What is the difference between arithmetic mean and CAGR?

Arithmetic mean is a simple average of returns, while CAGR (Compound Annual Growth Rate) is the geometric mean that accounts for compounding. CAGR is more accurate for measuring investment performance over multiple periods because it reflects the actual growth rate needed to reach the ending value from the starting value.

How is CAGR calculated?

CAGR is calculated using the formula: CAGR = (Ending Value / Beginning Value)^(1/n) - 1, where n is the number of years. For example, if an investment grows from $100 to $150 over 3 years, the CAGR would be approximately 14.47% per year.

What is a good Sharpe ratio?

A Sharpe ratio above 1 is considered good, above 2 is very good, and above 3 is excellent. The Sharpe ratio measures risk-adjusted returns by comparing excess returns (above risk-free rate) to volatility. Higher values indicate better risk-adjusted performance.

What does standard deviation tell me about my investment?

Standard deviation measures volatility - how much returns vary from the average. A higher standard deviation means more volatile and potentially risky investment. Generally, standard deviation below 10% is low volatility, 10-20% is moderate, and above 20% is high volatility.

What is maximum drawdown?

Maximum drawdown is the largest peak-to-trough decline in portfolio value during a specific period. It shows the worst-case scenario loss an investor would have experienced. For example, a 25% max drawdown means the portfolio fell 25% from its highest point.

When should I use cash flow mode vs cumulative mode?

Use cash flow mode when you have actual account balances and transaction history (deposits/withdrawals). Use cumulative mode when you have return percentages for different periods and want to calculate overall performance metrics like CAGR, volatility, and risk-adjusted returns.

Average Return Calculator - CAGR & Investment Return Calculator | AICalculator

Understanding Investment Returns

📊 CAGR vs Arithmetic Mean

CAGR (Compound Annual Growth Rate) reflects the actual growth rate with compounding:

CAGR = (End/Start)^(1/years) - 1

Arithmetic Mean is a simple average but can overstate performance when returns vary.

🎯 Risk-Adjusted Returns

Sharpe Ratio: Excess return per unit of risk
Standard Deviation: Volatility measure
Max Drawdown: Worst peak-to-trough loss
Risk-Free Rate: Typically 2-3% (Treasury)

Two Calculation Methods

📊 Cash Flow Method

Best for analyzing actual account performance:

• Input starting and ending balances
• Add all deposits and withdrawals
• Specify transaction dates
• Get time-weighted average return

📈 Cumulative Method

Best for analyzing return series:

• Input return percentages by period
• Specify holding duration (years/months)
• Get CAGR and arithmetic mean
• Calculate risk metrics and volatility

Understanding Risk Metrics

Sharpe Ratio Interpretation

below 1

Poor

1 - 2

Good

2 - 3

Very Good

above 3

Excellent

Standard Deviation (Volatility)

Low (below 10%)

Stable, lower returns

Moderate (10-20%)

Balanced risk/return

High (above 20%)

Volatile, higher potential

Real-World Examples

Conservative Portfolio

CAGR: 5-7%
Volatility: 5-8%
Sharpe: 0.5-1.0
Max DD: 5-10%

Balanced Portfolio

CAGR: 8-10%
Volatility: 10-15%
Sharpe: 0.7-1.5
Max DD: 15-25%

Aggressive Portfolio

CAGR: 10-15%+
Volatility: 18-25%+
Sharpe: 0.5-1.2
Max DD: 30-50%

Common Mistakes to Avoid

❌ Ignoring risk metrics: High returns mean nothing without considering volatility and drawdowns
❌ Using arithmetic mean for multi-period returns: Always use CAGR for accurate long-term performance
❌ Forgetting about taxes and fees: These significantly reduce actual returns
❌ Comparing different time periods: Ensure fair comparisons by using same timeframes
❌ Overlooking survivorship bias: Past performance does not guarantee future results

Advanced Investment Concepts

📊 Time-Weighted Return (TWR)

Best for evaluating investment manager performance. Eliminates the impact of cash flows (deposits/withdrawals) by breaking the measurement period into sub-periods.

Formula: TWR = [(1 + R₁) × (1 + R₂) × ... × (1 + Rₙ)] - 1

💰 Money-Weighted Return (MWR)

Also known as Internal Rate of Return (IRR). Accounts for the timing and size of cash flows. Better for evaluating your personal investment performance.

Use when: You control timing of deposits/withdrawals

📉 Sortino Ratio

Similar to Sharpe ratio but only considers downside volatility. Focuses on harmful volatility (losses) rather than total volatility.

Formula: (Return - Target) / Downside Deviation

📊 Calmar Ratio

Compares annualized return to maximum drawdown. Higher is better. Helps assess if returns justify the worst-case risk.

Formula: CAGR / |Maximum Drawdown|

Investment Return Formulas

Simple Return

R = (Ending Value - Beginning Value) / Beginning Value

Example: $100 grows to $110, return = ($110 - $100) / $100 = 10%

CAGR (Compound Annual Growth Rate)

CAGR = (Ending Value / Beginning Value)^(1/n) - 1

Example: $100 grows to $150 in 3 years, CAGR = ($150/$100)^(1/3) - 1 ≈ 14.47%

Standard Deviation

σ = √[Σ(Rᵢ - R̄)² / n]

Measures the dispersion of returns around the mean. Higher σ = higher volatility

Sharpe Ratio

Sharpe = (Rₚ - Rᶠ) / σₚ

Where: Rₚ = portfolio return, Rᶠ = risk-free rate, σₚ = portfolio standard deviation

When to Use Each Calculation Method

Scenario	Use This Method	Why
Evaluating fund manager	Time-Weighted Return	Eliminates cash flow timing impact
Personal portfolio performance	Money-Weighted Return (IRR)	Accounts for your contribution timing
Comparing multiple investments	CAGR	Standardized annualized measure
Quick average calculation	Arithmetic Mean	Simple but may overstate performance
Risk-adjusted comparison	Sharpe Ratio	Balances return with volatility

Practical Tips for Investors

✅ Do This

• Use CAGR for multi-year comparisons
• Consider both return AND risk metrics
• Track performance consistently
• Account for fees and taxes in calculations
• Compare to appropriate benchmarks
• Review performance quarterly

❌ Avoid This

• Chasing last year hot performers
• Ignoring volatility and drawdowns
• Using arithmetic mean for long periods
• Comparing different time periods
• Overlooking survivorship bias
• Making decisions on short-term results

Benchmark Comparisons

Historical annual returns (1928-2023 average):

S&P 500 (US Large Cap)~10.3%

Small Cap Stocks~12.1%

International Stocks~8.5%

Corporate Bonds~6.2%

Treasury Bills~3.3%

Inflation (CPI)~3.0%

*Past performance does not guarantee future results. Source: Historical market data

Cash Flow Inputs

Understanding Investment Returns

📊 CAGR vs Arithmetic Mean

🎯 Risk-Adjusted Returns

Two Calculation Methods

📊 Cash Flow Method

📈 Cumulative Method

Understanding Risk Metrics

Sharpe Ratio Interpretation

Standard Deviation (Volatility)

Real-World Examples

Conservative Portfolio

Balanced Portfolio

Aggressive Portfolio

Common Mistakes to Avoid

Advanced Investment Concepts

📊 Time-Weighted Return (TWR)

💰 Money-Weighted Return (MWR)

📉 Sortino Ratio

📊 Calmar Ratio

Investment Return Formulas

Simple Return

CAGR (Compound Annual Growth Rate)

Standard Deviation

Sharpe Ratio

When to Use Each Calculation Method

Practical Tips for Investors

✅ Do This

❌ Avoid This

Benchmark Comparisons

Related Investment Calculators

📊 Investment Calculator

🏖️ Retirement Calculator

📊 RMD Calculator

Average Return Calculator - Calculate CAGR, Sharpe Ratio, and Investment Risk Metrics

Cash Flow Inputs

Understanding Investment Returns

📊 CAGR vs Arithmetic Mean

🎯 Risk-Adjusted Returns

Two Calculation Methods

📊 Cash Flow Method

📈 Cumulative Method

Understanding Risk Metrics

Sharpe Ratio Interpretation

Standard Deviation (Volatility)

Real-World Examples

Conservative Portfolio

Balanced Portfolio

Aggressive Portfolio

Common Mistakes to Avoid

Advanced Investment Concepts

📊 Time-Weighted Return (TWR)

💰 Money-Weighted Return (MWR)

📉 Sortino Ratio

📊 Calmar Ratio

Investment Return Formulas

Simple Return

CAGR (Compound Annual Growth Rate)

Standard Deviation

Sharpe Ratio

When to Use Each Calculation Method

Practical Tips for Investors

✅ Do This

❌ Avoid This

Benchmark Comparisons

Related Investment Calculators

📊 Investment Calculator

🏖️ Retirement Calculator

📊 RMD Calculator