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📘 Portfolio Optimisation — Walk‑Through

Build, test and understand a simple stock portfolio in Python.

Table of Contents

👋 Welcome

If you’ve ever wondered how people pick a mix of stocks and test it on past data, this guide is for you. We’ll start with ten well‑known companies and show — with code — how to: choose a mix of stocks each year, test it on past data, and compare the outcome to the S&P 500 ETF (SPY). No PhD or heavy maths required — just curiosity and some Python.

🛠️ What We’re Building

  • Goal: Grow money over the long run while minimizing wild swings.
  • Universe: Ten large‑cap US stocks (Apple, Microsoft, Amazon, etc.).
  • Tactic: Every 1Y / 6M / 3M, find the weights that gave the best risk‑adjusted return (Sharpe Ratio) over the past period, then hold those weights for the next.
  • Benchmark: SPY, the go‑to yard‑stick for US equities.

🧰 Tools in the Toolbox

Tool Why we use it
VectorBT Quickly downloads price data from Yahoo Finance.
NumPy / Pandas Crunch numbers and wrangle data frames.
CVXPY Solves the optimisation problem that draws the efficient frontier.
Matplotlib Plots equity curves and other charts.

Everything runs on plain Python 3.10+; nothing fancy to install.

⚙️ How the Strategy Works

Picture a recipe book. Each recipe is a set of weights that tells us how much Apple, Microsoft, Amazon … to put in the pot. We want the recipe that offered the tastiest return per unit of risk last year.

Risk here is day‑to‑day ups and downs (volatility). The taste‑test score is the Sharpe Ratio:

\[ \text{Sharpe} = \frac{\text{Average daily return} \times 252 - r_f}{\text{Daily volatility} \times \sqrt{252}} \]

…where \(r_f\) is the tiny “free” return you could have earned in cash (we use 3 %).

Once we have that recipe, we cook with it for a year, then repeat the process.

🧮 Key Equations

Here are the handful of formulas you will see over and over in portfolio theory. MathJax is enabled, so feel free to copy‑paste these into your own notes.

\[ \mu_p = \mathbf{w}^\top \boldsymbol{\mu} \]
\[ \sigma_p = \sqrt{\mathbf{w}^\top \Sigma \,\mathbf{w}} \]
\[ \min_{\mathbf{w}} \;\sigma_p \quad\text{s.t.}\quad \begin{cases} \mathbf{w}^\top \boldsymbol{\mu} \;\ge\; \mu_{\text{target}} \\ \sum_{i=1}^{N} w_i = 1 \\ w_i \ge 0 \quad \forall i \end{cases} \]
\[ \text{CVaR}_{95\%} = -\frac{1}{N_{tail}}\sum_{i \in \text{worst }5\%} r_i \]

$$ \sum_{i=1}^{N} w_i^2 \xrightarrow{} 0 \quad\text{implies a well‑diversified portfolio} $$ (That last one is the Herfindahl index we plot each year.)

🧵 The Code — Step by Step

flowchart TD A[main.py] -->|Download| B[Daily Prices] B --> C[Daily % Returns] C -->|Sample 10 000 random recipes| D[Sharpe Scores] D -->|Pick the best| E[Yearly Weights] C -->|CVXPY loop| F[Efficient Frontier] E --> G[PortfolioBacktester] G --> H[Equity Curve] H --> I[Plot & Save Charts] F --> I G --> J[Write CSV Summaries] style A fill:#e8f4ff,stroke:#1c6fd3 style I fill:#fff7e6,stroke:#c99400
  1. Get the data from Yahoo Finance.
  2. Generate 10 000 random weight vectors with a Dirichlet distribution.
  3. Score each weight set by its Sharpe Ratio.
  4. Keep the top‑scoring weights.
  5. Test those weights on the actual returns for that year.
  6. Stitch together the yearly equity curves to form one long curve.
  7. Compare that curve with SPY and save everything (plots + CSV) in the reports/ and exports/ folders.

💡 Code Nuggets

Sometimes you just want to see one self‑contained example. The snippet below shows how we solve one point on the Efficient Frontier. 

import cvxpy as cp

# mus and cov are taken from historical returns
w = cp.Variable(len(tickers))
risk = cp.quad_form(w, cov)

prob = cp.Problem(
    cp.Minimize(risk),
    [
        cp.sum(w) == 1,      # fully invested
        w >= 0,              # long‑only
        mus @ w >= target    # hit desired return
    ]
)
prob.solve()

print("Weights:", w.value.round(4))
print("Portfolio σ:", (risk.value ** 0.5).round(4))

👉 Tip: swap cp.Minimize(risk) for cp.Maximize(sharpe) if you feel adventurous.
(Just remember to define the Sharpe expression first!)

📊 Results at a Glance

After running main.py you’ll find:

  • Equity & Drawdown Plot – see growth and the worst dips.
  • Efficient Frontier Plots – one fancy curve per year.
  • CSV summaries – handy for spreadsheets or deeper analysis.

(Files land in reports/ and exports/. Feel free to open them and poke around.)

🚀 Run It Yourself

# 1. Grab the code.
git clone https://github.com/your_user/portfolio-opt.git
cd portfolio-opt

# 2. Install requirements (about 1–2 min).
poetry install  # or: pip install -r requirements.txt

# 3. Launch the pipeline.
portfolio-opt --tickers AAPL MSFT NVDA --start-date 2020-01-01 --end-date 2024-12-31 --rebalance YE

Tinker Time
Open main.py to:

  • swap in different tickers.
  • widen the date range.
  • change the number of random portfolios (n_ports).

Then hit Run again and see how the story changes.

Happy exploring, and may your portfolios be ever in your favour! 🎉