Cfa Level 1 Question Weighting
Versie Rons
In the mock for this year lvl 3, 5 securities are given and we must select the weighting that gives the highest return. Here is my understanding of how to do the calculations but apparently I am wrong.
Now, in trying to find my error, I used both methods of calculation for price-weighted and market-cap weighted. Price-weighted gets the same answer with both approaches, as expected. However, given the numbers in the problem, the market cap weighted approachs give VERY DIFFERENT answers.
In practice, if one was weighting the individual securities at time 0, the ending market cap would not be known. Therefore, the weights on the individual securities would be based solely on (market cap starting for company 1 / sum of all market caps).
Are the weights of the individual positions determined correctly? Once the weights have been properly determined, the portfolio return is the sum of the position weights times the position returns. There has been no rebalancing so what would the change in market cap have to do with anything?
"The question says to assume there are no stock splits or stock dividends, but it does not assume away cash dividends. Your method of calculation (summing the products of the starting market cap weights and the price returns) assumes no cash dividends which is clearly not the case because the market cap returns are different than the price returns.
The sum of the products of the initial market cap weights and the change in market cap (the market cap return) is 13.5%, the same as the ending market cap divided by the beginning market cap minus 1."
The only way that the price appreciation could be less than the change in market cap is if 1) there is a stock dividend (we are told to assume this has not happened) or 2) the company raises equity capital via a secondary offering. In the case of the latter, the performance of an index that is constructed using the initial market cap weights and is not rebalanced (again, question said to assume no rebalancing) will be equal to the initial weights times the price appreciation.
Since each level of the CFA exam is going to take about 300 hours of study time, knowing how each topic is weighted for each exam level will allow you to budget and allocate your study time more effectively. This will help you study more efficiently based on your own strengths and weaknesses.
One of the major changes to the Level 1 scoring weight system is that the weights are given in ranges. This means that the testing candidates will no longer be able to figure out exactly how many questions will be asked per topic ahead of the testing date.
As you can see from these weight ranges, the most important topics to do well on are the Ethics component and the Financial Reporting and Analysis component. Successful test-takers recommend you spend approximately one-third of your total studying on these two topics.
While the exact number of questions cannot be known ahead of time, there are some fairly accurate assumptions that can be made based on the weight percentage breakdowns. The minimum and maximum possible number of questions, along with a ballpark expectation of the number of test questions are:
Based on the above data, you can see that the most important topics in the second level of the CFA exams are Equity Investments, Financial Reporting and Analysis, Fixed Income, Portfolio Management and Ethical and Professional Standards.
Level 2 has fewer questions than Level 1, but it does come with substantially more reading. The test is broken into item sets or mini-cases, each with four or six multiple-choice questions.
It is recommended that you spend around 60% of your study time focused on these five areas. With a suggested study time of 300 hours per testing level, you should be spending 180 hours on these five subjects alone.
The shorter topic list for Level 3 does not mean increased topic weight for all the subjects. In fact, the combination of just two of the seven topics comprises more than half of the entire exam grade. The topic weights for Level 3 are:
As you can see, the scoring for Fixed Income Investments and Portfolio Management and Wealth Planning can account for up to 60% of your total score, so that should be reflected in your study time and preparation. For example, if you are spending 300 hours preparing and studying for the Level 3 exam, then you should be spending a minimum of 150 hours between those two topics alone.
For level 2, it is recommended that you spend around 60% of your study time focused on the five areas of Equity Investments, Financial Reporting and Analysis, Fixed Income, Portfolio Management and Ethical and Professional Standards.
But are they sufficient for reducing selection bias6 in online opt-in surveys? Two studies that compared weighted and unweighted estimates from online opt-in samples found that in many instances, demographic weighting only minimally reduced bias, and in some cases actually made bias worse.7 In a previous Pew Research Center study comparing estimates from nine different online opt-in samples and the probability-based American Trends Panel, the sample that displayed the lowest average bias across 20 benchmarks (Sample I) used a number of variables in its weighting procedure that went beyond basic demographics, and it included factors such as frequency of internet use, voter registration, party identification and ideology.8 Sample I also employed a more complex statistical process involving three stages: matching followed by a propensity adjustment and finally raking (the techniques are described in detail below).
The present study builds on this prior research and attempts to determine the extent to which the inclusion of different adjustment variables or more sophisticated statistical techniques can improve the quality of estimates from online, opt-in survey samples. For this study, Pew Research Center fielded three large surveys, each with over 10,000 respondents, in June and July of 2016. The surveys each used the same questionnaire, but were fielded with different online, opt-in panel vendors. The vendors were each asked to produce samples with the same demographic distributions (also known as quotas) so that prior to weighting, they would have roughly comparable demographic compositions. The survey included questions on political and social attitudes, news consumption, and religion. It also included a variety of questions drawn from high-quality federal surveys that could be used either for benchmarking purposes or as adjustment variables. (See Appendix A for complete methodological details and Appendix F for the questionnaire.)
The analysis compares three primary statistical methods for weighting survey data: raking, matching and propensity weighting. In addition to testing each method individually, we tested four techniques where these methods were applied in different combinations for a total of seven weighting methods:
Because different procedures may be more effective at larger or smaller sample sizes, we simulated survey samples of varying sizes. This was done by taking random subsamples of respondents from each of the three (n=10,000) datasets. The subsample sizes ranged from 2,000 to 8,000 in increments of 500.9 Each of the weighting methods was applied twice to each simulated survey dataset (subsample): once using only core demographic variables, and once using both demographic and political measures.10 Despite the use of different vendors, the effects of each weighting protocol were generally consistent across all three samples. Therefore, to simplify reporting, the results presented in this study are averaged across the three samples.
For some methods, such as raking, this does not present a problem, because they only require summary measures of the population distribution. But other techniques, such as matching or propensity weighting, require a case-level dataset that contains all of the adjustment variables. This is a problem if the variables come from different surveys.
The next step was to statistically fill the holes of this large but incomplete dataset. For example, all the records from the ACS were missing voter registration, which that survey does not measure. We used a technique called multiple imputation by chained equations (MICE) to fill in such missing information.12 MICE fills in likely values based on a statistical model using the common variables. This process is repeated many times, with the model getting more accurate with each iteration. Eventually, all of the cases will have complete data for all of the variables used in the procedure, with the imputed variables following the same multivariate distribution as the surveys where they were actually measured.
This synthetic population dataset was used to perform the matching and the propensity weighting. It was also used as the source for the population distributions used in raking. This approach ensured that all of the weighted survey estimates in the study were based on the same population information. See Appendix B for complete details on the procedure.
For public opinion surveys, the most prevalent method for weighting is iterative proportional fitting, more commonly referred to as raking. With raking, a researcher chooses a set of variables where the population distribution is known, and the procedure iteratively adjusts the weight for each case until the sample distribution aligns with the population for those variables. For example, a researcher might specify that the sample should be 48% male and 52% female, and 40% with a high school education or less, 31% who have completed some college, and 29% college graduates. The process will adjust the weights so that gender ratio for the weighted survey sample matches the desired population distribution. Next, the weights are adjusted so that the education groups are in the correct proportion. If the adjustment for education pushes the sex distribution out of alignment, then the weights are adjusted again so that men and women are represented in the desired proportion. The process is repeated until the weighted distribution of all of the weighting variables matches their specified targets.