE shares. If you had them then you could engineer this short position through short selling them. (d) This is different from the academic sense of the word arbitrage. That involves zero risk and infinite gain. Here we do face a risk (see below) and our gains might be very high - but not infinite! (e) You would be taking the risk that the merger indeed goes through successfully. 4 Question 3 (a) The dealers are selling the Matif contract and buying the Liffe. (See below) (b) The horizontal axis would have price and the vertical axis would show gain and loss. (c) Since both Euribor and Euro BBA Libor are both European based rates, the profit would simply be scaled down - if all European interest rates would be dramatically lowered. 5 Selling Matif Gain Loss Price Gain Price Loss Buying Liffe Figure 1: 6 Chapter 3 Cash Flow Engineering and Forward Contracts Exercises Question 1 (a) BeforeFAS133, ifcompaniesqualifiedforhedgeaccounting, theirhedges were assumed to be perfect–no valuation or testing required. Now, un- der FAS 133, risk managers seeking hedge accounting treatment have to thoroughly document each hedge from the outset and explain why they are undertaking the transaction. They have to mark their derivatives to market every quarter (no small feat for many instruments), then prove they are effectively hedging the underlying exposure. It’s this sense of having to pay for the sins of others that accounts for the deep resentment toward FAS 133. Many finance executives suspect the new rules have less to do with improving financial statements than with discouraging treasury departments from speculating with derivatives. (b) Constructing synthetic swaps will involve replication of a swap by port- folios of bonds. These do not come under the considerations of FAS 133. So all the work that FAS 133 brings with it needs not be done now. Question 2 (Parts (a)-(c) answered together:)A gold miner risks losing money if the price of gold declines, between the time say, when she is mining the gold and when she would actually sell it. So, she sells futures. If the market prices fall, she has still locked in a rate (at the present time, based on the present day value of gold) high enough for her to make some profit on. This is how she can hedge against a steady decline in gold prices over the years. Unless she sets a futures price that is lower than the present day value of gold, she cannot have a loss. And this will typically not happen since this would also lead to arbitrage opportunities. But the hedge could lead to a ‘loss’ in the sense that if the market price appreciates then she would not make as much profit as she could have. 7 Question 3 (a) Synthetic for Contract A involves: ‘Sell EUR (to get USD)’ is equivalent to • Loan: Borrow EUR at t for maturity t 0 1 • Spot operation: Buy USD against EUR • Deposit: Deposit USD at t for maturity at t 0 1 Here, t is March 1, 2004 and t is March 15, 2004. The underlying sum 0 1 sold is 1,000,000 EUR. Synthetic for Contract B involves: ‘Buy EUR against USD’ is equivalent to • Loan: Borrow USD at t for maturity t 0 1 • Spot operation: Buy EUR against USD • Deposit: Deposit EUR at t for maturity at t 0 1 Here, t is March 1, 2004 and t is April 30, 2004. The underlying sum 0 1 bought is 1,000,000 EUR. (b) In this part of the question, if we have correctly identified our synthetics we can simply interpret the data given to us in the question and use the pricing equation (8) from Section 5 of this Chapter. This is given by B(t ,t )eur 0 1 F = e t0 t0B(t ,t )usd 0 1 Consider Contract A and its synthetic from the previous part of this question above. We borrow EUR at 2.36%, buy USD at spot rate 1.1500 and deposit USD at 2.25%. So, 2.36 F1 = 1.1500× = 1.2062 t 2.25 Now, consider Contract B and its synthetic from the previous part of this question above. We borrow USD at 2.27%, buy EUR at spot rate 8 1.1505 and deposit EUR at 2.35%. So, 2.35 F2 = 1.1505× = 1.1910 t 2.27 (c) The basic idea is as follows: now the outright forward spot rate is 1.1510/1.1525. With this new rate, consider both synthetics. Long the one that gives you higher profit and short the other. This will give arbitrage. Question 4 To rank the instruments we need to recall the conventions from Chapter 2. We review Section 5 from Chapter 2, and Table 2-1 in particular. According to the formula given there, we first calculate present day values of these instruments. • 30-day US T-bill: Daycountconvention: ACT/360. Yieldisquoted at discount rate, so we have (cid:2) (cid:3) (cid:2) (cid:3) T −t 30 B(t,T) = 100−RT 100 = 100−5.5 = 99.5479 365 365 • 30-day UK T-bill: Day count convention: ACT/365. Yield is quoted at discount rate, so we have (cid:2) (cid:3) (cid:2) (cid:3) T −t 30 B(t,T) = 100−RT 100 = 100−5.4 = 99.5561 365 365 • 30-day ECP: Day count convention: ACT/360. Yield is quoted at the money market yield, so we have 100 100 (cid:4) (cid:4) (cid:5)(cid:5) (cid:4) (cid:4) (cid:5)(cid:5) B(t,T) = = = 99.5744 1+RT T−t 1+0.052 30 365 365 • 30-day interbank deposit USD: Day count convention: ACT/360. Yield is quoted at the money market yield, so we have 100 100 (cid:4) (cid:4) (cid:5)(cid:5) (cid:4) (cid:4) (cid:5)(cid:5) B(t,T) = = = 99.5500 1+RT T−t 1+0.055 30 365 365 9 • 30-day US CP: Day count convention: ACT/360. Yield is quoted at the discount rate, so we have (cid:2) (cid:3) (cid:2) (cid:3) T −t 30 B(t,T) = 100−RT 100 = 100−5.6 = 99.5397 365 365 Yields on these instruments = 100−B(t,T), so to arrange these instruments inincreasingorderoftheiryields, wesimplyarrangethemindecreasingorder of their present day values. (a) Since we are dealing with an ECP (Euro), the day count convention used is ACT/360. So there are 62 days till maturity. Also, we have to use the money market yield rate to compute the present day value. (We have again used conventions from Chapter 2, Table 2-1). So, (cid:2) (cid:3) (cid:2) (cid:3) T −t 62 B(t,T) = 100−RT 100 = 100−3.2 = 99.4564384 365 365 is the present day of a bond that would yield 100 USD. So, we have to make a payment of 10,000,000 99.4564384× = 9945643.84 100 US Dollars for this ECP. 10
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