1) IF volatility is realized all to one side, that would be an extremely unlikely occurrence. Why would anyone want to give the 'number.' You already did that. You GUARANTEED the stock would drop to the level stated. I read exactly what you said. 2) You don't understand what you wrote. 3) You stated that if the implied volatility is realized - and that means the stock moves sufficiently so that the actual stock volatility turns out to be 42 between now and expiration - that it is GUARANTEED that the stock will reach a specific price. That is just wrong. 4) And the fact that you ask me to provide 'the numbers' is sufficient proof that you do not understand volatility and what it measures. 5) There ARE NO NUMBERS FOR ME TO PROVIDE. There are an infinite number of possible numbers (of course there are only billions of practical possibilities). The stock does not have to move DOWN enough to reach that specific price level you mentioned. SPY might move higher. Ok you eliminate that possibility. But, it's not enough. It might move up one day and down the next. They up and up. Then down and up. The possible combinations are infinite. You just don't get it. A daily move in EITHER direction contributes to the stock's volatility. You GUARANTEE it will drop to a specific price. That is simply wrong. If realized vol will be the same as currently implied (42.??), and if the current price of SPY ($82.76) is the top price during the next 38 days, we can say this with ABSOLUTE certainty: SPY will reach a price equal to or LESS than $58.75. That is $24 down (with certainty under the above two conditions which is not unrealistic). You can say it with the ABSOLUTE CERTAINTY that you are incorrect. Why: Stock goes down 5 points. Then 5 more. Then 6 points higher. then down 5. then up again - but never goes above today's top price. Never goes above today's top price. That does not mean it has to go down every day. Mark
I am sorry Mark, but you are wrong again. I asked the question not to get the answer, but to get your answer to the question so that you cannot stand on a fence, or change the question as you have done on multiple occasions. The result I gave is correct, and you are wrong, because I have the mathematical proof that what I wrote is correct. Just like the example of Pythagoras theorem. If A, then B. Maths are reliable. I gave A, and B. The only thing you can challenge is the B. My B is correct, and you are wrong as long as you find the B not correct because the maths do not lie. Mark: there is no problem if you are short on things such as mathematical stuff. Just do not try to play politics with it, as science (particularly math) is one of the few areas where politics and evasion do not work. It is black and white. No changing of questions and sitting on fences, etc. I think that what I wrote is above your head to be honest with you. You do not understand the significance of what I wrote, and I think that you doubt its validy because your mind cannot conceive of it, which was the reason why I gave the example. Re-read my IF in italic, and if you still find the result strange, it has to do with what is in your head, and does not have anything to do with the validity of the result.
riskfree: Please find volatility of the following daily closing prices: T+1=79.40, T+2=82.71, T+3=79.40, T+4=82.71,T=5=79.40, T+6=82.71... T+37=79.40,T+38=82.71 Odd days close at 79.40 and evens at 82.71.
All this "math" is making things more confusing then what it has to be. If your volatility is trading at 40% and the SPY is trading at 80.00 (just for an example), all this is saying is that the expected move over a year for the SPY is $32.00 EITHER way. A 10.00 stock trading at 100% volatility means that the expected move over a year is 10.00 either way. Keep it simple.
I have to disagree. Let's set aside for the moment the effect of lognormal distribution for simplicity's sake. If SPY is 80, then 40% volatility means a 1 standard deviation move over the next year is 32. That means there is approximately a 68% probability that one year from now, SPY will be no less than 48 (80-32) and no more than 112 (80+32). However, as Nitro correctly pointed out way back, that's not all it means. You can choose any period you like - weeks, days, months - and that volatility of 40% has an implication for the likely movement within those periods. Let's take weeks for example. There are 52 weeks in a year, and the square root of 52 is about 7.2. If you divide 40 by 7.2 you get 5.55%. So if SPY has a volatility of 40%, then there is a 68% probability that 1 week from now SPY will be no higher than 85.55, and no less than 74.45. It turns out that this is not just idle theory. Rather, it has important implications for practical option trading. To understand how, you need to understand how scalping gammas works. If you don't understand how scalping gammas works, I'm attaching an article that explains it pretty well. If you read it you will understand why - if you buy options with 1 year remaining - it DOES matter greatly how much the average daily and weekly movement is over the following year, even if SPY is unchanged at the end of that year.
Finally someone is showing an understanding. I would ask people to ponder a slight change in this sentence from DMO: "That means there is approximately a 68% probability that one year from now, SPY will be no less than 48 (80-32) and no more than 112 (80+32)." replace "one year from now" by "anytime between now and a year from now". What do you think will happen to the numbers in there? You might be shocked it you realize the significance of the NEW numbers.
I actually think it's right the way I said it - although I'm not a statistician and I could be wrong. For one thing, if we use "anytime between now and a year from now" as opposed to "one year from now," then there is of course a 100% probability that the price will be between those two points at some point during the next year - because it's there right now. So the question really is, what is the probability it will be outside of our range? I still think that the 32% figure (100-68) is correct for "one year from now." If the question is "at some point during the next year," well, statistically that's a different question. And if I'm not mistaken, the answer is different. I vaguely remember that Hoadley has some calculators on his website that distinguish between those two questions. I won't have time to look into it over the next few days but if someone else does I'd like to know the answer.
What you wrote in the earlier post is correct. What I wrote is rather to introduce the second question which you have rephrased nicely. cheers!