In finance Finance is the science of funds management. The general areas of finance are business finance, personal finance, and public finance. Finance includes saving money and often includes lending money. The field of finance deals with the concepts of time, money, and risk and how they are interrelated. It also deals with how money is spent and budgeted, rate of return (ROR), also known as return on investment (ROI), rate of profit or sometimes just return, is the ratio of money Money is any object 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, a standard of deferred payment gained or lost (whether realized or unrealized) on an investment Investment is the commitment of money or capital to purchase financial instruments or other assets in order to gain profitable returns in form of interest, income, or appreciation of the value of the instrument. It is related to saving or deferring consumption. Investment is involved in many areas of the economy, such as business management and relative to the amount of money invested. The amount of money gained or lost may be referred to as interest Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money, or, money earned by deposited funds. Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft, and even entire factories in finance lease arrangements. The interest is, profit In accounting, profit is the difference between 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/loss, gain/loss, or net income/loss. The money invested may be referred to as the 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. Simplistically stated, assets represent ownership of value that can be converted into cash . The balance sheet of a firm, capital In economics, capital, capital goods, or real capital are factors of production used to create goods or services that are not themselves significantly consumed in the production process. Capital goods may be acquired with money or financial capital, principal Debt is that which is owed; usually referencing assets owed, but the term can also cover moral obligations and other interactions not requiring money. In the case of assets, debt is a means of using future purchasing power in the present before a summation has been earned. Some companies and corporations use debt as a part of their overall, or the 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/(saves) taxes on a capital gain/(loss) that equals the amount realized on the sale minus the sold property's basis of the investment. ROI is usually expressed as a percentage rather than a fraction.
Contents |
Calculation
The initial value of an investment, Vi, does not always have a clearly defined monetary value 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 which can be exchanged. From this analysis came the concepts value in use and value in exchange, but for purposes of measuring ROI, the expected value must be clearly stated along with the rationale for this initial value. The multiple value of an investment, Vf, 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.[citation needed]
The rate of return can be calculated over a single period, or expressed as an average over multiple periods.
Single-period
Arithmetic return
The arithmetic return is:
rarith is sometimes referred to as the yield 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. Yield applies to various stated rates of return on stocks , fixed income instruments (bonds, notes, bills, strips, zero coupon), and some other investment type. See also: 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 annual interest between loans with different, effective annual 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 annual interest between loans with different (EAR) or 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. However, it does not account for the possibility of account fees affecting the net gain. APY generally refers (APY).
Logarithmic or continuously compounded return
The logarithmic return or continuously compounded return 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 . A loan, for example, may have its interest compounded every month: in this case, a loan with $100 initial principal and 1%, also known as force of 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 . A loan, for example, may have its interest compounded every month: in this case, a loan with $100 initial principal and 1%, is cleared as:
Multiperiod average returns
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 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.
Internal rate of return
Main article: Internal rate of return The 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 (DCFROR) or simply the rate of return (ROR). In the context of savings and loans the IRR is also called the effective interest rate. The term internal refers toThe internal rate of return (IRR), also known as the dollar-weighted rate of return, is defined as the value(s) of that satisfies the following equation:
where:
- NPV = net present value In finance, the net present value or net present worth (NPW) of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows. In case when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the of the investment
- Ct = cashflow Cash flow is a generic term used differently depending on the context. It may be defined by users for their own purposes. It can refer to actual past flows, or to projected future flows. It can refer to the total of all the flows involved or to only a subset of those flows. Subset terms include 'net cash flow', operating cash flow and free cash at time t
When the rate of return r is smaller than the IRR rate , the investment is profitable, i.e., NPV > 0. Otherwise, the investment is not profitable.
Comparisons between various rates of return
Arithmetic and logarithmic return
The value of an investment is doubled over a year if the annual ROR or . The value falls to zero when or .
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, Vi | $100 | $100 | $100 | $100 | $100 |
|---|---|---|---|---|---|
| Final investment, Vf | $0 | $50 | $100 | $150 | $200 |
| Profit/loss, Vf − Vi | -$100 | -$50 | $0 | $50 | $100 |
| Arithmetic return, rarith | -100% | -50% | 0% | 50% | 100% |
| Logarithmic return, rlog | -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. [1] 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, geometric 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[citation needed] generated by or lost due to the investment. It measures the cash flow or income stream from the investment to the investor The term has taken on a specific meaning in finance to describe the particular types of people and companies that regularly purchase equity or debt securities for financial gain in exchange for funding an expanding company. Less frequently, the term is applied to parties who purchase real estate, currency, commodity derivatives, personal property, relative to the amount invested. Cash flow Cash flow is a generic term used differently depending on the context. It may be defined by users for their own purposes. It can refer to actual past flows, or to projected future flows. It can refer to the total of all the flows involved or to only a subset of those flows. Subset terms include 'net cash flow', operating cash flow and free cash 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 yield The dividend yield or the dividend-price ratio on a company stock is the company's annual dividend payments divided by its market cap, or the dividend per share, divided by the price per share. It is often expressed as a percentage. Its reciprocal is the Price/Dividend ratio, Net profit margin Profit margin, net margin, net profit margin or net profit ratio all refer to a measure of profitability. It is calculated by finding the net profit as a percentage of the revenue, Return on equity Return on Equity (requity) measures the rate of return on the ownership interest (shareholders' equity) of the common stock owners. It measures a firm's efficiency at generating profits from every unit of shareholders' equity (also known as net assets or assets minus liabilities). ROE shows how well a company uses investment funds to generate, and Return on assets This number tells you what the company can do with what it has, i.e. how many dollars of earnings they derive from each dollar of assets they control. It's a useful number for comparing competing companies in the same industry. The number will vary widely across different industries. Return on assets gives an indication of the capital intensity of.[2]
- During capital budgeting Capital budgeting is the planning process used to determine whether a firm's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing. It is budget for major capital, or investment, expenditures, 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 value In finance, the net present value or net present worth (NPW) of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows. In case when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the, profitability index Profitability Index is also known as Profit Investment Ratio, abbreviated to P.I. and Value Investment Ratio . Profitability index is a good tool for ranking projects because it allows you to clearly identify the amount of value created per unit of investment, thus if you are capital constrained you wish to invest in those projects which create, and internal rate of return The 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 (DCFROR) or simply the rate of return (ROR). In the context of savings and loans the IRR is also called the effective interest rate. The term internal refers to for various projects. [3]
- A return may be adjusted for taxes To tax is to impose a financial charge or other levy upon a taxpayer (an individual or legal entity) by a state or the functional equivalent of a state such that failure to pay is punishable by law 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 inflation In 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 price level rises, each unit of currency buys fewer goods and services; consequently, inflation is also an erosion in the purchasing power of money – a loss of real value in the internal medium of exchange and unit to better indicate its true value in purchasing power Purchasing 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 power in the 1950s. Currency can be either a. Any investment with a nominal rate of return less than the annual inflation rate In 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 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 power Purchasing 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 power in the 1950s. Currency can be either a. If an ROI value is adjusted for inflation, it is stated explicitly, such as “The return, adjusted for inflation, was 2%.”
- Many online poker tools Poker tools are a variety of software or web-based applications that allow the statistical analysis of poker players, games or tournaments include ROI in a player's tracked statistics, assisting users in evaluating an opponent's profitability.
Cash or potential cash returns
Time value of money
Investments generate cash flow to the investor to compensate the investor for the time value of money For example, 100 dollars of today's money invested for one year and earning 5 percent interest will be worth 105 dollars after one year. Therefore, 100 dollars paid now or 105 dollars paid exactly one year from now both have the same value to the recipient who assumes 5 percent interest; using time value of money terminology, 100 dollars invested.
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 An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for deferring the use of funds and instead lending it to that banks Banking is generally a highly regulated industry, and government restrictions on financial activities by banks have varied over time and location. The current set of global bank capital standards are called Basel II. In some countries such as Germany, banks have historically owned major stakes in industrial corporations while in other countries offer for deposits 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 bank, and represent the amount owed by the bank to, and also in the interest rates that banks charge for loans such as home mortgages. The “risk-free The risk-free interest rate is the interest rate that it is assumed can be obtained by investing in financial instruments with no default risk. However, the financial instrument can carry other types of risk, e.g. market risk , liquidity risk (the risk of being unable to sell the instrument for cash at short notice without significant costs), etc” rate is the rate on U.S. Treasury Bills A United States Treasury security is a government debt issued by the United States Department of the Treasury through the Bureau of the Public Debt. Treasury securities are the debt financing instruments of the United States Federal government, and they are often referred to simply as Treasuries. There are four types of marketable treasury, 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 The discount rate is an interest rate a central bank charges depository institutions that borrow reserves from it. Each investment has a different discount rate, based on the cash flow expected in future from the investment. The higher the risk Risk concerns the deviation of one or more results of one or more future events from their expected value. Technically, the value of those results may be positive or negative. However, general usage tends to focus only on potential harm that may arise from a future event, which may accrue either from incurring a cost or by failing to attain some, the higher the discount rate (rate of return) the investor will demand from the investment.
Compounding or reinvesting
Compound 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 . A loan, for example, may have its interest compounded every month: in this case, a loan with $100 initial principal and 1% 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 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. However, it does not account for the possibility of account fees affecting the net gain. APY generally refers, 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 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 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. However, it does not account for the possibility of account fees affecting the net gain. APY generally refers or Future value Future value 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 function[citation needed] 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.
Returns when capital is at risk
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 volatility.” 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:
- Vi is the initial investment ($100)
- Vf is the final value ($103.02)
- .
Mutual fund and investment company returns
Mutual funds A mutual fund is a professionally managed type of collective investment scheme that pools money from many investors and invests typically in investment securities . The mutual fund will have a fund manager that trades (buys and sells) the fund's investments in accordance with the fund's investment objective. In the U.S., a fund registered with the, exchange-traded funds (ETFs), and other equitized investments (such as unit investment trusts or UITs, insurance separate accounts 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 affect 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.
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.
- .
- .
- .
- .
- .
Total Return = ((Final Price x Last Reinvestment Factor) - Beginning Price) / Beginning Price
Average annual total return (geometric)
Average Annual Return (geometric) US mutual funds are to compute total return as proscribed 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:[4]
P(1+T)n = ERV
Where:
P = a hypothetical initial investment 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).
Example
| 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% return. An investor who did not reinvest received total cash payments 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.
See also
- Average for a discussion of annualization of returns.
- Compound interest
- Capital budgeting
- Compound annual growth rate
- Dollar cost averaging
- Economic value added
- Expected return
- Internal rate of return
- Net Present Value
- Rate of profit
- Return on assets
- Return on capital
- Return of capital
- Value investing
References
- ^ Damato,Karen. Doing the Math: Tech Investors' Road to Recovery is Long. Wall Street Journal, pp.C1-C19, May 18, 2001
- ^ A. A. Groppelli and Ehsan Nikbakht (2000). Barron's Finance, 4th Edition. New York. pp. 442–456. ISBN 0-7641-1275-9.
- ^ Barron's Finance. pp. 151–163.
- ^ U.S. Securities and Exchange Commission (1998). [http://www.sec.gov/rules/final/33-7512f.htm#E12E2 "Final Rule: Registration Form Used by Open-End Management Investment Companies: Sample Form and instructions"]. http://www.sec.gov/rules/final/33-7512f.htm#E12E2.
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
External links
Categories: Financial ratios | Basic financial concepts
|
Tue, 27 Jul 2010 15:30:04 GMT+00:00
Lexology (registration) In a surprising development, the Act makes permanent the increase in the deposit insurance coverage limit of $25000 that was otherwise scheduled to return ... Bond Rating Agencies Now Held Liable, Which Is a Good Thing Seeking Alpha (blog) Executive compensation, corporate governance and other securities disclosure ... Lexology (registration) Regulations, not regulators, needed ; market view istockAnalyst.com (press release)
admin
ue, 22 Jun 2010 17:51:20 GM
I know of NO other method of investing, be it real estate, or some other form of investing all together different from real estate that offers NO risk in . return. for such an awesome profit potential! I mean WHAT A . RETURN. ON OUR ...
Q. I've had the new 2009 corolla over a month now and because no one will finance me they want me to bring back the car. Do I get my old car back? What about the transfer back? Gas? What am I to expect when I do bring the car back; don't know anything about it.
Asked by Yvonne - Wed Sep 3 12:57:55 2008 - - 2 Answers - 0 Comments
A. Sounds like you let them talk you into a "drive-off sale" which means it's contingent on financing approval. Read the paperwork you signed - what does it say about financing refusal?
Answered by jlf - Wed Sep 3 15:28:04 2008


