Blog Posts

Stochastic Portfolio Theory (SPT) is a mathematical framework used to analyze and manage portfolios of assets in probabilistic terms. It extends the classical Markowitz portfolio theory by incorporating the randomness inherent in financial markets.   Key Takeaways – Stochastic Portfolio Theory & Chance-Constrained Portfolio Selection Stochastic Portfolio Theory (SPT) focuses on understanding and exploiting patterns […]

Behavioral Portfolio Theory (BPT) is based on a newer understanding of how traders and investors construct portfolios based on psychological factors. This theory deviates from traditional models by emphasizing the influence of cognitive biases and emotions in trading and investment decisions.   Key Takeaways – Behavioral Portfolio Theory Multiple Goals Behavioral Portfolio Theory posits that […]

Roy’s Safety-First Criterion, formulated by A.D. Roy in 1952, is a risk management approach in portfolio selection. This criterion focuses on minimizing the probability of portfolio returns falling below a threshold level, known as the disaster level. It’s particularly relevant for investors who prioritize capital preservation over high returns.   Theoretical Framework Roy’s criterion is […]

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets. Developed by John L. Kelly Jr. in 1956, it has found application in gambling, trading, investing, and risk management. The criterion aims to maximize the logarithm of wealth. This offers a strategic edge in scenarios where the […]

Intertemporal portfolio choice is a financial strategy focusing on how investors allocate assets over time to optimize returns. It’s rooted in the theory that trading decisions made today impact future wealth and consumption. This approach contrasts with static portfolio choices where decisions are made for a single time period without considering future implications.   Key […]

Correlation and covariance are statistical measures in asset allocation. They provide information on how different financial assets move in relation to each other. Covariance measures the directional relationship between the returns of two assets. When the covariance is positive, asset returns move together; if negative, they move inversely. Correlation, meanwhile, standardizes this relationship, expressing it […]

Particle Filters or Sequential Monte Carlo Methods – a Bayesian inference technique and machine learning algorithm – is increasingly relevant in quantitative finance and high-frequency trading (HFT). This method employs a set of random samples, or “particles,” to approximate the posterior distribution of a stochastic process. In the context of HFT, particle filtering can help […]

The Cramer-Rao Lower Bound (CRLB) is a fundamental concept in statistical estimation theory. It provides a lower bound on the variance of unbiased estimators of a parameter in a statistical model (i.e., there’s always going to be some amount of unavoidable unpredictability in a model). The significance of the CRLB lies in its role as […]

Kalman Filters are used for estimating the state of a dynamic system from a series of incomplete and noisy measurements. Originating from control theory and employed in signal processing and finance, Kalman filters enable the efficient and real-time estimation of variables in systems governed by linear equations.   Key Takeaways – Kalman Filters Predicting Market […]

Extreme Value Theory (EVT) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It focuses on understanding the behavior of the tails of distributions, which is important in finance and risk management.   Key Takeaways – Extreme Value Theory (EVT) Risk Assessment EVT assesses the risks of rare, […]