Return - Parallax API

Return measures the percentage change in investment value over a period, including any income received. It’s the most fundamental measure of investment performance.

Beginner

What It Means

Return tells you how much you made (or lost) on an investment, expressed as a percentage of your starting value.

Basic Calculation

Return = (Ending Value - Beginning Value + Income) / Beginning Value

Example:
- Buy stock at $100
- Receive $3 dividend
- Sell at $110
- Return = ($110 - $100 + $3) / $100 = 13%

Types of Returns

Type	What It Includes
Price Return	Price change only
Total Return	Price change + dividends/income
Annualized Return	Return expressed as yearly rate
Cumulative Return	Total return over entire period

Why It Matters

Return is the bottom line - did your investment make money? Everything else (risk, volatility, Sharpe ratio) provides context, but return is what you actually earn.

Advanced

Return Calculation Methods

Method	Formula	Use Case
Simple	(End - Start) / Start	Single period
Logarithmic	ln(End / Start)	Continuous compounding
Time-Weighted	Geometric link of sub-periods	Manager evaluation
Money-Weighted	IRR of cash flows	Investor experience

Time-Weighted vs. Money-Weighted

Type	Considers Cash Flows?	Best For
Time-Weighted (TWR)	No	Manager performance
Money-Weighted (MWR)	Yes	Investor experience

Time-weighted return removes the effect of when money was added/withdrawn, isolating manager skill. Money-weighted return shows what the investor actually earned.

Annualization

Converting returns to annual rates:

Annualized Return = (1 + Total Return)^(1/Years) - 1

Example:
- 50% cumulative return over 3 years
- Annualized = (1.50)^(1/3) - 1 = 14.5% per year

Geometric vs. Arithmetic Mean

Type	Formula	When to Use
Arithmetic	Sum / N	Expected single-period return
Geometric	(Product)^(1/N) - 1	Actual compound growth

Example: Years with +50% then -50%
- Arithmetic mean: (50 + -50) / 2 = 0%
- Geometric mean: √(1.5 × 0.5) - 1 = -13.4%
- Reality: $100 → $150 → $75 (you lost money!)

Arithmetic mean overstates compound returns. Always use geometric mean for multi-period performance.

Real vs. Nominal Returns

Type	Definition
Nominal	Return before inflation adjustment
Real	Return after subtracting inflation

Real Return ≈ Nominal Return - Inflation

Example:
- Nominal return: 8%
- Inflation: 3%
- Real return: ~5%

After-Tax Returns

Different return measures for tax impact:

Measure	Description
Pre-Tax	Return before taxes
After-Tax (Pre-Liquidation)	After taxes paid during holding
After-Tax (Post-Liquidation)	After all taxes including sale

Return Attribution

Breaking down where returns came from:

Component	Description
Market Return	Broad market movement
Sector Allocation	Sector over/underweights
Stock Selection	Individual stock picks
Interaction	Combined effects

Historical Context

Long-term annualized returns (US):

Asset	Return	Period
Stocks	10%	1926-present
Bonds	5%	1926-present
T-Bills	3%	1926-present
Inflation	3%	1926-present

Return Expectations

Historical returns don’t guarantee future returns. Current valuations, interest rates, and economic conditions affect forward expectations.

Alpha

Excess return vs. benchmark

Risk-Adjusted Returns

Return relative to risk

Benchmark

Standard for comparison

​Beginner

​What It Means

​Basic Calculation

​Types of Returns

​Why It Matters

​Advanced

​Return Calculation Methods

​Time-Weighted vs. Money-Weighted

​Annualization

​Geometric vs. Arithmetic Mean

​Real vs. Nominal Returns

​After-Tax Returns

​Return Attribution

​Historical Context

​Return Expectations

​Related Terms

Alpha

Risk-Adjusted Returns

Benchmark

Beginner

What It Means

Basic Calculation

Types of Returns

Why It Matters

Advanced

Return Calculation Methods

Time-Weighted vs. Money-Weighted

Annualization

Geometric vs. Arithmetic Mean

Real vs. Nominal Returns

After-Tax Returns

Return Attribution

Historical Context

Return Expectations

Related Terms