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Lecture Quantitative investment analysis: Chapter 5 – CFA Institute

Chapter 5 – Common probability distributions. This chapter define and explain a probability distribution; distinguish between and give examples of discrete and continuous random variables; define a probability function, state its two key properties, and determine whether a given function satisfies those properties;. | Common Probability distributions 1 Probability distribution The set of probabilities for the possible outcomes of a random variable is called a “probability distribution.” The underlying foundation of most inferential statistical analysis is the concept of a probability distribution. The focus in the investments arena is on four probability distributions. Uniform Binomial Normal Lognormal An understanding of probability distributions is critical to using such quantitative methods as hypothesis testing, regression, and time-series analysis. 2 LOS: Define and explain a probability distribution. Page 171 An understanding of basic probability distribution is critical to the next four chapters, so time spent here is well spent. Inferential statistical analysis that has a prespecified (assumed) or derived known statistical distribution as its foundation is known as parametric statistical analysis, although we often omit the term “parametric.” 2 Discrete and continuous random variables A . | Common Probability distributions 1 Probability distribution The set of probabilities for the possible outcomes of a random variable is called a “probability distribution.” The underlying foundation of most inferential statistical analysis is the concept of a probability distribution. The focus in the investments arena is on four probability distributions. Uniform Binomial Normal Lognormal An understanding of probability distributions is critical to using such quantitative methods as hypothesis testing, regression, and time-series analysis. 2 LOS: Define and explain a probability distribution. Page 171 An understanding of basic probability distribution is critical to the next four chapters, so time spent here is well spent. Inferential statistical analysis that has a prespecified (assumed) or derived known statistical distribution as its foundation is known as parametric statistical analysis, although we often omit the term “parametric.” 2 Discrete and continuous random variables A random variable is a variable whose future values are uncertain. Discrete random variables have a theoretically countable number of outcomes. There may be an infinite number of them, but they are countable. Price is a discrete random variable. Continuous random variables have a theoretically uncountable number of outcomes. Rate of return is a continuous random variable. Temperature is a continuous random variable. 3 LOS: Distinguish between and give examples of discrete and continuous random variables. Pages 171–172 By convention, uppercase letters represent a random variable in the broad sense (all possible values of that variable); lowercase letters are used to represent a specific outcome of a particular random variable. The reason that price is discrete lies in its “incrementation.” A price of $1.257 doesn’t actually exist. Prices move from $1.25 to $1.26; in other words, they change with a measurable interval. This is not the case for rates of return, which can be measured with .