Chapter 2 - Risk and Return

Chapter 2: Risk and Return Chapter Outline 1.Statistics and concepts 1.1. Univariate statistics 1.2. Bivariate statistic 2. Risk and Return 2.1. Risk and return trade-off relation 2.2. Risk appetite 3. Portfolio diversification 3.1. Definition of portfolio 3.2. Benefits of portfolio diversification 2 1. Statistics and Concepts When one measurement is made on each observation, univariate analysis is applied. If more than one measurement is made on each observation, multivariate analysis is applied. 16/03/2020 3 1.1 Univariate statistics A population is a collection of units being studied. This might be the set of all people in a country. Units can be people, places, objects, years, drugs, or many other things. The term population is also used for the infinite population of all possible results of a sequence of statistical trials, for example, tossing a coin. . A parameter is a numerical value of a population, such as the population mean. The population values are often modelled from a distribution. Then the shape of the distribution depends on its parameters. For example the parameters of the normal distribution are the mean, μ and the standard deviation, σ 4 Univariate statistics A sample is a group of units, selected from a larger group (the population). By studying the sample it is hoped to draw valid conclusions (inferences) about the population. A sample is usually used because the population is too large to study in its entirety. The sample should be representative of the population. This is best achieved by random sampling. The sample is then called a random sample. An estimator is a quantity calculated from the sample data, which is used to give information about an unknown quantity (usually a parameter) in the population. For example, the sample mean is an estimator of the population mean. 16/03/2020 5 Mean (μ) The Mean is a measure of the “middle”, sometimes called the “average”. It is often given the symbol μ To calculate the mean, sum all the data values, and divide by the number of them [2-1] 6