08年FRM考试Quantitative Analysis考点解析

来源：Kaplan Schweser　作者：Vivian　时间：2008-09-10　点击：

Quantitative analysis accounts for 10% of the 2008 FRM exam. A good foundation in QA is necessary for understanding other topics and solving problems in fixed income, market risk measurements, and credit risk, as well as the investment management portion of the exam.

• Despite its title, do not make the mistake of thinking that all of the questions in this section will require calculations. You should be prepared for questions that will ask you about definitions and interpretations of the material.
• Understand time value of money. There is no specific topic on time value of money in the 2008 FRM curriculum, but don't let the absence of an assigned reading on this concept throw you off on the exam. Every valuation problem(e.g., bonds, futures, options, swaps)requires your knowledge of time value of money on a discrete or continuous basis.
• Fortunately, the problems relating to time value can easily be solved with the use of a financial calculator. As soon as you purchase a TI BA II Plus® or HP 12C® calculator(both approved for the FRM exam), start learning how to use it. The more proficient you are in the use of your calculator, the more efficient you will be on exam questions, in both accuracy and time spent.
• Know how the Taylor series approximation can adjust for the curvature of a nonlinear derivative in addition to the slope.
• Understand conditional probability, along with Bayes' theorem.
• Understand the probability of occurence for two or more independent events. You will also see this concept used when calculating default probabilities in the credit risk material.
• Know that if two or more events are not independent, calculating their joint probability will require a joint probability table.
• Understand the properties of a normal distribution and memorize the percentage of observations that fall within various intervals.
• Know how to calculate probabilities using a standard normal distribution. A potential exam question could give you multiple N(d)s, and ask you to calculate the area between certain values. On exam day, you will not be given a normal distribution table, but the questions you will be given will not require one. However, make sure you understand how probabilities from a Z-table are determined and know how to look up positive and negative values in the Z-table in the back of your Kaplan Schweser Study Notes. When working on sample problems, it may help to draw a normal distribution and shade in the probabilities you are working with.
• Be ready for variance, standard deviation, correlation coefficient, and the measures of central tendency by skewness and kurtosis. These classic topics are always possible areas for exam questions.
• Memorize the confidence interval formula and the common z reliability factors. Confidence interval calculations will come back into play in the value at risk(VAR) section.
• Tests of hypotheses are critical. This is a must-read and a must-practice concept!
• Understand Type 1 and Type 2 errors in hypothesis testing. Make sure you can evaluate(reject or fail to reject) your null hypothesis based on both the value of the t-test(two-sided versus one-sided) and the p-value. Note that the higher the value of your computed t, the lower p-value, and the higher the chance of rejecting your null. The types of errors in hypothesis testing are often confusing. Only through practice can you overcome the possible confusion.
• Note the difference between the chi-square test and the F-test. Both are used to evaluate the difference in variances. In the case of the chi-square test, you are dealing with the variance of the same population. In the case of the F-test, you are comparing the variances of two distinct populations. For example, if you want to test whether the variance of your portfolio has changed over time, use the chi-square test. If you want to verify if the variance of your population is different from that of another portfolio, such as the S&P500, use the F-test.
• Understand the meaning and the computation of the coefficient of determination. Do not confuse the following concepts and their notations: total variation(total sum of the squares=TSS), unexplained variation(residual sum of the squares=RSS), and explained variation(explained sum of squares=ESS).
• Know how to calculate a correlation coefficient. Understand that a correlation of 1 indicates a perfect positive relationship and that a correlation of -1 indicates a perfect negative relationship. Correlation is also an important concept in other sections.
• Covariance, variance, and correlation—know how to solve for each based on the others. Be prepared to manipulate the formulas to solve  for their various components. Remember that standard deviation is the square root of the variance—even though you are moving quickly on the exam, do not make the mistake of using a variance value when you need standard deviation and vice versa.
• Be familiar with the difference between simple and multiple linear regression analysis.
• Be able to apply the concept of the coefficient of determination as well as the adjusted R^2.
• Note that RiskMetrics^TM and GARCH approaches are both exponential smoothing weighting methods and that RiskMetrics is a special case of the GARCH approach.
• Understand the three historical-based approaches of measuring VAR: parametric, nonparametric, and hybrid. Know the difference between historical approaches and exponential smoothing approaches when calculating standard deviation.
• Expect some easy and descriptive questions related to Monte Carlo simulation and extreme value theory(EVT).