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What Is Return?

Investment return is the gain or loss your portfolio generates over time — the basic measure of how much your money grows.

Why Return Matters

1. Shows growth: Return is the engine of long-term wealth.
2. Compare investments: Different assets can have identical prices but different return histories.
3. Shapes goals: Higher return → faster progress to your goals.
4. Optimizer input: Return feeds efficient frontier construction, expected performance estimates, and Sharpe calculations.

Types of Return (Beginner-friendly)

• Total Return — includes price change, dividends, interest, and distributions.
  $$\mathrm{Total\ Return}=\frac{\mathrm{Ending\ Value}-\mathrm{Beginning\ Value}+\mathrm{Income}}{\mathrm{Beginning\ Value}}$$
• Annualized Return (CAGR) — average yearly growth rate that smooths volatility.
  $$\mathrm{CAGR}=\left(\frac{\mathrm{Ending\ Value}}{\mathrm{Beginning\ Value}}\right)^{1/n}-1$$
• Real Return — return after inflation. Approximation:
  $$\mathrm{Real\ Return}\approx\mathrm{Nominal\ Return}-\mathrm{Inflation}$$
• Expected Return — a forecast (not a guarantee), often a weighted average of historical or modelled returns.
• Risk‑Adjusted Return — return measured relative to risk (e.g., via Sharpe ratio).

Key Formulas

• Total Return — shown above.
• CAGR — shown above.
• Expected portfolio return (for weights $w$ and asset returns $r$):
  $$\mathrm{E}[R_p]=w^T r$$

Simple Examples

Example 1 — Basic Return
Invest $1,000 → $1,150. Return = 15%.

Example 2 — Including Dividends
Price gain: $80; Dividends: $20; Beginning value: $1,000 → Total return = 10%.

Example 3 — Annualized Return
$1,000 → $1,331 over 3 years → CAGR = 10%.

Return vs Risk: The Real Relationship

Return without context is incomplete. Two portfolios can both return 10% but differ wildly in volatility. Your optimizer targets risk‑adjusted return to find efficient portfolios.

How Your Optimizer Uses Return

• Estimates expected performance for each asset and portfolio.
• Combines expected return with the covariance matrix to build the efficient frontier.
• Computes risk‑adjusted measures (e.g., Sharpe) to compare portfolios.
• Flags inefficient allocations and suggests rebalancing or diversification.

Common Misunderstandings About Return

• “High return means good investment.” Not if achieved with excessive risk.
• “Past returns predict future returns.” Past performance offers context but is not a guarantee.
• “Dividends don’t matter.” Dividends are a significant component of long-term total return.
• “Crypto returns are always higher.” Crypto has had high returns historically but with large volatility and regime risk.

How to Interpret Your Portfolio’s Return

• Low Return (0–4%) — Very stable, often bond-heavy.
• Moderate Return (4–8%) — Balanced, typical for diversified portfolios.
• High Return (8%+) — Higher growth potential, usually higher volatility.