01 — Returns and Compounding¶

Objectives¶

Explain and calculate simple return, log return, portfolio return, and geometric compounding.

Free learning pack¶

1. MIT OCW Portfolio Theory I–III
   https://ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/pages/video-lectures-and-slides/portfolio-theory/
2. CFA Portfolio Risk and Return Part I
   https://www.cfainstitute.org/insights/professional-learning/refresher-readings/2026/portfolio-risk-return-part-1
3. resources/portfolio_foundations.md

Do not search for more material until these are insufficient.

PREDICT¶

Without code: an asset rises 50% and then falls 50%. Is cumulative return 0%? Write the ending value of $100.

Formula¶

Simple return: r_t = P_t/P_(t-1) - 1

Portfolio return: r_p = w^T r

Cumulative return: prod(1+r_t)-1

HAND CALCULATION¶

Compute:

• $100 → +50% → ?
• then −50% → ?
• cumulative return = ?

MANUAL FIRST¶

Type the following structure yourself rather than pasting from the reference page.

In [ ]:

import numpy as np
import pandas as pd

prices = pd.Series([100.0, 105.0, 102.0, 108.0])

def my_simple_returns(prices):
    # TODO: type your implementation
    raise NotImplementedError

import numpy as np import pandas as pd prices = pd.Series([100.0, 105.0, 102.0, 108.0]) def my_simple_returns(prices): # TODO: type your implementation raise NotImplementedError

Code to type after your attempt¶

Open reference/concepts/portfolio_return.md only after trying. Then manually type the vector dot-product implementation and compare results.

Experiment¶

Compare arithmetic average return against actual compounded return.

Promote¶

Compare with src/pm/returns.py. Do not simply replace your notebook code; understand each line.

Test¶

pytest tests/test_returns.py

ORAL CHECK¶

Why does volatility drag make +x% and -x% asymmetric?