some background: A few months ago, Nathan presented his free web tool for performing Monte Carlo sims on a position. For the distribution of future price action, he uses a Normal Distribution. During the presentation, Jim Riggio asked about substituting a different distribution: Possibly collecting historic data for the distribution. The response was something, like "it is not easy to do" (I forget, the reasoning, and at the time did not give it adequate thought). so: Now, I would like to revisit the topic, of substituting a real distribution, as a proxy for estimating future price action. The theory: using a real distribution associated with the underlying should produce more accurate results than using a Normal Distribution. (Seems logical) I do not have a strong statistics background, so would like feedback from those with statistical background on likely errors/assumptions in my pursuit. It is my desire to produce a Cumulative Distribution Function from binning Historical returns, that can be applied to Future time values, by indexing by STD DEV, where I merely map the STD DEV to the CDF bin for all bins! My first concern is if errors are introduced by using historic "daily returns" to map to larger time estimates (1->100 Days). -- I should be able to work out the CDF (will probably merely use the BIN probabilities) -- I do not yet anticipate difficulty here. Using Excel's "Descriptive Statistics" Analysis tool for examining both a daily % Return and a weekly % Return on data from 1986 to present, produces the following results: DailyMean0.037449Standard Error0.01275Median0.057263Mode0Standard Deviation1.139284Sample Variance1.297968Kurtosis21.35565Skewness-0.8324Range32.04696Minimum-20.4669Maximum11.58004Sum298.9918Count7984Largest(1)11.58004Smallest(1)-20.4669Confidence Level(95.0%)0.024994weeklyMean0.144179Standard Error0.062901Median0.291831Mode#N/AStandard Deviation2.290484Sample Variance5.246317Kurtosis5.409974Skewness-0.72341Range28.90254Minimum-18.1955Maximum10.70707Sum191.1809Count1326Largest(1)10.70707Smallest(1)-18.1955Confidence Level(95.0%)0.123396~ Note: The Weekly is sloppily created by only capturing each Friday close, vs the prior Friday close, therefore occurrences of non-trading Fridays, will result in one less sample, but the period of the next will cover 2 weeks instead of one. I don't think this sloppy sampling introduces significant error. All data is % return (sample-sample[-1])/sample[-1])% (where "-1" means prior sample) Can someone with a good grasp on statistics confirm that the above Daily and Weekly summaries do NOT suggest a flaw in using Daily return data to produce a CDF that will be used to infer different ranges of future time deltas? BTW: This is for SPX only! Thanks in advance. PS: After this, other questions will be pursued, such as relevance of some historic periods, etc.