CFA Level 1 Exam-tips Blog Quantitative Methods By Dr. R. Douglas Van Eaton, CFA - Level 1 Manager Quantitative Methods--Study Session 3

The statistics material in Study Session 3 is much more application-oriented than the theoretical and descriptive statistics material covered in Study Session 2. This is important material, indicated by its appearance throughout the entire CFA curriculum.

Common Probability Distributions

The normal distribution is very important here. Do not enter the exam room without an understanding (both conceptual and computational) of z-scores, confidence intervals, and the computation of probabilities.
You should definitely be able to look up probabilities in a normal table based on computed z-scores.
Computations using the binomial formula are also possible, and look for a question on Roy's safety-first criterion (SFRatio). Notice the similarity between the Sharpe ratio and the SFRatio--you want to pick the portfolio with the highest Sharpe and SFRatios.

Samples and Estimates

I know it doesn't look like it at first glance, but the central limit theorem (CLT) is the crux of what is happening in the quant material. The CLT says that if you draw n samples from a population and compute the sample means for each of the n samples, the resulting distribution of sample means will be approximately normally distributed as the number of samples, n, gets large.

The reason this is so important is that we can use the properties of the normal distribution to develop confidence intervals around the sample mean irrespective of whether the underlying population is normally distributed. Hence, the really important information from this chapter includes the computation of the standard error, confidence intervals, and issues relating to sample size.

Remember that if the sample size is small (i.e., the number of sample means is small), we cannot use the normal distribution and must use the t-distribution to create confidence intervals instead.

Hypothesis Testing

Traditionally, hypothesis testing has not been a big part of the Level 1 exam. However, you should definitely be able to look up critical values of the t-statistic or z-statistic in the tables and compare these critical values to the computed values. Basically, you use the z-statistic when the variance is known and the t-statistic when it is not.

Remember that in a hypothesis test, you reject the null hypothesis when the absolute value of the computed test statistic exceeds its critical value at a given level of significance. As the significance level of the test falls, it becomes more difficult to reject the null hypothesis because the critical value of the test statistic rises (recall that as the significance level falls, the confidence level rises—in fact, significance = 1 – confidence).

Once you understand the similarity between confidence intervals and the critical values for hypothesis tests, you'll be in good shape here.

Technical Analysis