What is a return?
A return is the gain or loss that an investment generates over a period of time. It can be expressed in dollars (nominal dollars gained or lost) or as a percentage (return per dollar invested). Returns can be shown before or after fees, taxes and inflation (gross vs net), and are commonly measured for specific holding periods (monthly, annual, multi‑year).
Key concepts and definitions
– Holding period return (HPR): The total return earned over the time an investor owns an asset. Can be expressed in dollars or as a percentage (rate of return).
– Nominal return: The dollar gain or percentage gain before adjustments for fees, taxes, inflation or other factors.
Example (nominal dollar): Buy at $1,000, sell at $1,200 => nominal return = $200.
– Percentage return / ROI: Return divided by initial investment, expressed as a percentage.
Formula: ROI = (Ending value − Beginning value + Distributions) ÷ Beginning value × 100%.
Example: $200 gain on $1,000 investment => ROI = (200 ÷ 1,000) × 100% = 20%.
– Real return: Nominal return adjusted for inflation (or other external price changes) to reflect change in purchasing power.
Formula: Real return ≈ (1 + nominal return) ÷ (1 + inflation rate) − 1.
Example: Nominal 20% with 3% inflation => Real ≈ (1.20 ÷ 1.03) − 1 ≈ 16.5%.
– Annualization: Converting returns for different periods to a common (usually annual) basis so they can be compared. (See practical steps below for the standard annualization formula.)
– Gross return vs net return: Gross excludes fees, taxes and expenses; net includes them.
– Positive return vs negative return: Positive = profit; negative = loss.
Common return ratios (useful for evaluating companies/investments)
– Return on Investment (ROI): See the percentage return formula above.
– Return on Equity (ROE): Measures net income generated per dollar of shareholder equity.
Formula: ROE = Net income ÷ Average shareholder’s equity.
Example: $10,000 net income ÷ $100,000 average equity = 10%.
– Return on Assets (ROA): Measures net income generated per dollar of assets.
Formula: ROA = Net income ÷ Average total assets.
Example: $10,000 net income ÷ $100,000 average assets = 10%.
Yield vs return
– Yield typically refers to income generated by an investment, most commonly in fixed income (e.g., coupon income as a percentage of bond face value or price).
Example: $50 annual coupon on a $1,000 bond = 5% yield.
– Return includes yield (income) plus capital gains or losses from price changes. In most contexts, return is the broader term.
Is it possible to have a negative return?
Yes. A negative return means the investor lost money (or purchasing power). Negative nominal returns occur when ending value plus distributions are less than the initial investment. Negative real returns can occur even with positive nominal returns if inflation exceeds nominal gains.
Risk–return tradeoff
Higher expected returns are typically associated with higher risk. Investors must balance expected return versus the amount of risk they can tolerate, considering both nominal and real returns. Use diversification and asset allocation to align expected returns with risk tolerance.
How diversification impacts returns
Diversification reduces unsystematic (asset‑specific) risk by spreading investments across assets that do not move perfectly together. Proper diversification can improve the portfolio’s risk‑adjusted returns, though it cannot eliminate market (systematic) risk.
Practical steps — how to measure and manage returns (step‑by‑step)
1. Define the holding period
• Decide the start and end dates of the investment period (e.g., 1 year, 3 years, 6 months).
2. Calculate nominal return (dollars)
• Nominal dollar return = Ending value + Distributions − Beginning value.
3. Calculate percentage return (ROI / HPR)
• HPR (as %): = (Ending value + Distributions − Beginning value) ÷ Beginning value.
• Multiply by 100 for a percent.
• Example: Bought $1,000, sold for $1,200, no distributions => HPR = (1,200 − 1,000) ÷ 1,000 = 20%.
4. Annualize returns if comparing across timeframes
• Standard formula: Annualized return = (1 + HPR)^(1 / n) − 1, where n = number of years.
• Example: 20% total return over 2 years => Annualized = (1.20)^(1/2) − 1 ≈ 9.54% per year.
5. Adjust for inflation to get real return
• Real return = (1 + nominal return) ÷ (1 + inflation rate) − 1.
• Use consumer price index (CPI) or an appropriate inflation measure for the currency/time period.
6. Separate gross vs net returns
• Subtract transaction costs, management fees, and taxes to get net return. Always compare net returns for apples‑to‑apples comparisons.
7. Compare to appropriate benchmarks
• Use relevant market indices or peer group returns to judge performance.
8. Evaluate return ratios for businesses
• Calculate ROE and ROA to assess how efficiently a company uses equity and assets to generate income.
9. Consider risk and risk‑adjusted returns
• Ask: Did the return compensate adequately for the risk taken? Use diversification, asset allocation and rebalancing to manage risk.
10. Report and monitor consistently
• Track returns on a regular schedule, consistently apply the same formulas, and document assumptions (fees, taxes, inflation).
Practical tips for improving/maintaining real returns
– Minimize fees and trading costs: Fees reduce net return over time.
– Use tax‑advantaged accounts when appropriate (401(k), IRAs) to reduce tax drag.
– Diversify across asset classes and geographies to lower unrewarded risk.
– Rebalance periodically to maintain target asset allocation and harvest gains.
– Use long‑term perspective for equities; short‑term volatility does not always reflect long‑term expected returns.
– Compare net (after fees/taxes) and real (after inflation) returns, not just nominal returns.
– Match investments to objectives and risk tolerance—higher return targets usually require accepting higher volatility.
Short formulas summary
– Nominal dollar return = Ending value + Distributions − Beginning value
– HPR (%) = (Ending value + Distributions − Beginning value) ÷ Beginning value × 100%
– Annualized return = (1 + HPR)^(1/n) − 1
– Real return = (1 + nominal return) ÷ (1 + inflation) − 1
– ROI (%) = (Profit ÷ Initial investment) × 100%
– ROE = Net income ÷ Average shareholder’s equity
– ROA = Net income ÷ Average total assets
The bottom line
“Return” is a flexible term whose practical meaning depends on how you define the holding period, whether you use nominal or real terms, and whether you report gross or net figures. To make meaningful comparisons, always: (1) use the same time basis (annualize when needed), (2) specify gross vs net and nominal vs real, (3) include distributions, and (4) compare to relevant benchmarks while taking risk into account.
Reference
Investopedia, “Return” —
Source: Investopedia — “Return” (Julie Bang)
CONTINUATION AND EXPANSION
Pay attention to the context within which the terms “yield” and “return” are used. In many cases yield refers only to periodic income (coupons, dividends, rent) while return is the broader concept that also includes capital gains or losses. Below we expand on remaining topics, give additional examples, and offer practical steps investors can take.
IS IT POSSIBLE TO HAVE A NEGATIVE RETURN?
– Definition: A negative return means the investor’s ending value plus any distributions received is less than the investor’s beginning value plus any additional contributions — i.e., a net loss.
– Common situations:
• Selling an asset for less than the purchase price (capital loss).
• A stock declines in price and dividends don’t fully offset the price decline.
• A business reports an operational loss that reduces equity value.
– Example:
• Buy a stock for $1,000; receive $10 in dividends; sell later for $900.
• Nominal return in dollars = ($900 + $10) − $1,000 = −$90 (negative $90).
• Percentage return (HPR) = −$90 ÷ $1,000 = −9%.
WHAT IS RISK-RETURN TRADEOFF?
– Concept: Investments that offer the possibility of higher returns typically come with higher risk (greater chance of loss or higher volatility). Lower-risk investments generally deliver lower expected returns.
– Practical considerations:
• Risk tolerance: An investor must weigh how much volatility and potential loss they can tolerate against expected returns.
• Time horizon: Longer horizons can tolerate more short-term volatility for higher long-term expected returns.
• Diversification and risk management: Proper diversification can reduce non-systematic risk but cannot eliminate market (systematic) risk.
– Example comparison:
• Short-term government bonds: low expected return, low volatility, low default risk.
• Equities (stocks): higher expected return over long periods, higher short-term volatility.
• Venture capital or start-ups: potentially very high returns but very high probability of complete loss for many investments.
– Quantifying tradeoff:
• Common measures include standard deviation (volatility), beta (sensitivity to market), and Sharpe ratio (return per unit of volatility).
WHAT ARE GROSS RETURN AND NET RETURN?
– Gross return:
• The change in value plus distributions before subtracting any fees, taxes, transaction costs, or inflation adjustments.
• Useful for comparing pre-cost performance between funds or assets.
– Net return:
• Gross return after subtracting fees, commissions, taxes, and any other investor-specific outlays.
• What matters to an investor’s wallet — the true increase or decrease in wealth.
– Example:
• Investment grows from $10,000 to $11,200 in a year and pays $200 in distributions.
• Gross dollar return = ($11,200 + $200) − $10,000 = $1,400 → gross % return = 14%.
• If fees = $150 and taxes on distributions = $50, net dollar return = $1,400 − $150 − $50 = $1,200 → net % return = 12%.
HOW DOES DIVERSIFICATION IMPACT RETURNS?
– Principle: Diversification reduces idiosyncratic (asset-specific) risk by holding assets whose returns are not perfectly positively correlated. It does not guarantee higher returns, but it can lower volatility for a given expected return.
– Effects:
• Reduces the chance that a single bad outcome will devastate a portfolio.
• Can improve risk-adjusted returns (e.g., higher Sharpe ratio) even if absolute return is similar.
– Example (toy numbers):
• Portfolio A: 100% Stock X — expected return 8%, volatility 20%.
• Portfolio B: 50% Stock X, 50% Bond Y — expected return 6.5%, volatility 10% (because bond returns are less correlated with stock returns).
• Investor choosing B trades some expected return for considerably less volatility; on a risk-adjusted basis B might be preferable.
– Practical design:
• Combine assets with different risk-return profiles (e.g., equities, bonds, cash, real assets).
• Use correlation data to select assets that offset each other during different market conditions.
• Rebalance regularly to maintain target allocations.
ADDITIONAL SECTIONS AND EXAMPLES
Holding Period Return (HPR) and Annualization
– Holding Period Return (HPR) formula:
• HPR = (Ending Value + Distributions − Beginning Value) ÷ Beginning Value
– Example:
• Buy an ETF for $500, receive $10 in dividends, and sell for $540 after 9 months.
• HPR = ($540 + $10 − $500) / $500 = $50 / $500 = 10% over 9 months.
– Annualization:
• To compare across investments, convert to an annualized rate.
• Simple annualization (compounding): Annualized return = (1 + HPR)^(12 / months) − 1
• ExampleAnnualized = (1 + 0.10)^(12/9) − 1 ≈ 0.133 or 13.3% annualized.
Real Return (adjusting for inflation)
– Formula approximation: Real return ≈ ((1 + nominal return) ÷ (1 + inflation rate)) − 1
– Example:
• Nominal return = 8%, inflation = 3% → Real return ≈ (1.08 ÷ 1.03) − 1 ≈ 4.85%.
Return Ratios (practical use)
– ROI (Return on Investment): ROI = (Gain from Investment − Cost of Investment) ÷ Cost of Investment
• Business example: Spend $5,000 on marketing and generate $8,000 in incremental profit → ROI = ($8,000 − $5,000) ÷ $5,000 = 60%.
– ROE (Return on Equity): ROE = Net Income ÷ Average Shareholders’ Equity
• Use to judge how efficiently a firm uses equity capital.
– ROA (Return on Assets): ROA = Net Income ÷ Average Total Assets
• Use to assess how efficiently assets are producing profits.
Yield vs. Return — concrete example
– Bond example:
• Face value $1,000, coupon $50 annually → current yield (coupon ÷ price). If price = $1,000, yield = 5%.
• Total return if bond sold at $900 later and coupons received:
• Purchase $1,000, receive $50 coupon, sell for $900: dollar return = ($900 + $50) − $1,000 = −$50 → negative total return of −5%.
• Thus yield (coupon rate at purchase) did not capture the capital loss from selling below par; total return did.
Practical Steps for Investors — How to evaluate and track returns
1. Define the goal and horizon
• Short-term trading vs long-term investing require different evaluation windows and risk tolerance.
2. Choose the right return metric
• Use HPR for single-period results; annualize for comparisons across years.
• Use nominal return for raw performance, real return for purchasing power, and net return to know actual benefit after costs.
3. Include all cash flows
• Incorporate purchases, sales, dividends, interest, fees, and taxes into return calculations.
4. Adjust for timing of cash flows
• For multiple inflows/outflows, use money-weighted returns (XIRR) or time-weighted returns (TWRR) depending on whether you want to reflect investor behavior or manager performance.
5. Annualize to compare
• Convert returns to an annual basis for comparability.
6. Evaluate risk alongside return
• Look at volatility, drawdowns, and risk-adjusted measures (Sharpe ratio).
7. Account for inflation and taxes
• Compute real returns and after-tax returns to understand true gains.
8. Compare to benchmarks
• Use appropriate benchmarks (e.g., S&P 500 for U.S. large caps, Bloomberg Aggregate for U.S. bonds).
9. Track net returns over time
• Prefer net-of-fees performance for assessing actual wealth accumulation.
10. Rebalance and diversify
• Rebalance periodically to maintain target allocation and use diversification to manage risk.
EXAMPLE: CALCULATING NET ANNUALIZED RETURN WITH MULTIPLE CASH FLOWS
– Scenario:
• Jan 1: Invest $10,000.
• Jul 1: Add $2,000.
• Dec 31: Portfolio value $13,500.
– Use XIRR (money-weighted return) to account for timing of cash flows.
• Rough estimate: the $10,000 invested for full year grows to part of $13,500; the $2,000 invested mid-year has less time.
• Plugging dates/cash flows into an XIRR calculator yields the actual annualized return (use spreadsheet XIRR function).
– Practical tip: When you add or withdraw money, money-weighted returns measure the investor’s actual gain/loss, while time-weighted returns isolate the investment vehicle’s performance.
COMMON MISTAKES TO AVOID
– Ignoring fees: A small recurring fee can materially reduce net returns over time.
– Comparing nominal to real returns: Don’t compare a nominal return to an inflation-adjusted benchmark.
– Failing to annualize: Comparing a 3-month return directly to a 1-year return is misleading unless both are annualized.
– Overlooking taxes: Tax-inefficient strategies can reduce after-tax returns substantially.
– Using the wrong benchmark: Compare to an appropriate peer or index.
THE BOTTOM LINE
– A return measures the gain or loss on an investment; it can be expressed in dollars (nominal) or as a percentage (rate of return).
– Returns must be interpreted in context: gross vs net, nominal vs real, single-period vs annualized, and income (yield) vs total return (income + capital change).
– Risk matters: higher expected returns usually come with higher risk. Assess both absolute and risk-adjusted returns.
– Practical investing requires tracking net returns, adjusting for inflation and taxes, comparing to relevant benchmarks, and managing risk through diversification and rebalancing.
CONCLUDING SUMMARY — PRACTICAL TAKEAWAYS
– Always record all cash flows and fees when calculating returns.
– Use appropriate metrics: HPR for single-period; annualize for comparison; XIRR/TWRR for multiple cash flows.
– Convert nominal returns to real returns to understand purchasing-power gains.
– Evaluate returns alongside volatility and drawdown to measure risk-adjusted performance.
– Diversify to reduce unsystematic risk and rebalance to keep the portfolio in line with your goals.
– Net-of-fees and after-tax returns are what ultimately matter to investors — focus on these when making decisions.
References
– Investopedia, “Return,” Julie Bang.