ADM CHEAT SHEET PT2

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Feb 20, 2024

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Find the minimum possible forward rate ($/£),no bid-ask spread on the forward market, in spot exchange bid-ask rates are 1.55-1.57$/£, you can freely invest $s and £s at 5% and 7% respectively while your borrowing rates in $s and £s are 5.5% and 8% Solution: 1.55*1.05/1.08=1.5069 Find the price of 1-year European call option for 1£ with the strike price of 1.77$/£ if today's spot rate is 1.7$/£, next year it can either go up to 1.9$/£ (with 67% probability) or go down to 1.6$/£ (with 33% probability). The interest rates in U.S. and U.K. are 4% and 7% respectively. Answer: $0.0218 Ignoring time value of money, what is your maximum possible loss if you bought a put option on £1 with strike price of 1.8$/£ for $0.11 and, at the same time, bought a call option on £1 with strike price of 1.7$/£ for $0.16? Answer: $0.27 ABC inc. has £20M account receivables that will be paid next year and it wants to hedge it using money market hedge. ABC has $40M debt at 7%, can borrow £s at 4% and can invest $s at 5%. If today's spot rate is 1.8$/£, into how much dollars the money market hedge will effectively transfer £20M account receivables? Answer: 20/1.04*1.8*1.07=$37.038M ABC inc. has £20M account receivables that will be paid next year and it wants to hedge it using money market hedge. ABC has $20M debt at 7%, can borrow £s at 4% and can invest $s at 5%. If today's spot rate is 1.8$/£, indo how much dollars the money market hedge will effectively transfer £20M account receivables? Answer: 20*1.07+(20/1.04*1.8-20)*1.05=$36.746M Assume there are only 3 banks on the FOREX market and there are only two currencies: $ and £. Assume the bid-ask spread posted by the first bank is 0.602£/$-0.606£/$, the bid-ask spread posted by the second bank is 1.641$/£-1.684$/£, and the bid-ask spread posted by the third bank is 1.637$/£-1.678$/£. If you would like to exchange 1000£ for dollars, what is the maximum amount of dollars that you can get? Ans: 1000/0.606=$1,650.17 What is the $/£ cross ask rate if $/€ bid-ask rates are 1.31-1.33 and €/£ bid-ask rates are 1.19-1.20. IMPORTANT: you need to find ask rate, not bid rate!!! Ans: 1.33*1.2=1.596 Assume that you have the following info: Spot $/£ (bid-ask): 2.08 - 2.10, Forward $/£ (bid-ask): 2.13 - 2.16, Inflation in the UK is 6%, real interest rate is 4%, US real interest rate is 5%. What is the maximum possible rate of inflation in the US that is consistent with the above information? Answer: 9.03% Solution: 1 + i = (F/S)( 1 + i*), i*=1.06*1.04-1=10.24% ,1.1024*2.13/2.1≤1 + i≤1.1024*2.16/2.08, where min (F/S)=2.13/2.1 and max(F/S)=2.16/2.08, 11.815% ≤ i ≤14.48%% for the US nominal interest rate. Since 1 + i = (1 + real)( 1 + infl), 7.5%≤ inflation rate ≤9.03% Find nominal exchange between US and Canadian dollars (in USD/CAD) if you know that as of October 1, 2014 the real exchange rate between these two currencies was 0.98, US Bureau of Labor Statistics was reporting the consumer price index (CPI) of USD216 and Statistics Canada was reporting Canadian CPI of CAD136. c) 1.556471 USD/CAD Calculate maximum possible loss (including the price of the options) from a short positon in Feb 2015 ₤ put option and a long position in Feb 2015 call option. Strike price of the put is 1.45 $/₤, strike price of the call is 1.35 $/₤. Assume that put’s premium was $0.1 per 1₤ while calls’ premium was $0.2 per 1₤ and the size of each contract is ₤65,500. b) $101,525 Consider and investor who switches his investment portfolio from Optimal Domestic Portfolio (ODP) to Optimal International Portfolio (OIP). By how much his Sharpe ratio will increase if the expected returns on OIP and ODP are the same while the standard deviation of the OIP is by 30% less than the standard deviation of the ODP? a) by more than 40% Solution: 1/0.7=42% Find 1-year forward rate on £s if 1-year call option for 1£ with the strike price of 1.8$/£ is selling for $0.15; 1-year put option for 1£ with the same strike price is selling for $0.27 and 1-year U.S. interest rate is 8% Sol: (0.15-0.27)*1.08+1.8=1.6704 Assume the spot exchange rate is 1.9$/£ and next year the spot rate can be either 2.1$/£ or 1.7$/£. The U.S. interest rate is 10% and the U.K interest rate is 7%. a) (2 points) Find the price of a 1-year European call option for £1 with strike price of 1.8$/£ Answer: (1.9/1.07-1.7/1.1)*0.3/0.4=$0.1727 b) (1 point) What is the time value of the option in part (a)? Ans: 0.1727-0.1=$0.0727 What is the 1-year forward $/£ exchange rate if next year spot rate can be either 1.8$/£ or 1.6$/£, interest rate in the U.S. is 4%, interest rate in the U.K. is 5% and 1-year call option with strike price of 1.65 $/£ is selling for $0.07 Solution: 0.15/0.2*(S/1.05-1.6/1.04)=$0.07 . Thus, S=(0.07*0.2/0.15+1.6/1.04)*1.05=1.713385 Thus, F=1.713385*1.04/1.05=1.6971

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