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Strategies & Market Trends : Waiting for the big Kahuna -- Ignore unavailable to you. Want to Upgrade?

To: Defrocked who wrote (9199)	11/5/1997 8:39:00 PM
From: Bilow	Read Replies (4) \| Respond to of 94695

Regarding index options. They are always less volatile then their constituents. The best case for this statement is when the under- lying securities are independent (this is not the case when market risk is present. Market risk is risk that the market as a whole will change, non-market risk is risk that the particular stock will change relative to the market. Example calculation: Four stocks, A, B, C, and D make up index X, X = (A+B+C+D)/4. Suppose A, B, C, and D will be each be worth either $4 or $6 three weeks from now, with equal probability. (I.e. I am using simple probability examples that can be worked without calculus.) Further, suppose they each currently sell for $5.00. Easy to calculate their current variances: 0.5 * (5-4)^2 + 0.5 * (5-6)^2 = 1. So standard deviation = sqrt of variance = 1. Therefore their options should be priced with an implied volatility of 1. Now look at the index. Here are the possible outcomes, with probabilities: (4+4+4+4)/4 = 4.00 Prob = 1/16 = 0.0625 (4+4+4+6)/4 = 4.50 Prob = 4/16 = 0.2500 (4+4+6+6)/4 = 5.00 Prob = 6/16 = 0.3750 (4+6+6+6)/4 = 5.50 Prob = 4/16 = 0.2500 (6+6+6+6)/4 = 6.00 Prob = 1/16 = 0.0625 So variance is: 0.0625(5-4.0)^2 + 0.2500(5-4.5)^2 + 0.3750(5-5.0)^2 +0.2500(5-5.5)^2 + 0.0625*(5-6.0)^2 = 0.2500 So standard deviation is sqrt(0.25) = 0.5 So the index options should (in this case of 4 independent stocks) be priced with an implied volatility just half that of the constituent stocks. This is a theoretical calculation, and not an indication that one or the other is a better deal. These calculations compute the "fair" deal. This shows why it is that indexes are supposed to carry lower implied volatility than the constituent stocks that make them up. Similarly, the SPX should have lower implied volatility than the SOX or XCI, for example. The point is that just because INTC has higher implied volatility, doesn't mean that its options are a worse deal. If that were the case, then options buyers would only buy index options. In fact, options are more or less fairly priced. The problem with purchasing them is the spreads, the commissions, and the decay of time premium... :) To do this comparison on real-life stocks and indexs, look up time premiums for same expiration calls/puts struck at the money. -- Carl