Web2 refers to the version of the internet that we know today. The internet (Web2) is dominated by companies that provide services in exchange for your personal data. Web3 refers to the collection of dApps that run on a blockchain. As described in a lesson before, dApps allow anyone to […]

## Introduction to DeFi (Decentralised Finance)

Decentralised Finance, or DeFi, is a term for a variety of peer-to-peer financial services or applications that is build on top of public blockchains, ready to start disrupting today’s financial third party services. With DeFi, you can do most of the things that in general banks support, like earning interest, […]

## What are Decentralised Applications (dApps)?

A standard web app, such as Facebook or Amazon, is owned and maintained by an organisation. This organisation has the full authority over the app and how it operates. There may be multiple users on one side, but the backend is controlled by a single organisation. To compare this to […]

## Digital Assets: Cryptocurrencies vs Crypto Tokens

Until now, we have generalised the term cryptocurrencies, but not all assets in the crypto market are cryptocurrencies. There is a crucial difference between cryptocurrencies and crypto tokens. The most important difference is that cryptocurrencies have their own blockchain. Crypto tokens are built on an existing blockchain. In the context […]

## Holding and Transferring Cryptos – Introduction to Public Keys and Private Keys

Public and private keys are an integral part of cryptocurrencies. They allow you to send and receive cryptocurrencies without requiring a third party to verify the transactions. These keys are a part of the public-key cryptography (PKC) framework. You can use these keys to send your cryptocurrency to anyone, anywhere, […]

## Introduction to Cryptocurrencies

Cryptocurrencies are electronic peer-to-peer currencies. They don’t physically exist. You can’t pick up a bitcoin and hold it in your hand, or pull one out of your wallet. Bitcoin was the first cryptocurrency of its kind and was created by Satoshi Nakamoto to be an electronic and decentralised peer-to-peer cash […]

## Prospect Theory and Stock Returns

This lesson about prospect theory is based on an article by Barbaris, Mukherjee and Wang. Prospect theory is a behavioural economic theory that described the way people choose between probabilistic alternatives that involve risk, where the probabilities of outcomes are known. The main empirical prediction of the article is that […]

## Investment Sentiment in the Stock Market and Market Anomalies

The previous lesson was about noise trader risk. Noise and investor sentiment are terms that are often used interchangeably. Investor sentiment can be defined as the overall attitude of investors towards a particular asset or larger financial market. Market sentiment is the feeling or tone of a market, or its […]

## Limits to Arbitrage

The efficient market hypothesis states that prices are equal to their fundamental value. All deviations will be undone by rational arbitrageurs. In theory, arbitrage is done by an infinite number of small risk-neutral investors. This leads to a direct price adjustment. In reality, arbitrage is done by a small number […]

## Momentum and Mean Reversion

To what extend are past returns related to future returns? This question alone is already a direct attack on the weak-form theory of market efficiency. Theory about the three levels of market efficiency theoryWeak-form – The weak form suggests today’s stock prices reflect all the data of past prices and […]

## Improving the ‘Two Factor Model’ & Fama and French (1992, 1993, 2015)

Are there any other characteristics than beta that predict the expected return of an asset or portfolio? This lesson will elaborate on three important articles that introduced new parameters to the original CAPM model. Fama and French, 1992 and 1993 In this new publication, the data quality was better compared […]

## Capital Asset Pricing Model (CAPM) & Fama and MacBeth (1973)

The capital asset pricing model (CAPM) was one of the first laws in finance and it’s still widely used or, in other cases, part of new (improved) models. The CAPM describes the relationship between systematic risk and expected return for assets, generally stocks. But how do we quantify this specific […]

## Basic (Quadratic) Utility – Effect on Market Portfolio Demand

From portfolio theory, we know that investors hold a combination of the risk free asset and the market portfolio. The weights regarding the diversification depends on the so called utility function. Utility is a term in economics that refers to the total satisfaction received from consuming a good or service. […]

## Introduction to Asset Pricing and the Modern Portfolio Theory

Asset pricing is about the determinants of stock returns and how to optimise the performance of stock portfolios, not about the valuation of stocks. Asset prices are the prices for which financial instruments, such as stocks and bonds, are bought and sold. Fundamentals, risks, and sentiment may be derived from […]

## Eigenvectors and Eigenvalues

This lesson will recap the theory on eigenvectors and eigenvalues, which you most probably studies during a linear algebra or calculus course. If not, do not worry, we will elaborate on this content. Eigenvector versus eigenvalue By theorem, an eigenvector of an matrix A is a nonzero vector x, such […]

## Least-Squares in Linear Algebra

The least-squares method is very important in the area of data fitting. The lesson will give an overview of how to use the least-squares method, in order to find the best fitting model on data. Consider a stock, for which you can assume that the stock price increases linearly during […]

## Orthogonal Projections and the Gram-Schmidt Process

This lesson will elaborate on orthogonal projections and the Gram-Schmidt process, which will lay the foundation to understand least-squares problems (important in any statistical analysis). The orthogonal projection of a vector y on plane P is interesting, because it gives us the shortest distance of the vector y on plane […]

## The Inner Product and Orthogonality

Up to now, we have added and multiplied vectors and matrices with each other. There is much more to be said about vectors. Take for example a vector a and b. We might be interested in the length of a vector, the distance between vectors or the angle between vectors. […]

## Cramer’s Rule

This lesson will elaborate on how determinants can be used to solve a system of n linear equations and n variables, if the solution is unique. This technique is called the Cramer’s rule. Consider a system of n equations and n unknowns, so we have Ax = b for an […]