IBUS 700 Professor Robert B.H. Hauswald International Finance Kogod School of Business, AU Solutions 1. Sing Dollar Quotations. (a) Bid-ask: the bid quote in European terms of 1.6056 signifies that an FX dealer stands ready to buy USD 1 for SGD 1.6056 while the ask quote means that she will sell USD 1 for SGD 1.611. (b) Midpoint: SSGD/USD mid = Sbid SGD/USD +Sask SGD/USD = 1.6056+1.611 = SGD 1.6084/USD. (c) American bid-ask from European bid-ask quotes: American quotes are USD per unit of foreign currency, European quotes foreign currency per unit of USD. By the reciprocal rule of FX calculus we know that American terms need to be reciprocals of European terms. However, with bid-ask FX quotations we have to remember that the rip-off rule applies whereby the customer always gets the more unfavorable price. This means that an American bid is the reciprocal of a European ask (and vice versa) and an American ask the reciprocal of a European bid. Otherwise, there would be arbitrage opportunities. As a verification the American bid has to be lower than the American ask (why?). Hence, we have Quote Rule Result American bid American ask S bid USD/SGD = 1 S ask SGD/USD S ask USD/SGD = 1 S bid SGD/USD 1 1.611 = USD 0.607/SGD 1 1.6056 = USD 0.68/SGD. Euro Currency Markets. Here, one relentlessly applies IRP to carry out the money market hedge in disguise. Note that the calculations mirror the computations of the FXF price approximation. (a) From the FT data i USD i DKK S F 5.5% 3.50% 5.5330 5.5065 one gets a theoretical yield r USD in USD of ( ) 1 + r USD = S [ ( )] 1 + i DKK F so that r USD = 0.0544 > 0.055 = i USD. = 5.5330 [ ( )] 5.5065 1 + 0.035 From the preceding information it is clear that investing in the DKK Euro money market is more advantageous. This could also have been concluded from the implied forward rate F = 1+iDKK ( ) 1+0.035( S = ) 5.5330 = 5. 5091 > 5.5065 = F quote 1+i USD ( ) 1+0.055( ) or directly from the data (F = 5.5083).
Correspondingly, one should borrow in the USD Euro-currency market. Arbitrage is carried out via the money market hedge: borrow in the USD Euro money market and invest in the DKK Euro money market. The usual roundtrip argument or the initial return comparison yields a profit of USD [ 1 + 0.0544 1 4 ( 1 + 0.055 1 4)] = 0.000475 or 4.75 pts per USD borrowed (annualized return: 0.0544 0.055 = 19 bpts). (b) Repeating the initial return comparison we now find that r USD = 0.0579 > 0.055 + 0.005 = 0.0550 = i USD new so that the operation is even more profitable yielding an arbitrage return of 9 bpts (which is unsurprising since the yield curve shifted by more in the market we are investing in). 3. Dual Currency Bonds. In order to analyze the bond one decomposes it into its constituent parts (valuation: constituent cash flows) and values each separately. (a) The bond has a European call on BRL embedded for the investor. Granting an American BRL call would not make any sense at all unless the holder could ask for early reimbursement of principal. If principal is repaid at maturity the option can only be European. (b) Put-call parity principle for FXOs: p t c t = e r(t t) [K F t,t ] in the continuous case; the discrete analog is p t c t = (1 + r t,t ) 1 [K F t,t ]. (c) By the double nature of FXOs (USD call on BRL = BRL put on USD) the instrument also is a BRL bond with an embedded put option on USD struck at K = BRL.0000/USD. (d) Since USD call on BRL is equivalent to a BRL put on USD the put-call-parity principle should reflect this fact, which is easily verified using the reciprocal rule of FX calculus. (e) From a Brazilian investor s point of view we have a 10 year BRL 0,000 bond with embedded European put on USD with a face value of BRL 0,000 and strike K = BRL.0000/USD. (f) The theoretical option value is computed from the binomial FXO spreadsheet FXoption.xls as USD 0.05761 (European call). By comparison, the Black-Scholes-Merton model prices the call as c t = e r(t t) [F t,t N (d 1 ) KN (d )] = USD 0.05445/BRL where K = 0.5, S = 0.5556, r $ = r DM = 0.059, σ = 0.11, F t,t = e (r$ r DM )(T t) S t so that d 1 = log F t,t K + 1 σ (T t) σ = 0.49 N (d 1 ) = 0.6664 T t d = d 1 σ T t = 0.1186 N (d ) = 0.544 4. International Bond Offering. This question goes to the heart of pricing bond offerings by exploring the arts and science involved. Obviously, there are many different structures and the following proposals are by way of illustration only.
(a) Issue terms and pricing elements: Terms Euro Sovereign Euro Sovereign Euro Corporate Denomination USD Brady USD CAD Redemption at par: 1,000 at par: 1,000 at par: 1,000 Coupon 10.50% 1.50% 5.00% YTM 10.30% 1.80% 5.35% Maturity 30Y 30Y 7Y Issue price: PRICE( ) 1,018.378 977.174 980.001 Enhancements: guarantee Coupon, ppal None None Call provision/protection None/none None/none None/none All-in-cost: IRR( ) 10.4648% 13.0016% 5.565% The initial price is established by yield-to-maturity pricing with the help of a benchmark: for maturity T, par P T, coupon c and cash flows C, yield y one has P 0 = T C t (1+y) t where C t = c for t < T and C T = c + P T. (b) Pricing: AA+ benchmark corporates in the Euro CAD segment currently yield between 5.31% and 5.35%, the latter being a floating rate note (FRN) with variable coupon. For a fixed coupon one should probably price closer to 5.31% but anything between 5.30% and 5.35% is acceptable. Let us price the corporate conservatively and the sovereign aggressively. In the Latin American segment you have a choice in terms of enhancements fixing on the nature of the bond. The enhancements refer to rolling interest and partial principal guarantees through sinking funds held in US government securities. Such partially collateralized emerging market bonds are referred to as Brady bonds. BB benchmark Brady sovereigns in the Euro USD segment are priced at a yield around 9.40% to 9.85% for Latin American emerging markets: Mexico s issue (9.40%) matures in 019 so that one is better off with taking Argentina s 03 at 9.85%. Without the enhancements, the yield rises for the same two countries to 1.9% and 1.56%, respectively. Hence, 10.30% or 1.80% seem to be good choices correcting for the somewhat longer maturity of our issue relative to the benchmarks. In terms of determining an appropriate yield one has y = y b (υ) + h 1 (T ) + h (ρ) + h 3 (λ) where y b (υ) is the benchmark yield as a function of the rating υ = AAA, AA+,..., BB,..., h 1 (T ) the adjustment for differing maturity, h (ρ) an adjustment for differently perceived risks and h 3 (λ) an adjustment for liquidity. Using Excel s PRICE( ) formula now allows to price the issues on the basis of the appropriate yields. (c) Increasing the size of the CAD corporate from CAD 300m to CAD 500m presumably lowers the liquidity premium so that your required yield-to-maturity decreases translating into a slightly higher price. Decreasing the size of the USD sovereign does the reverse: liquidity premium and yield rise decreasing the issue price. (d) All-in-cost are calculated as the IRR that equates your net proceeds with future payment streams, i.e., r solving P 0 γp 0 g T C t = 0 where γ is the fee (100 or 50 bpts) (1+r) t and g legal, administrative and swap costs. In particular, one finds the above all-in costs 3
setting r such that 1018.378 (1 0.01) 0.5 977.174 (1 0.01) 0.5 980.001 (1 0.005) 0.5 5. JPY Arbitrage and Speculation. 30 30 7 105 (1 + r) 30 = 0 105 (1 + r) 30 = 0 50 (1 + r) 7 = 0 (a) JPY-covered interest rate parity: With the quoted forward rates a simple money-marketforward arbitrage argument shows that the quoted forward rate is too high. Hence, you would like to sell USD forward at this high price which means that your money-market hedge for this position should replicate a long forward position, i.e., you wish to have USD at the end of the three months. But then, you need to borrow in the Japanese money market, change spot into USD and invest in the US money market and sell the receipts forward against JPY. Note that interest rates are quoted per annum so that you need to convert them to three month rates (e.g., Japanese rates become i J = 0.005 4 = 0.0015). Here is the full transaction starting out with JPY 300m Instrument Cashflows t Cashflows T Borrow JPY 300m @ 0.5% p.a.for 3M 300m -300,375,000 Buy USD @ JPY 10.50,489,66 Invest USD @ 4.15% p.a. for 3M -,489,66, 515, 300 Sell USD 3M fwd @ JPY 119.60 300, 89, 880 JPY-CIA profits 454,880 (b) JPY-uncovered interest rate parity: speculation is much harder since the trader has to assess the impact of the interest rate hike before taking a position. Increasing US rates by 5 bpts (basis points: 100th of a percentage point) presumably attracts capital from Japan to the US so that the USD spot might well appreciate to JPY 11 or 1, say. At the same time, the IRP argument shows that 3M forward rates should weaken for current spot rates from JPY 119.60/USD3M to JPY 119.3453: F = 10.50 1 + 0.005 1 + 0.04375 = 119.3453. However, this is only a guess since the spot rate will change, too. Uncovered arbitrage now means that the trader borrows JPY and exchanges them spot for USD at the current JPY 10.50 rate before it moves but invests the proceeds immediately after the Federal Reserve Board meeting when interest rates will have risen by 5 bpts (timing is critical!). After these transaction one usually leaves the position uncovered until spot and forward rate movements allow to lock in the hoped-for return through a later forward transaction. The bet here is that the USD will further strengthen against the JPY so that the return in JPY increases. To build up a speculative position you have several choices: speculate intra-day in the FFX market or engaging in an uncovered speculation via UIP. In the first case, you would 4
sell JPY 3M forward at 119.60 hoping to buy them back after the FOMC announcement later in the day at 119.34 3M forward or, at least, below 119.60 - transaction costs. The second transaction is obviously much more risky as FX spot and forward rates might be all over the place. So, let us assume that after an initial weakening of the USD it appreciates against the JPY to 11 after 3M Instrument Cashflows t Cashflows T Borrow JPY 300m @ 0.5% p.a.for 3M 300m -300,375,000 Buy USD @ JPY 10.50,489,66 Invest USD @ 4.375 % p.a. for 3M -,489,66, 516, 856 Sell USD spot in 3M @ JPY 11 304, 539, 610 JPY-CIA profits 4,164,610 Any depreciation of the JPY beyond the new implied FFX rate of F = 119.3453 is pure profit. When you engage in this kind of speculation you always compute break-even rates, i.e., future spot rates for which your speculative position breaks even which is, unsurprisingly, S = 119.34. Then you estimate the probability of the JPY appreciating beyond this magical number given the current rate of 10.50 which will give you the position s VAR. 5