# CFA Level I: Quantitative Methods (Part II)

By Stella Goh – Market Data Analyst | 26 June 2019 As discussed earlier in my previous Article of “CFA Level I Quantitative Methods (Part I)”, I believe that all of you have a better understanding of what reading six until reading 9. Today, I would like to continue to talk about what content we can learn from reading 10 to reading 13 on the topic of Quantitative Methods.

In this reading, the random variable plays a vital role in making an investment decision. The probability distribution used to specify the probabilities of possible outcomes of a random variable such as price and return. Besides, candidates are also able to learn how to distinguish the difference between the types of variables with their functions. For examples, Discrete uniform random variable, Bernoulli random variables, Binomial random variables, and so on. The types of distributions and their features also will be discussed in this reading, such as Discrete uniform distribution, Binomial distribution, Normal distribution and Lognormal distribution. All of these probabilities distribution will be used extensively in the basic valuation models such as the Black-Scholes-Merton option pricing model, Binomial option pricing model, and the Capital asset pricing model. Besides, candidates must also learn to distinguish between the univariate and a multivariate distribution and explain the role of correlation in the multivariate normal distribution.

At the last part of this reading, it discusses the Monte Carlo simulation. Monte Carlo simulation is a type of computer-based tool for obtaining the information on the multiple options for which no simple pricing formula exists. Usually, it is a technique people used to identify the risk factors associated with the uncertainty and specify the probability distributions in the prediction and forecasting models. From this reading, candidates can know more about the applications, limitations and also the comparison between Monte Carlo simulation and Historical Simulation.

First of all, in this reading, it focuses more on sample, sampling and estimation. An example is a subset containing the characteristics of a large population. Any statistics that we compute with sample information are only the estimates of the underlying population parameters. The analyst uses the samples such as S&P500 and the Nikkei-Dow Jones Average as valid indicators of the whole population’s behaviour to assess how various the markets from the world are performing.

Sampling is the process of obtaining a sample. Candidates can learn more about what is random sampling, sampling distribution, sampling error, purely random, and stratified random sampling, etc. Besides, candidates are also able to know what is the central limit theorem and its importance, how to interpret the standard error of a sample mean, properties of an estimator, features of Student’s T-Distribution, degree of freedom, time series data, cross-sectional data and so on.

Furthermore, Mean also will be used as a measure of central tendency of random variables, such as return and earnings per share. The central limit theorem and estimation will be used together with other statistical techniques to the financial data to interpret the results to decide what works and what does not work in the investment.

In this reading, it’s more focusing on the concepts of hypothesis testing.  Candidates able to learn on what is a hypothesis, describe the steps in hypothesis testing, describe and interpret the choice of the null and alternative hypothesis. Hypothesis testing is a systematic way used to select the samples from a group or population with the intent to decide whether a hypothesis will be accepted or not. Besides, it is also a part of the branch of statistics known as statistical inference. The statistical inference can break into two subdivisions, such as estimation and hypothesis testing. The evaluation will be used to address questions while the hypothesis is defined as a statement about one or more population.

In this reading, candidates can also learn on how to distinguish between one-tailed versus two-tailed test of hypotheses, Type I Error versus Type II Error, P-Value, Significance level, and how the significance levels are used in the hypothesis testing.