Portfolio Theory and Risk Metrics

Master portfolio theory and risk metrics with applications in probability and combinatorics.

26 min read
Advanced

Introduction

Learning Objectives:

  • Apply portfolio variance formula
  • Calculate Sharpe ratio
  • Understand diversification

Portfolio Variance

For portfolio w1X1+cdots+wnXnw_1 X_1 + cdots + w_n X_n:

eq j} w_i w_j ext{Cov}(X_i, X_j)$$ **Diversification**: Correlation reduces as portfolio grows

Applications

Apply these concepts to solve real-world problems in probability and statistics.

python
import numpy as np
import matplotlib.pyplot as plt

# Example implementation
print("Apply concepts from Portfolio Theory and Risk Metrics")

Key Takeaways

Master these advanced concepts to complete your probability and combinatorics journey!

๐ŸŽฒ

Combinatorics and Probability: From Counting to Inference

Master the mathematical foundations of counting, probability, and randomness. This comprehensive course bridges pure combinatorics with computational probability, covering everything from basic counting principles to advanced probabilistic methods, limit theorems, and real-world applications in algorithms, finance, and data science.