To assist you, here are the parameter estimates for the DJIA, 8/30/00 = 4/22/05 mu_daily -0.000006 sigma_daily 0.011932547 mu_annual -0.001390045 sigma_annual 0.189423317 ------------------------ r_bar -0.00008 sigma 0.011932547 _____________________________________ A tip on calculating p-values: The Paper tables and even STATTABLES are useless for z-scores greater than 3.9. One has to use the Excel function to get small p-values. To calculate in Excel: --------------------- Cell A1: 1.96 # z score cell A2: =2*(1-NORMSDIST(abs(A1))) # p-value (2-sided) test it with +/- 1.96! cell A3: 1/A2 # number of days for event to happen cell A4: A3/252 # number of years for this event to happen e.g., if p-value is 0.001, then this should happen every 1000 days, which is 4 trading years. Even EXCEL cannot handle |z|> 8.200 which calculates p-value to 2.22045E-16 (corresponding to once in 1.78714E+13 years, but keep in mind the age of the universe is 4E10, so this would occur only once in the age of the universe times TEN PARALLEL UNIVERSES!) ____________________________________ Some general guideline: Don't turn in all the data, just what is germane and helps make your point. This would include a few data summary tables, etc. Remember, Management is NEVER going to look at a bunch of attachments with raw data. I trust that you have looked carefully at all the data. There's no reason to include up to 140 pages of of NEEDLESS DATA, excluding the charts/graphs! Save a Tree! That is [(4stocks + 3indexs)*(1318 days)* (4 columns per stock)]/(8 columns/page)/(25 lines per page) = 138 pages. One of the purposes of the course was to teach data reduction techniques; so if you can display pages and pages of prices as a single chart, this is in the spirit of the beginning of the course. ____________________________________ Note: Daily Estimates:l sigma_daily = stdev(daily data) sigma_annual = sigma_daily * sqrt(252) mu_daily = r_bar + (sigma_daily^2)/2 mu_annual = mu_daily * 252 (no square root) ______________________________________________________ >Dear DR. Dobelman, > >What is volatility, is it square root of variance ? in the text book variance >is given as sigma squared but here you mention it as sigma ? volatility is variability of the returns; it is quoted in terms of standard deviation, which is just sigma, the square root of s^2. >S small r -is it Standard deviation of daily "r".? YES! ______________________________________________________ To: CLASS Subject: lab 99 Dr. Dobelman, I would like a clarification for question number 2 in lab 99. Is a price chart a time series? Thanks, From: J.A. Dobelman To: CLASS Subject: Re: lab 99 Yes, just a time plot like a stock chart (www.stockcharts.com) ________________________________________________________ From: J.A. Dobelman To: CLASS Subject: Re: Lab 99 > Dear Professor Dobelman, > > I've been working on Lab 99 and I have a few questions. On question #3, what > would you like us to use for our x-component and what would you like us to use > for our y-component of the regression and correlation analysis? We put the "independent" variable (the reference index) on the x-axis and the "dependent" variable (a stock of interest) on the y-axis. > Then on question #5, would you like us to present 8 correlations (ie > each stock with G-ISCO and each stock with D-ISCO)? Yes, but this is just s single number, the correlation. We expect a good writeup to compute a regression equation and discuss its intercept and slope! _________________________________________________ From: J.A. Dobelman To: CLASS Subject: Re: lab 99 questions! Here is some help provided so far. > > 1) question number 1 says to calculate the annual and daily growth and > volatility estimates for the DJIA and 4 stocks. we were confused in the > explanation of the clarity of which definitions to use in order to compute > these calculations. if you could clarify these statistics for us that would > be great! See below, sorry for the confustion > 2) in question number 4, in order to scale to the value of the DJIA, do we > multiply the indexes by A/I which would be 11103/specific index or is the > scaled value A/I? We were confused bc if we are to multiply the index value > by A/I, then this just yields the value of A and this is not > helpful/informative and we werent sure how to approach the calculations! its 11103/specific index on day 1 (see below) > 3) in number 5 we are supposed to find the correlations between the 4 stocks > and the indexes. are the indexes we are supposed to use the originally > calculated indexes or the scaled indexes from number 4? Either one, they divide out, just say which one you use ______________________________________________________ From: J.A. Dobelman To: CLASS Subject: Re: lab99 > on number 4, i cant seem to do the geometric mean on excel. i think that > the values of the numbers may be too large for the program to handle. in =geomean(d3:f3) remember you are calculating it across a particular row, and just copying that down the column > addition, the scaling of the numbers... it says that "if we wish to scale > the indexes to 11,000 on day 1, we multiply each calculaion by A/I. what > is "each calculation" refer to? the geomean or the average in each cell. > so far i have done to problem 4 and i am > experiencing extreme confusion on this lab (and stress)! thanks for your > understanding. WTG! Sorry for the stress.. ________________________________________________________________ > Dr. Dobelman, > > Our group is unsure how to answer question 9 & 10 on the project. How > should we approach these questions? Basic idea on question 9 after you get the z-scores, is if 10% results in a very rare event, and if all stokcs underwent this rare event, and the rare event happens every few months instead of every few hundred milliion years, then one might question the normality assumption. On Question 9 you could explore normality with QQ plots, or just calculate z-scores for EVERY DAY on EVERY STOCK and sort them and count them and see how many there are greater than 3 sigma; then know that P(|z| < 3sigma) = P(-3sig < z < 3sig) = .997, or the opposite which is .003, or about 4 out of 1000; If you get more than 3 |z|>3 sigm days, then you would have even more questions about the normality assumptions of the log of the return of X. You could plot these returns and they would look normal, but might be far from it, always in the far tails. Some questions for #10 that people int he past have raised are things like these, but you might have already addressed them in your writeup: o General probabilistic question: What is the probability that an individual stock increases and how does this relate to its GBM growth parameters? o Is there fruit in coefficient of variation analysis for stocks (sigma.mu)? o What do the intercepts mean on the stock regressions, especially when they are negative, or if Dow = 4320 -> CSC = 0? o Why are the DISCO and GISCO not 100% correlated? Does it have something to do with the different type of averaging? o How does one measure "consumer confidence," and does it attempt to discover individual psychology As you can see, it would take a short time of brainstorming to come up with a nice batch of questions like these.