# Performance Thinking & Technologies, Inc.

## Hierarchical Clustering Optimization

### Modern Portfolio Theory (MPT) is based on the idea that diversification of holdings reduces risk. Thus, the challenge is to pick assets with the least variance of expected returns while maximizing differences between these holdings. These differences, or factors, can be asset type, industry, country, volatility, etc..

### MPT relies on linear algebra to produce statistics such as covariance and correlation matrices. The problem is that modern investments exhibit non-linear patterns. At some point, the benefits of diversification are outweighed by variances in expected returns. This produces a non-optimal portfolio.

### The following pages introduce aspects of hierarchical clustering optimization and graph theory that can be used in portfolio management. As the example diagram below shows, this includes the ability to identify clusters of similar behavior based on the previous year's returns.

### This mini-app will allow you to upload a portfolio and

- Create a correlation matrix
- Identify clusters within that portfolio
- Produce a network map of that portfolio