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In
finance,
rate of return (
ROR) or
return on investment (
ROI), or sometimes just
return, is the ratio of money gained or lost on an
investment relative to the amount of money invested. The amount of money gained or lost may be referred to as
interest, profit/loss, gain/loss, or net income/loss. The money invested may be referred to as the asset, capital,
Debt, or the
cost basis of the investment.
ROI is also known as
rate of profit.
Return can also refer to the monetary amount of gain or loss. ROI is the return on a past or current investment, or the estimated return on a future investment. ROI is usually given as a percent rather than decimal value.
ROI does not indicate how long an investment is held. However, ROI is most often stated as an annual or annualized rate of return, and it is most often stated for a calendar or fiscal year. In this article, “ROI” indicates an
annual or annualized rate of return, unless otherwise noted.
ROI is used to compare returns on investments where the money gained or lost -- or the money invested – are not easily compared using monetary values. For instance, a $1,000 investment that earns $50 in interest obviously generates more cash than a $100 investment that earns $20 in interest, but the $100 investment earns a higher return on investment.
- $50/$1,000 = 5% ROI
- $20/$100 = 20% ROI
Since rates of return are percentages, negative rates cannot be averaged with positive rates for purposes of calculating monetary returns. However, it is common practice in finance to estimate monetary returns by averaging periodic rates of return; these estimations are most useful when the averaged periodic returns are all positive, all negative, or have low variances.
Measuring rate of return
The initial value of an investment does not always have a clearly defined monetary value, but for purposes of measuring ROI,
the initial value must be clearly stated -- along with the rationale for this initial value. The final value of an investment also does not always have a clearly defined monetary value, but for purposes of measuring ROI,
the final value must be clearly stated -- along with the rationale for this final value.
Return on investment is a rate of profit or income (realized or unrealized). The return is sometimes adjusted for taxes in geographical areas or historical times in which taxes consumed or consume a significant portion of profits or income. Taxes are an expense which may or may not be considered when calculating ROI. Similarly, a return may be adjusted for inflation to better indicate its true value in purchasing power.
Cash flow (income stream)
{| class="wikitable" style="text-align:center" align="right"|+ Cash Flow Example on $1,000 Investment! !! Year 1 !! Year 2 !! Year 3 !! Year 4|-! Dollar Return| $100 || $55 || $60 || $50|-! ROI| 10% || 5.5% || 6% || 5%|}
ROI is a measure of cash (or potential cash) generated by an investment, or the cash lost due to the investment. It measures the cash flow or income stream from the investment to the investor.
Cash flow to the investor can be in the form of profit, interest, dividends, or capital gain/loss. Capital gain/loss occurs when the market value or resale value of the investment increases or decreases. Cash flow here does not include the return of invested capital.
To the right is a simple example of cash flow on a $1,000 investment.
Annual returns
An
Annual Rate of Return is the return on an investment over a one-year period, such as January 1st through December 31st, or June 3rd 2006 through June 2nd 2007. Each ROI in the cash flow example above is an annual rate of return. An
Annualized Rate of Return is the return on an investment over a period other than one year (such as a month, or two years) multiplied or divided to give a comparable one-year return. For instance, a one-month ROI of 1% could be stated as an annualized rate of return of 12%. Or a two-year ROI of 10% could be stated as an annualized rate of return of 5%.
In the cash flow example above, the dollar returns for the four years add up to $265. The annualized rate of return for the four years is$265 ÷ ($1,000 x 4 years) = 6.625%.
Arithmetic return
In mathematical terms, the
arithmetic return is defined as the following:
\text{ROI}_\text{Arith}=\frac{V_f - V_i}{V_i}
where
- V_i is the initial investment value and
- V_f is the final investment value
This return has the following characteristics:
- \text{ROI}_\text{Arith}=+1.00=+100% when the final value is twice the initial value
- \text{ROI}_\text{Arith}>0 when the investment is profitable
- \text{ROI}_\text{Arith}0 is profit
- \text{ROI}_\text{Log}+1.
- {\rm Year\; 3\; Reinvestment\; Factor\;} = \frac{{\rm Year\; 3\; Total\; Distribution} \times {\rm Year\; 2\; Reinvestment\; Factor\;-->+1.
- {\rm Year\; 4\; Reinvestment\; Factor\;} = \frac{{\rm Year\; 4\; Total\; Distribution} \times {\rm Year\; 3\; Reinvestment\; Factor\;-->+1.
- {\rm Year\; 5\; Reinvestment\; Factor\;} = \frac{{\rm Year\; 5\; Total\; Distribution} \times {\rm Year\; 4\; Reinvestment\; Factor\;-->+1.
Total Return = ((Final Price x Last Reinvestment Factor) - Beginning Price) / Beginning Price
Average annual return (geometric)
Average Annual Return (geometric)
= \left {\left(1 + \frac{100}\right)}^{{\rm Time\; in\; years}^{-1--> - 1 \right \times 100
Example
{| class="wikitable" style="text-align:center"|+Example: Mutual Fund with low volatility and a regular annual dividend, reinvested at year-end share price, initial share value $100|-! End of: !! Year 1 !! Year 2!! Year 3 !! Year 4 !! Year 5|-! Dividend| $5 || $5 || $5 || $5 || $5|-! Capital Gain Distribution| || || $2 || |||-! Total Distribution| $5 || $5 || $7 || $5 || $5|-! Share Price| $98 || $101 || $102 || $99 ||
$101|-! Shares Purchased| 0.05102 || 0.04950 || 0.06863 || 0.05051 || 0.04950|-! Shares Owned| 1.05102 || 1.10053 || 1.16915 || 1.21966 || 1.26916|-! Reinvestment Factor
| 1.05102 || 1.05203 || 1.07220 || 1.05415 ||
1.05219|}
- Total Return = (($101 x 1.05219) - $100) / $100 = 6.27% (net of expenses)
- Average Annual Return (geometric) = (((28.19)/100)+1) ^ (1/5)) – 1) x 100 = 5.09%
Using a
Holding Period Return calculation, after 5 years, an investor who reinvested owned 1.26916 share valued at $101 per share ($128.19 in value). ($128.19-$100)/$100/5 = 5.638% yield. An investor who did not reinvest received a total of $27 in dividends and $1 in capital gain. ($27+$1)/$100/5 = 5.600% return.
Mutual funds include capital gains as well as dividends in their return calculations. Since the market price of a mutual fund share is based on net asset value, a capital gain distribution is offset by an equal decrease in mutual fund share value/price. From the shareholder's perspective, a capital gain distribution is not a net gain in assets, but it is a realized capital gain.
Summary: overall rate of return
Rate of Return and
Return on Investment indicate cash flow from an investment to the investor over a specified period of time, usually a year.
ROI is a measure of investment profitability, not a measure of investment size. While compound interest and dividend reinvestment can increase the size of the investment (thus potentially yielding a higher dollar return to the investor),
Return on Investment is a percentage return based on capital invested.
In general, the higher the investment risk, the greater the potential investment return, and the greater the potential investment loss.
References
See also
Further reading
- A. A. Groppelli and Ehsan Nikbakht. Barron’s Finance, 4th Edition. New York: Barron’s Educational Series, Inc., 2000. ISBN 0-7641-1275-9
- Zvi Bodie, Alex Kane and Alan J. Marcus. Essentials of Investments, 5th Edition. New York: McGraw-Hill/Irwin, 2004. ISBN 0-07-251077-3
- Richard A. Brealey, Stewart C. Myers and Franklin Allen. Principals of Corporate Finance, 8th Edition. McGraw-Hill/Irwin, 2006
- Walter B. Meigs and Robert F. Meigs. Financial Accounting, 4th Edition. New York: McGraw-Hill Book Company, 1970. ISBN 0-07-041534-X
- Bruce J. Feibel. Investment Performance Measurement. New York: Wiley, 2003. ISBN 0471268496
In
finance,
rate of return (
ROR) or
return on investment (
ROI), or sometimes just
return, is the ratio of
money gained or lost on an
investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest,
profit/loss, gain/loss, or net income/loss. The money invested may be referred to as the asset,
capital, Debt, or the
cost basis of the investment.
ROI is also known as
rate of profit.
Return can also refer to the monetary amount of gain or loss. ROI is the return on a past or current investment, or the estimated return on a future investment. ROI is usually given as a percent rather than decimal value.
ROI does not indicate how long an investment is held. However, ROI is most often stated as an annual or annualized rate of return, and it is most often stated for a calendar or fiscal year. In this article, “ROI” indicates an
annual or annualized rate of return, unless otherwise noted.
ROI is used to compare returns on investments where the money gained or lost -- or the money invested – are not easily compared using monetary values. For instance, a $1,000 investment that earns $50 in interest obviously generates more cash than a $100 investment that earns $20 in interest, but the $100 investment earns a higher return on investment.
- $50/$1,000 = 5% ROI
- $20/$100 = 20% ROI
Since rates of return are percentages, negative rates cannot be averaged with positive rates for purposes of calculating monetary returns. However, it is common practice in finance to estimate monetary returns by averaging periodic rates of return; these estimations are most useful when the averaged periodic returns are all positive, all negative, or have low variances.
Measuring rate of return
The initial value of an investment does not always have a clearly defined monetary value, but for purposes of measuring ROI,
the initial value must be clearly stated -- along with the rationale for this initial value. The final value of an investment also does not always have a clearly defined monetary value, but for purposes of measuring ROI,
the final value must be clearly stated -- along with the rationale for this final value.
Return on investment is a rate of profit or income (realized or unrealized). The return is sometimes adjusted for taxes in geographical areas or historical times in which taxes consumed or consume a significant portion of profits or income. Taxes are an expense which may or may not be considered when calculating ROI. Similarly, a return may be adjusted for
inflation to better indicate its true value in purchasing power.
Cash flow (income stream)
{| class="wikitable" style="text-align:center" align="right"|+ Cash Flow Example on $1,000 Investment! !! Year 1 !! Year 2 !! Year 3 !! Year 4|-! Dollar Return| $100 || $55 || $60 || $50|-! ROI| 10% || 5.5% || 6% || 5%|}
ROI is a measure of cash (or potential cash) generated by an investment, or the cash lost due to the investment. It measures the cash flow or income stream from the investment to the investor.
Cash flow to the investor can be in the form of profit, interest, dividends, or capital gain/loss. Capital gain/loss occurs when the market value or resale value of the investment increases or decreases. Cash flow here does not include the return of invested capital.
To the right is a simple example of cash flow on a $1,000 investment.
Annual returns
An
Annual Rate of Return is the return on an investment over a one-year period, such as January 1st through December 31st, or June 3rd 2006 through June 2nd 2007. Each ROI in the cash flow example above is an annual rate of return. An
Annualized Rate of Return is the return on an investment over a period other than one year (such as a month, or two years) multiplied or divided to give a comparable one-year return. For instance, a one-month ROI of 1% could be stated as an annualized rate of return of 12%. Or a two-year ROI of 10% could be stated as an annualized rate of return of 5%.
In the cash flow example above, the dollar returns for the four years add up to $265. The annualized rate of return for the four years is$265 ÷ ($1,000 x 4 years) = 6.625%.
Arithmetic return
In mathematical terms, the
arithmetic return is defined as the following:
\text{ROI}_\text{Arith}=\frac{V_f - V_i}{V_i}
where
- V_i is the initial investment value and
- V_f is the final investment value
This return has the following characteristics:
- \text{ROI}_\text{Arith}=+1.00=+100% when the final value is twice the initial value
- \text{ROI}_\text{Arith}>0 when the investment is profitable
- \text{ROI}_\text{Arith}0 is profit
- \text{ROI}_\text{Log}+1.
- {\rm Year\; 3\; Reinvestment\; Factor\;} = \frac{{\rm Year\; 3\; Total\; Distribution} \times {\rm Year\; 2\; Reinvestment\; Factor\;-->+1.
- {\rm Year\; 4\; Reinvestment\; Factor\;} = \frac{{\rm Year\; 4\; Total\; Distribution} \times {\rm Year\; 3\; Reinvestment\; Factor\;-->+1.
- {\rm Year\; 5\; Reinvestment\; Factor\;} = \frac{{\rm Year\; 5\; Total\; Distribution} \times {\rm Year\; 4\; Reinvestment\; Factor\;-->+1.
Total Return = ((Final Price x Last Reinvestment Factor) - Beginning Price) / Beginning Price
Average annual return (geometric)
Average Annual Return (geometric)
= \left {\left(1 + \frac{100}\right)}^{{\rm Time\; in\; years}^{-1--> - 1 \right \times 100
Example
{| class="wikitable" style="text-align:center"|+Example: Mutual Fund with low volatility and a regular annual dividend, reinvested at year-end share price, initial share value $100|-! End of: !! Year 1 !! Year 2!! Year 3 !! Year 4 !! Year 5|-! Dividend| $5 || $5 || $5 || $5 || $5|-! Capital Gain Distribution| || || $2 || |||-! Total Distribution| $5 || $5 || $7 || $5 || $5|-! Share Price| $98 || $101 || $102 || $99 ||
$101|-! Shares Purchased| 0.05102 || 0.04950 || 0.06863 || 0.05051 || 0.04950|-! Shares Owned| 1.05102 || 1.10053 || 1.16915 || 1.21966 || 1.26916|-! Reinvestment Factor
| 1.05102 || 1.05203 || 1.07220 || 1.05415 ||
1.05219|}
- Total Return = (($101 x 1.05219) - $100) / $100 = 6.27% (net of expenses)
- Average Annual Return (geometric) = (((28.19)/100)+1) ^ (1/5)) – 1) x 100 = 5.09%
Using a
Holding Period Return calculation, after 5 years, an investor who reinvested owned 1.26916 share valued at $101 per share ($128.19 in value). ($128.19-$100)/$100/5 = 5.638% yield. An investor who did not reinvest received a total of $27 in dividends and $1 in capital gain. ($27+$1)/$100/5 = 5.600% return.
Mutual funds include capital gains as well as dividends in their return calculations. Since the market price of a mutual fund share is based on net asset value, a capital gain distribution is offset by an equal decrease in mutual fund share value/price. From the shareholder's perspective, a capital gain distribution is not a net gain in assets, but it is a realized capital gain.
Summary: overall rate of return
Rate of Return and
Return on Investment indicate cash flow from an investment to the investor over a specified period of time, usually a year.
ROI is a measure of investment profitability, not a measure of investment size. While compound interest and dividend reinvestment can increase the size of the investment (thus potentially yielding a higher dollar return to the investor),
Return on Investment is a percentage return based on capital invested.
In general, the higher the investment risk, the greater the potential investment return, and the greater the potential investment loss.
References
See also
Further reading
- A. A. Groppelli and Ehsan Nikbakht. Barron’s Finance, 4th Edition. New York: Barron’s Educational Series, Inc., 2000. ISBN 0-7641-1275-9
- Zvi Bodie, Alex Kane and Alan J. Marcus. Essentials of Investments, 5th Edition. New York: McGraw-Hill/Irwin, 2004. ISBN 0-07-251077-3
- Richard A. Brealey, Stewart C. Myers and Franklin Allen. Principals of Corporate Finance, 8th Edition. McGraw-Hill/Irwin, 2006
- Walter B. Meigs and Robert F. Meigs. Financial Accounting, 4th Edition. New York: McGraw-Hill Book Company, 1970. ISBN 0-07-041534-X
- Bruce J. Feibel. Investment Performance Measurement. New York: Wiley, 2003. ISBN 0471268496
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