Rate of return
Encyclopedia
In finance
, rate of return (ROR), also known as return on investment (ROI), rate of profit or sometimes just return, is the ratio of money
gained or lost (whether realized or unrealized) 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
, principal
, or the cost basis
of the investment. ROI is usually expressed as a percentage.
, does not always have a clearly defined monetary value
, but for purposes of measuring ROI, the expected value must be clearly stated along with the rationale for this initial value. Similarly, 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.
The rate of return can be calculated over a single period, or expressed as an average over multiple periods of time.
is sometimes referred to as the yield
. See also: effective interest rate
, effective annual rate (EAR) or annual percentage yield
(APY).
It is the reciprocal of the e-folding
time.
The geometric average rate of return calculated over n years is also known as the annualized return.
Time-weighted rates of return (TWRR) are important because they eliminate the impact of cash flows. This is helpful when assessing the job that a money manager did for his/her clients, where typically the clients control these cash flows.
that satisfies the following equation:
where:
When the cost of capital
is smaller than the IRR rate 
, the investment is profitable, i.e., 
. Otherwise, the investment is not profitable.
MWRR are helpful in that they take cash flows into consideration. This is especially helpful when evaluating cases where the money manager controls cash flows (for private equity investments, for example, as well as sub-portfolio rates of return) as well as to provide the investor with their return. Contrast with TWRR.
= +100%, that is, if 
= ln($200 / $100) = ln(2) = 69.3%. The value falls to zero when 
= -100%, that is, if 
= -∞.
Arithmetic and logarithmic returns are not equal, but are approximately equal for small returns.
The difference between them is large only when percent changes are high. For example, an arithmetic return of +50% is equivalent to a logarithmic return of 40.55%, while an arithmetic return of -50% is equivalent to a logarithmic return of -69.31%.
Logarithmic returns are often used by academics in their research. The main advantage is that the continuously compounded return is symmetric, while the arithmetic return is not: positive and negative percent arithmetic returns are not equal. This means that an investment of $100 that yields an arithmetic return of 50% followed by an arithmetic return of -50% will result in $75, while an investment of $100 that yields a logarithmic return of 50% followed by an logarithmic return of -50% it will remain $100.
A 10% gain followed by a 10% loss is a 1% loss. The order in which the loss and gain occurs does not affect the result. A 50% gain and a 50% loss is a 25% loss. An 80% gain plus an 80% loss is a 64% loss. To recover from a 50% loss, a 100% gain is required. The mathematics of this are beyond the scope of this article, but since investment returns are often published as "average returns", it is important to note that average returns do not always translate into dollar returns.
An annual rate of return is the return on an investment over a one-year period, such as January 1 through December 31, or June 3, 2006 through June 2, 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%. **For GIPS compliance: you do not annualize portfolios or composites for periods of less than one year. You start on the 13th month.
In the cash flow example below, 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%.
Investors usually seek a higher rate of return on taxable investment returns than on non-taxable investment returns.
.
Except for rare periods of significant deflation where the opposite may be true, a dollar in cash is worth less today than it was yesterday, and worth more today than it will be worth tomorrow.
The main factors that are used by investors to determine the rate of return at which they are willing to invest money include:
The time value of money is reflected in the interest rates that bank
s offer for deposit
s, and also in the interest rates that banks charge for loans such as home mortgages. The “risk-free
” rate is the rate on U.S. Treasury Bills, because this is the highest rate available without risking capital.
The rate of return which an investor expects from an investment is called the Discount Rate
. Each investment has a different discount rate, based on the cash flow expected in future from the investment. The higher the risk
, the higher the discount rate (rate of return) the investor will demand from the investment.
or other reinvestment of cash returns (such as interest and dividends) does not affect the discount rate of an investment, but it does affect the Annual Percentage Yield
, because compounding/reinvestment increases the capital invested.
For example, if an investor put $1,000 in a 1-year Certificate of Deposit (CD) that paid an annual interest rate of 4%, compounded quarterly, the CD would earn 1% interest per quarter on the account balance. The account balance includes interest previously credited to the account.
The concept of 'income stream' may express this more clearly. At the beginning of the year, the investor took $1,000 out of his pocket (or checking account) to invest in a CD at the bank. The money was still his, but it was no longer available for buying groceries. The investment provided a cash flow of $10.00, $10.10, $10.20 and $10.30. At the end of the year, the investor got $1,040.60 back from the bank. $1,000 was return of capital.
Once interest is earned by an investor it becomes capital
. Compound interest involves reinvestment of capital; the interest earned during each quarter is reinvested. At the end of the first quarter the investor had capital of $1,010.00, which then earned $10.10 during the second quarter. The extra dime was interest on his additional $10 investment. The Annual Percentage Yield
or Future value
for compound interest is higher than for simple interest because the interest is reinvested as capital and earns interest. The yield on the above investment was 4.06%.
Bank accounts offer contractually guaranteed returns, so investors cannot lose their capital. Investors/Depositors lend money to the bank, and the bank is obligated to give investors back their capital plus all earned interest. Because investors are not risking losing their capital on a bad investment, they earn a quite low rate of return. But their capital steadily increases.
.” If the price often changes a great deal, the stock has “high volatility.” All stock shares have some volatility, and the change in price directly affects ROI for stock investments.
Stock returns are usually calculated for holding periods such as a month, a quarter or a year.
Yield is the compound rate of return that includes the effect of reinvesting interest or dividends.
To the right is an example of a stock investment of one share purchased at the beginning of the year for $100.
To calculate the rate of return, the investor includes the reinvested dividends in the total investment. The investor received a total of $4.06 in dividends over the year, all of which were reinvested, so the investment amount increased by $4.06.
The disadvantage of this ROI calculation is that it does not take into account the fact that not all the money was invested during the entire year (the dividend reinvestments occurred throughout the year). The advantages are: (1) it uses the cost basis of the investment, (2) it clearly shows which gains are due to dividends and which gains/losses are due to capital gains/losses, and (3) the actual dollar return of $3.02 is compared to the actual dollar investment of $104.06.
For U.S. income tax purposes, if the shares were sold at the end of the year, dividends would be $4.06, cost basis of the investment would be $104.06, sale price would be $103.02, and the capital loss would be $1.04.
Since all returns were reinvested, the ROI might also be calculated as a continuously compounded return or logarithmic return. The effective continuously compounded rate of return is the natural log of the final investment value divided by the initial investment value:
.
s, exchange-traded fund
s (ETFs), and other equitized investments (such as unit investment trusts or UITs, insurance separate account
s and related variable products such as variable universal life insurance
policies and variable annuity contracts, and bank-sponsored commingled funds, collective benefit funds or common trust funds) are essentially portfolios of various investment securities such as stocks, bonds and money market instruments which are equitized by selling shares or units to investors. Investors and other parties are interested to know how the investment has performed over various periods of time.
Performance is usually quantified by a fund's total return. In the 1990s, many different fund companies were advertising various total returns—some cumulative, some averaged, some with or without deduction of sales loads or commissions, etc. To level the playing field and help investors compare performance returns of one fund to another, the U.S. Securities and Exchange Commission (SEC) began requiring funds to compute and report total returns based upon a standardized formula—so called "SEC Standardized total return" which is the average annual total return assuming reinvestment of dividends and distributions and deduction of sales loads or charges. Funds may compute and advertise returns on other bases (so-called "non-standardized" returns), so long as they also publish no less prominently the "standardized" return data.
Subsequent to this, apparently investors who'd sold their fund shares after a large increase in the share price in the late 1990s and early 2000s were ignorant of how significant the impact of income/capital gain taxes was on their fund "gross" returns. That is, they had little idea how significant the difference could be between "gross" returns (returns before federal taxes) and "net" returns (after-tax returns). In reaction to this apparent investor ignorance, and perhaps for other reasons, the SEC made further rule-making to require mutual funds to publish in their annual prospectus, among other things, total returns before and after the impact of U.S federal individual income taxes. And further, the after-tax returns would include 1) returns on a hypothetical taxable account after deducting taxes on dividends and capital gain distributions received during the illustrated periods and 2) the impacts of the items in #1) as well as assuming the entire investment shares were sold at the end of the period (realizing capital gain/loss on liquidation of the shares). These after-tax returns would apply of course only to taxable accounts and not to tax-deferred or retirement accounts such as IRAs.
Lastly, in more recent years, "personalized" investment returns have been demanded by investors. In other words, investors are saying more or less the fund returns may not be what their actual account returns are based upon the actual investment account transaction history. This is because investments may have been made on various dates and additional purchases and withdrawals may have occurred which vary in amount and date and thus are unique to the particular account. More and more fund and brokerage firms have begun providing personalized account returns on investor's account statements in response to this need.
With that out of the way, here's how basic earnings and gains/losses work on a mutual fund. The fund records income for dividends and interest earned which typically increases the value of the mutual fund shares, while expenses set aside have an offsetting impact to share value. When the fund's investments increase in market value, so too does the value of the fund shares (or units) owned by the investors. When investments increase (decrease) in market value, so too the fund shares value increases (or decreases). When the fund sells investments at a profit, it turns or reclassifies that paper profit or unrealized gain into an actual or realized gain. The sale has no effect on the value of fund shares but it has reclassified a component of its value from one bucket to another on the fund books—which will have future impact to investors. At least annually, a fund usually pays dividends from its net income (income less expenses) and net capital gains realized out to shareholders as an IRS requirement. This way, the fund pays no taxes but rather all the investors in taxable accounts do. Mutual fund share prices are typically valued each day the stock or bond markets are open and typically the value of a share is the net asset value
of the fund shares investors own.
Mutual funds report total returns assuming reinvestment of dividend and capital gain distributions. That is, the dollar amounts distributed are used to purchase additional shares of the funds as of the reinvestment/ex-dividend date. Reinvestment rates or factors are based on total distributions (dividends plus capital gains) during each period.
Where:
P = a hypothetical initial payment of $1,000.
T = average annual total return.
n = number of years.
ERV = ending redeemable value of a hypothetical $1,000 payment made at the beginning of the 1-, 5-, or 10-year periods at the end of the 1-, 5-, or 10-year periods (or fractional portion).
Solving for T gives
Using a Holding Period Return
calculation, after five years, an investor who reinvested owned 91.314 shares valued at $19.90 per share. ((($19.90 × 91.314) / $1,000) - 1) / 5 = 16.34% return. An investor who did not reinvest received total cash payments of $5.78 per share. ((($19.90 + $5.78) / $14.21) - 1) / 5 = 16.14% 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.
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.
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, rate of return (ROR), also known as return on investment (ROI), rate of profit or sometimes just return, is the ratio of money
Money
Money is any object or record that is generally accepted as payment for goods and services and repayment of debts in a given country or socio-economic context. The main functions of money are distinguished as: a medium of exchange; a unit of account; a store of value; and, occasionally in the past,...
gained or lost (whether realized or unrealized) on an investment
Investment
Investment has different meanings in finance and economics. Finance investment is putting money into something with the expectation of gain, that upon thorough analysis, has a high degree of security for the principal amount, as well as security of return, within an expected period of time...
relative to the amount of money invested. The amount of money gained or lost may be referred to as interest
Interest
Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....
, profit
Profit (accounting)
In accounting, profit can be considered to be the difference between the purchase price and the costs of bringing to market whatever it is that is accounted as an enterprise in terms of the component costs of delivered goods and/or services and any operating or other expenses.-Definition:There are...
/loss, gain/loss, or net income
Net income
Net income is the residual income of a firm after adding total revenue and gains and subtracting all expenses and losses for the reporting period. Net income can be distributed among holders of common stock as a dividend or held by the firm as an addition to retained earnings...
/loss. The money invested may be referred to as the asset
Asset
In financial accounting, assets are economic resources. Anything tangible or intangible that is capable of being owned or controlled to produce value and that is held to have positive economic value is considered an asset...
, capital
Capital (economics)
In economics, capital, capital goods, or real capital refers to already-produced durable goods used in production of goods or services. The capital goods are not significantly consumed, though they may depreciate in the production process...
, principal
Debt
A debt is an obligation owed by one party to a second party, the creditor; usually this refers to assets granted by the creditor to the debtor, but the term can also be used metaphorically to cover moral obligations and other interactions not based on economic value.A debt is created when a...
, or the cost basis
Cost basis
Basis , as used in United States tax law, is the original cost of property, adjusted for factors such as depreciation. When property is sold, the taxpayer pays/ taxes on a capital gain/ that equals the amount realized on the sale minus the sold property's basis.The taxpayer deserves a tax-free...
of the investment. ROI is usually expressed as a percentage.
Calculation
The initial value of an investment,, does not always have a clearly defined monetary valueValue (economics)
An economic value is the worth of a good or service as determined by the market.The economic value of a good or service has puzzled economists since the beginning of the discipline. First, economists tried to estimate the value of a good to an individual alone, and extend that definition to goods...
, but for purposes of measuring ROI, the expected value must be clearly stated along with the rationale for this initial value. Similarly, 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.The rate of return can be calculated over a single period, or expressed as an average over multiple periods of time.
Arithmetic return
The arithmetic return is: is sometimes referred to as the yieldYield (finance)
In finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return...
. See also: effective interest rate
Effective interest rate
The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.It is used to compare the...
, effective annual rate (EAR) or annual percentage yield
Annual Percentage Yield
Annual percentage yield is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow for a reasonable, single-point comparison of different offerings with varying compounding schedules...
(APY).
Logarithmic or continuously compounded return
The logarithmic return or continuously compounded return, also known as force of interest, is defined as:It is the reciprocal of the e-folding
E-folding
In science, e-folding is the time interval in which an exponentially growing quantity increases by a factor of e. This term is often used in theoretical physics, especially when cosmic inflation is investigated...
time.
Arithmetic average rate of return
The arithmetic average rate of return over n periods is defined as:Geometric average rate of return
The geometric average rate of return, also known as the True Time-Weighted Rate of Return, over n periods is defined as:The geometric average rate of return calculated over n years is also known as the annualized return.
Time-weighted rates of return (TWRR) are important because they eliminate the impact of cash flows. This is helpful when assessing the job that a money manager did for his/her clients, where typically the clients control these cash flows.
Internal rate of return
The internal rate of return (IRR), also known as the dollar-weighted rate of return or the money-weighted rate of return (MWRR), is defined as the value(s) of that satisfies the following equation:where:
- NPV = net present valueNet present valueIn finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...
of the investment 
= cashflow at time 
When the cost of capital
is smaller than the IRR rate , the investment is profitable, i.e., . Otherwise, the investment is not profitable.MWRR are helpful in that they take cash flows into consideration. This is especially helpful when evaluating cases where the money manager controls cash flows (for private equity investments, for example, as well as sub-portfolio rates of return) as well as to provide the investor with their return. Contrast with TWRR.
Arithmetic and logarithmic return
The value of an investment is doubled over a year if the annual ROR = +100%, that is, if = ln($200 / $100) = ln(2) = 69.3%. The value falls to zero when = -100%, that is, if = -∞.Arithmetic and logarithmic returns are not equal, but are approximately equal for small returns.
The difference between them is large only when percent changes are high. For example, an arithmetic return of +50% is equivalent to a logarithmic return of 40.55%, while an arithmetic return of -50% is equivalent to a logarithmic return of -69.31%.
Logarithmic returns are often used by academics in their research. The main advantage is that the continuously compounded return is symmetric, while the arithmetic return is not: positive and negative percent arithmetic returns are not equal. This means that an investment of $100 that yields an arithmetic return of 50% followed by an arithmetic return of -50% will result in $75, while an investment of $100 that yields a logarithmic return of 50% followed by an logarithmic return of -50% it will remain $100.
Initial investment,  |
$100 | $100 | $100 | $100 | $100 |
|---|---|---|---|---|---|
Final investment,  |
$0 | $50 | $100 | $150 | $200 |
Profit/loss,  |
−$100 | −$50 | $0 | $50 | $100 |
Arithmetic return,  |
−100% | −50% | 0% | 50% | 100% |
Logarithmic return,  |
−∞ | −69.31% | 0% | 40.55% | 69.31% |
Arithmetic average and geometric average rates of return
Both arithmetic and geometric average rates of returns are averages of periodic percentage returns. Neither will accurately translate to the actual dollar amounts gained or lost if percent gains are averaged with percent losses. A 10% loss on a $100 investment is a $10 loss, and a 10% gain on a $100 investment is a $10 gain. When percentage returns on investments are calculated, they are calculated for a period of time – not based on original investment dollars, but based on the dollars in the investment at the beginning and end of the period. So if an investment of $100 loses 10% in the first period, the investment amount is then $90. If the investment then gains 10% in the next period, the investment amount is $99.A 10% gain followed by a 10% loss is a 1% loss. The order in which the loss and gain occurs does not affect the result. A 50% gain and a 50% loss is a 25% loss. An 80% gain plus an 80% loss is a 64% loss. To recover from a 50% loss, a 100% gain is required. The mathematics of this are beyond the scope of this article, but since investment returns are often published as "average returns", it is important to note that average returns do not always translate into dollar returns.
| Year 1 | Year 2 | Year 3 | Year 4 | |
|---|---|---|---|---|
| Rate of Return | 5% | 5% | 5% | 5% |
| Geometric Average at End of Year | 5% | 5% | 5% | 5% |
| Capital at End of Year | $105.00 | $110.25 | $115.76 | $121.55 |
| Dollar Profit/(Loss) | $5.00 | $10.25 | $15.76 | $21.55 |
| Compound Yield | 5% | 5.4% |
| Year 1 | Year 2 | Year 3 | Year 4 | |
|---|---|---|---|---|
| Rate of Return | 50% | -20% | 30% | -40% |
| Geometric Average at End of Year | 50% | 9.5% | 16% | -1.6% |
| Capital at End of Year | $150.00 | $120.00 | $156.00 | $93.60 |
| Dollar Profit/(Loss) | ($6.40) | |||
| Compound Yield | -1.6% |
| Year 1 | Year 2 | Year 3 | Year 4 | |
|---|---|---|---|---|
| Rate of Return | -95% | 0% | 0% | 115% |
| Geometric Average at End of Year | -95% | -77.6% | -63.2% | -42.7% |
| Capital at End of Year | $5.00 | $5.00 | $5.00 | $10.75 |
| Dollar Profit/(Loss) | ($89.25) | |||
| Compound Yield | -22.3% |
Annual returns and annualized returns
Care must be taken not to confuse annual and annualized returns. An annual rate of return is a single-period return, while an annualized rate of return is a multi-period, arithmetic average return.An annual rate of return is the return on an investment over a one-year period, such as January 1 through December 31, or June 3, 2006 through June 2, 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%. **For GIPS compliance: you do not annualize portfolios or composites for periods of less than one year. You start on the 13th month.
In the cash flow example below, 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%.
Uses
- ROI is a measure of cash generated by or lost due to the investment. It measures the cash flow or income stream from the investment to the investorInvestorAn investor is a party that makes an investment into one or more categories of assets --- equity, debt securities, real estate, currency, commodity, derivatives such as put and call options, etc...
, relative to the amount invested. Cash flowCash flowCash flow is the movement of money into or out of a business, project, or financial product. It is usually measured during a specified, finite period of time. Measurement of cash flow can be used for calculating other parameters that give information on a company's value and situation.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.
| Year 1 | Year 2 | Year 3 | Year 4 | |
|---|---|---|---|---|
| Dollar Return | $100 | $55 | $60 | $50 |
| ROI | 10% | 5.5% | 6% | 5% |
- ROI values typically used for personal financial decisions include Annual Rate of Return and Annualized Rate of Return. For nominal risk investments such as savings accounts or Certificates of Deposit, the personal investor considers the effects of reinvesting/compounding on increasing savings balances over time. For investments in which capital is at risk, such as stock shares, mutual fund shares and home purchases, the personal investor considers the effects of price volatility and capital gain/loss on returns.
- Profitability ratios typically used by financial analysts to compare a company’s profitability over time or compare profitability between companies include Gross Profit Margin, Operating Profit Margin, ROI ratio, Dividend yieldDividend yieldThe dividend yield or the dividend-price ratio on a company stock is the company's total annual dividend payments divided by its market capitalization, or the dividend per share, divided by the price per share. It is often expressed as a percentage...
, Net profit margin, Return on equityReturn on equityReturn on equity measures the rate of return on the ownership interest of the common stock owners. It measures a firm's efficiency at generating profits from every unit of shareholders' equity . ROE shows how well a company uses investment funds to generate earnings growth...
, and Return on assets.
- During capital budgetingCapital budgetingCapital budgeting is the planning process used to determine whether an organization's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing...
, companies compare the rates of return of different projects to select which projects to pursue in order to generate maximum return or wealth for the company's stockholders. Companies do so by considering the average rate of return, payback period, net present valueNet present valueIn finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...
, profitability indexProfitability indexProfitability index , also known as profit investment ratio and value investment ratio , is the ratio of payoff to investment of a proposed project...
, and internal rate of returnInternal rate of returnThe internal rate of return is a rate of return used in capital budgeting to measure and compare the profitability of investments. It is also called the discounted cash flow rate of return or the rate of return . In the context of savings and loans the IRR is also called the effective interest rate...
for various projects.
- A return may be adjusted for taxes to give the after-tax rate of return. This is done in geographical areas or historical times in which taxes consumed or consume a significant portion of profits or income. The after-tax rate of return is calculated by multiplying the rate of return by the tax rate, then subtracting that percentage from the rate of return.
- A return of 5% taxed at 15% gives an after-tax return of 4.25%
-
- 0.05 x 0.15 = 0.0075
- 0.05 - 0.0075 = 0.0425 = 4.25%
- A return of 10% taxed at 25% gives an after-tax return of 7.5%
- 0.10 x 0.25 = 0.025
- 0.10 - 0.025 = 0.075 = 7.5%
Investors usually seek a higher rate of return on taxable investment returns than on non-taxable investment returns.
- A return may be adjusted for inflationInflationIn economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...
to better indicate its true value in purchasing powerPurchasing powerPurchasing power is the number of goods/services that can be purchased with a unit of currency. For example, if you had taken one dollar to a store in the 1950s, you would have been able to buy a greater number of items than you would today, indicating that you would have had a greater purchasing...
. Any investment with a nominal rate of return less than the annual inflation rateInflation rateIn economics, the inflation rate is a measure of inflation, the rate of increase of a price index . It is the percentage rate of change in price level over time. The rate of decrease in the purchasing power of money is approximately equal.The inflation rate is used to calculate the real interest...
represents a loss of value, even though the nominal rate of return might well be greater than 0%. When ROI is adjusted for inflation, the resulting return is considered an increase or decrease in purchasing powerPurchasing powerPurchasing power is the number of goods/services that can be purchased with a unit of currency. For example, if you had taken one dollar to a store in the 1950s, you would have been able to buy a greater number of items than you would today, indicating that you would have had a greater purchasing...
. If an ROI value is adjusted for inflation, it is stated explicitly, such as “The return, adjusted for inflation, was 2%.”
- Many online poker toolsPoker toolsPoker tools are a variety of software or web-based applications that allow the statistical analysis of poker players, games or tournaments.-Hand converters:...
include ROI in a player's tracked statistics, assisting users in evaluating an opponent's profitability.
Time value of money
Investments generate cash flow to the investor to compensate the investor for the time value of moneyTime value of money
The time value of money is the value of money figuring in a given amount of interest earned over a given amount of time. The time value of money is the central concept in finance theory....
.
Except for rare periods of significant deflation where the opposite may be true, a dollar in cash is worth less today than it was yesterday, and worth more today than it will be worth tomorrow.
The main factors that are used by investors to determine the rate of return at which they are willing to invest money include:
- estimates of future inflation rates
- estimates regarding the risk of the investment (e.g. how likely it is that investors will receive regular interest/dividend payments and the return of their full capital)
- whether or not the investors want the money available (“liquid”) for other uses.
The time value of money is reflected in the interest rates that bank
Bank
A bank is a financial institution that serves as a financial intermediary. The term "bank" may refer to one of several related types of entities:...
s offer for deposit
Deposit account
A deposit account is a current account, savings account, or other type of bank account, at a banking institution that allows money to be deposited and withdrawn by the account holder. These transactions are recorded on the bank's books, and the resulting balance is recorded as a liability for the...
s, and also in the interest rates that banks charge for loans such as home mortgages. The “risk-free
Risk-free interest rate
Risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss. The risk-free rate represents the interest that an investor would expect from an absolutely risk-free investment over a given period of time....
” rate is the rate on U.S. Treasury Bills, because this is the highest rate available without risking capital.
The rate of return which an investor expects from an investment is called the Discount Rate
Discount rate
The discount rate can mean*an interest rate a central bank charges depository institutions that borrow reserves from it, for example for the use of the Federal Reserve's discount window....
. Each investment has a different discount rate, based on the cash flow expected in future from the investment. The higher the risk
Risk
Risk is the potential that a chosen action or activity will lead to a loss . The notion implies that a choice having an influence on the outcome exists . Potential losses themselves may also be called "risks"...
, the higher the discount rate (rate of return) the investor will demand from the investment.
Compounding or reinvesting
Compound interestCompound interest
Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...
or other reinvestment of cash returns (such as interest and dividends) does not affect the discount rate of an investment, but it does affect the Annual Percentage Yield
Annual Percentage Yield
Annual percentage yield is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow for a reasonable, single-point comparison of different offerings with varying compounding schedules...
, because compounding/reinvestment increases the capital invested.
For example, if an investor put $1,000 in a 1-year Certificate of Deposit (CD) that paid an annual interest rate of 4%, compounded quarterly, the CD would earn 1% interest per quarter on the account balance. The account balance includes interest previously credited to the account.
| 1st Quarter | 2nd Quarter | 3rd Quarter | 4th Quarter | |
|---|---|---|---|---|
| Capital at the beginning of the period | $1,000 | $1,010 | $1,020.10 | $1,030.30 |
| Dollar return for the period | $10 | $10.10 | $10.20 | $10.30 |
| Account Balance at end of the period | $1,010.00 | $1,020.10 | $1,030.30 | $1,040.60 |
| Quarterly ROI | 1% | 1% | 1% | 1% |
The concept of 'income stream' may express this more clearly. At the beginning of the year, the investor took $1,000 out of his pocket (or checking account) to invest in a CD at the bank. The money was still his, but it was no longer available for buying groceries. The investment provided a cash flow of $10.00, $10.10, $10.20 and $10.30. At the end of the year, the investor got $1,040.60 back from the bank. $1,000 was return of capital.
Once interest is earned by an investor it becomes capital
Financial capital
Financial capital can refer to money used by entrepreneurs and businesses to buy what they need to make their products or provide their services or to that sector of the economy based on its operation, i.e. retail, corporate, investment banking, etc....
. Compound interest involves reinvestment of capital; the interest earned during each quarter is reinvested. At the end of the first quarter the investor had capital of $1,010.00, which then earned $10.10 during the second quarter. The extra dime was interest on his additional $10 investment. The Annual Percentage Yield
Annual Percentage Yield
Annual percentage yield is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow for a reasonable, single-point comparison of different offerings with varying compounding schedules...
or Future value
Future value
Future value is the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of return; it is the present value multiplied by the accumulation...
for compound interest is higher than for simple interest because the interest is reinvested as capital and earns interest. The yield on the above investment was 4.06%.
Bank accounts offer contractually guaranteed returns, so investors cannot lose their capital. Investors/Depositors lend money to the bank, and the bank is obligated to give investors back their capital plus all earned interest. Because investors are not risking losing their capital on a bad investment, they earn a quite low rate of return. But their capital steadily increases.
Capital gains and losses
Many investments carry significant risk that the investor will lose some or all of the invested capital. For example, investments in company stock shares put capital at risk. The value of a stock share depends on what someone is willing to pay for it at a certain point in time. Unlike capital invested in a savings account, the capital value (price) of a stock share constantly changes. If the price is relatively stable, the stock is said to have “low volatilityVolatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
.” If the price often changes a great deal, the stock has “high volatility.” All stock shares have some volatility, and the change in price directly affects ROI for stock investments.
Stock returns are usually calculated for holding periods such as a month, a quarter or a year.
Reinvestment when capital is at risk: rate of return and yield
| End of: | 1st Quarter | 2nd Quarter | 3rd Quarter | 4th Quarter |
|---|---|---|---|---|
| Dividend | $1 | $1.01 | $1.02 | $1.03 |
| Stock Price | $98 | $101 | $102 | $99 |
| Shares Purchased | 0.010204 | 0.01 | 0.01 | 0.010404 |
| Total Shares Held | 1.010204 | 1.020204 | 1.030204 | 1.040608 |
| Investment Value | $99 | $103.04 | $105.08 | $103.02 |
| Quarterly ROI | -1% | 4.08% | 1.98% | -1.96% |
Yield is the compound rate of return that includes the effect of reinvesting interest or dividends.
To the right is an example of a stock investment of one share purchased at the beginning of the year for $100.
- The quarterly dividend is reinvested at the quarter-end stock price.
- The number of shares purchased each quarter = ($ Dividend)/($ Stock Price).
- The final investment value of $103.02 is a 3.02% Yield on the initial investment of $100. This is the compound yield, and this return can be considered to be the return on the investment of $100.
To calculate the rate of return, the investor includes the reinvested dividends in the total investment. The investor received a total of $4.06 in dividends over the year, all of which were reinvested, so the investment amount increased by $4.06.
- Total Investment = Cost Basis = $100 + $4.06 = $104.06.
- Capital gain/loss = $103.02 - $104.06 = -$1.04 (a capital loss)
- ($4.06 dividends - $1.04 capital loss ) / $104.06 total investment = 2.9% ROI
The disadvantage of this ROI calculation is that it does not take into account the fact that not all the money was invested during the entire year (the dividend reinvestments occurred throughout the year). The advantages are: (1) it uses the cost basis of the investment, (2) it clearly shows which gains are due to dividends and which gains/losses are due to capital gains/losses, and (3) the actual dollar return of $3.02 is compared to the actual dollar investment of $104.06.
For U.S. income tax purposes, if the shares were sold at the end of the year, dividends would be $4.06, cost basis of the investment would be $104.06, sale price would be $103.02, and the capital loss would be $1.04.
Since all returns were reinvested, the ROI might also be calculated as a continuously compounded return or logarithmic return. The effective continuously compounded rate of return is the natural log of the final investment value divided by the initial investment value:
is the initial investment ($100)
is the final value ($103.02)
.Mutual fund and investment company returns
Mutual fundMutual fund
A mutual fund is a professionally managed type of collective investment scheme that pools money from many investors to buy stocks, bonds, short-term money market instruments, and/or other securities.- Overview :...
s, exchange-traded fund
Exchange-traded fund
An exchange-traded fund is an investment fund traded on stock exchanges, much like stocks. An ETF holds assets such as stocks, commodities, or bonds, and trades close to its net asset value over the course of the trading day. Most ETFs track an index, such as the S&P 500 or MSCI EAFE...
s (ETFs), and other equitized investments (such as unit investment trusts or UITs, insurance separate account
Separate account
A separate account is a segregated accounting and reporting account held by an insurance company not in or "separate" from its general account. A separate account allows an investor to choose an investment category according to his individual risk tolerance, and desire for performance...
s and related variable products such as variable universal life insurance
Variable universal life insurance
Variable Universal Life Insurance is a type of life insurance that builds a cash value. In a VUL, the cash value can be invested in a wide variety of separate accounts, similar to mutual funds, and the choice of which of the available separate accounts to use is entirely up to the contract owner...
policies and variable annuity contracts, and bank-sponsored commingled funds, collective benefit funds or common trust funds) are essentially portfolios of various investment securities such as stocks, bonds and money market instruments which are equitized by selling shares or units to investors. Investors and other parties are interested to know how the investment has performed over various periods of time.
Performance is usually quantified by a fund's total return. In the 1990s, many different fund companies were advertising various total returns—some cumulative, some averaged, some with or without deduction of sales loads or commissions, etc. To level the playing field and help investors compare performance returns of one fund to another, the U.S. Securities and Exchange Commission (SEC) began requiring funds to compute and report total returns based upon a standardized formula—so called "SEC Standardized total return" which is the average annual total return assuming reinvestment of dividends and distributions and deduction of sales loads or charges. Funds may compute and advertise returns on other bases (so-called "non-standardized" returns), so long as they also publish no less prominently the "standardized" return data.
Subsequent to this, apparently investors who'd sold their fund shares after a large increase in the share price in the late 1990s and early 2000s were ignorant of how significant the impact of income/capital gain taxes was on their fund "gross" returns. That is, they had little idea how significant the difference could be between "gross" returns (returns before federal taxes) and "net" returns (after-tax returns). In reaction to this apparent investor ignorance, and perhaps for other reasons, the SEC made further rule-making to require mutual funds to publish in their annual prospectus, among other things, total returns before and after the impact of U.S federal individual income taxes. And further, the after-tax returns would include 1) returns on a hypothetical taxable account after deducting taxes on dividends and capital gain distributions received during the illustrated periods and 2) the impacts of the items in #1) as well as assuming the entire investment shares were sold at the end of the period (realizing capital gain/loss on liquidation of the shares). These after-tax returns would apply of course only to taxable accounts and not to tax-deferred or retirement accounts such as IRAs.
Lastly, in more recent years, "personalized" investment returns have been demanded by investors. In other words, investors are saying more or less the fund returns may not be what their actual account returns are based upon the actual investment account transaction history. This is because investments may have been made on various dates and additional purchases and withdrawals may have occurred which vary in amount and date and thus are unique to the particular account. More and more fund and brokerage firms have begun providing personalized account returns on investor's account statements in response to this need.
With that out of the way, here's how basic earnings and gains/losses work on a mutual fund. The fund records income for dividends and interest earned which typically increases the value of the mutual fund shares, while expenses set aside have an offsetting impact to share value. When the fund's investments increase in market value, so too does the value of the fund shares (or units) owned by the investors. When investments increase (decrease) in market value, so too the fund shares value increases (or decreases). When the fund sells investments at a profit, it turns or reclassifies that paper profit or unrealized gain into an actual or realized gain. The sale has no effect on the value of fund shares but it has reclassified a component of its value from one bucket to another on the fund books—which will have future impact to investors. At least annually, a fund usually pays dividends from its net income (income less expenses) and net capital gains realized out to shareholders as an IRS requirement. This way, the fund pays no taxes but rather all the investors in taxable accounts do. Mutual fund share prices are typically valued each day the stock or bond markets are open and typically the value of a share is the net asset value
Net asset value
Net asset value is a term used to describe the value of an entity's assets less the value of its liabilities. The term is most commonly used in relation to open-ended or mutual funds because shares of such funds registered with the U.S. Securities and Exchange Commission are redeemed at their net...
of the fund shares investors own.
Total returns
This section addresses only total returns without the impact of U.S. federal individual income and capital gains taxes.Mutual funds report total returns assuming reinvestment of dividend and capital gain distributions. That is, the dollar amounts distributed are used to purchase additional shares of the funds as of the reinvestment/ex-dividend date. Reinvestment rates or factors are based on total distributions (dividends plus capital gains) during each period.
Average annual total return (geometric)
US mutual funds are to compute average annual total return as prescribed by the U.S. Securities and Exchange Commission (SEC) in instructions to form N-1A (the fund prospectus) as the average annual compounded rates of return for 1-year, 5-year and 10-year periods (or inception of the fund if shorter) as the "average annual total return" for each fund. The following formula is used:Where:
P = a hypothetical initial payment of $1,000.
T = average annual total return.
n = number of years.
ERV = ending redeemable value of a hypothetical $1,000 payment made at the beginning of the 1-, 5-, or 10-year periods at the end of the 1-, 5-, or 10-year periods (or fractional portion).
Solving for T gives
Example
| Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
|---|---|---|---|---|---|
| Dividend per share | $0.26 | $0.29 | $0.30 | $0.50 | $0.53 |
| Capital gain distribution per share | $0.06 | $0.39 | $0.47 | $1.86 | $1.12 |
| Total Distribution Per Share | $0.32 | $0.68 | $0.77 | $2.36 | $1.65 |
| Share Price At End Of Year | $17.50 | $19.49 | $20.06 | $20.62 | $19.90 |
| Reinvestment factor | 1.01829 | 1.03553 | 1.03975 | 1.11900 | 1.09278 |
| Shares owned before distribution | 70.373 | 71.676 | 74.125 | 76.859 | 84.752 |
| Total distribution | $22.52 | $48.73 | $57.10 | $181.73 | $141.60 |
| Share price at distribution | $17.28 | $19.90 | $20.88 | $22.98 | $21.31 |
| Shares purchased | 1.303 | 2.449 | 2.734 | 7.893 | 6.562 |
| Shares owned after distribution | 71.676 | 74.125 | 76.859 | 84.752 | 91.314 |
- Total return = (($19.90 × 1.09278) / $14.21) - 1 = 53.04%
- Average annual total return (geometric) = ((($19.90 × 91.314) / $1,000) ^ (1 / 5)) - 1 = 12.69%
Using a Holding Period Return
Holding Period Return
In finance, holding period return is the total return on an asset or portfolio over the period during which it was held. It is one of the simplest measures of investment performance....
calculation, after five years, an investor who reinvested owned 91.314 shares valued at $19.90 per share. ((($19.90 × 91.314) / $1,000) - 1) / 5 = 16.34% return. An investor who did not reinvest received total cash payments of $5.78 per share. ((($19.90 + $5.78) / $14.21) - 1) / 5 = 16.14% 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.
See also
- AverageAverageIn mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....
for a discussion of annualization of returns - Capital budgetingCapital budgetingCapital budgeting is the planning process used to determine whether an organization's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing...
- Compound annual growth rateCompound annual growth rateCompound annual growth rate is a business and investing specific term for the smoothed annualized gain of an investment over a given time period...
- Compound interestCompound interestCompound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...
- Dollar cost averagingDollar cost averagingDollar cost averaging is an investment strategy that may be used with any currency. It takes the form of investing equal monetary amounts regularly and periodically over specific time periods in a particular investment or portfolio. By doing so, more shares are purchased when prices are low and...
- Economic value addedEconomic value addedIn corporate finance, Economic Value Added or EVA, a registered trademark of Stern Stewart & Co., is an estimate of a firm's economic profit – being the value created in excess of the required return of the company's investors . Quite simply, EVA is the profit earned by the firm less the cost of...
- Expected returnExpected returnThe expected return is the weighted-average outcome in gambling, probability theory, economics or finance.It isthe average of a probability distribution of possible returns, calculated by using the following formula:...
- Internal rate of returnInternal rate of returnThe internal rate of return is a rate of return used in capital budgeting to measure and compare the profitability of investments. It is also called the discounted cash flow rate of return or the rate of return . In the context of savings and loans the IRR is also called the effective interest rate...
- Modified Dietz MethodModified Dietz MethodThe Modified Dietz Method is a calculation used to determine an approximation of the performance of an investment portfolio based on money-weighted cash flow...
- Net present valueNet present valueIn finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...
- Rate of profitRate of profitIn economics and finance, the profit rate is the relative profitability of an investment project, of a capitalist enterprise, or of the capitalist economy as a whole...
- Return of capitalReturn of capitalReturn of capital refers to payments back to "capital owners" that exceed the growth of a business. It should not be confused with return on capital which measures a 'rate of return'....
- Return on assets
- Return on capital
- Simple Dietz MethodSimple Dietz MethodSimple Dietz Method is a means of calculating an approximation of investment portfolio performance during a period of external cash flows into/out of the portfolio...
- True Time-Weighted Rate of ReturnTrue time-weighted rate of returnTrue Time-Weighted Rate of Return is a way to measure the performance of an investing portfolio in the presence of external cash flows. It determines the return for an investor who has not invested any additional cash flows during the investment period:...
- Value investingValue investingValue investing is an investment paradigm that derives from the ideas on investment and speculation that Ben Graham and David Dodd began teaching at Columbia Business School in 1928 and subsequently developed in their 1934 text Security Analysis...
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. Principles 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