Financial Management in IB Exercises
I. Foreign Exchange Market Locational Arbitrage Paris Interbank market: EUR/USD 1.2548/1.2552 London Interbank market: EUR/USD 1.2543/1.2546 =(1.2548-1.2546)*10000000= USD 2,000 2
I. Foreign Exchange Market Triangular Arbitrage EUR/USD 1.3000 EUR/CZK 28.490 USD/CZK 21.900 =(10000000*28.49/21.9/1.3)-10000000= EUR 7,024.92 3
I. Foreign Exchange Market Triangular Arbitrage EUR/USD 1.2900/1.2980 EUR/CZK 28.150/28.200 USD/CZK 21.900/21.930 =(10000000*1.29*21.9/28.2)-10000000= EUR 18,085.11 4
I. Foreign Exchange Market Currency Speculations Assume you expect Euro to appreciate from EUR/USD 1.40 to 1.47 in 60 days. What is your expected profit from the speculation if your borrowing capacity is 10 MEUR or 14 MUSD and annualized interest rates are as follows: EUR 4.00% - 4.30% USD 3.00% - 3.25% Borrow USD and lend out EUR Profit=(14000000/1.4)*(1+0.04/6)*1.47-14000000*(1+0.0325/6) = USD 722,166.67 5
II. Currency Derivatives FX Forwards Covered Interest Arbitrage Spot rate EUR/USD 1.3500 Interest rate USD Interest rate EUR 8 % p.a. 4 % p.a. 3-month Forward rate 1.3600 (1.36/1.35) is lower than (1.02/1.01), thus I borow EUR: Profit = Gain-Cost =10,000,000*1.35*(1.02)/1.36-10000000*(1.01)=EUR 25,000 6
II. Currency Derivatives FX Forwards Non Deliverable Forward Contracts Spot rate: EUR/PHP 70.7660 Contracted 6-month rate: EUR/PHP 72.6431 Reference spot rate in 6 months: EUR/PHP 73.7712 Compute a net payment resulting from the contract for the buyer of EUR 100,000. =(73.7712-72.6431)*100000=PHP 112,810 7
II. Currency Derivatives: Currency Futures Currency Futures Assume you have bought 10 FED contracts on the LIFFE at the price 125.00. Suppose you hold the position for 5 days and then you close out the position. Compute the gains and losses on the position if daily settlement prices are as follows: Day D O D 1 D 2 D 3 D 4 D 5 Settlement Price 125.00 125.30 125.10 125.40 124.90 124.80 Gain/Loss ----- 600-400 600-1000 - 200 Total ----- 600 200 800-200 - 400 D1=(125.3-125)*10*200= USD 600 D2=(125.1-125.3)*10*200= - USD 400 8
II. Currency Derivatives: Currency Options Speculating with Currency Put Options Assume you have purchased a put option on 100,000 Euros against U. S. Dollars with following parameters: Option premium: 0.04 USD per 1 EUR Spot price: EUR/USD 1.30 Underlying currency: 100,000 Maturity: 3 months Strike price: EUR/USD 1.30 What is your net profit/loss on the option if the spot rate at the expiration date is: EUR/USD 1.25 Put is exercised, (1.3-1.25)*100,000-4,000 = + USD 1,000 EUR/USD 1.28 Put is exercised, (1.3-1.28)*100,000-4,000 = - USD 2,000 EUR/USD 1.35 Put is not exercised, - USD 4,000 9
II. Currency Derivatives: Currency Options Speculating with Currency Call Options Assume you have sold a call option on 50,000 Euros against U. S. Dollars with following parameters: Option premium: 0.05 USD per 1 EUR Spot price: EUR/USD 1.30 Underlying currency: 50,000 Maturity: 3 months Strike price: EUR/USD 1.25 What is your net profit/loss on the option if the spot rate at the expiration date is: EUR/USD 1.20 No to call, you make the premium, i.e. +USD 2,500 EUR/USD 1.25 No to call, you make the premium, i.e. +USD 2,500 EUR/USD 1.33 Yes to call, (1.25-1.33)*50,000+2,500 = - USD 1,500 10
II. Currency Derivatives: Currency Options Speculating with Currency Call Options Assume you have bought a call option on 100,000 Euros against Czech Crowns. The strike price is 27.000 CZK = 1 EUR and the premium is 0.054 CZK per Euro. What will be your net profit (loss) on the position if the spot rate at the expiration day is 27.150 EUR/CZK? Yes to call, thus (27.15-27.0)*100000-0.054*100000= CZK 9,600 11
III. Foreign Exchange Exposure Value at Risk 1. Assume that your corporation will receive 2.8 million euros dollars in one month. Spot rate equals EUR/USD 1.40. You estimate the standard deviation of monthly percentage changes of the EUR/USD to be 0.5. Assume further that these monthly percentage changes are normally distributed. What is the maximum expected loss on the position at 95% confidence level over 1 month? VaR=2,800,000*1.4*1.65*0.005= USD 32,340 12
III. Foreign Exchange Exposure Hedging with options and forwards Assume you have sold chocolate invoiced at EUR 500,000. Payment for the invoice is due in 30 days. You have following information: 30-day forward rate is EUR/USD 1.18. 30-day put option on 100,000 with the strike price EUR/USD 1.18 costs 0.04 USD per 1 EUR. Which strategy would you prefer if you expect the spot rate at the expiration day to be: 1.25 Put: (1.25-0.04) = 1.21 which is better than forward (1.18) 1.20 Put: (1.2-0.04) = 1.16 which is worse than forward (1.18) 1.15 Put: (1.18-0.04) = 1.14 which is worse than forward (1.18) 13
III. Foreign Exchange Exposure Hedging with Risk Reversal Assume you sold bicycles invoiced at EUR 400,000. Payment for the invoice is due in 6 moths. Assume you want to hedge the position without any hedging costs. Spot rate is EUR/USD 1.18. You have following options to chose: 6-Moths Call EUR/USD Strike: 1.22 EUR/USD Option premium: 4% 6-Moths Put EUR/USD Strike: 1.10 EUR/USD Option premium: 4% What would be the effective exchange rate for the receivables if the spot rate in 6 moths were: o EUR/USD 1.25 Bank exercises its call, thus I sell at 1.22 o EUR/USD 1.17 no to call, no to put, thus we sell at 1.17 (market) o EUR/USD 1.07 I will exercise my put, thus I sell at 1.1 14
III. Foreign Exchange Exposure Money Market Hedge Assume you have sold bicycles invoiced at EUR 200,000. Payment for the invoice is due in 90 days. You have following information: Spot rate EUR/USD 1.22 1.24 Annual IR USD 2.00% - 2.40% EUR 1.80% - 2.20% I borrow EUR: 200,000/(1+0,022/4) = EUR 198,906.0169 I will sell it at 1.22 and lend out USD: 198,906.0169*1.22*(1+0.02/4) = USD 243,878.6673 EF. Rate 243,878.6673/200,000 = 1.2194 15
III. Foreign Exchange Exposure Comparing different hedging strategies Assume you plan to pay EUR 500,000 for the bicycles imported from Germany in 30 days. You have following information: 30-day forward EUR/USD 1.18 1-Moth Call EUR/USD Strike: 1.25 Option premium: 3.00% 1-Moth Put EUR/USD Strike: 1.13 Option premium: 3.00% Which strategy (forward, plain vanilla option, Risk Reversal) would you prefer if you have following scenarios of future exchange rate: Premium: =0.03*500,000 = EUR15,000, Let s assume SR = 1.8, then 15,000*1.18= USD 17,700, thus 0.0354 EUR/USD 1.32 20% EUR/USD 1.18 40% EUR/USD 1.07 40% Forward: 1.18 Second best Call Hedge: =(1.25+0.0354)*0.2+(1.18+0.0354)*0.4+(1.07+0.0354)*0.4= 1.1854 The worst Risk Reversal: =1.25*0.2+1.18*0,4+1.13*0.4=1.174 The best 16