Rosy The basket is determined by either price or capitalisation weightings, or a ratio thereof. I'm also at a loss as to what you mean, but more I'm than happy to be enlightened....
rosy, my apologies for jumping on you. The context of the basket was not crystal clear, and generally speaking a basket is constructed as opposed to an index which is fixed (relatively speaking). Perhaps you had an insight that was not expressed? Let's pose a situation: You have an index (say OEX) and from those 100 stocks you wish to construct a basket of a dozen or so stocks that would outperform the index. This is in fact a situation similar to that facing dispersion traders doing partial replication (although the partial replication is usually over 50% of the index). So are you saying that there is a way to do that?
The synthetic asset is the sum of the weighted asset prices. What do you mean the weights are given? Are you referring to the constituent weights as specified by the index? Using the index weights will not yield good results if you are trying to find a proxy for the entire basket of constituents (Index). -segv
We can. Your statement is not true unless the basket contains all of the constituents of the index. If the basket contains fewer than all of the index constitutents, you need to optimize the weighting and asset selection to find the best proxy for the index price. -segv
best proxy works good only in reverse dispersion ; you need to find a pair(s) that will go to diff directions and contribute zero to index's move , when playing long
Evidently you have not read my last post above where I clarify the confusion between an index and a basket. The title of the thread says "index" so I thought that was the subject -- understanding how the vol of the index is computed from its constituents -- which have fixed weighting. Now you want to talk about a basket which contains only some of the stocks in the index? Fine. If you only have some of the index stocks and not all in the basket then it is obviously true that using the index weights will not replicate the index. So how would you select the stocks in the basket and optimize their weighting to find the best proxy for the index?
When playing long what? Finish the sentence. First you need to have a decision or at least a leaning toward either dispersion or reverse dispersion based on the index and its total constituent stocks (100% replication). Then you can carry out your decision by the selection of stocks for the partial replication basket, and this will usually be based on IV, correlation, or both.
Well at least we are on the same page now. The money is these days is being made in proxy selection. I do not know anyone who is actually trading full replications, dispersion, arbitrage, basket, or otherwise. The methodology depends on the objectives. If you want spread risk, hedging, or simply index tracking you can use a cointegration approach to create a best-fit synthetic instrument. If you want correlation risk, you can use a weighted-sum approach using correlations. Based on your initial post, I think that you want the correlation risk. If thats true, see this dispersion trading guide for a quick tutorial: http://www.nuclearphynance.com/User...ueless 1.1.pdf#search="dispersion fdaxhunter" The only way to get pure correlation exposure is through a swap. -segv
The dispersion of the full index is need not necessarily be a factor in your decision for the basket trade. I understand that you want it, but you do not need it to trade a dispersion basket. -segv