Since you do 100% replication, I'm surprised that you are arguing for a small basket of stocks, or are you arguing against that -- I can't tell. Please clarify what you are saying. Here is how I am trying to interpret it: It is true that with less components the greater chance they will all be on the same side, but according to that logic let's just use 1 stock. And that logic cuts both ways. The same odds (3%) say that the 5 stocks will be on the other side. There is no right side or wrong side unless the index has made a directional move. And the less stocks you have, the more chances there are for tracking errors which could be more serious. Here are some questions: Is it necessarily "good" to have all 5 stocks on the same side of the "axis"? Why or when? What do you mean by "the longs you recieved on your short index"? What do you mean by "if 2 will be negative and 3 positive .... that's a home run."? I would think a home run would be when the index stays stagnant and the stocks disperse greatly (like fireworks) to either one side or the other.
mastic , that what I meant when I said i'm not trying to confuse anyone... In my answer to Alassio , I try to point to all pros and cons when one uses fewer amount of stocks. This time I will put it in numbers . Index conditions : price=100 , IV=14. Basket : 4 stocks(A,B,C,D) , price=100(each) , IV=21(each),price weight contribution toward Index=25%(each) Action : Sell 12 Index ATM straddles for 3$ each. Buy 2 ATM straddles (for each stock , total 8) for 4.50$ each. No intra position action , all final numbers based on intrinsic value. Scenario 1: each stock went up 4% (hence , Index up 4%) Index lost 1200$ (1 per combo*12) Basket loss 400$ (50 cents*8) Portfolio P&L is -4.76 (and -8.76 vs. benchmark/market) Scenario 2: A,B +4 and B,C -4 ( hence , Index=no change) Index gain is 3600 (3*12) Basket loss is 400$ (50 cents*8) Portfolio P&L is 9.5% the above 2 scenarios will be very unlikely for higher amount of stocks/components , much smoother results vs. Disaster or Home Run that described in this sample. Anyway , good luck to all , I will consider somehow "cheap/expensive" IV rating next time I take position like it was suggested here.
Thanks IV_Trader for putting numbers to these scenarios. I assume that the time period is about a month. What your scenarios are telling me if the index moves you lose (#1) and if it is stagnant you win (#2). I don't know what your main point is here regarding the distribution of the component stocks. It seems to me that under the losing scenario #1 it doesn't matter how many stocks you have. Since the stocks track the index, regardless of their number, then their distribution will be centered on the mean of 104 (+4%), so given a normal distribution, the P&L of the straddles will be the roughly the same regardless of the number of stocks. I did a quick check on a hypothetical scenario #3, with A,B +4, C +2, D +6, and the resulting loss comes out the same. By the way, how are you calculating the portfolio P&L? You scenarios are interesting but I have a nagging feeling that something isn't amiss in how they are set up. Right now I can't put my finger on exactly what it is. I think it has to do with the fact that the IV of the stocks is 50% greater than the index, and you pay 50% more for the straddles, but in the end the example distribution of both the stocks and the index is the same.
Why do index options have negative IV skew, whereas the component parts (individual equity options) don't ? Is there any way to trade this anomaly ?
The reverse (or negative) skew of index options has been there since the crash of 87. The dispersion strategy we have discussed here so far involves ATM option straddles. McMillan has discussed a variant of the dispersion strategy whereby OTM index puts are sold and OTM puts of components are bought.
I was thinking along the lines of shorting a representative basket of individual equity Calls, and hedging by going long the index Calls. My reasoning being that index Calls are cheap (realative to index Puts). Anyone have any experience here, comments, or suggestions ?
This is another attempt at a reverse dispersion. The index calls are cheap compared to the puts, but you are not hedging against puts. Even the index calls will be somewhat expensive compared to the index SV. You don't say what kind of equity calls these are and your reasoning for selling them. Why don't you give us an example of your strategy or say why you think it would work?
I don't have an example yet, I'm in the early days and it may amount to diddly squat. The reason I think it should work is because the vol smile of individual equity options is broadly symmetrical, whereas the composite index has a negative skew to the upside. This cannot be correct, and I'm looking at any and all ways to profit from the discrepancy. Any help from anyone appreciated.
You would kinda expect that in a panic-driven selloff everything correlates, while in a rally things disperse based on their relative value. From this, being long correlation (long index puts, short component puts) on the downside and short correlation (short index calls, long component calls) might be a good way to go. Sort-of opposite from your thinking