Portfolio theory, developed by Markowitz, provides a framework for how investors can distribute their wealth to achieve optimal outcomes, while balancing the desire to maximize expected returns and to minimize risk. It remains a cornerstone of modern investment strategies. The objective of this document is to illustrate the principles that underpin this theory by developing an algorithm to obtain optimal portfolios via simulations, starting with a set of only two stocks and later generalizing it to multiple risky assets.

Creditors invest significant efforts in creating algorithms to predict the likelihood of a customer defaulting on a loan (PD). Defaults can result in substantial financial losses, impacting both the profitability and stability of financial institutions. To mitigate these risk, it is essential to develop robust predictive models that help to identify potential defaulters before credit is granted. Our aim here is to develop such models.

Momentum investment strategies involve taking long positions on stocks that show positive momentum (winners) and shorting those with negative momentum (losers). By relying on past information to predict future performance, momentum exploits a market anomaly. In this document I illustrate the strategy by generating a signal to buy (long position) or sell (short position) based on historical information.

The description of the efficient market hypothesis (EMH) states that prices in financial markets fully reflect all available information. In this document we study and test the hypothesis, using tickers for the largest US companies by market cap.