If you click on the avatar picture you will see a slightly enlarged version of it and you will see it's a tank with a Ukrainian flag and the words "Go Ukraine!" inside of it. It's too late to bring home the packing tape dispenser and the boxes now he's hooked on Roblox. LOL
War is a racket imho. "War is mass murder wrapped in a pretty flag." Mike Rivero. No box in there TD?
Here's the extended formula that gives the above numbers for -1SD and +1SD in Normal Distribution (ND), with some explanations: The trick is: we set Volatility V = 34.1345% (wikipedia says just "34.1%", but we use some more precision, ie. more decimals). Code: S = 100 ; V = 34.1345 ; DTE = 365 ; SD1 = S * V / 100 * sqrt(DTE / 365) ; SD1 ; S - SD1 ; S + SD1 34.13450 ( the value for 1SD; here it of course equals V b/c DTE=1 year, the same as V is for too ) 65.86550 ( the value for -1SD around S ) 134.13450 ( the value for +1SD around S ) S is of course the current stock price. DTE: time frame, 365 means 1 year. Via this parameter we can calculate also for other time frames, for example for 90 days etc. My above quoted calculation uses even more precision, so the minuscule differences are neglectable. In my above quoted posting I've extended this to be used in the Lognormal Distribution (LogND) case --> see there.
Follow-up: A more precise value is 34.134474% : s = 100 ; v = 34.134474 ; dte = 365 ; sd1 = s * v / 100 * sqrt(dte / 365) ; sd1 ; s - sd1 ; s + sd1 34.134474 65.865526 134.134474
I just thought I’d update this thread for anyone who is still following it or in case someone comes across it in the future. After discussing OP’s objectives with him, I was able to clarify that he wanted to get a *very rough* indication of possible future prices for a stock by using the following model: price_in_future = price_now + X, where X is a ‘random variable’ that follows some statistical distribution (eg: normal, lognormal, etc). X is assumed to have a mean of 0 (ie: assume that “on average” the stock will end up at the same price it is at now) and X represents the change in price of the stock over 1 year. In particular, OP wanted to know estimates for price_in_future_+1SD and price_in_future_-1SD. In other words, we needed to find the values for +1SD and -1SD on the distribution of X and then add (/“subtract”) them from the price_now. (OP also wanted to adjust the calculations for times less than 1 full year into the future; I assumed OP did those calculations correctly and I did not look at them.) In the course of our conversation, I confirmed that OP made a relatively common mistake among those who do not have a lot of experience with statistics: namely, that the standard deviation of a normal curve is (always) 34.1%. This, of course, is false and could lead to drawing wildly erroneous conclusions. The reason for the confusion lay in the fact that if a process follows a normal distribution, then approximately 34% of observations will fall between the mean and one standard deviation. This is true. If one is not thinking carefully, however, one can confuse this with the idea that for a normal distribution one standard deviation is equal to 34%! This is patently false. If it were true, then it would mean every process that follows a normal distribution has exactly the same variance (/“volatility”), which is obviously false! For what it’s worth, I've seen this and similar mistakes before and they can obviously have disastrous consequences if they are not caught early. To correctly specify a normal distribution, one must specify and/or estimate two quantities: the mean and the standard deviation. (Technically, one could specify two different quantities but that is well beyond what is needed here and adds nothing from a practical perspective.) These quantities either need to be assumed (specified) or estimated (computed) from data. OP disclosed that for various reasons using data to estimate these quantities is undesirable and moreover unnecessary considering he only needs very rough approximations for his application. Fair enough. So, in the end, OP settled on specifying the mean = 0 and the standard deviation to range from 25 to 45 based on his personal knowledge of how these stocks typically behave. From there he made several estimates for the range of possible future values of stock prices. Obviously, these estimates are incredibly rough, but presumably sufficient for his purposes.