# 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.

Technical Analysis is a type of security analysis that always used by traders or investors with the price and volume data to make their investment decision. In this reading, candidates can learn on principles of technical analysis, its application, and underlying assumption. Besides, this reading also provides a brief introduction about the field, comparison of technical analysis with other schools, and describes some of the tools used. The uses of trends, support, resistance lines, and changes in polarity are essential in this reading.

Last but not least, common technical analysis indicators such as price-based, momentum, oscillators, sentiment, and flow of funds also will be discussed with some of the examples provided in the textbook. The most exciting content in this subject is the critical tenets of Elliot Wave and the importance of the Fibonacci numbers. Eliot Wave principle is a type of technical analysis which will be used by the traders to analyse the financial market cycles to forecast the market trends by identifying extremes in the investor’s psychology such as high and low in price and other collective factors.

Conclusion

In conclusion, it is essential to know how the standard probability distribution used to describe the behaviour of random variables, what the use of hypothesis testing is, what the coverage of technical analysis is, how to estimate the measures of a population such as mean, standard deviation, etc. All of these are the main content that will be tested in the exam from this reading.

# CFA Level I: Quantitative Methods (Part I)

By Stella Goh – Market Data Analyst | 12 June 2019

Continued from the previous article, In this topic, candidates can learn how to apply quantitative concepts and techniques in financial analysis and investment decision making. It covers the time value of money, probability, normal distribution, hypothesis testing, descriptive statistics, and so forth. Time value of money and discounted cash flow analysis play as an essential role in this session because they form a basis for cash flow and security valuation. Both of them will be standalone problems or crucial parts problems throughout the curriculum. Besides, candidates are also able to learn the descriptive statistics which will be used for conveying the critical data such as central tendency, location and dispersion are presented. However, all investment forecasts and decision involve uncertainty. Therefore, probability played as conceptual part to quantifying risk and return in the investment decision. (For reading 1 – 5, please refer to the previous article).

Reading 6: Time Value of Money

In this reading, candidates can have a better understanding more on time value of money. Time value of money is the concept that the money available at the current time is worth more than an equal sum in the future. In this reading, candidates can learn three interpretations of interest rates such as the required rate of return, discount rates, or opportunity costs and can know what the components in the interest rate are.  For examples, risk-free rate, inflation, default risk and another risk premium. Besides, candidates are also required to explain an interest rate as the sum of a real risk-free rate and premiums that used to compensate investors for bearing the distinct types of risks. The calculation and interpretation of effective annual rate, given stated of yearly interest rate and frequency of compounding also will be teaching with some examples provided in the textbook.

In this reading, candidates are also able to learn how to demonstrate the use of a timeline in modelling and solve the time value of problems. However, the most critical thing in this reading is that they need to be familiar and comfortable on interpretation and discounting Present Value (PV) and Future Value (FV) of cash flow in the exam. It was due to the logic here applies to many other applications through this area topic. Besides PV and FV, candidates are also able to learn the annuity calculation for an ordinary annuity, annuity due, perpetuities a series of unequal cash flows.

Reading 7: Discounted Cash Flow (DCF)

In this reading, candidates can learn to use the Net Present Value (NPV) and Internal Rate of Return (IRR) for comparing projects with different payoffs to determine whether the company should invest into the plans or not. Net Present Value (NPV) of a project is the difference between the sum of all cash inflows and the amount of all cash outflows, discounted using by a required rate of return over a period of time. A positive NPV indicates that the project is making money for the company; while for negative NPV shows that the plan of the company is losing money. Therefore, the company should consider the investment with positive NPV because it is profitable.

Besides, candidates are also able to know what the advantages and disadvantages are by using NPV compares to IRR. The NPV and IRR rule also will be discussed in this reading, together with the problems associated with IRR rule. However, there are several essential types of returns you also need to know such as Holding Period Return (HPR), Money Weighted-Rate of Return (MWRR), and Time Weighted Rate of Return (TWRR) to measure and evaluate the performance of the portfolio. Besides, candidates are also able to learn bank discount yield, effective annual yield, money market yield and the relationships between them.

Reading 8: Statistical Concepts and Market Returns

In this reading, candidates need to learn on how to measure the central tendency, and dispersion such as the population mean, the sample means, arithmetic mean, weighted average, geometric mean, harmonic mean, median mean, mode, etc. Besides, they also can learn how to distinguish the difference between descriptive statistics and inferential statistics or variance and standard deviation, between a population and sample, and among the types of measurement scales.

Candidates also should know what parameter, sample statistic, frequency distribution, relative frequencies and cumulative relative frequencies are. Besides, they also must learn how to calculate and interpret the quartiles, quintiles, deciles and percentiles. The interpretation of coefficient of variation, Sharpe ratio, and the meaning of positively or negatively skewed of return distribution also will be discussed in this reading with examples provided.