Explanations please

Problem 7.11 Mystery at Baker Street Arthur Doyle is a currency trader for Baker Street, a private investment house in London. Baker Street's clients are a collection of wealthy private investors who, with a minimum stake of 250,000 each, wish to speculate on the movement of currencies. The investors expect annual returns in excess of 25%. Although officed in London, all accounts and expectations are based in U.S. dollars. Arthur is convinced that the British pound will slide significantly -- possibly to $1.3200/ -- in the coming 30 to 60 days. The current spot rate is $1.4260/. Arthur wishes to buy a put on pounds which will yield the 25% return expected by his investors. Which of the following put options would you recommend he purchase. Prove your choice is the preferable combination of strike price, maturity, and up-front premium expense. Strike Price $1.36/ $ $1.34/ $1.32/4 $1.36/ $1.34/ $1.32/ Maturity 30 days 30 days 30 days 60 days 60 days 60 days Premium $0.00081/ $0.00021/ $0.00004/ $0.00333/ $0.00150/ $0.00060/ Assumptions Current spot rate (US$/) Expected endings spot rate in 30 to 60 days (US$/) Potential investment principal per person () Values 51.4260 S1.3200 250,000.00 Put options on pounds Strike price (USS/L) Maturity (days) Premium (USS/) Put #1 S1.36 30 S0.0008 Put #2 S1 34 30 S0.0002 Put #3 $1.32 30 S0.0000 Put options on pounds Strike price (USSE) Maturity (days) Premium (US$/) Put #4 1.36 60 S0.0033 Put #5 $1.34 60 $0.0015 Put #6 $1.32 60 $0.0006 Issues for Sydney to consider: 1. Because his expectation is for "30 to 60 days" he should confine his choices to the 60 day options to be sure and capture the timing of the exchange rate change. (We have no explicit idea of why he believes this specific timing.) 2. The choice of which strike price is an interesting debate. The lower the strike price (1.34 or 1.32), the cheaper the option price. * The reason they are cheaper is that, statistically speaking, they are increasingly less likely to end up in the money * The choice, given that all the options are relatively "cheap," is to pick the strike price which will yield the required return The $1.32 strike price is too far 'down,' given that Sydney only expects the pound to fall to about $1.32 Strike price Less expected spot rate Less premium Profit Put #4 Net profit $1.36000 (1.32000) (0.00333) $0.03667 Put #5 Net profit $1.34000 (1.32000) (0.00150) S0.01850 $ Put #6 Net profit $1.32000 (1.32000) (0.00060) (S0.00060) If Sydney invested an individual's principal purely in this specific option, they would purchase an option of the following notional principal () 75,075,075.08 166,666,666,67 416,666,666.67 Expected profit, in total (profit ratex notional): Initial investment at current spot rate Return on Investment (ROI) Risk: They could lose it all (full premium) $2,753,003.00 S356,500.00 772% $3,083,333.33 S356,500.00 865% -$250,000.00 $356,500.00 -70% % Problem 7.11 Mystery at Baker Street Arthur Doyle is a currency trader for Baker Street, a private investment house in London. Baker Street's clients are a collection of wealthy private investors who, with a minimum stake of 250,000 each, wish to speculate on the movement of currencies. The investors expect annual returns in excess of 25%. Although officed in London, all accounts and expectations are based in U.S. dollars. Arthur is convinced that the British pound will slide significantly -- possibly to $1.3200/ -- in the coming 30 to 60 days. The current spot rate is $1.4260/. Arthur wishes to buy a put on pounds which will yield the 25% return expected by his investors. Which of the following put options would you recommend he purchase. Prove your choice is the preferable combination of strike price, maturity, and up-front premium expense. Strike Price $1.36/ $ $1.34/ $1.32/4 $1.36/ $1.34/ $1.32/ Maturity 30 days 30 days 30 days 60 days 60 days 60 days Premium $0.00081/ $0.00021/ $0.00004/ $0.00333/ $0.00150/ $0.00060/ Assumptions Current spot rate (US$/) Expected endings spot rate in 30 to 60 days (US$/) Potential investment principal per person () Values 51.4260 S1.3200 250,000.00 Put options on pounds Strike price (USS/L) Maturity (days) Premium (USS/) Put #1 S1.36 30 S0.0008 Put #2 S1 34 30 S0.0002 Put #3 $1.32 30 S0.0000 Put options on pounds Strike price (USSE) Maturity (days) Premium (US$/) Put #4 1.36 60 S0.0033 Put #5 $1.34 60 $0.0015 Put #6 $1.32 60 $0.0006 Issues for Sydney to consider: 1. Because his expectation is for "30 to 60 days" he should confine his choices to the 60 day options to be sure and capture the timing of the exchange rate change. (We have no explicit idea of why he believes this specific timing.) 2. The choice of which strike price is an interesting debate. The lower the strike price (1.34 or 1.32), the cheaper the option price. * The reason they are cheaper is that, statistically speaking, they are increasingly less likely to end up in the money * The choice, given that all the options are relatively "cheap," is to pick the strike price which will yield the required return The $1.32 strike price is too far 'down,' given that Sydney only expects the pound to fall to about $1.32 Strike price Less expected spot rate Less premium Profit Put #4 Net profit $1.36000 (1.32000) (0.00333) $0.03667 Put #5 Net profit $1.34000 (1.32000) (0.00150) S0.01850 $ Put #6 Net profit $1.32000 (1.32000) (0.00060) (S0.00060) If Sydney invested an individual's principal purely in this specific option, they would purchase an option of the following notional principal () 75,075,075.08 166,666,666,67 416,666,666.67 Expected profit, in total (profit ratex notional): Initial investment at current spot rate Return on Investment (ROI) Risk: They could lose it all (full premium) $2,753,003.00 S356,500.00 772% $3,083,333.33 S356,500.00 865% -$250,000.00 $356,500.00 -70% %