phobos 12/08

This question was set by the previous examiner, and although the calculations in his answer are correct, he should have explained his logic in the choice of exercise price better.

As I illustrate in my lectures, the approximate maximum effective interest rates for each of the exercise prices can be calculated as follows:

The rate equivalent to the strike price + the premium + the extra 0.5% at which Phobos borrows.

Using this gives:

93.75: 6.25% + 0.045% + 0.5% = 6.795%
94.00: 6% + 0.168% + 0.5% = 6.668%
94.25: 5.75% + 0.3% + 0.5% = 6.55%

Given that the treasurer wishes to keep the maximum borrowing rate at or below 6.6%, I would have chosen 94.25 as the exercise price. (The exact effective rate will obviously be a little different because of basis risk.) Provided that I explained my logic in choosing this, then it would get full marks.

The examiner chose 94.00 as the exercise price, but this does go over the limit of 6.6%. As you can see from the examiners answer, the exact maximum turns out to be 6.63%. The one factor that could make it a better choice despite this, is that if the option ends up not being exercised then the premium will still have to be paid and is a lot lower at 94:00 that at 94.25.

Fortunately the current examiner does not suffer from the same problems as the previous examiner 🙂

You are welcome 🙂