1. Investments Chapter 17: Macroeconomic Analysis

23. Arbitrage Invest £800 at i £ = 11.56% In one year £800 will be worth £892.48 = £800  (1+ i £ ) Step 4: repatriate to the U.S.A. If F £ (360) > $1.20/£ , £892.48 will be more than enough to repay your dollar obligation of $1,071; the excess is your profit. Step 1: borrow $1,000 Step 2: buy pounds Step 3: Step 5: Repay your dollar loan with $1,071<$1,098 £892.48 $1,098 $1,000 £800 £800 = $1,000× $1.25 £1 $1,071 < £892.48 × £1 $1.23

25. IRP and a Forward Market Hedge To form a forward market hedge: Borrow $ 112.05 million in the U.S. (in one year your debt will be $120 million). Translate $ 112.05 million into £ at the spot rate S £ (0) = $1.25/ £ to receive £89.64 million . Invest £ 89.64 million in the UK at i £ = 11.56% for one year. In one year your investment will have grown to £100 million = $120 million, i.e. exactly enough to pay your supplier.

26. Forward Market Hedge Where do the numbers come from? We owe our supplier £100 million in one year—so we know that we need to have an investment with an FV of £100 million. Since i £ = 11.56% we need to invest £89.64 million at the start of the year. How many dollars will it take to acquire £89.64 million at the start of the year if S £ (0) = $1.25/ £? £89.64 = £100 1.1156 $112.05 = £89.64 × $100 £1.25

27. Lufthansa’s decision (A true case,1985) On January 1985, signed Lufthansas CEO Heinz Ruhnau to buy 20, 737 Boeing, for $500 million. Lufthansa would pay in $ in a year (at delivery). Meanwhile, $ had increased continiously since Reagan became president and cost around 3.20 DM. By the delivery of planes it could cost up to 3.50 DM and made the purchase of planes 0.3*500 = DM150 million more expensive. At Lufthansa’s board meetings the following alternative strategies were discussed: (a) No hedge and pay what the dollar value will be at delivery (risky) (b) Hedge the entire amount with forward contract at 3.2 DM/$ (c) Hedge half amount only with forward contract at 3.2 DM/$ (d) Hedge the entire amount with currency options at exercise rate 3.2 DM/$

28. Finally, the CEO hedged half the amount ($ 250 m) at 3.2 DM/$, i.e. the alternative (c) was selected. In (d) case, a put option on DM with strike 3.2 DM/$ and 1 year to maturity, cost 6 pfennig, i.e. the right to sell their DM and buy $ at that rate, would cost 0.06*1.6DM billion) = DM96 million. Lufthansas decision (1985) What happened one year later? DM was strengthened dramatically to 2.3 DM/$ and Mr Ruhnau lost his jobb, because his political opponents argued that he ” speculated” with currencies !!! (although in fact he hedged !)

29. DM/$ actual & PPP exchange rate, 1977-2000

30. Billion DM 1.5 1.6 1.375 Non-hedged (a) 2.8 1.7 1.8 3.0 3.4 3.2 DM/$ Currency forward (b) Lufthansa’s alternatives Hedge half (c) 3.6 Put option (d) 1.150 2.3 Here it ended… At a rate of 3.6 DM/$, pay 250*3.6 + 250*3.2 = 1.7 billion Below 3.2 do not exercise the option (buy $ cheaper)

32. Equilibrium Exchange Rate Relationships  $ –  £ IRP PPP Fisher Effect Forward PPP Intern. FisherEffect Forward Premium i $ – i ¥ F – S S E ( e )