Project 7: Efficient Frontier & Portfolio Optimization

Build a portfolio optimizer that generates an efficient frontier.

Project Overview

Attribute Value
Difficulty Level 2: Intermediate
Time Estimate 1-2 weeks
Main Language Python
Alternative Languages R, Julia
Knowledge Area Portfolio theory
Tools Optimization library
Main Book “Portfolio Selection” by Harry Markowitz

What you’ll build: A tool that computes portfolio weights for target returns and plots the efficient frontier.

Why it teaches quant: You learn how covariance and expected returns shape optimal portfolios.

Core challenges you’ll face:

  • Estimating returns and covariance
  • Solving constrained optimization problems
  • Interpreting risk-return tradeoffs

Real World Outcome

You will input a set of assets and generate an efficient frontier plot and sample optimal weights.

Example Output:

$ python optimize.py --symbols AAPL MSFT SPY
Generated 50 portfolios
Saved frontier to charts/frontier.png

Verification steps:

  • Confirm frontier is upward sloping
  • Check that weights sum to 1

The Core Question You’re Answering

“How do I balance risk and return systematically?”

This is the foundation of portfolio construction.

Concepts You Must Understand First

Stop and research these before coding:

  1. Expected return and covariance
    • How do you estimate these from historical data?
    • Book Reference: “Portfolio Selection” by Harry Markowitz, Ch. 3
  2. Quadratic optimization
    • Why is portfolio variance a quadratic form?
    • Book Reference: “Numerical Optimization” by Nocedal & Wright, Ch. 16
  3. Risk-return tradeoff
    • What does it mean for a portfolio to be efficient?
    • Book Reference: “Investments” by Bodie, Kane, and Marcus, Ch. 7

Questions to Guide Your Design

  1. Constraints
    • Will you allow short selling?
    • How will you enforce weight sums?
  2. Visualization
    • How will you display individual assets vs frontier?
    • Will you highlight the minimum-variance portfolio?

Thinking Exercise

Covariance Intuition

If two assets are perfectly correlated, what happens to diversification benefits?

Questions while working:

  • Why is correlation important for risk reduction?
  • What happens if correlation is negative?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “What is the efficient frontier?”
  2. “Why does diversification reduce risk?”
  3. “What is covariance in portfolio terms?”
  4. “How do constraints change the frontier?”
  5. “What are the limits of mean-variance optimization?”

Hints in Layers

Hint 1: Starting Point Start with two assets to visualize the curve.

Hint 2: Next Level Use a solver to minimize variance for target returns.

Hint 3: Technical Details Ensure weights are constrained to sum to one.

Hint 4: Tools/Debugging Check results against simple two-asset analytic cases.

Books That Will Help

Topic Book Chapter
Markowitz theory “Portfolio Selection” by Harry Markowitz Ch. 3
Quadratic optimization “Numerical Optimization” by Nocedal & Wright Ch. 16
Risk-return “Investments” by Bodie, Kane, and Marcus Ch. 7

Implementation Hints

  • Standardize returns frequency (daily/weekly).
  • Use covariance matrix symmetry to validate calculations.
  • Plot the frontier with risk on x-axis and return on y-axis.

Learning Milestones

  1. First milestone: You can compute a covariance matrix.
  2. Second milestone: You can optimize weights for target return.
  3. Final milestone: You can interpret the efficient frontier meaningfully.