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.

Reading 9: Probability Concepts

Probability concepts will be used to predict the outcomes when faced with uncertainty.  In this reading, candidates can learn on how to define a random variable, a consequence of an event, mutually exclusive events, and exhaustive events. Besides, there are many types of probabilities such as the conditional probability, unconditional probability, multiplication rule of probability, addition rule of probability, total probability rule, joint probability rule, can find out in this reading.

Moreover, candidates also must understand how to use a Tree Diagram of probability to represent an investment problem. By calculating the chances can be hard, because sometimes we add them, sometimes we multiply them, and often it is hard to figure out what to do. By using the tree diagram, candidates can find it easy to find a probability. Bayes’ formula is also essential because it applies to compute conditional probability or posterior probability. Last but not least, candidates are also able to learn to calculate the covariance and correlation, understand more about the properties of correlation and how it affects the risks. Besides covariance and correlation, they also must know how to interpret the expected value, variance, and standard deviation of a random variable and returns on the portfolio.


In conclusion, candidates must be familiar with the formulas in this chapter because the logic here may apply to many other applications in other topics. For the different readings that include in Quantitative Methods, we will discuss on the next coming articles which I categorised it as Quantitative Method (Part II).

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