Shortfall Risk, Safety-first Ratio, and Identification of an Optimal Portfolio Using Roy’s Safety-first Criterion

Shortfall risk refers to the probability that a portfolio will not exceed the minimum (benchmark) return that an investor has set. In other words, it is the risk that a portfolio will fall short of the level of return an…

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Selecting Data Visualization Types

Guide to Selecting Visualization Types For numerical data, use a histogram, frequency polygon, or cumulative distribution chart. For category-based data, use a bar chart, tree-map, or heat map. For unstructured data, use a word cloud. For displaying relationships between two…

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Alternative Mean Definitions for Different Investment Problems

Suitability of Alternative Mean Definitions for Different Investment Problems $$ \begin{array}{l|l} \textbf { Type of Data } & \textbf { Mean to Use } \\ \hline \text { Single period data } & \text { Arithmetic mean } \\ \hline…

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CFA Level 1 Study Notes – Quantitative Methods

2023 Syllabus Study Session 1 R01 2023 – Time Value of Money -LOS a: interpret interest rates as required rates of return, discount rates, or opportunity costs -LOS b: explain an interest rate as the sum of a real risk-free…

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