RETURN ON INVESTMENT : Comprehensive Encyclopedia

This article or section is in need of attention from an expert on the subject.
Please help recruit one or improve this article yourself. See the talk page for details.
Please consider using {{Expert-subject}} to associate this request with a WikiProject

It has been suggested that Rate of return on investment be merged into this article or section. (Discuss)

In finance, rate of return (ROR) or return on investment (ROI), or sometimes just return, is a comparison of the money earned (or lost) on an investment to the amount of money invested.

[edit] Income from Investment

Rate of Return or Return on Investment (ROI) is the ratio of money gained or lost on an investment 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 also known as rate of profit, rate of return or return. Return can also refer to the dollar amount of gain or loss. ROI is the return on a past or current investment, or the estimated return on a future investment. ROI is usually given as a percent rather than decimal value.

ROI does not indicate how long an investment is held. However, ROI is most often stated as an annual or annualized rate of return, and it is most often stated for a calendar or fiscal year. In this article, “ROI” indicates an annual or annualized rate of return, unless otherwise noted.

ROI is used to compare returns on investments where the money gained or lost -- or the money invested – are not easily compared using dollar values. For instance, a $1,000 investment that earns $50 in interest obviously generates more cash than a $100 investment that earns $20 in interest, but the $100 investment earns a higher return on investment.

[edit] Arithmetic Return

[edit] Cash Flow (Income Stream)

ROI is a measure of cash (or potential cash) generated by an investment, or the cash lost due to the investment. It measures the cash flow or income stream from the investment to the investor.

Cash flow to the investor can be in the form of profit, interest, dividends, or capital gain/loss. Capital gain/loss occurs when the market value or resale value of the investment increases or decreases. Cash flow does not include the return of invested capital.

[edit] Annual Returns

An Annual Rate of Return is the return on an investment over a one-year period, such as January 1st through December 31st, or June 3rd 2006 through June 2nd 2007. Each ROI in the cash flow example above is an annual rate of return.

An Annualized Rate of Return is the return on an investment over a period other than one year (such as a month, or two years) multiplied or divided to give a comparable one-year return. For instance, a one-month ROI of 1% could be stated as an annualized rate of return of approximately 12%. Or a two-year ROI of 10% could be stated as an annualized rate of return of approximately 5%.

In the cash flow example above, the dollar returns for the four years add up to $215. The annualized rate of return for the four years is approximately $215/($1,000 x 4 years) = 5.375% ROI.

[edit] Yield

In financial economics, the term yield indicates a rate of return that is based on compounding, reinvestment, and/or the changing market value of a security. Effective annual rate (EAR) or Annual percentage yield APY indicates an annual compound yield.

Yield indicates that the amount of money invested increases or decreases during the investment period.

[edit] ROI Calculations for Various Uses

ROI values typically used for personal financial decisions include Annual Rate of Return and Annualized Rate of Return. For risk-free investments such as savings accounts or Certificates of Deposit, it’s useful to consider the effects of reinvesting/compounding on increasing savings balances over time. For risky investments such as stock shares, mutual fund shares and home purchases, in which capital is at risk, it’s also useful to consider the effects of price volatility and capital gain/loss on ROI.

ROI values typically used within a company to select which projects to pursue in order to generate cash flow into the company include Average rate of return, Net present value, Profitability index, and Internal rate of return.

[edit] Cash or Potential Cash Returns

[edit] Time Value of Money

Investments generate cash flow to the investor to compensate the investor for the time value of money.

A dollar in cash is worth less today than it was yesterday, and worth more today than it will be worth tomorrow. The value of cash decreases over time due to inflation, uncertainty about the future (risk), and the preference for current cash to pay everyday expenses or invest elsewhere.

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 banks offer for deposits, 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.

Any investment with an ROI less than the annual inflation rate represents a loss of value, even though the ROI might well be greater than 0%. When ROI is adjusted for inflation, the resulting return is considered an increase or decrease in purchasing power. If an ROI value is adjusted for inflation, it’s stated explicitly, such as “The return, adjusted for inflation, was 2%.”

[edit] Compounding or Reinvesting

Compound interest 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. Since investors are not risking losing their capital on a bad investment, they earn a quite low rate of return. But their capital steadily increases.

[edit] 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.

A stock share is partial ownership of a company, and the value of the stock depends on many factors, including the likelihood that the company will pay a dividend (a distribution of profit to shareholders). When stock shares are first offered for sale, the company receives the capital from the stock purchaser and uses the capital to operate its business. Once stock shares are sold to investors, the investors can sell the shares to other investors. Publicly-traded companies’ stock shares are bought and sold (traded) on the stock markets.

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.

[edit] Holding Period Return

Holding-Period Return = (Ending Price – Beginning Price + Cash Dividend) / Beginning Price.

The following is an example of a stock investment of one share purchased at the beginning of the year for $100.

Note that at the end of the first quarter the stock price is $98. This is a capital loss. The stock share bought for $100 can only be sold for $98, which is the value of the investment at the end of the first quarter. The first quarter return is:

($99 ending price - $100 beginning price + $4 dividends) / $100 beginning price = 3% ROI.

($95 ending price - $100 beginning price + $4 dividends) / $100 beginning price = -1% ROI.

[edit] Reinvestment When Capital is at Risk: Rate of Return and Yield

Yield is the compound rate of return that includes the effect of reinvesting interest/dividends.

The following 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 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.

($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 American 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:

$ROI_{Log} = \ln\left(\frac{V_f}{V_i}\right) = \ln\left(\frac{103.02}{100}\right) = 2.98%$ .

[edit] Average Returns When Capital Is at Risk

Most Average Returns that are published by financial institutions are actually Annualized Returns. Some published "Average Returns" are actually a geometric average of a type of compound yield (e.g. Mutual Fund Average Annual Total Returns).

When Average Returns are calculated by averaging periodic percentage returns, the results can be misleading.

There are three common ways investment returns are calculated over multiple periods of time

All of these calculations entail calculating averages of periodic percentage returns. None will accurately translate to dollar gains or losses if percent losses are averaged with percent gains.

Of course a 10% loss on a $100 investment is a $10 loss, and a 10% gain on a $100 investment is a 10% gain. But 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% dollar loss. The order in which the loss and gain occurs does not effect the result. A 50% gain and a 50% loss is a 25% loss. An 80% gain and 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’s important to note that most "Average Returns" are Annualized Returns.

Without getting into complex mathematics, here are some examples of what can happen to a 4-year $100 investment with an Arithmetic Average Rate of Return of 5%:

[edit] Annualized Rate of Return

Annualized returns express the rate of return over a given time period on an annual basis, or a return per year. Reference Source

[edit] Mutual Fund Returns

Mutual Funds and Exchange Traded Funds (ETFs) hold portfolios of various companies' stock shares. When the companies pay a dividend, and when the fund trades shares, dividends and capital gains are distributed to the mutual fund shareholders. Mutual funds trade at the net asset value of the stock shares.

[edit] Total Returns

Mutual funds report total returns based on reinvestment factors. Reinvestment 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

[edit] Average Annual Return (geometric)

[edit] Example

Average Annual Return (geometric) = (((28.19)/100)+1) ^ (1/5)) – 1) x 100 = 5.09%

After 5 years, an investor who reinvested owned 1.26916 share valued at $101 per share ($128.19 in value). ($128.19-$100)/$100/5 = 5.638% yield.

After 5 years, an investor who did not reinvest received a total of $27 in dividends and $1 in capital gain. ($27+$1)/$100/5 = 5.600% return.

Mutual funds include capital gains as well as dividends in their return calculations. Since the market price of a mutual fund share is based on net asset value, a capital gain distribution is offset by an equal decrease in mutual fund share value/price. From the shareholder's perspective, a capital gain distribution is not a net gain in assets, but it is a realized capital gain.

[edit] Logarithmic or Continuously Compounded Return

Academics use in their research natural log return called logarithmic return or continuously compounded return. The continuously compounded return is asymmetric thus clearly indicating that positive and negative percent returns are not equal. A 10% return results in 9.53% continuously compounded return while a -10% results in -10.53%. This clearly indicates that the investment will result in a dollar amount loss corresponding to the difference between the two numbers: 1%.

[edit] Exponential Decay of Returns

Exponential Decay of Returns is a gambling concept, based on random probability. It can be expected that the larger amount of capital employed, the lower the amount of return. For example, the difference between gambling in the Powerball lottery and investing in the entire world marketable equity market. If one were to win the Powerball when it is paying instantly somewhere around $300,000,000, the rate of return would be 30,000,000,000% -- but the probability of winning this amount is miniscule. Most gamblers lose money on gambling. If one were to own all of the marketable equity in the world, the return would be somewhere around 6% annually (give or take).

[edit] 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.

RETURN ON INVESTMENT

Contents