I'm having some trouble understanding the solution to question 1 of this. Hull says that if a fund replicates an index then to minimize the variance at hedge expiry the number of futures to short is P / A where: P is the current portfolio value A is the current value of stock underlying one futures contract. This makes sense as the fund has beta of 1 so this should be the minmum variance hedge ratio. In this case, this would give 100mil/(62000*exp(-yT)) (as futures holders don't get dividends) = 1637. The model solution gives 100mil/62623 = 1567 - i.e. dividing by the futures price (not the current value of stock underlying one future). The solution seems to derive this by trying to minimise the variance when t = 0, not when t = T (i.e. when the hedge expires as Hull does). If we try to minimize at t = T, I think we get the same answer as above though. Can anyone see why the model solution would be correct?
ST6 2007 Mock Q1 Your formula P/A ignores the daily settlement of the futures contract as stated in Hull on p63. See the footnote at the bottom of p63 for a clue as to how to allow for this daily settlement.
Thanks - I can see that the mock answer would be correct based on the Rendlemann paper formula but: 1. Would it not be acceptable in the exam to ignore daily settlement as Hull has done in his example at the bottom of page 63? 2. The derivation of current value / futures price given in the solution still seems erroneuous (even though it happens to give the right answer) - it doesn't seem to argue that we need to 'tail the hedge' as in the Rendelmann paper to allow for daily settlement.
1. Yes, if the marks on offer were less, but not for 4 marks. 2. "Tailing the hedge" is mentioned at the end of the solution, but as there's only a brief mention of it in Hull and not a full explanation, I felt it wasn't fair to expect people to cover this aspect in the solution. We're at t=0 and the question asks for the futures position, so I wouldn't expect answers to cover how this starting position might change over time, given this wording. In exam questions, you're unlikely to judge the level of detail required precisely, but as long as you're not too far off on too many questions, you should still be OK. I hope the rest of mock went well for you.
OK - I would have thought 2 acceptable possibilities would be to 1. Use the P/A formula from Hull to minimize the variance at hedge expiry - this doesn't allow for daily settlement but Hull gives an example to show this is an acceptable approximation. 2. Set up a dynamic hedge where we adjust the futures position every day to allow for daily settlement (a la Rendlemann) - the starting position is then the Acted solution, but won't be like this for long (as hinted at at the end of the Acted answer). I would have though the Acted solution, and the method used to derive it is the worst of both worlds. A static hedge at time 0 of our position / futures price doesn't consider the variance at hedge expiry (but at outset), and doesn't allow for daily settlement. Anyway, guess we'll have to agree to differ on this one Rest of the mock was ok - 86% overall, but reckon that's about 86% higher than I'd get on some of the recent ST6's - they seem much harder One other question - on Q8 part (iii) - is it actually possible to calculate the swaption value? - doesn't a swaption usually have a strike rate, or is it always true that the strike rate is the initial swap rate?
ST6 2007 Mock I would be happy to give “Possibility 1” equivalent credit provided it’s pointed out that it’s an approximation, which ignores daily marking to market. I agree “Possibility 2” is ideal and it’s this approach that the solution was referring to. The solution calculated the starting hedge and said that this would need to change over time. Apologies if our wording doesn’t make this clear. 86% sounds like a very good score for this paper. As for your query on Q8(iii), the swap rate quoted for 2 years ago should have been the 5-year forward swap rate, which would typically be used as the strike rate for such an option, but it would have been clearer if we’d actually stated it was used as the strike rate. However, if you didn’t realise this initially, you would have wondered why that rate had been given in the question – if it’s not the strike rate, then it serves no purpose. I think most students must have made this assumption OK as you're the first one to query this. On a related note, a recent actual exam question missed out information on the strike price and full credit was given provided an assumption was stated and the correct option value derived from this.
