1.x — Chapter 1 summary and quiz#

Chapter summary#

This chapter covered the return and volatility concepts needed to compute backtest performance metrics.

Key concepts#

• Simple return: $(P_t-P_{t-1})/P_{t-1}$; in pandas, pct_change().
• Volatility: standard deviation of returns; annualize with ${\sigma }_{\text{daily}}\sqrt{252}$ for daily data.
• Annualized return: scale mean daily return or total return to a yearly equivalent.
• Sharpe ratio: (annualized return − risk-free rate) / annualized volatility; risk-adjusted performance.

What we learned#

1. 1.1 Returns and volatility: How to compute simple returns, total return, volatility, annualization, and a simple Sharpe ratio for use in Project 1 — Backtesting Engine.

Application#

Use these definitions in your backtester to report total return, annualized return, annualized volatility, and Sharpe ratio. Combine with Python & Pandas for data and Quant Research for interpreting results and risk.

Quiz time#

Question 1

What is the difference between simple return and log return? When might you use each?

Show Solution

Simple return is $(P_t-P_{t-1})/P_{t-1}$; log return is $\ln (P_t/P_{t-1})$. For small returns they are close. Simple returns are intuitive and easy to compound over a few periods; log returns add over time (sum of log returns = log of total gross return) and are often used in models and for long-horizon aggregation.

Question 2

If daily returns have mean 0.0005 and standard deviation 0.01, what are (approximately) the annualized return and annualized volatility (252 trading days)?

Show Solution

Annualized return (approximate): $(1+0.0005{)}^{252}-1\approx 0.134$ (about 13.4%). Annualized volatility: $0.01\times \sqrt{252}\approx 0.159$ (about 15.9%).

Question 3

Why do we annualize returns and volatility when reporting backtest performance?

Show Solution

So we can compare strategies run over different lengths (e.g. 6 months vs. 2 years) and compare to benchmarks or risk-free rates quoted in annual terms. Annualization puts everything on a common scale (per year).