Way to go, ymc!
liaaba Wrote: ------------------------------------------------------- > >>>"I would like to give them some benefit of the > doubt, but that’s just wrong. Are the readings > right? " > > —in readings 9, this is the reading when they > first introduce confidence interval, first, they > mention: > > approximately 68% of observations is b/w miu +/- 1 > sigma > approximately 95% of observations is b/w miu +/- 2 > sigma > … > (which are correct) > > then, they said, > “In general we do not observe the population mean > or the population standard deviation of a > distribution, so we need to estimate them. we > estimate the population mean, miu, using the > sample mean, xbar, and estimate the population > standard deviation, sigma, using hte sample > standard deviation, s. using the sample mean and > the sample standard deviation, to estimate the > population mean and population standard deviation, > respectively, we can make the following > probability statements about a normally > distributed random variable X, in which we use the > more precise numbers for standard deviation in > stating intervals.” > > And they basically showed, > > > "The 90% confidence interval for X is +/- > 1.65s. > > > > The 95% confidence interval for X is +/- 1.96s. > > > > The 99% confidence interval for X is +/- 2.58s. > > These are ALL from reading 9, where I think they > really meant to teach prediction interval, and > they used it for that purpose as well (and they > never used standard error). YUCK > > Then in reading 10, they introduce central limit > theorem and standard error, then they showed the > correct confidence levels…
While we are at it, can someone explain to me how those polls in newspaper arrive at their margin of error like +/-3% or something like that. This bugged me since I was a teenager. Suppose there is a poll of 1000 people who were asked who they are going to pick in the democratic primary Hilary 42% Obama 23% Edwards 9% Others 17% No opinon 9% And then it says the margin of error is 1.5% for example. Can you explain to me how to find the margin of error in this example? I don’t know how to model this problem to find it. Can someone enlighten me please? Thanks!
It’s not even exactly clear, particularly when they say the margin of error is the same for all those people. However, it’s usually the radius of the 95% C.I. for the people who would vote for each candidate. So Hillary’s margin of error shou be 1.96*Sqrt(0.42*(1-0.42)/1000) = 3%. If they reported the margin of error is 1.5% here they were reporting the standard error as the margin of error which happens all the time. Note that Edwards error is much smaller, standard error = 0.9% vs Hillary’s 1.5%.
Wikipedia actually has a pretty nice entry on C.I.'s. (I love Wikipedia, btw). Anyway, the first sentence of that entry is “In statistics, a confidence interval (CI) is an interval estimate of a population parameter”. Apparently, the curriculum committee at CFAI doesn’t understand that.
So I just sent the following letter to CFAI: I spend a significant amount of time teaching the CFA curriculum. I am having deep trouble with the following LOS: > “Construct and explain confidence intervals for a > normally distributed random variable and interpret > the probability that a normally distributed random > variable takes its value inside the constructed > confidence interval.” The LOS barely makes sense and then the readings that go with it are simply wrong. The writers of this LOS need to go back to any elementary statistics book and look up the definition of confidence interval. The first sentence from the Wikipedia entry (which is pretty good, incidentally, and far better than the CFA readings) might help: “In statistics, a confidence interval (CI) is an interval estimate of a population parameter” So the first problem with the LOS is that it asks candidates to construct a C.I. for a random variable. Ouch. Confidence intervals are interval estimates for parameters, not random variables. At the risk of being condescending, parameters are unknown but not random and are certainly not random variables. Adding in “normally distributed” just makes it more unintelligible. The second part about “interpret the probability a normally distributed random variable takes its value in the constructed C.I.” barely makes sense. Given any distribution and some interval, I can tell you what the probability is that a r.v. drawn from that distribution lies in the interval. However, this is not what’s being discussed in the readings which are something like a weird discussion of asymptotic prediction intervals. So: 1) “Twenty observations are drawn from a normal distribution. X-bar = 10 and s = 5. Calculate a 95% C.I. for an observation drawn from this distribution” Ans: Question makes no sense. A C.I. is an estimate for a parameter. An observation is not a parameter. 2) “Twenty observations are drawn from a normal distribution. X-bar = 10 and s = 5. Calculate a 95% prediction interval for an observation drawn from this distribution” Ans: Now this makes sense, but the appropriate formula is not given in the readings. It is X-bar ± t*s*Sqrt(1 + 1/n) 3) “Twenty Bazillion observations are drawn from a normal distribution. X-bar = 10 and s = 5. Calculate a 95% prediction interval for an observation drawn from this distribution” Ans: Since a t-distribution with 20 bazillion - 1 d.f. is about a z and 1/20 Bazillion is about 0 the answer is X-Bar ± z*s as given in the C.R… Note this is a prediction interval, not a confidence interval. 4) “Twenty observations are drawn from a normal distribution. X-bar = 10 and s = 5. Calculate a 95% confidence interval for the mean of this distribution” Ans: Now we are talking confidence intervals because we are estimating a mean which is a parameter and not a random variable. The answer to this kind of problem is correctly done in the CR’s and is X-bar ± t*s/Sqrt(n) This is a really serious problem. The CFA curriculum is supposed to be post-graduate level material, but this level of understanding of C.I.'s would be poor for someone completing a basic statistics class at the undergraduate level. To be frank, if I’m talking to someone and they say that a C.I. for a random variable is [anything], I just think they are an idiot and can’t have anything very sensible to add to the discussion (with a little caveat about some pretty sophisticated Bayesian statistics that are clearly not what is being discussed in the curriculum). Clearly, that is not the way that we want CFA charterholders to be regarded. Regards - JoeyDVivre Ph.D, Statistics.
Way to go, Joey! You are the man! As to my “margin of error” question, are you assuming a Binomial distribution with n=1 for each choice?
Got a “We received your letter and will be responding in three days”
I got the following e-mail today: Thank you for your email. We appreciate your pointing out this problem, which will be addressed in the near future. Thank you again for taking the time to inform us of this. Regards, Wanda Lauziere Curriculum Development CFA Institute So, what are they going to do about it?
Looks like not much content in this reply though. But they did give me detailed reply when I asked them how to deal with market value of stock options to comply with GIPS. ----------------------------------- Re: GIPS and stock options fund Thank you for your interest in the GIPS® standards. Portfolio valuations must be based on market values. In the case of thinly traded securities, firms may use a reasonable method for valuation as long as the method is consistently applied. The following Q&A is available in the GIPS Q&A database at http://www.gipsstandards.org/programs/faqs/index.asp under the category “valuation”: Firm B has several portfolios invested in emerging market debt and other thinly traded securities. What is a reasonable method for valuation of these securities? Firm B must determine a reasonable valuation method for the thinly traded securities held in its portfolios. One example of a “reasonable method” is to seek out three separate bids from three non-affiliated brokers, average those three prices, and consider this average to be a fair and acceptable representation of the market value. The valuation method policy developed by the firm must be applied consistently over time to ensure relatively consistent asset valuations. Source: GIPS Handbook, 2nd Edition Added: March 2006 The proposed Guidance Statement on the Use of Leverage and Derivatives at http://www.gipsstandards.org/standards/guidance/develop/pdf/Leverage_Derivatives_Guidance.pdf may provide useful information on leverage and derivative instruments; please note it is still pending final approval following a period of public comment. The GIPS Q&A database also provides valuation guidance for leverage and derivatives. The GIPS standards are located at http://www.cfainstitute.org/centre/ips/gips/pdf/GIPS_2006.pdf. The above response is based on an understanding of the facts presented in your question. Omission, misstatement or misrepresentation of the facts may affect the response provided. A number of resources for the Standards are available and include the following: The GIPS Interpretations Library, including Guidance Statements and Questions and Answers on the GIPS standards that are applicable to all firms claiming compliance with the GIPS standards, available at http://www.gipsstandards.org/standards; the GIPS Handbook, available to be ordered at http://www.efastcom.com/CFABookstore/control/productdetails?item_id=061101; information on upcoming workshops and conferences is available at http://www.cfainstitute.org/memresources/conferences/gips.html. To receive bi-monthly e-mail updates on the GIPS standards, please email your contact information to gipshelpdesk@cfainstitute.org. Once again, thank you for your interest in the GIPS standards. If you need any additional information, please feel free to contact us.
ymc - What question did you ask them about GIPS that resulted in that reply? I sent Wanda back the following e-mail: So what are you going to do about it, so I can tell my students what they should do about it? I would be happy to teach them confidence intervals, prediction intervals, sampling problems, but it’s just not clear what I should teach under that LOS. Regards - B IMHO, chances of a reply = 0.0001 but it’s fun to try.
I got a generic answer after my first try, too. So it is good that you follow up. My second email looks like: ---------------------------------- To: GIPS Helpdesk Subject: RE: Stock Options Fund and GIPS What if there was no market value on the day of interest? It is quite often that there is no volume in option trading. Do I just average out the last bid/ask (not sure if I can find this info however…)? Actually can GIPS explicitly devote a section to deal with derivatives? Thanks
The problem is much deeper than that and their answer wasn’t very satisfying. Even the part about “consistently” is a little troubling (for example, this month/stock we might be in “sticky delta” and in another month/stock “sticky strike” - if they aren’t trading you need your trader to tell you which to use). One of the big problems with these methodologies is that applying a valuation method “consistently” means applying a valuation methodology that says your investment is riskless. For example, suppose I buy some claim in a bankruptcy court. I judge that I will get paid out between $0.6 and $0.7 on the dollar and it will happen in 12 - 18 months. I pay $0.5 for the privilege. A decent valuation methodology is to average everything and say I’m getting 0.65 in 15 months which sounds like a 23% annual return. So everyday I follow GIPS’s “consistently” and accrue that 23% return and collect incentive fees and put out advertising literature based on my riskless 23% returns. A guy can collect a lot of money under management that way blessed by GIPS until it turns out that he’s getting 0.48 in 24 months. But your track record is so good you have collected enough capital that these early faux pas’s are not material to the billions in your portfolio now, which are still accruing 23% annually in a riskless way. Eventually, you could have your GIPS-compliant $3B hedge fund go to 0 in 6 months. It really sucks.
So I did get an e-mail back: To be fair to all candidates, a correction/clarification will be posted on the Errata listing when it is next updated so that all candidates are informed at the same time. Regards, Wanda Lauziere