| | Problem 7.10 Arthur Doyle 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 | | Maturity | | Premium |
| | $1.36/£ | | 30 days | | $0.00081/£ |
| | $1.34/£ | | 30 days | | $0.00021/£ |
| | $1.32/£ | | 30 days | | $0.00004/£ |
| | $1.36/£ | | 60 days | | $0.00333/£ |
| | $1.34/£ | | 60 days | | $0.00150/£ |
| | $1.32/£ | | 60 days | | $0.00060/£ |
| | Assumptions | | Values |
| | Current spot rate (US$/£) | | $1.4260 |
| | Expected endings spot rate in 30 to 60 days (US$/£) | | $1.3200 |
| | Potential investment principal per person (£) | | £250,000.00 |
| | Put options on pounds | | Put #1 | | Put #2 | | Put #3 |
| | Strike price (US$/£) | | $1.36 | | $1.34 | | $1.32 |
| | Maturity (days) | | 30 | | 30 | | 30 |
| | Premium (US$/£) | | $0.00081 | | $0.00021 | | $0.00004 |
| | Put options on pounds | | Put #4 | | Put #5 | | Put #6 |
| | Strike price (US$/£) | | $1.36 | | $1.34 | | $1.32 |
| | Maturity (days) | | 60 | | 60 | | 60 |
| | Premium (US$/£) | | $0.0033 | | $0.0015 | | $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. |
| | | | Put #4 | | Put #5 | | Put #6 |
| | | | Net profit | | Net profit | | Net profit |
| | Strike price | | $1.36000 | | $1.34000 | | $1.32000 |
| | Less expected spot rate | | (1.32000) | | (1.32000) | | (1.32000) |
| | Less premium |
| | Profit |
| | If Sydney invested an individual's principal purely |
| | in this specific option, they would purchase an |
| | option of the following notional principal (£): |
| | Expected profit, in total (profit rate x notional): |
| | Initial investment at current spot rate |
| | Return on Investment (ROI) |
| | Risk: They could lose it all (full premium) |
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Q7-10.xlsx
