6085:
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
6072:
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 rulemaking to require mutual funds to publish in their annual prospectus, among other things, total returns before and after the impact of US federal individual income taxes. And further, the after-tax returns would include 1) returns on a hypothetical taxable account after deducting
6068:(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.
3599:
36:
5200:. For nominal risk investments such as savings accounts or Certificates of Deposit, the investor considers the effects of reinvesting/compounding on increasing savings balances over time to project expected gains into the future. For investments in which capital is at risk, such as stock shares, mutual fund shares and home purchases, the investor also takes into consideration the effects of price volatility and risk of loss.
5447:(CD) that pays an annual interest rate of 4%, paid quarterly, the CD would earn 1% interest per quarter on the account balance. The account uses compound interest, meaning the account balance is cumulative, including interest previously reinvested and credited to the account. Unless the interest is withdrawn at the end of each quarter, it will earn more interest in the next quarter.
6081:
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 funds and brokerage firms are now providing personalized account returns on investor's account statements in response to this need.
2856:
6106:
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
6080:
Lastly, in more recent years, "personalized" brokerage account statements have been demanded by investors. In other words, the investors are saying more or less that the fund returns may not be what their actual account returns are, based upon the actual investment account transaction history. This
6076:
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
412:
For example, if someone purchases 100 shares at a starting price of 10, the starting value is 100 x 10 = 1,000. If the shareholder then collects 0.50 per share in cash dividends, and the ending share price is 9.80, then at the end the shareholder has 100 x 0.50 = 50 in cash, plus 100 x 9.80 = 980 in
6279:
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
4120:
Ordinary returns and logarithmic returns are only equal when they are zero, but they are approximately equal when they are small. 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
3667:
also takes cash flows into consideration. They are useful evaluating and comparing cases where the money manager controls cash flows, for example private equity. (Contrast with the true time-weighted rate of return, which is most applicable to measure the performance of a money manager who does not
6084:
With that out of the way, here is 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
5602:
As explained above, the return, or rate or return, depends on the currency of measurement. In the example given above, a US dollar cash deposit which returns 2% over a year, measured in US dollars, returns 12.2% measured in
Japanese yen, over the same period, if the US dollar increases in value by
5237:
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
4409:
Logarithmic returns are symmetric, while ordinary returns are not: positive and negative percent ordinary returns of equal magnitude do not cancel each other out and result in a net change, but logarithmic returns of equal magnitude but opposite signs will cancel each other out. This means that an
238:
The overall period may, however, instead be divided into contiguous subperiods. This means that there is more than one time period, each sub-period beginning at the point in time where the previous one ended. In such a case, where there are multiple contiguous subperiods, the return or the holding
5114:
Care must be taken not to confuse annual with annualized returns. An annual rate of return is a return over a period of one year, such as
January 1 through December 31, or June 3, 2006, through June 2, 2007, whereas an annualized rate of return is a rate of return per year, measured over a period
687:
For example, let us suppose that US$ 20,000 is returned on an initial investment of US$ 100,000. This is a return of US$ 20,000 divided by US$ 100,000, which equals 20 percent. The US$ 20,000 is paid in 5 irregularly-timed installments of US$ 4,000, with no reinvestment, over a 5-year period, and
6063:
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
5808:
Investments carry varying amounts of risk that the investor will lose some or all of the invested capital. For example, investments in company stock shares put capital at risk. Unlike capital invested in a savings account, the share price, which is the market value of a stock share at a certain
5765:
A portfolio increases in value in
Singapore dollars by 10% over the 2015 calendar year (with no flows in or out of the portfolio over the year). In the first month of 2016, it increases in value by another 7%, in US dollars. (Again, there are no inflows or outflows over the January 2016 period.)
5541:
At the beginning of the second quarter, the account balance is $ 1,010.00, which then earns $ 10.10 interest altogether during the second quarter. The extra dime was interest on the additional $ 10 investment from the previous interest accumulated in the account. The annualized return (annual
6505:
An investor who did not reinvest would have received total distributions (cash payments) of $ 5.78 per share. The return over the five-year period for such an investor would be ($ 19.90 + $ 5.78) / $ 14.21 − 1 = 80.72%, and the arithmetic average rate of return would be 80.72%/5 = 16.14% per
2864:
In cases where there are inflows and outflows, the formula applies by definition for time-weighted returns, but not in general for money-weighted returns (combining the logarithms of the growth factors based on money-weighted returns over successive periods does not generally conform to this
5747:
This holds true if either the time-weighted method is used, or there are no flows in or out over the period. If using one of the money-weighted methods, and there are flows, it is necessary to recalculate the return in the second currency using one of the methods for compensating for flows.
6071:
Subsequent to this, apparently investors who had 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
3257:
576:
This is the rate of return experienced either by an investor who starts with yen, converts to dollars, invests in the USD deposit, and converts the eventual proceeds back to yen; or for any investor, who wishes to measure the return in
Japanese yen terms, for comparison purposes.
480:
The return, or rate of return, depends on the currency of measurement. For example, suppose a US$ 10,000 (US dollar) cash deposit earns 2% interest over a year, so its value at the end of the year is US$ 10,200 including interest. The return over the year is 2%, measured in USD.
6119:(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:
1100:
Note that this does not apply to interest rates or yields where there is no significant risk involved. It is common practice to quote an annualized rate of return for borrowing or lending money for periods shorter than a year, such as overnight interbank rates.
4646:
For example, a return of +10%, followed by −10%, gives an arithmetic average return of 0%, but the overall result over the 2 subperiods is 110% x 90% = 99% for an overall return of −1%. The order in which the loss and gain occurs does not affect the result.
468:
A negative initial value usually occurs for a liability or short position. If the initial value is negative, and the final value is more negative, then the return will be positive. In such a case, the positive return represents a loss rather than a profit.
4410:
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 a logarithmic return of −50% will come back to $ 100.
6020:
To calculate the capital gain for US income tax purposes, include the reinvested dividends in the cost basis. The investor received a total of $ 4.06 in dividends over the year, all of which were reinvested, so the cost basis increased by $ 4.06.
2257:
5756:
It is not meaningful to compound together returns for consecutive periods measured in different currencies. Before compounding together returns over consecutive periods, recalculate or adjust the returns using a single currency of measurement.
3584:
To measure returns net of fees, allow the value of the portfolio to be reduced by the amount of the fees. To calculate returns gross of fees, compensate for them by treating them as an external flow, and exclude accrued fees from valuations.
3021:
4659:
This pattern is not followed in the case of logarithmic returns, due to their symmetry, as noted above. A logarithmic return of +10%, followed by −10%, gives an overall return of 10% − 10% = 0% and an average rate of return of zero also.
5121:
For example, a return over one month of 1% converts to an annualized rate of return of 12.7% = ((1+0.01) − 1). This means if reinvested, earning 1% return every month, the return over 12 months would compound to give a return of 12.7%.
6032:
For U.S. income tax purposes therefore, dividends were $ 4.06, the cost basis of the investment was $ 104.06 and if the shares were sold at the end of the year, the sale value would be $ 103.02, and the capital loss would be $ 1.04.
6089:
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
2664:
5809:
point in time, depends on what someone is willing to pay for it, and the price of a stock share tends to change continually when the market for that share is open. If the price is relatively stable, the stock is said to have "low
5431:
The annualized return of an investment depends on whether or not the return, including interest and dividends, from one period is reinvested in the next period. If the return is reinvested, it contributes to the starting value of
1295:
1096:
Annualizing a return over a period of less than one year might be interpreted as suggesting that the rest of the year is most likely to have the same rate of return, effectively projecting that rate of return over the whole year.
5125:
As another example, a two-year return of 10% converts to an annualized rate of return of 4.88% = ((1+0.1) − 1), assuming reinvestment at the end of the first year. In other words, the geometric average return per year is 4.88%.
3266:
periods, converted into a rate of return per period. Where the individual sub-periods are each equal (say, 1 year), and there is reinvestment of returns, the annualized cumulative return is the geometric average rate of return.
3985:
Note that the money-weighted return over multiple sub-periods is generally not equal to the result of combining the money-weighted returns within the sub-periods using the method described above, unlike time-weighted returns.
5273:
Investors usually seek a higher rate of return on taxable investment returns than on non-taxable investment returns, and the proper way to compare returns taxed at different rates of tax is after tax, from the end-investor's
4620:
3496:
1200:
5129:
In the cash flow example below, the dollar returns for the four years add up to $ 265. Assuming no reinvestment, the annualized rate of return for the four years is: $ 265 ÷ ($ 1,000 x 4 years) = 6.625% (per year).
3803:
484:
Let us suppose also that the exchange rate to
Japanese yen at the start of the year is 120 yen per USD, and 132 yen per USD at the end of the year. The value in yen of one USD has increased by 10% over the period.
184:
To compare returns over time periods of different lengths on an equal basis, it is useful to convert each return into a return over a period of time of a standard length. The result of the conversion is called the
2367:
3063:
3569:
In the presence of external flows, such as cash or securities moving into or out of the portfolio, the return should be calculated by compensating for these movements. This is achieved using methods such as the
6270:
3576:. Time-weighted returns compensate for the impact of cash flows. This is useful to assess the performance of a money manager on behalf of his/her clients, where typically the clients control these cash flows.
3375:
1685:
5603:
10% against the
Japanese yen over the same period. The return in Japanese yen is the result of compounding the 2% US dollar return on the cash deposit with the 10% return on US dollars against Japanese yen:
5360:, i.e. the uncertainty of returns (including how likely it is that investors will receive interest/dividend payments they expect and the return of their full capital, with or without any possible additional
1092:
This is because an annualized rate of return over a period of less than one year is statistically unlikely to be indicative of the annualized rate of return over the long run, where there is risk involved.
571:
5775:
If the return in 2015 was 10% in
Singapore dollars, and the Singapore dollar rose by 5% against the US dollar over 2015, then so long as there were no flows in 2015, the return over 2015 in US dollars is:
6014:
1460:
For example, if a stock is priced at US$ 3.570 per share at the close on one day, and at US$ 3.575 per share at the close the next day, then the logarithmic return is: ln(3.575/3.570) = 0.0014, or 0.14%.
4634:
The geometric average rate of return is in general less than the arithmetic average return. The two averages are equal if (and only if) all the sub-period returns are equal. This is a consequence of the
1948:
1745:
For example, if the logarithmic return of a security per trading day is 0.14%, assuming 250 trading days in a year, then the annualized logarithmic rate of return is 0.14%/(1/250) = 0.14% x 250 = 35%
938:
5222:
of different projects to decide which projects to pursue in order to maximize returns for the company's stockholders. Other tools employed by companies in capital budgeting include payback period,
2618:
1619:
6499:
After five years, an investor who reinvested all distributions would own 91.314 shares valued at $ 19.90 per share. The return over the five-year period is $ 19.90 × 91.314 / $ 1,000 − 1 = 81.71%
6179:
1389:
2490:
6195:
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)
342:
4069:= -100%. The ordinary return can be calculated for any non-zero initial investment value, and any final value, positive or negative, but the logarithmic return can only be calculated when
488:
The deposit is worth 1.2 million yen at the start of the year, and 10,200 x 132 = 1,346,400 yen at the end of the year. The return on the deposit over the year in yen terms is therefore:
3554:
4413:
Logarithmic return is also called the continuously compounded return. This means that the frequency of compounding does not matter, making returns of different assets easier to compare.
5104:
6734:
4953:
455:
2072:
1872:
6289:
Example: Balanced mutual fund during boom times with regular annual dividends, reinvested at time of distribution, initial investment $ 1,000 at end of year 0, share price $ 14.21
988:
5679:
4496:
4455:
5592:
4668:
Investment returns are often published as "average returns". In order to translate average returns into overall returns, compound the average returns over the number of periods.
4802:
4531:
4377:
4047:
2656:
1720:
1537:
1502:
1430:
4115:
3944:), the investment adds value, i.e. the net present value of cash flows, discounted at the cost of capital, is greater than zero. Otherwise, the investment does not add value.
2861:
This formula applies with an assumption of reinvestment of returns and it means that successive logarithmic returns can be summed, i.e. that logarithmic returns are additive.
682:
2149:
4656:
In cases of leveraged investments, even more extreme results are possible: A return of +200%, followed by −200%, has an average return of 0% but an overall return of −300%.
3975:
6932:
Hudson, Robert; Gregoriou, Andros (2010-02-07). "Calculating and
Comparing Security Returns is Harder than you Think: A Comparison between Logarithmic and Simple Returns".
807:
3977:
depends on the pattern of cash flows). There may also be more than one real solution to the equation, requiring some interpretation to determine the most appropriate one.
3029:
This formula can also be used when there is no reinvestment of returns, any losses are made good by topping up the capital investment and all periods are of equal length.
4272:
2903:
1753:
When the return is calculated over a series of sub-periods of time, the return in each sub-period is based on the investment value at the beginning of the sub-period.
6763:
5203:
Ratios typically used by financial analysts to compare a company's performance over time or compare performance between companies include return on investment (ROI),
3930:
3901:
3846:
2141:
2108:
5741:
5712:
4207:
4155:
1821:
406:
375:
5440:
reflects the effect of the return in one period on the return in the next period, resulting from the change in the capital base at the start of the latter period.
6789:
3872:
2851:{\displaystyle R_{\mathrm {log} }=\sum _{i=1}^{n}R_{\mathrm {log} ,i}=R_{\mathrm {log} ,1}+R_{\mathrm {log} ,2}+R_{\mathrm {log} ,3}+\cdots +R_{\mathrm {log} ,n}}
1978:
4317:
4067:
4012:
3708:
2895:
2517:
2418:
2398:
2021:
1998:
1794:
1774:
1740:
1557:
1454:
1318:
1077:
1057:
1037:
1017:
850:
830:
753:
733:
713:
646:
623:
603:
277:
5303:, even when the nominal annual return is greater than 0%, and the purchasing power at the end of the period is less than the purchasing power at the beginning.
1215:
5542:
percentage yield, compound interest) is higher than for simple interest because the interest is reinvested as capital and then itself earns interest. The
5772:
The answer is that there is insufficient data to compute a return, in any currency, without knowing the return for both periods in the same currency.
3932:, net of any other flows at the beginning and at the end respectively. (The initial value is treated as an inflow, and the final value as an outflow.)
6280:
gain distribution is not a net gain in assets, but it is a realized capital gain (coupled with an equivalent decrease in unrealized capital gain).
3947:
Note that there is not always an internal rate of return for a particular set of cash flows (i.e. the existence of a real solution to the equation
4536:
3386:
1129:
6996:
3716:
3252:{\displaystyle {\bar {r}}_{\mathrm {geometric} }=\left(\prod _{i=1}^{n}(1+r_{i})\right)^{\frac {1}{n}}-1={\sqrt{\prod _{i=1}^{n}(1+r_{i})}}-1}
2265:
3043:
If compounding is performed, (i.e. if gains are reinvested and losses accumulated), and if all periods are of equal length, then using the
6056:
contracts, and bank-sponsored commingled funds, collective benefit funds or common trust funds, all derive their value from an underlying
7197:
6203:
5743:
is the return on the first currency against the second currency (which in our example is the return on US dollars against
Japanese yen).
3276:
1627:
7172:
6845:
168:. It may be measured either in absolute terms (e.g., dollars) or as a percentage of the amount invested. The latter is also called the
6812:
494:
5969:
7048:
6116:
6065:
6830:
5399:
5046:
The geometric average return over the 4-year period was −42.74%. Over 4 years, this translates back into an overall return of:
4639:. The difference between the annualized return and average annual return increases with the variance of the returns – the more
1980:
are reinvested, i.e. they are not withdrawn or paid out, then the value of the investment at the start of the second period is
1880:
6860:
7277:
6916:
6891:
4653:
A return of +100%, followed by −100%, has an average return of 0% but an overall return of −100% since the final value is 0.
2519:
over the overall time period using the time-weighted method is the result of compounding all of the growth factors together:
858:
152:(or securities, or other investments) which the investor receives from that investment over a specified time period, such as
100:
2525:
1565:
7024:
72:
6124:
7418:
5959:
The final investment value of $ 103.02 compared with the initial investment of $ 100 means the return is $ 3.02 or 3.02%.
5115:
either longer or shorter than one year, such as a month, or two years, annualized for comparison with a one-year return.
4895:
The geometric average return over the 4-year period was −1.64%. Over 4 years, this translates into an overall return of:
1326:
688:
with no information provided about the timing of the installments. The rate of return is 4,000 / 100,000 = 4% per year.
79:
7140:
7130:
7116:
7078:
6980:
6060:. Investors and other parties are interested to know how the investment has performed over various periods of time.
6049:
3646:
3038:
2423:
119:
17:
3628:
285:
5332:
Factors that investors may use to determine the rate of return at which they are willing to invest money include:
3270:
For example, assuming reinvestment, the cumulative return for four annual returns of 50%, -20%, 30%, and −40% is:
7348:
7099:
3620:
3507:
53:
5949:
To the right is an example of a stock investment of one share purchased at the beginning of the year for $ 100.
239:
period return over the overall period can be calculated by combining the returns within each of the subperiods.
86:
7423:
7165:
7092:
5052:
3624:
57:
7053:"Final Rule: Registration Form Used by Open-End Management Investment Companies: Sample Form and instructions"
5611:
In more general terms, the return in a second currency is the result of compounding together the two returns:
4650:
For a return of +20%, followed by −20%, this again has an average return of 0%, but an overall return of −4%.
7428:
6663:
6502:
Geometric average annual total return with reinvestment = ($ 19.90 × 91.314 / $ 1,000) ^ (1 / 5) − 1 = 12.69%
4901:
2377:, or geometric linking, or compounding together the holding period returns in the two successive subperiods.
416:
2029:
1829:
949:
68:
5617:
4460:
4419:
6532:
5549:
5406:
207:(ROI) is return per dollar invested. It is a measure of investment performance, as opposed to size (c.f.
4765:
4501:
4347:
4017:
2626:
2252:{\displaystyle (1+R_{1})(1+R_{2})=\left({\frac {B}{A}}\right)\left({\frac {C}{B}}\right)={\frac {C}{A}}}
1690:
1507:
1472:
1400:
7408:
7330:
1120:
216:
5310:
include ROI in a player's tracked statistics, assisting users in evaluating an opponent's performance.
4759:
The geometric average rate of return was 5%. Over 4 years, this translates into an overall return of:
4072:
654:
413:
shares, totalling a final value of 1,030. The change in value is 1,030 − 1,000 = 30, so the return is
7413:
7403:
7342:
7158:
3026:
This formula can be used on a sequence of logarithmic rates of return over equal successive periods.
177:
3950:
7289:
7135:
Carl Bacon. Practical
Portfolio Performance Measurement and Attribution. West Sussex: Wiley, 2003.
3609:
3016:{\displaystyle {\bar {r}}={\frac {1}{n}}\sum _{i=1}^{n}{r_{i}}={\frac {1}{n}}(r_{1}+\cdots +r_{n})}
761:
3686:(IRR) (which is a variety of money-weighted rate of return) is the rate of return which makes the
7433:
7376:
6831:"rate of return: definition of rate of return in Oxford dictionary (British & World English)"
6572:
6557:
6516:
5395:
5338:
5219:
4237:
3677:
3613:
46:
5444:
1115:
6957:
6883:
6816:
5417:, the higher the discount rate (rate of return) the investor will demand from the investment.
7301:
7283:
7226:
6739:
6657:
6577:
6567:
6552:
6542:
5769:
What is the return on the portfolio, from the beginning of 2015, to the end of January 2016?
5394:, and also in the interest rate that a bank charges for a loan such as a home mortgage. The "
5368:
3906:
3877:
3822:
2113:
2080:
192:
Typically, the period of time is a year, in which case the rate of return is also called the
169:
165:
6875:
93:
7365:
7318:
7215:
6627:
6547:
5810:
5803:
5719:
5690:
4640:
4636:
4625:
The use of logarithmic returns prevents investment prices in models from becoming negative.
4185:
4133:
3572:
3044:
2374:
1799:
384:
353:
204:
5118:
The appropriate method of annualization depends on whether returns are reinvested or not.
4125:
Comparison of ordinary returns and logarithmic returns for an initial investment of $ 100
8:
7255:
7203:
6768:
6622:
6617:
6612:
6057:
5405:
The rate of return which an investor requires from a particular investment is called the
5326:
5320:
5227:
3855:
1957:
235:, can be calculated over a single period. The single period may last any length of time.
141:
6990:
6945:
5784:
The return between the beginning of 2015 and the end of January 2016 in US dollars is:
4302:
4052:
3997:
3693:
2880:
2502:
2403:
2383:
2006:
1983:
1779:
1759:
1725:
1542:
1439:
1303:
1290:{\displaystyle r_{\mathrm {log} }={\frac {\ln \left({\frac {V_{f}}{V_{i}}}\right)}{t}}}
1062:
1042:
1022:
1002:
835:
815:
738:
718:
698:
631:
608:
588:
262:
6077:
only to taxable accounts and not to tax-deferred or retirement accounts such as IRAs.
5714:
is the return on the investment in the first currency (US dollars in our example), and
7354:
7324:
7192:
7136:
7126:
7112:
7088:
7074:
7052:
6976:
6953:
6949:
6912:
6887:
6876:
6607:
6597:
6582:
6537:
6527:
5437:
5433:
5426:
5223:
5215:
3687:
692:
7336:
7312:
7266:
6937:
6602:
6053:
6045:
5288:
5208:
5204:
4498:
are logarithmic returns in successive periods, then the overall logarithmic return
3262:
The geometric average return is equivalent to the cumulative return over the whole
1796:. If there are no inflows or outflows during the period, the holding period return
1469:
Under an assumption of reinvestment, the relationship between a logarithmic return
212:
208:
157:
7181:
6813:"return: definition of return in Oxford dictionary (British & World English)"
6637:
6632:
6562:
6091:
5410:
5391:
3937:
1082:
According to the CFA Institute's Global Investment Performance Standards (GIPS),
465:
Return measures the increase in size of an asset or liability or short position.
6115:
US mutual funds are to compute average annual total return as prescribed by the
5822:
Example: Stock with low volatility and a regular quarterly dividend, reinvested
5436:
invested for the next period (or reduces it, in the case of a negative return).
5325:
Investments generate returns to the investor to compensate the investor for the
7231:
7221:
6592:
5414:
5355:
5296:
4121:
an arithmetic return of −50% is equivalent to a logarithmic return of −69.31%.
3049:
5813:". If the price often changes a great deal, the stock has "high volatility".
4629:
7397:
7382:
7371:
7307:
6587:
5956:
The number of shares purchased each quarter = ($ Dividend)/($ Stock Price).
5383:
4615:{\displaystyle R_{\mathrm {log} }=R_{\mathrm {log} ,1}+R_{\mathrm {log} ,2}}
7360:
6073:
5361:
3491:{\displaystyle {\sqrt{(1+0.50)(1-0.20)(1+0.30)(1-0.40)}}-1=-0.0164=-1.64\%}
6791:) the terms have an arithmetic average of 100% but product less than 100%.
1195:{\displaystyle R_{\mathrm {log} }=\ln \left({\frac {V_{f}}{V_{i}}}\right)}
7261:
6941:
6041:
5307:
3798:{\displaystyle {\mbox{NPV}}=\sum _{t=0}^{n}{\frac {C_{t}}{(1+r)^{t}}}=0}
3501:
The annualized cumulative return and geometric return are related thus:
2623:
If the returns are logarithmic returns, however, the logarithmic return
7047:
149:
145:
5402:, because this is the highest rate available without risking capital.
2362:{\displaystyle (1+R_{1})(1+R_{2})-1={\frac {C}{A}}-1={\frac {C-A}{A}}}
943:
For example, a 33.1% return over 3 months is equivalent to a rate of:
7295:
7271:
7237:
5346:
5280:
3849:
161:
5953:
The quarterly dividend is reinvested at the quarter-end stock price.
3989:
3598:
35:
7249:
7150:
5291:
between the start and the end of the period. Any investment with a
1087:"Returns for periods of less than one year must not be annualized."
153:
6970:
6265:{\displaystyle \mathrm {T=\left({\frac {ERV}{P}}\right)^{1/n}-1} }
6028:
Capital gain/loss = $ 103.02 − $ 104.06 = -$ 1.04 (a capital loss)
4049:= ln($ 200 / $ 100) = ln(2) = 69.3%. The value falls to zero when
3980:
3370:{\displaystyle (1+0.50)(1-0.20)(1+0.30)(1-0.40)-1=-0.0640=-6.40\%}
2003:
If the value of the investment at the end of the second period is
1680:{\displaystyle r_{\mathrm {log} }={\frac {R_{\mathrm {log} }}{t}}}
6521:
5751:
133:
1104:
472:
If the initial value is zero, then no return can be calculated.
7243:
7025:"Time Value of Money - How to Calculate the PV and FV of Money"
566:{\displaystyle {\frac {1,346,400-1,200,000}{1,200,000}}=12.2\%}
5962:
The continuously compounded rate of return in this example is:
5258:
A return of 10% taxed at 25% gives an after-tax return of 7.5%
5241:
A return of 5% taxed at 15% gives an after-tax return of 4.25%
4959:
Example #3 Highly volatile rates of return, including losses
3559:
2400:
periods, assuming returns are reinvested, if the returns over
691:
Assuming returns are reinvested however, due to the effect of
7209:
6036:
6009:{\displaystyle \ln \left({\frac {103.02}{100}}\right)=2.98\%}
2369:
is the holding period return over the two successive periods.
2000:, i.e. the same as the value at the end of the first period.
148:. It comprises any change in value of the investment, and/or
6911:. Mason, Ohio: South-Western Cengage Learning. p. 527.
6415:
Total distribution (distribution per share x shares owned)
5387:
4630:
Comparing geometric with arithmetic average rates of return
6110:
1687:
is the annualized logarithmic rate of return for a return
7097:
Richard A. Brealey, Stewart C. Myers and Franklin Allen.
6274:
6086:
5234:
1943:{\displaystyle 1+R_{1}=1+{\frac {B-A}{A}}={\frac {B}{A}}}
196:, and the conversion process, described below, is called
6843:
Overview of the Global Investment Performance Standards
5283:. When return is adjusted for inflation, the resulting
5109:
1756:
Suppose the value of the investment at the beginning is
4808:
Example #2 Volatile rates of return, including losses
4533:
is the sum of the individual logarithmic returns, i.e.
4416:
Logarithmic returns are time-additive, meaning that if
2077:
Multiplying together the growth factors in each period
933:{\displaystyle r=(1+R)^{\frac {1}{t}}-1={\sqrt{1+R}}-1}
7073:. New York: Barron's Educational Series, Inc., 2000.
5816:
5374:
whether or not the investors want the money available
5295:(i.e., unadjusted annual return) less than the annual
4663:
3955:
3721:
2613:{\displaystyle 1+R=(1+R_{1})(1+R_{2})\cdots (1+R_{n})}
1614:{\displaystyle R_{\mathrm {log} }=r_{\mathrm {log} }t}
1464:
999:
is the process described above of converting a return
6771:
6742:
6666:
6206:
6127:
5972:
5722:
5693:
5620:
5552:
5443:
For example, if an investor puts $ 1,000 in a 1-year
5055:
4904:
4768:
4539:
4504:
4463:
4422:
4350:
4305:
4240:
4188:
4136:
4075:
4055:
4020:
4000:
3953:
3936:
When the internal rate of return is greater than the
3909:
3880:
3858:
3825:
3719:
3696:
3510:
3389:
3279:
3066:
2906:
2883:
2667:
2629:
2528:
2505:
2426:
2406:
2386:
2268:
2152:
2116:
2083:
2032:
2023:, the holding period return in the second period is:
2009:
1986:
1960:
1883:
1832:
1802:
1782:
1762:
1728:
1693:
1630:
1568:
1545:
1510:
1475:
1442:
1403:
1329:
1306:
1218:
1132:
1065:
1045:
1025:
1005:
952:
861:
838:
818:
764:
741:
721:
701:
657:
634:
611:
591:
497:
419:
387:
356:
288:
265:
181:, assuming the amount invested is greater than zero.
6174:{\displaystyle \mathrm {P\left(1+T\right)^{n}=ERV} }
3994:
The value of an investment is doubled if the return
2868:
5218:process, companies would traditionally compare the
3032:
60:. Unsourced material may be challenged and removed.
6909:Portfolio construction, management, and protection
6783:
6757:
6728:
6264:
6173:
6008:
5792:
5735:
5706:
5673:
5586:
5098:
4947:
4796:
4614:
4525:
4490:
4449:
4371:
4311:
4266:
4201:
4149:
4109:
4061:
4041:
4006:
3969:
3924:
3895:
3866:
3840:
3797:
3702:
3548:
3490:
3369:
3251:
3015:
2889:
2850:
2650:
2612:
2511:
2484:
2412:
2392:
2361:
2251:
2135:
2102:
2066:
2015:
1992:
1972:
1942:
1866:
1815:
1788:
1768:
1734:
1714:
1679:
1613:
1551:
1531:
1496:
1448:
1424:
1384:{\displaystyle V_{f}=V_{i}e^{r_{\mathrm {log} }t}}
1383:
1312:
1289:
1194:
1071:
1051:
1031:
1011:
982:
932:
844:
824:
801:
747:
727:
707:
676:
640:
617:
597:
565:
449:
400:
369:
336:
271:
3990:Comparing ordinary return with logarithmic return
7395:
6064:performance returns of one fund to another, the
5546:or annualized return on the above investment is
3588:
3047:, the appropriate average rate of return is the
1748:
6931:
5409:, and is also referred to as the (opportunity)
5398:" rate on US dollar investments is the rate on
3981:Money-weighted return over multiple sub-periods
2485:{\displaystyle R_{1},R_{2},R_{3},\cdots ,R_{n}}
377:= final value, including dividends and interest
279:over a single period of any length of time is:
6455:Shares purchased (total distribution / price)
6186:P = a hypothetical initial payment of $ 1,000
5752:Foreign currency returns over multiple periods
337:{\displaystyle R={\frac {V_{f}-V_{i}}{V_{i}}}}
7166:
7111:. New York: McGraw-Hill Book Company, 1970.
5420:
4643:the performance, the greater the difference.
1105:Logarithmic or continuously compounded return
175:A loss instead of a profit is described as a
6858:
6524:for a discussion of annualization of returns
6044:, unit investment trusts or UITs, insurance
5382:The time value of money is reflected in the
2897:time periods of equal length is defined as:
1059:is measured in years and the rate of return
695:, the relationship between a rate of return
6971:A. A. Groppelli and Ehsan Nikbakht (2000).
5597:
3627:. Unsourced material may be challenged and
3560:Comparisons between various rates of return
3549:{\displaystyle {\sqrt{1-0.0640}}-1=-0.0164}
7173:
7159:
6995:: CS1 maint: location missing publisher (
6037:Mutual fund and investment company returns
3671:
475:
7083:Zvi Bodie, Alex Kane and Alan J. Marcus.
5099:{\displaystyle (1-0.4274)^{4}-1=-89.25\%}
3647:Learn how and when to remove this message
1950:is the growth factor in the first period.
460:
120:Learn how and when to remove this message
5134:Cash flow example on $ 1,000 investment
1776:, and at the end of the first period is
812:which can be used to convert the return
7049:U.S. Securities and Exchange Commission
6729:{\displaystyle (x+y)(x-y)=x^{2}-y^{2}.}
6117:U.S. Securities and Exchange Commission
6111:Average annual total return (geometric)
6066:U.S. Securities and Exchange Commission
5472:Capital at the beginning of the period
4948:{\displaystyle (1-0.0164)^{4}-1=-6.4\%}
450:{\displaystyle {\frac {30}{1,000}}=3\%}
14:
7396:
7087:. New York: McGraw-Hill/Irwin, 2004.
7085:Essentials of Investments, 5th Edition
6906:
6882:. Cambridge University Press. p.
6873:
6275:Mutual fund capital gain distributions
6048:and related variable products such as
6025:Cost Basis = $ 100 + $ 4.06 = $ 104.06
5797:
5314:
5196:Rates of return are useful for making
2067:{\displaystyle R_{2}={\frac {C-B}{B}}}
1867:{\displaystyle R_{1}={\frac {B-A}{A}}}
7278:Present value of growth opportunities
7198:Cyclically adjusted price-to-earnings
7154:
7107:Walter B. Meigs and Robert F. Meigs.
6878:Introductory Econometrics for Finance
5506:Account balance at end of the period
5110:Annual returns and annualized returns
3690:of cash flows zero. It is a solution
983:{\displaystyle {\sqrt{1.331}}-1=10\%}
27:Finance term; profit on an investment
7244:Enterprise value/gross cash invested
7180:
7069:A. A. Groppelli and Ehsan Nikbakht.
6333:Capital gain distribution per share
5674:{\displaystyle (1+r_{i})(1+r_{c})-1}
4491:{\displaystyle R_{\mathrm {log} ,2}}
4450:{\displaystyle R_{\mathrm {log} ,1}}
3940:, (which is also referred to as the
3625:adding citations to reliable sources
3592:
58:adding citations to reliable sources
29:
5817:US income tax on investment returns
5587:{\displaystyle 4.06\%=(1.01)^{4}-1}
4664:Average returns and overall returns
3710:satisfying the following equation:
3668:have control over external flows.)
3659:Like the time-weighted return, the
1465:Annualization of logarithmic return
1300:or equivalently it is the solution
585:Without any reinvestment, a return
252:The direct method to calculate the
24:
7123:Investment Performance Measurement
7063:
6752:
6250:
6232:
6228:
6225:
6222:
6208:
6167:
6164:
6161:
6153:
6144:
6129:
6094:of the fund shares investors own.
6003:
5556:
5093:
4942:
4797:{\displaystyle 1.05^{4}-1=21.55\%}
4791:
4672:Example #1 Level rates of return
4600:
4597:
4594:
4573:
4570:
4567:
4552:
4549:
4546:
4526:{\displaystyle R_{\mathrm {log} }}
4517:
4514:
4511:
4476:
4473:
4470:
4435:
4432:
4429:
4405:Advantages of logarithmic return:
4372:{\displaystyle r_{\mathrm {log} }}
4363:
4360:
4357:
4042:{\displaystyle r_{\mathrm {log} }}
4033:
4030:
4027:
3485:
3364:
3106:
3103:
3100:
3097:
3094:
3091:
3088:
3085:
3082:
2836:
2833:
2830:
2803:
2800:
2797:
2776:
2773:
2770:
2749:
2746:
2743:
2722:
2719:
2716:
2680:
2677:
2674:
2651:{\displaystyle R_{\mathrm {log} }}
2642:
2639:
2636:
1715:{\displaystyle R_{\mathrm {log} }}
1706:
1703:
1700:
1666:
1663:
1660:
1643:
1640:
1637:
1602:
1599:
1596:
1581:
1578:
1575:
1532:{\displaystyle r_{\mathrm {log} }}
1523:
1520:
1517:
1497:{\displaystyle R_{\mathrm {log} }}
1488:
1485:
1482:
1425:{\displaystyle r_{\mathrm {log} }}
1416:
1413:
1410:
1370:
1367:
1364:
1231:
1228:
1225:
1145:
1142:
1139:
977:
560:
444:
25:
7445:
7146:
7109:Financial Accounting, 4th Edition
6395:Shares owned before distribution
6050:variable universal life insurance
4997:Geometric average at end of year
4846:Geometric average at end of year
4710:Geometric average at end of year
3564:
3380:The geometric average return is:
3039:True time-weighted rate of return
2875:arithmetic average rate of return
2869:Arithmetic average rate of return
2658:over the overall time period is:
1504:and a logarithmic rate of return
1039:, where the length of the period
6475:Shares owned after distribution
6189:T = average annual total return
6097:
4110:{\displaystyle V_{f}/V_{i}>0}
3597:
3033:Geometric average rate of return
1539:over a period of time of length
677:{\displaystyle r={\frac {R}{t}}}
580:
242:
34:
7349:Risk-adjusted return on capital
7100:Principles of Corporate Finance
7041:
7017:
7003:
5793:Returns when capital is at risk
2420:successive time subperiods are
45:needs additional citations for
6975:. New York. pp. 442–456.
6964:
6925:
6900:
6867:
6859:John Simpson (6 August 2012).
6852:
6837:
6823:
6805:
6694:
6682:
6679:
6667:
6650:
5820:
5662:
5643:
5640:
5621:
5569:
5562:
5251:0.05 − 0.0075 = 0.0425 = 4.25%
5069:
5056:
4918:
4905:
3970:{\displaystyle {\mbox{NPV}}=0}
3874:, including the initial value
3777:
3764:
3665:dollar-weighted rate of return
3450:
3438:
3435:
3423:
3420:
3408:
3405:
3393:
3337:
3325:
3322:
3310:
3307:
3295:
3292:
3280:
3232:
3213:
3161:
3142:
3074:
3010:
2978:
2913:
2607:
2588:
2582:
2563:
2560:
2541:
2310:
2291:
2288:
2269:
2194:
2175:
2172:
2153:
1116:continuously compounded return
881:
868:
790:
777:
222:
13:
1:
7071:Barron's Finance, 4th Edition
6973:Barron's Finance, 4th Edition
6861:"CIPM Exam Tips & Tricks"
6798:
6353:Total distribution per share
5489:Dollar return for the period
5279:A return may be adjusted for
5233:A return may be adjusted for
3661:money-weighted rate of return
3589:Money-weighted rate of return
1749:Returns over multiple periods
993:per month with reinvestment.
832:to a compound rate of return
802:{\displaystyle 1+R=(1+r)^{t}}
7210:Cash return on cash invested
6435:Share price at distribution
6283:
1432:= logarithmic rate of return
1019:to an annual rate of return
7:
7029:Corporate Finance Institute
6533:Compound annual growth rate
6510:
6373:Share price at end of year
5299:represents a loss of value
5268:0.10 − 0.025 = 0.075 = 7.5%
4267:{\displaystyle V_{f}-V_{i}}
10:
7450:
7419:Factor income distribution
7331:Return on capital employed
7125:. New York: Wiley, 2003.
5801:
5788:1.155 x 1.07 − 1 = 23.585%
5760:
5451:Compound interest example
5424:
5421:Compounding or reinvesting
5318:
3675:
3036:
2373:This method is called the
1207:logarithmic rate of return
217:return on capital employed
7343:Return on tangible equity
7188:
7104:. McGraw-Hill/Irwin, 2006
2380:Extending this method to
247:
7296:Price-earnings to growth
6643:
5598:Foreign currency returns
5238:from the rate of return.
5220:internal rates of return
3053:of returns, which, over
1954:If the gains and losses
1823:in the first period is:
7238:Enterprise value/EBITDA
6907:Strong, Robert (2009).
6758:{\displaystyle x=100\%}
6573:Internal rate of return
6558:Effective interest rate
6517:Annual percentage yield
5339:risk-free interest rate
5287:measures the change in
5190:
5014:Capital at end of year
4863:Capital at end of year
4727:Capital at end of year
3942:required rate of return
3925:{\displaystyle {C_{n}}}
3896:{\displaystyle {C_{0}}}
3841:{\displaystyle {C_{t}}}
3812:NPV = net present value
3684:internal rate of return
3678:Internal rate of return
3672:Internal rate of return
3579:
2136:{\displaystyle 1+R_{2}}
2103:{\displaystyle 1+R_{1}}
1456:= length of time period
476:Currency of measurement
7250:Enterprise value/sales
6874:Brooks, Chris (2008).
6785:
6759:
6730:
6266:
6175:
6010:
5780:1.1 x 1.05 − 1 = 15.5%
5737:
5708:
5675:
5607:1.02 x 1.1 − 1 = 12.2%
5588:
5445:certificate of deposit
5100:
4949:
4798:
4616:
4527:
4492:
4451:
4373:
4313:
4268:
4203:
4151:
4111:
4063:
4043:
4008:
3971:
3926:
3897:
3868:
3842:
3799:
3750:
3704:
3550:
3492:
3371:
3253:
3212:
3141:
3017:
2952:
2891:
2852:
2709:
2652:
2614:
2513:
2486:
2414:
2394:
2363:
2253:
2137:
2104:
2068:
2017:
1994:
1974:
1944:
1868:
1817:
1790:
1770:
1742:is measured in years.
1736:
1716:
1681:
1615:
1553:
1533:
1498:
1450:
1426:
1385:
1314:
1291:
1196:
1073:
1053:
1033:
1013:
984:
934:
846:
826:
803:
749:
735:over a length of time
729:
709:
678:
642:
619:
605:over a period of time
599:
567:
461:Negative initial value
451:
402:
371:
338:
273:
7424:Investment indicators
6786:
6760:
6731:
6658:difference of squares
6578:Modified Dietz method
6568:Holding period return
6553:Effective annual rate
6543:Dollar cost averaging
6267:
6176:
6011:
5738:
5736:{\displaystyle r_{c}}
5709:
5707:{\displaystyle r_{i}}
5676:
5589:
5293:nominal annual return
5101:
5031:Dollar profit/(loss)
4950:
4880:Dollar profit/(loss)
4799:
4744:Dollar profit/(loss)
4617:
4528:
4493:
4452:
4374:
4314:
4269:
4204:
4202:{\displaystyle V_{f}}
4152:
4150:{\displaystyle V_{i}}
4112:
4064:
4044:
4014:= +100%, that is, if
4009:
3972:
3927:
3898:
3869:
3843:
3800:
3730:
3705:
3551:
3493:
3372:
3254:
3192:
3121:
3037:Further information:
3018:
2932:
2892:
2853:
2689:
2653:
2615:
2514:
2487:
2415:
2395:
2364:
2254:
2138:
2105:
2069:
2018:
1995:
1975:
1945:
1869:
1818:
1816:{\displaystyle R_{1}}
1791:
1771:
1737:
1717:
1682:
1616:
1554:
1534:
1499:
1451:
1427:
1386:
1315:
1292:
1197:
1074:
1054:
1034:
1014:
985:
935:
847:
827:
804:
750:
730:
710:
679:
643:
620:
600:
568:
452:
403:
401:{\displaystyle V_{i}}
372:
370:{\displaystyle V_{f}}
339:
274:
258:holding period return
233:holding period return
170:holding period return
7429:Mathematical finance
7319:Return on net assets
6942:10.2139/ssrn.1549328
6769:
6740:
6664:
6628:Time-weighted return
6548:Economic value added
6204:
6198:Solving for T gives
6192:n = number of years
6125:
6102:Mutual funds report
6058:investment portfolio
5970:
5804:volatility (finance)
5720:
5691:
5618:
5550:
5344:estimates of future
5285:return in real terms
5248:0.05 x 0.15 = 0.0075
5198:investment decisions
5053:
4902:
4766:
4537:
4502:
4461:
4420:
4348:
4344:Logarithmic return,
4303:
4238:
4186:
4134:
4130:Initial investment,
4073:
4053:
4018:
3998:
3951:
3907:
3878:
3856:
3823:
3717:
3694:
3621:improve this section
3573:time-weighted return
3508:
3387:
3277:
3064:
3045:time-weighted method
2904:
2881:
2665:
2627:
2526:
2503:
2424:
2404:
2384:
2375:time-weighted method
2266:
2150:
2114:
2081:
2030:
2007:
1984:
1958:
1881:
1830:
1800:
1780:
1760:
1726:
1691:
1628:
1566:
1543:
1508:
1473:
1440:
1401:
1327:
1304:
1216:
1130:
1063:
1043:
1023:
1003:
950:
859:
836:
816:
762:
739:
719:
699:
655:
632:
609:
589:
495:
417:
385:
354:
286:
263:
205:return on investment
54:improve this article
7204:Capitalization rate
7013:. pp. 151–163.
6784:{\displaystyle x=1}
6623:Time value of money
6618:Simple Dietz method
6613:Returns (economics)
6313:Dividend per share
6290:
5823:
5798:Risk and volatility
5452:
5400:U.S. Treasury bills
5327:time value of money
5321:time value of money
5315:Time value of money
5265:0.10 x 0.25 = 0.025
5228:profitability index
5135:
4960:
4809:
4673:
4126:
3867:{\displaystyle {t}}
1973:{\displaystyle B-A}
7377:Sustainable growth
6781:
6755:
6726:
6288:
6262:
6171:
6074:taxes on dividends
6006:
5895:Total shares held
5821:
5733:
5704:
5671:
5584:
5450:
5413:. The higher the
5353:assessment of the
5308:online poker tools
5133:
5096:
4958:
4945:
4807:
4794:
4671:
4612:
4523:
4488:
4447:
4369:
4309:
4264:
4199:
4182:Final investment,
4147:
4124:
4107:
4059:
4039:
4004:
3967:
3959:
3922:
3893:
3864:
3838:
3795:
3725:
3700:
3546:
3488:
3367:
3249:
3013:
2887:
2848:
2648:
2610:
2509:
2482:
2410:
2390:
2359:
2249:
2133:
2100:
2064:
2013:
1990:
1970:
1940:
1864:
1813:
1786:
1766:
1732:
1712:
1677:
1611:
1549:
1529:
1494:
1446:
1422:
1381:
1310:
1287:
1192:
1111:logarithmic return
1069:
1049:
1029:
1009:
980:
930:
842:
822:
799:
745:
725:
705:
674:
638:
615:
595:
563:
447:
398:
367:
334:
269:
7409:Financial markets
7391:
7390:
7325:Return on capital
7193:Buffett indicator
7121:Bruce J. Feibel.
6918:978-0-324-66510-9
6893:978-0-521-87306-2
6608:Return on capital
6598:Return of capital
6583:Net present value
6538:Compound interest
6528:Capital budgeting
6496:
6495:
6235:
6046:separate accounts
5991:
5947:
5946:
5912:Investment value
5878:Shares purchased
5539:
5538:
5523:Quarterly return
5427:compound interest
5358:of the investment
5224:net present value
5216:capital budgeting
5188:
5187:
5044:
5043:
4893:
4892:
4757:
4756:
4403:
4402:
4312:{\displaystyle r}
4299:Ordinary return,
4062:{\displaystyle r}
4007:{\displaystyle r}
3958:
3787:
3724:
3703:{\displaystyle r}
3688:net present value
3657:
3656:
3649:
3529:
3459:
3241:
3177:
3077:
2976:
2930:
2916:
2890:{\displaystyle n}
2512:{\displaystyle R}
2494:cumulative return
2413:{\displaystyle n}
2393:{\displaystyle n}
2357:
2330:
2247:
2230:
2212:
2062:
2016:{\displaystyle C}
1993:{\displaystyle B}
1938:
1925:
1862:
1789:{\displaystyle B}
1769:{\displaystyle A}
1735:{\displaystyle t}
1675:
1552:{\displaystyle t}
1449:{\displaystyle t}
1320:to the equation:
1313:{\displaystyle r}
1285:
1275:
1186:
1121:force of interest
1072:{\displaystyle r}
1052:{\displaystyle t}
1032:{\displaystyle r}
1012:{\displaystyle R}
963:
922:
892:
845:{\displaystyle r}
825:{\displaystyle R}
748:{\displaystyle t}
728:{\displaystyle R}
708:{\displaystyle r}
672:
641:{\displaystyle r}
625:corresponds to a
618:{\displaystyle t}
598:{\displaystyle R}
552:
436:
332:
272:{\displaystyle R}
194:annualized return
130:
129:
122:
104:
18:Investment return
16:(Redirected from
7441:
7414:Financial ratios
7404:Finance theories
7337:Return on equity
7313:Return on assets
7267:Operating margin
7182:Financial ratios
7175:
7168:
7161:
7152:
7151:
7057:
7056:
7045:
7039:
7038:
7036:
7035:
7021:
7015:
7014:
7011:Barron's Finance
7007:
7001:
7000:
6994:
6986:
6968:
6962:
6961:
6929:
6923:
6922:
6904:
6898:
6897:
6881:
6871:
6865:
6864:
6856:
6850:
6849:
6846:"GIPS Standards"
6841:
6835:
6834:
6827:
6821:
6820:
6819:on July 8, 2012.
6815:. Archived from
6809:
6792:
6790:
6788:
6787:
6782:
6764:
6762:
6761:
6756:
6735:
6733:
6732:
6727:
6722:
6721:
6709:
6708:
6654:
6603:Return on assets
6291:
6287:
6271:
6269:
6268:
6263:
6261:
6254:
6253:
6249:
6240:
6236:
6231:
6220:
6180:
6178:
6177:
6172:
6170:
6157:
6156:
6151:
6147:
6054:variable annuity
6015:
6013:
6012:
6007:
5996:
5992:
5984:
5824:
5742:
5740:
5739:
5734:
5732:
5731:
5713:
5711:
5710:
5705:
5703:
5702:
5680:
5678:
5677:
5672:
5661:
5660:
5639:
5638:
5593:
5591:
5590:
5585:
5577:
5576:
5453:
5449:
5392:deposit accounts
5289:purchasing power
5209:return on assets
5205:return on equity
5136:
5132:
5105:
5103:
5102:
5097:
5077:
5076:
4961:
4957:
4954:
4952:
4951:
4946:
4926:
4925:
4810:
4806:
4803:
4801:
4800:
4795:
4778:
4777:
4674:
4670:
4637:AM–GM inequality
4621:
4619:
4618:
4613:
4611:
4610:
4603:
4584:
4583:
4576:
4557:
4556:
4555:
4532:
4530:
4529:
4524:
4522:
4521:
4520:
4497:
4495:
4494:
4489:
4487:
4486:
4479:
4456:
4454:
4453:
4448:
4446:
4445:
4438:
4378:
4376:
4375:
4370:
4368:
4367:
4366:
4318:
4316:
4315:
4310:
4273:
4271:
4270:
4265:
4263:
4262:
4250:
4249:
4208:
4206:
4205:
4200:
4198:
4197:
4156:
4154:
4153:
4148:
4146:
4145:
4127:
4123:
4116:
4114:
4113:
4108:
4100:
4099:
4090:
4085:
4084:
4068:
4066:
4065:
4060:
4048:
4046:
4045:
4040:
4038:
4037:
4036:
4013:
4011:
4010:
4005:
3976:
3974:
3973:
3968:
3960:
3956:
3931:
3929:
3928:
3923:
3921:
3920:
3919:
3903:and final value
3902:
3900:
3899:
3894:
3892:
3891:
3890:
3873:
3871:
3870:
3865:
3863:
3847:
3845:
3844:
3839:
3837:
3836:
3835:
3804:
3802:
3801:
3796:
3788:
3786:
3785:
3784:
3762:
3761:
3752:
3749:
3744:
3726:
3722:
3709:
3707:
3706:
3701:
3652:
3645:
3641:
3638:
3632:
3601:
3593:
3555:
3553:
3552:
3547:
3530:
3528:
3523:
3512:
3497:
3495:
3494:
3489:
3460:
3458:
3453:
3391:
3376:
3374:
3373:
3368:
3258:
3256:
3255:
3250:
3242:
3240:
3235:
3231:
3230:
3211:
3206:
3190:
3179:
3178:
3170:
3168:
3164:
3160:
3159:
3140:
3135:
3111:
3110:
3109:
3079:
3078:
3070:
3022:
3020:
3019:
3014:
3009:
3008:
2990:
2989:
2977:
2969:
2964:
2963:
2962:
2951:
2946:
2931:
2923:
2918:
2917:
2909:
2896:
2894:
2893:
2888:
2857:
2855:
2854:
2849:
2847:
2846:
2839:
2814:
2813:
2806:
2787:
2786:
2779:
2760:
2759:
2752:
2733:
2732:
2725:
2708:
2703:
2685:
2684:
2683:
2657:
2655:
2654:
2649:
2647:
2646:
2645:
2619:
2617:
2616:
2611:
2606:
2605:
2581:
2580:
2559:
2558:
2518:
2516:
2515:
2510:
2491:
2489:
2488:
2483:
2481:
2480:
2462:
2461:
2449:
2448:
2436:
2435:
2419:
2417:
2416:
2411:
2399:
2397:
2396:
2391:
2368:
2366:
2365:
2360:
2358:
2353:
2342:
2331:
2323:
2309:
2308:
2287:
2286:
2258:
2256:
2255:
2250:
2248:
2240:
2235:
2231:
2223:
2217:
2213:
2205:
2193:
2192:
2171:
2170:
2142:
2140:
2139:
2134:
2132:
2131:
2109:
2107:
2106:
2101:
2099:
2098:
2073:
2071:
2070:
2065:
2063:
2058:
2047:
2042:
2041:
2022:
2020:
2019:
2014:
1999:
1997:
1996:
1991:
1979:
1977:
1976:
1971:
1949:
1947:
1946:
1941:
1939:
1931:
1926:
1921:
1910:
1899:
1898:
1873:
1871:
1870:
1865:
1863:
1858:
1847:
1842:
1841:
1822:
1820:
1819:
1814:
1812:
1811:
1795:
1793:
1792:
1787:
1775:
1773:
1772:
1767:
1741:
1739:
1738:
1733:
1721:
1719:
1718:
1713:
1711:
1710:
1709:
1686:
1684:
1683:
1678:
1676:
1671:
1670:
1669:
1653:
1648:
1647:
1646:
1620:
1618:
1617:
1612:
1607:
1606:
1605:
1586:
1585:
1584:
1558:
1556:
1555:
1550:
1538:
1536:
1535:
1530:
1528:
1527:
1526:
1503:
1501:
1500:
1495:
1493:
1492:
1491:
1455:
1453:
1452:
1447:
1431:
1429:
1428:
1423:
1421:
1420:
1419:
1390:
1388:
1387:
1382:
1380:
1379:
1375:
1374:
1373:
1352:
1351:
1339:
1338:
1319:
1317:
1316:
1311:
1296:
1294:
1293:
1288:
1286:
1281:
1280:
1276:
1274:
1273:
1264:
1263:
1254:
1241:
1236:
1235:
1234:
1201:
1199:
1198:
1193:
1191:
1187:
1185:
1184:
1175:
1174:
1165:
1150:
1149:
1148:
1119:, also known as
1078:
1076:
1075:
1070:
1058:
1056:
1055:
1050:
1038:
1036:
1035:
1030:
1018:
1016:
1015:
1010:
989:
987:
986:
981:
964:
962:
954:
939:
937:
936:
931:
923:
921:
916:
905:
894:
893:
885:
851:
849:
848:
843:
831:
829:
828:
823:
808:
806:
805:
800:
798:
797:
754:
752:
751:
746:
734:
732:
731:
726:
714:
712:
711:
706:
683:
681:
680:
675:
673:
665:
647:
645:
644:
639:
624:
622:
621:
616:
604:
602:
601:
596:
572:
570:
569:
564:
553:
551:
534:
499:
456:
454:
453:
448:
437:
435:
421:
407:
405:
404:
399:
397:
396:
376:
374:
373:
368:
366:
365:
343:
341:
340:
335:
333:
331:
330:
321:
320:
319:
307:
306:
296:
278:
276:
275:
270:
213:return on assets
209:return on equity
125:
118:
114:
111:
105:
103:
69:"Rate of return"
62:
38:
30:
21:
7449:
7448:
7444:
7443:
7442:
7440:
7439:
7438:
7394:
7393:
7392:
7387:
7284:Price/cash flow
7227:Dividend payout
7184:
7179:
7149:
7066:
7064:Further reading
7061:
7060:
7046:
7042:
7033:
7031:
7023:
7022:
7018:
7009:
7008:
7004:
6988:
6987:
6983:
6969:
6965:
6930:
6926:
6919:
6905:
6901:
6894:
6872:
6868:
6857:
6853:
6844:
6842:
6838:
6829:
6828:
6824:
6811:
6810:
6806:
6801:
6796:
6795:
6770:
6767:
6766:
6741:
6738:
6737:
6717:
6713:
6704:
6700:
6665:
6662:
6661:
6655:
6651:
6646:
6633:Value investing
6563:Expected return
6513:
6286:
6277:
6245:
6241:
6221:
6219:
6215:
6214:
6207:
6205:
6202:
6201:
6152:
6137:
6133:
6132:
6128:
6126:
6123:
6122:
6113:
6100:
6092:net asset value
6039:
5983:
5979:
5971:
5968:
5967:
5819:
5806:
5800:
5795:
5763:
5754:
5727:
5723:
5721:
5718:
5717:
5698:
5694:
5692:
5689:
5688:
5656:
5652:
5634:
5630:
5619:
5616:
5615:
5600:
5572:
5568:
5551:
5548:
5547:
5429:
5423:
5411:cost of capital
5378:for other uses.
5323:
5317:
5193:
5112:
5072:
5068:
5054:
5051:
5050:
4980:Rate of return
4921:
4917:
4903:
4900:
4899:
4829:Rate of return
4773:
4769:
4767:
4764:
4763:
4693:Rate of return
4666:
4632:
4593:
4592:
4588:
4566:
4565:
4561:
4545:
4544:
4540:
4538:
4535:
4534:
4510:
4509:
4505:
4503:
4500:
4499:
4469:
4468:
4464:
4462:
4459:
4458:
4428:
4427:
4423:
4421:
4418:
4417:
4356:
4355:
4351:
4349:
4346:
4345:
4304:
4301:
4300:
4258:
4254:
4245:
4241:
4239:
4236:
4235:
4193:
4189:
4187:
4184:
4183:
4141:
4137:
4135:
4132:
4131:
4095:
4091:
4086:
4080:
4076:
4074:
4071:
4070:
4054:
4051:
4050:
4026:
4025:
4021:
4019:
4016:
4015:
3999:
3996:
3995:
3992:
3983:
3954:
3952:
3949:
3948:
3938:cost of capital
3915:
3911:
3910:
3908:
3905:
3904:
3886:
3882:
3881:
3879:
3876:
3875:
3859:
3857:
3854:
3853:
3831:
3827:
3826:
3824:
3821:
3820:
3780:
3776:
3763:
3757:
3753:
3751:
3745:
3734:
3720:
3718:
3715:
3714:
3695:
3692:
3691:
3680:
3674:
3653:
3642:
3636:
3633:
3618:
3602:
3591:
3582:
3567:
3562:
3524:
3513:
3511:
3509:
3506:
3505:
3454:
3392:
3390:
3388:
3385:
3384:
3278:
3275:
3274:
3236:
3226:
3222:
3207:
3196:
3191:
3189:
3169:
3155:
3151:
3136:
3125:
3120:
3116:
3115:
3081:
3080:
3069:
3068:
3067:
3065:
3062:
3061:
3041:
3035:
3004:
3000:
2985:
2981:
2968:
2958:
2954:
2953:
2947:
2936:
2922:
2908:
2907:
2905:
2902:
2901:
2882:
2879:
2878:
2871:
2829:
2828:
2824:
2796:
2795:
2791:
2769:
2768:
2764:
2742:
2741:
2737:
2715:
2714:
2710:
2704:
2693:
2673:
2672:
2668:
2666:
2663:
2662:
2635:
2634:
2630:
2628:
2625:
2624:
2601:
2597:
2576:
2572:
2554:
2550:
2527:
2524:
2523:
2504:
2501:
2500:
2476:
2472:
2457:
2453:
2444:
2440:
2431:
2427:
2425:
2422:
2421:
2405:
2402:
2401:
2385:
2382:
2381:
2343:
2341:
2322:
2304:
2300:
2282:
2278:
2267:
2264:
2263:
2239:
2222:
2218:
2204:
2200:
2188:
2184:
2166:
2162:
2151:
2148:
2147:
2127:
2123:
2115:
2112:
2111:
2094:
2090:
2082:
2079:
2078:
2048:
2046:
2037:
2033:
2031:
2028:
2027:
2008:
2005:
2004:
1985:
1982:
1981:
1959:
1956:
1955:
1930:
1911:
1909:
1894:
1890:
1882:
1879:
1878:
1848:
1846:
1837:
1833:
1831:
1828:
1827:
1807:
1803:
1801:
1798:
1797:
1781:
1778:
1777:
1761:
1758:
1757:
1751:
1727:
1724:
1723:
1699:
1698:
1694:
1692:
1689:
1688:
1659:
1658:
1654:
1652:
1636:
1635:
1631:
1629:
1626:
1625:
1595:
1594:
1590:
1574:
1573:
1569:
1567:
1564:
1563:
1544:
1541:
1540:
1516:
1515:
1511:
1509:
1506:
1505:
1481:
1480:
1476:
1474:
1471:
1470:
1467:
1441:
1438:
1437:
1409:
1408:
1404:
1402:
1399:
1398:
1363:
1362:
1358:
1357:
1353:
1347:
1343:
1334:
1330:
1328:
1325:
1324:
1305:
1302:
1301:
1269:
1265:
1259:
1255:
1253:
1249:
1242:
1240:
1224:
1223:
1219:
1217:
1214:
1213:
1180:
1176:
1170:
1166:
1164:
1160:
1138:
1137:
1133:
1131:
1128:
1127:
1107:
1064:
1061:
1060:
1044:
1041:
1040:
1024:
1021:
1020:
1004:
1001:
1000:
958:
953:
951:
948:
947:
917:
906:
904:
884:
880:
860:
857:
856:
837:
834:
833:
817:
814:
813:
793:
789:
763:
760:
759:
740:
737:
736:
720:
717:
716:
715:, and a return
700:
697:
696:
664:
656:
653:
652:
633:
630:
629:
610:
607:
606:
590:
587:
586:
583:
535:
500:
498:
496:
493:
492:
478:
463:
425:
420:
418:
415:
414:
408:= initial value
392:
388:
386:
383:
382:
361:
357:
355:
352:
351:
326:
322:
315:
311:
302:
298:
297:
295:
287:
284:
283:
264:
261:
260:
250:
245:
225:
178:negative return
166:stock dividends
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
7447:
7437:
7436:
7434:Temporal rates
7431:
7426:
7421:
7416:
7411:
7406:
7389:
7388:
7386:
7385:
7380:
7374:
7369:
7366:Short interest
7363:
7358:
7352:
7346:
7340:
7334:
7328:
7322:
7316:
7310:
7305:
7299:
7293:
7290:Price-earnings
7287:
7281:
7275:
7269:
7264:
7259:
7253:
7247:
7241:
7235:
7232:Earnings yield
7229:
7224:
7222:Dividend cover
7219:
7216:Debt-to-equity
7213:
7207:
7201:
7195:
7189:
7186:
7185:
7178:
7177:
7170:
7163:
7155:
7148:
7147:External links
7145:
7144:
7143:
7133:
7119:
7105:
7095:
7081:
7065:
7062:
7059:
7058:
7040:
7016:
7002:
6981:
6963:
6924:
6917:
6899:
6892:
6866:
6851:
6836:
6822:
6803:
6802:
6800:
6797:
6794:
6793:
6780:
6777:
6774:
6754:
6751:
6748:
6745:
6725:
6720:
6716:
6712:
6707:
6703:
6699:
6696:
6693:
6690:
6687:
6684:
6681:
6678:
6675:
6672:
6669:
6648:
6647:
6645:
6642:
6641:
6640:
6635:
6630:
6625:
6620:
6615:
6610:
6605:
6600:
6595:
6593:Rate of profit
6590:
6585:
6580:
6575:
6570:
6565:
6560:
6555:
6550:
6545:
6540:
6535:
6530:
6525:
6519:
6512:
6509:
6508:
6507:
6503:
6500:
6494:
6493:
6488:
6485:
6482:
6479:
6476:
6472:
6471:
6468:
6465:
6462:
6459:
6456:
6452:
6451:
6448:
6445:
6442:
6439:
6436:
6432:
6431:
6428:
6425:
6422:
6419:
6416:
6412:
6411:
6408:
6405:
6402:
6399:
6396:
6392:
6391:
6386:
6383:
6380:
6377:
6374:
6370:
6369:
6366:
6363:
6360:
6357:
6354:
6350:
6349:
6346:
6343:
6340:
6337:
6334:
6330:
6329:
6326:
6323:
6320:
6317:
6314:
6310:
6309:
6306:
6303:
6300:
6297:
6294:
6285:
6282:
6276:
6273:
6260:
6257:
6252:
6248:
6244:
6239:
6234:
6230:
6227:
6224:
6218:
6213:
6210:
6169:
6166:
6163:
6160:
6155:
6150:
6146:
6143:
6140:
6136:
6131:
6112:
6109:
6099:
6096:
6038:
6035:
6030:
6029:
6026:
6018:
6017:
6005:
6002:
5999:
5995:
5990:
5987:
5982:
5978:
5975:
5964:
5963:
5960:
5957:
5954:
5945:
5944:
5941:
5938:
5935:
5932:
5931:Quarterly ROI
5928:
5927:
5922:
5919:
5916:
5913:
5909:
5908:
5905:
5902:
5899:
5896:
5892:
5891:
5888:
5885:
5882:
5879:
5875:
5874:
5871:
5868:
5865:
5862:
5858:
5857:
5854:
5851:
5848:
5845:
5841:
5840:
5837:
5834:
5831:
5828:
5818:
5815:
5802:Main article:
5799:
5796:
5794:
5791:
5790:
5789:
5782:
5781:
5762:
5759:
5753:
5750:
5745:
5744:
5730:
5726:
5715:
5701:
5697:
5682:
5681:
5670:
5667:
5664:
5659:
5655:
5651:
5648:
5645:
5642:
5637:
5633:
5629:
5626:
5623:
5609:
5608:
5599:
5596:
5583:
5580:
5575:
5571:
5567:
5564:
5561:
5558:
5555:
5537:
5536:
5533:
5530:
5527:
5524:
5520:
5519:
5516:
5513:
5510:
5507:
5503:
5502:
5499:
5496:
5493:
5490:
5486:
5485:
5482:
5479:
5476:
5473:
5469:
5468:
5465:
5462:
5459:
5456:
5425:Main article:
5422:
5419:
5380:
5379:
5372:
5365:
5351:
5342:
5319:Main article:
5316:
5313:
5312:
5311:
5304:
5297:inflation rate
5276:
5275:
5271:
5270:
5269:
5266:
5260:
5259:
5255:
5254:
5253:
5252:
5249:
5243:
5242:
5239:
5231:
5212:
5201:
5192:
5189:
5186:
5185:
5182:
5179:
5176:
5173:
5169:
5168:
5165:
5162:
5159:
5156:
5155:Dollar return
5152:
5151:
5148:
5145:
5142:
5139:
5111:
5108:
5107:
5106:
5095:
5092:
5089:
5086:
5083:
5080:
5075:
5071:
5067:
5064:
5061:
5058:
5042:
5041:
5038:
5036:
5034:
5032:
5028:
5027:
5024:
5021:
5018:
5015:
5011:
5010:
5007:
5004:
5001:
4998:
4994:
4993:
4990:
4987:
4984:
4981:
4977:
4976:
4973:
4970:
4967:
4964:
4956:
4955:
4944:
4941:
4938:
4935:
4932:
4929:
4924:
4920:
4916:
4913:
4910:
4907:
4891:
4890:
4887:
4885:
4883:
4881:
4877:
4876:
4873:
4870:
4867:
4864:
4860:
4859:
4856:
4853:
4850:
4847:
4843:
4842:
4839:
4836:
4833:
4830:
4826:
4825:
4822:
4819:
4816:
4813:
4805:
4804:
4793:
4790:
4787:
4784:
4781:
4776:
4772:
4755:
4754:
4751:
4749:
4747:
4745:
4741:
4740:
4737:
4734:
4731:
4728:
4724:
4723:
4720:
4717:
4714:
4711:
4707:
4706:
4703:
4700:
4697:
4694:
4690:
4689:
4686:
4683:
4680:
4677:
4665:
4662:
4631:
4628:
4627:
4626:
4623:
4609:
4606:
4602:
4599:
4596:
4591:
4587:
4582:
4579:
4575:
4572:
4569:
4564:
4560:
4554:
4551:
4548:
4543:
4519:
4516:
4513:
4508:
4485:
4482:
4478:
4475:
4472:
4467:
4444:
4441:
4437:
4434:
4431:
4426:
4414:
4411:
4401:
4400:
4397:
4394:
4391:
4388:
4385:
4382:
4379:
4365:
4362:
4359:
4354:
4341:
4340:
4337:
4334:
4331:
4328:
4325:
4322:
4319:
4308:
4296:
4295:
4292:
4289:
4286:
4283:
4280:
4277:
4274:
4261:
4257:
4253:
4248:
4244:
4231:
4230:
4227:
4224:
4221:
4218:
4215:
4212:
4209:
4196:
4192:
4179:
4178:
4175:
4172:
4169:
4166:
4163:
4160:
4157:
4144:
4140:
4106:
4103:
4098:
4094:
4089:
4083:
4079:
4058:
4035:
4032:
4029:
4024:
4003:
3991:
3988:
3982:
3979:
3966:
3963:
3934:
3933:
3918:
3914:
3889:
3885:
3862:
3834:
3830:
3814:
3813:
3806:
3805:
3794:
3791:
3783:
3779:
3775:
3772:
3769:
3766:
3760:
3756:
3748:
3743:
3740:
3737:
3733:
3729:
3699:
3676:Main article:
3673:
3670:
3655:
3654:
3605:
3603:
3596:
3590:
3587:
3581:
3578:
3566:
3565:External flows
3563:
3561:
3558:
3557:
3556:
3545:
3542:
3539:
3536:
3533:
3527:
3522:
3519:
3516:
3499:
3498:
3487:
3484:
3481:
3478:
3475:
3472:
3469:
3466:
3463:
3457:
3452:
3449:
3446:
3443:
3440:
3437:
3434:
3431:
3428:
3425:
3422:
3419:
3416:
3413:
3410:
3407:
3404:
3401:
3398:
3395:
3378:
3377:
3366:
3363:
3360:
3357:
3354:
3351:
3348:
3345:
3342:
3339:
3336:
3333:
3330:
3327:
3324:
3321:
3318:
3315:
3312:
3309:
3306:
3303:
3300:
3297:
3294:
3291:
3288:
3285:
3282:
3260:
3259:
3248:
3245:
3239:
3234:
3229:
3225:
3221:
3218:
3215:
3210:
3205:
3202:
3199:
3195:
3188:
3185:
3182:
3176:
3173:
3167:
3163:
3158:
3154:
3150:
3147:
3144:
3139:
3134:
3131:
3128:
3124:
3119:
3114:
3108:
3105:
3102:
3099:
3096:
3093:
3090:
3087:
3084:
3076:
3073:
3050:geometric mean
3034:
3031:
3024:
3023:
3012:
3007:
3003:
2999:
2996:
2993:
2988:
2984:
2980:
2975:
2972:
2967:
2961:
2957:
2950:
2945:
2942:
2939:
2935:
2929:
2926:
2921:
2915:
2912:
2886:
2870:
2867:
2859:
2858:
2845:
2842:
2838:
2835:
2832:
2827:
2823:
2820:
2817:
2812:
2809:
2805:
2802:
2799:
2794:
2790:
2785:
2782:
2778:
2775:
2772:
2767:
2763:
2758:
2755:
2751:
2748:
2745:
2740:
2736:
2731:
2728:
2724:
2721:
2718:
2713:
2707:
2702:
2699:
2696:
2692:
2688:
2682:
2679:
2676:
2671:
2644:
2641:
2638:
2633:
2621:
2620:
2609:
2604:
2600:
2596:
2593:
2590:
2587:
2584:
2579:
2575:
2571:
2568:
2565:
2562:
2557:
2553:
2549:
2546:
2543:
2540:
2537:
2534:
2531:
2508:
2498:overall return
2479:
2475:
2471:
2468:
2465:
2460:
2456:
2452:
2447:
2443:
2439:
2434:
2430:
2409:
2389:
2371:
2370:
2356:
2352:
2349:
2346:
2340:
2337:
2334:
2329:
2326:
2321:
2318:
2315:
2312:
2307:
2303:
2299:
2296:
2293:
2290:
2285:
2281:
2277:
2274:
2271:
2260:
2259:
2246:
2243:
2238:
2234:
2229:
2226:
2221:
2216:
2211:
2208:
2203:
2199:
2196:
2191:
2187:
2183:
2180:
2177:
2174:
2169:
2165:
2161:
2158:
2155:
2130:
2126:
2122:
2119:
2097:
2093:
2089:
2086:
2075:
2074:
2061:
2057:
2054:
2051:
2045:
2040:
2036:
2012:
1989:
1969:
1966:
1963:
1952:
1951:
1937:
1934:
1929:
1924:
1920:
1917:
1914:
1908:
1905:
1902:
1897:
1893:
1889:
1886:
1875:
1874:
1861:
1857:
1854:
1851:
1845:
1840:
1836:
1810:
1806:
1785:
1765:
1750:
1747:
1731:
1708:
1705:
1702:
1697:
1674:
1668:
1665:
1662:
1657:
1651:
1645:
1642:
1639:
1634:
1622:
1621:
1610:
1604:
1601:
1598:
1593:
1589:
1583:
1580:
1577:
1572:
1548:
1525:
1522:
1519:
1514:
1490:
1487:
1484:
1479:
1466:
1463:
1458:
1457:
1445:
1434:
1433:
1418:
1415:
1412:
1407:
1392:
1391:
1378:
1372:
1369:
1366:
1361:
1356:
1350:
1346:
1342:
1337:
1333:
1309:
1298:
1297:
1284:
1279:
1272:
1268:
1262:
1258:
1252:
1248:
1245:
1239:
1233:
1230:
1227:
1222:
1203:
1202:
1190:
1183:
1179:
1173:
1169:
1163:
1159:
1156:
1153:
1147:
1144:
1141:
1136:
1106:
1103:
1090:
1089:
1068:
1048:
1028:
1008:
991:
990:
979:
976:
973:
970:
967:
961:
957:
941:
940:
929:
926:
920:
915:
912:
909:
903:
900:
897:
891:
888:
883:
879:
876:
873:
870:
867:
864:
841:
821:
810:
809:
796:
792:
788:
785:
782:
779:
776:
773:
770:
767:
744:
724:
704:
685:
684:
671:
668:
663:
660:
637:
627:rate of return
614:
594:
582:
579:
574:
573:
562:
559:
556:
550:
547:
544:
541:
538:
533:
530:
527:
524:
521:
518:
515:
512:
509:
506:
503:
477:
474:
462:
459:
446:
443:
440:
434:
431:
428:
424:
410:
409:
395:
391:
379:
378:
364:
360:
345:
344:
329:
325:
318:
314:
310:
305:
301:
294:
291:
268:
249:
246:
244:
241:
224:
221:
187:rate of return
162:cash dividends
128:
127:
42:
40:
33:
26:
9:
6:
4:
3:
2:
7446:
7435:
7432:
7430:
7427:
7425:
7422:
7420:
7417:
7415:
7412:
7410:
7407:
7405:
7402:
7401:
7399:
7384:
7381:
7378:
7375:
7373:
7370:
7367:
7364:
7362:
7359:
7356:
7353:
7350:
7347:
7344:
7341:
7338:
7335:
7332:
7329:
7326:
7323:
7320:
7317:
7314:
7311:
7309:
7308:Profit margin
7306:
7303:
7300:
7297:
7294:
7291:
7288:
7285:
7282:
7279:
7276:
7273:
7272:Price-to-book
7270:
7268:
7265:
7263:
7260:
7257:
7256:Loan-to-value
7254:
7251:
7248:
7245:
7242:
7239:
7236:
7233:
7230:
7228:
7225:
7223:
7220:
7217:
7214:
7211:
7208:
7205:
7202:
7199:
7196:
7194:
7191:
7190:
7187:
7183:
7176:
7171:
7169:
7164:
7162:
7157:
7156:
7153:
7142:
7141:0-470-85679-3
7138:
7134:
7132:
7131:0-471-26849-6
7128:
7124:
7120:
7118:
7117:0-07-041534-X
7114:
7110:
7106:
7103:
7102:, 8th Edition
7101:
7096:
7094:
7090:
7086:
7082:
7080:
7079:0-7641-1275-9
7076:
7072:
7068:
7067:
7054:
7050:
7044:
7030:
7026:
7020:
7012:
7006:
6998:
6992:
6984:
6982:0-7641-1275-9
6978:
6974:
6967:
6959:
6955:
6951:
6947:
6943:
6939:
6935:
6928:
6920:
6914:
6910:
6903:
6895:
6889:
6885:
6880:
6879:
6870:
6862:
6855:
6847:
6840:
6832:
6826:
6818:
6814:
6808:
6804:
6778:
6775:
6772:
6749:
6746:
6743:
6723:
6718:
6714:
6710:
6705:
6701:
6697:
6691:
6688:
6685:
6676:
6673:
6670:
6659:
6656:Consider the
6653:
6649:
6639:
6636:
6634:
6631:
6629:
6626:
6624:
6621:
6619:
6616:
6614:
6611:
6609:
6606:
6604:
6601:
6599:
6596:
6594:
6591:
6589:
6588:Profit margin
6586:
6584:
6581:
6579:
6576:
6574:
6571:
6569:
6566:
6564:
6561:
6559:
6556:
6554:
6551:
6549:
6546:
6544:
6541:
6539:
6536:
6534:
6531:
6529:
6526:
6523:
6520:
6518:
6515:
6514:
6504:
6501:
6498:
6497:
6492:
6489:
6486:
6483:
6480:
6477:
6474:
6473:
6469:
6466:
6463:
6460:
6457:
6454:
6453:
6449:
6446:
6443:
6440:
6437:
6434:
6433:
6429:
6426:
6423:
6420:
6417:
6414:
6413:
6409:
6406:
6403:
6400:
6397:
6394:
6393:
6390:
6387:
6384:
6381:
6378:
6375:
6372:
6371:
6367:
6364:
6361:
6358:
6355:
6352:
6351:
6347:
6344:
6341:
6338:
6335:
6332:
6331:
6327:
6324:
6321:
6318:
6315:
6312:
6311:
6307:
6304:
6301:
6298:
6295:
6293:
6292:
6281:
6272:
6258:
6255:
6246:
6242:
6237:
6216:
6211:
6199:
6196:
6193:
6190:
6187:
6184:
6181:
6158:
6148:
6141:
6138:
6134:
6120:
6118:
6108:
6107:each period.
6105:
6104:total returns
6098:Total returns
6095:
6093:
6088:
6082:
6078:
6075:
6069:
6067:
6061:
6059:
6055:
6052:policies and
6051:
6047:
6043:
6034:
6027:
6024:
6023:
6022:
6000:
5997:
5993:
5988:
5985:
5980:
5976:
5973:
5966:
5965:
5961:
5958:
5955:
5952:
5951:
5950:
5942:
5939:
5936:
5933:
5930:
5929:
5926:
5923:
5920:
5917:
5914:
5911:
5910:
5906:
5903:
5900:
5897:
5894:
5893:
5889:
5886:
5883:
5880:
5877:
5876:
5872:
5869:
5866:
5863:
5860:
5859:
5855:
5852:
5849:
5846:
5843:
5842:
5838:
5835:
5832:
5829:
5826:
5825:
5814:
5812:
5805:
5787:
5786:
5785:
5779:
5778:
5777:
5773:
5770:
5767:
5758:
5749:
5728:
5724:
5716:
5699:
5695:
5687:
5686:
5685:
5668:
5665:
5657:
5653:
5649:
5646:
5635:
5631:
5627:
5624:
5614:
5613:
5612:
5606:
5605:
5604:
5595:
5581:
5578:
5573:
5565:
5559:
5553:
5545:
5534:
5531:
5528:
5525:
5522:
5521:
5517:
5514:
5511:
5508:
5505:
5504:
5500:
5497:
5494:
5491:
5488:
5487:
5483:
5480:
5477:
5474:
5471:
5470:
5466:
5463:
5460:
5457:
5455:
5454:
5448:
5446:
5441:
5439:
5435:
5428:
5418:
5416:
5412:
5408:
5407:discount rate
5403:
5401:
5397:
5393:
5389:
5385:
5384:interest rate
5377:
5373:
5371:
5370:
5369:currency risk
5366:
5363:
5359:
5357:
5352:
5350:
5348:
5343:
5341:
5340:
5335:
5334:
5333:
5330:
5328:
5322:
5309:
5305:
5302:
5301:in real terms
5298:
5294:
5290:
5286:
5282:
5278:
5277:
5272:
5267:
5264:
5263:
5262:
5261:
5257:
5256:
5250:
5247:
5246:
5245:
5244:
5240:
5236:
5232:
5229:
5225:
5221:
5217:
5213:
5210:
5206:
5202:
5199:
5195:
5194:
5183:
5180:
5177:
5174:
5171:
5170:
5166:
5163:
5160:
5157:
5154:
5153:
5149:
5146:
5143:
5140:
5138:
5137:
5131:
5127:
5123:
5119:
5116:
5090:
5087:
5084:
5081:
5078:
5073:
5065:
5062:
5059:
5049:
5048:
5047:
5039:
5037:
5035:
5033:
5030:
5029:
5025:
5022:
5019:
5016:
5013:
5012:
5008:
5005:
5002:
4999:
4996:
4995:
4991:
4988:
4985:
4982:
4979:
4978:
4974:
4971:
4968:
4965:
4963:
4962:
4939:
4936:
4933:
4930:
4927:
4922:
4914:
4911:
4908:
4898:
4897:
4896:
4888:
4886:
4884:
4882:
4879:
4878:
4874:
4871:
4868:
4865:
4862:
4861:
4857:
4854:
4851:
4848:
4845:
4844:
4840:
4837:
4834:
4831:
4828:
4827:
4823:
4820:
4817:
4814:
4812:
4811:
4788:
4785:
4782:
4779:
4774:
4770:
4762:
4761:
4760:
4752:
4750:
4748:
4746:
4743:
4742:
4738:
4735:
4732:
4729:
4726:
4725:
4721:
4718:
4715:
4712:
4709:
4708:
4704:
4701:
4698:
4695:
4692:
4691:
4687:
4684:
4681:
4678:
4676:
4675:
4669:
4661:
4657:
4654:
4651:
4648:
4644:
4642:
4638:
4624:
4607:
4604:
4589:
4585:
4580:
4577:
4562:
4558:
4541:
4506:
4483:
4480:
4465:
4442:
4439:
4424:
4415:
4412:
4408:
4407:
4406:
4398:
4395:
4392:
4389:
4386:
4383:
4380:
4352:
4343:
4342:
4338:
4335:
4332:
4329:
4326:
4323:
4320:
4306:
4298:
4297:
4293:
4290:
4287:
4284:
4281:
4278:
4275:
4259:
4255:
4251:
4246:
4242:
4234:Profit/loss,
4233:
4232:
4228:
4225:
4222:
4219:
4216:
4213:
4210:
4194:
4190:
4181:
4180:
4176:
4173:
4170:
4167:
4164:
4161:
4158:
4142:
4138:
4129:
4128:
4122:
4118:
4104:
4101:
4096:
4092:
4087:
4081:
4077:
4056:
4022:
4001:
3987:
3978:
3964:
3961:
3945:
3943:
3939:
3916:
3912:
3887:
3883:
3860:
3851:
3832:
3828:
3819:
3818:
3817:
3811:
3810:
3809:
3792:
3789:
3781:
3773:
3770:
3767:
3758:
3754:
3746:
3741:
3738:
3735:
3731:
3727:
3713:
3712:
3711:
3697:
3689:
3685:
3679:
3669:
3666:
3662:
3651:
3648:
3640:
3637:February 2020
3630:
3626:
3622:
3616:
3615:
3611:
3606:This section
3604:
3600:
3595:
3594:
3586:
3577:
3575:
3574:
3543:
3540:
3537:
3534:
3531:
3525:
3520:
3517:
3514:
3504:
3503:
3502:
3482:
3479:
3476:
3473:
3470:
3467:
3464:
3461:
3455:
3447:
3444:
3441:
3432:
3429:
3426:
3417:
3414:
3411:
3402:
3399:
3396:
3383:
3382:
3381:
3361:
3358:
3355:
3352:
3349:
3346:
3343:
3340:
3334:
3331:
3328:
3319:
3316:
3313:
3304:
3301:
3298:
3289:
3286:
3283:
3273:
3272:
3271:
3268:
3265:
3246:
3243:
3237:
3227:
3223:
3219:
3216:
3208:
3203:
3200:
3197:
3193:
3186:
3183:
3180:
3174:
3171:
3165:
3156:
3152:
3148:
3145:
3137:
3132:
3129:
3126:
3122:
3117:
3112:
3071:
3060:
3059:
3058:
3057:periods, is:
3056:
3052:
3051:
3046:
3040:
3030:
3027:
3005:
3001:
2997:
2994:
2991:
2986:
2982:
2973:
2970:
2965:
2959:
2955:
2948:
2943:
2940:
2937:
2933:
2927:
2924:
2919:
2910:
2900:
2899:
2898:
2884:
2876:
2866:
2862:
2843:
2840:
2825:
2821:
2818:
2815:
2810:
2807:
2792:
2788:
2783:
2780:
2765:
2761:
2756:
2753:
2738:
2734:
2729:
2726:
2711:
2705:
2700:
2697:
2694:
2690:
2686:
2669:
2661:
2660:
2659:
2631:
2602:
2598:
2594:
2591:
2585:
2577:
2573:
2569:
2566:
2555:
2551:
2547:
2544:
2538:
2535:
2532:
2529:
2522:
2521:
2520:
2506:
2499:
2495:
2477:
2473:
2469:
2466:
2463:
2458:
2454:
2450:
2445:
2441:
2437:
2432:
2428:
2407:
2387:
2378:
2376:
2354:
2350:
2347:
2344:
2338:
2335:
2332:
2327:
2324:
2319:
2316:
2313:
2305:
2301:
2297:
2294:
2283:
2279:
2275:
2272:
2262:
2261:
2244:
2241:
2236:
2232:
2227:
2224:
2219:
2214:
2209:
2206:
2201:
2197:
2189:
2185:
2181:
2178:
2167:
2163:
2159:
2156:
2146:
2145:
2144:
2128:
2124:
2120:
2117:
2095:
2091:
2087:
2084:
2059:
2055:
2052:
2049:
2043:
2038:
2034:
2026:
2025:
2024:
2010:
2001:
1987:
1967:
1964:
1961:
1935:
1932:
1927:
1922:
1918:
1915:
1912:
1906:
1903:
1900:
1895:
1891:
1887:
1884:
1877:
1876:
1859:
1855:
1852:
1849:
1843:
1838:
1834:
1826:
1825:
1824:
1808:
1804:
1783:
1763:
1754:
1746:
1743:
1729:
1695:
1672:
1655:
1649:
1632:
1608:
1591:
1587:
1570:
1562:
1561:
1560:
1546:
1512:
1477:
1462:
1443:
1436:
1435:
1405:
1397:
1396:
1395:
1376:
1359:
1354:
1348:
1344:
1340:
1335:
1331:
1323:
1322:
1321:
1307:
1282:
1277:
1270:
1266:
1260:
1256:
1250:
1246:
1243:
1237:
1220:
1212:
1211:
1210:
1208:
1188:
1181:
1177:
1171:
1167:
1161:
1157:
1154:
1151:
1134:
1126:
1125:
1124:
1122:
1118:
1117:
1112:
1102:
1098:
1094:
1088:
1085:
1084:
1083:
1080:
1079:is per year.
1066:
1046:
1026:
1006:
998:
997:Annualization
994:
974:
971:
968:
965:
959:
955:
946:
945:
944:
927:
924:
918:
913:
910:
907:
901:
898:
895:
889:
886:
877:
874:
871:
865:
862:
855:
854:
853:
839:
819:
794:
786:
783:
780:
774:
771:
768:
765:
758:
757:
756:
742:
722:
702:
694:
689:
669:
666:
661:
658:
651:
650:
649:
635:
628:
612:
592:
581:Annualization
578:
557:
554:
548:
545:
542:
539:
536:
531:
528:
525:
522:
519:
516:
513:
510:
507:
504:
501:
491:
490:
489:
486:
482:
473:
470:
466:
458:
441:
438:
432:
429:
426:
422:
393:
389:
381:
380:
362:
358:
350:
349:
348:
327:
323:
316:
312:
308:
303:
299:
292:
289:
282:
281:
280:
266:
259:
255:
243:Single-period
240:
236:
234:
230:
220:
218:
214:
210:
206:
201:
199:
198:annualization
195:
190:
188:
182:
180:
179:
173:
171:
167:
163:
159:
155:
151:
147:
143:
139:
135:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
7122:
7108:
7098:
7084:
7070:
7043:
7032:. Retrieved
7028:
7019:
7010:
7005:
6972:
6966:
6933:
6927:
6908:
6902:
6877:
6869:
6854:
6839:
6825:
6817:the original
6807:
6652:
6490:
6388:
6278:
6200:
6197:
6194:
6191:
6188:
6185:
6182:
6121:
6114:
6103:
6101:
6083:
6079:
6070:
6062:
6042:Mutual funds
6040:
6031:
6019:
5948:
5924:
5861:Stock price
5839:4th quarter
5807:
5783:
5774:
5771:
5768:
5764:
5755:
5746:
5683:
5610:
5601:
5543:
5540:
5467:4th quarter
5442:
5430:
5404:
5381:
5375:
5367:
5362:capital gain
5354:
5345:
5337:
5331:
5324:
5300:
5292:
5284:
5274:perspective.
5197:
5128:
5124:
5120:
5117:
5113:
5045:
4894:
4758:
4667:
4658:
4655:
4652:
4649:
4645:
4633:
4404:
4119:
3993:
3984:
3946:
3941:
3935:
3815:
3807:
3683:
3681:
3664:
3660:
3658:
3643:
3634:
3619:Please help
3607:
3583:
3571:
3568:
3500:
3379:
3269:
3263:
3261:
3054:
3048:
3042:
3028:
3025:
2874:
2872:
2863:
2860:
2622:
2497:
2493:
2379:
2372:
2076:
2002:
1953:
1755:
1752:
1744:
1623:
1468:
1459:
1393:
1299:
1206:
1204:
1114:
1110:
1108:
1099:
1095:
1091:
1086:
1081:
996:
995:
992:
942:
811:
690:
686:
626:
584:
575:
487:
483:
479:
471:
467:
464:
411:
346:
257:
253:
251:
237:
232:
228:
226:
202:
197:
193:
191:
186:
183:
176:
174:
137:
131:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
7355:Risk return
7302:Price-sales
7240:(EV/EBITDA)
5836:3rd quarter
5833:2nd quarter
5830:1st quarter
5518:$ 1,040.60
5484:$ 1,030.30
5464:3rd quarter
5461:2nd quarter
5458:1st quarter
5438:Compounding
5390:offers for
2492:, then the
693:compounding
223:Calculation
7398:Categories
7252:(EV/Sales)
7206:(Cap Rate)
7093:0073226386
7034:2020-10-06
6799:References
5811:volatility
5515:$ 1,030.30
5512:$ 1,020.10
5509:$ 1,010.00
5481:$ 1,020.10
5376:(“liquid”)
5040:($ 89.25)
3663:(MWRR) or
2865:formula).
156:payments,
150:cash flows
146:investment
110:April 2021
80:newspapers
6991:cite book
6950:235264677
6753:%
6711:−
6689:−
6660:formula,
6430:$ 141.60
6256:−
6004:%
5977:
5907:1.040608
5890:0.010404
5844:Dividend
5666:−
5579:−
5557:%
5396:risk-free
5347:inflation
5281:inflation
5094:%
5088:−
5079:−
5063:−
4943:%
4937:−
4928:−
4912:−
4889:($ 6.40)
4792:%
4780:−
4739:$ 121.55
4252:−
3850:cash flow
3732:∑
3608:does not
3541:−
3532:−
3518:−
3486:%
3480:−
3471:−
3462:−
3445:−
3415:−
3365:%
3359:−
3350:−
3341:−
3332:−
3302:−
3244:−
3194:∏
3181:−
3123:∏
3075:¯
2995:⋯
2934:∑
2914:¯
2819:⋯
2691:∑
2586:⋯
2467:⋯
2348:−
2333:−
2314:−
2053:−
1965:−
1916:−
1853:−
1247:
1158:
978:%
966:−
925:−
896:−
561:%
517:−
445:%
309:−
231:, or the
7246:(EV/GCI)
7051:(1998).
6511:See also
6450:$ 21.31
6427:$ 181.73
5925:$ 103.02
5921:$ 105.08
5918:$ 103.04
5904:1.030204
5901:1.020204
5898:1.010204
5881:0.010204
5501:$ 10.30
5026:$ 10.75
4875:$ 93.60
4872:$ 156.00
4869:$ 120.00
4866:$ 150.00
4753:$ 21.55
4736:$ 115.76
4733:$ 110.25
4730:$ 105.00
4641:volatile
3852:at time
1205:and the
154:interest
7383:Treynor
7372:Sortino
7351:(RAROC)
7212:(CROCI)
6958:1549328
6522:Average
6447:$ 22.98
6444:$ 20.88
6441:$ 19.90
6438:$ 17.28
6424:$ 57.10
6421:$ 48.73
6418:$ 22.52
6410:84.752
6389:$ 19.90
6385:$ 20.62
6382:$ 20.06
6379:$ 19.49
6376:$ 17.50
6368:$ 1.65
6348:$ 1.12
6328:$ 0.53
6308:Year 5
6284:Example
6183:Where:
5943:−1.96%
5856:$ 1.03
5827:End of:
5761:Example
5498:$ 10.20
5495:$ 10.10
5478:$ 1,010
5475:$ 1,000
5434:capital
5386:that a
5214:In the
5150:Year 4
5009:−42.7%
4975:Year 4
4824:Year 4
4688:Year 4
4399:69.31%
4387:−1.005%
4384:−69.31%
3808:where:
3629:removed
3614:sources
1394:where:
347:where:
256:or the
158:coupons
134:finance
94:scholar
7361:Sharpe
7345:(ROTE)
7333:(ROCE)
7321:(RONA)
7286:(P/CF)
7280:(PVGO)
7200:(CAPE)
7139:
7129:
7115:
7091:
7077:
6979:
6956:
6948:
6915:
6890:
6765:(i.e.
6491:91.314
6487:84.752
6484:76.859
6481:74.125
6478:71.676
6470:6.562
6407:76.859
6404:74.125
6401:71.676
6398:70.373
6365:$ 2.36
6362:$ 0.77
6359:$ 0.68
6356:$ 0.32
6345:$ 1.86
6342:$ 0.47
6339:$ 0.39
6336:$ 0.06
6325:$ 0.50
6322:$ 0.30
6319:$ 0.29
6316:$ 0.26
6305:Year 4
6302:Year 3
6299:Year 2
6296:Year 1
5986:103.02
5853:$ 1.02
5850:$ 1.01
5684:where
5336:their
5226:, and
5207:, and
5147:Year 3
5144:Year 2
5141:Year 1
5066:0.4274
5023:$ 5.00
5020:$ 5.00
5017:$ 5.00
5006:−63.2%
5003:−77.6%
4972:Year 3
4969:Year 2
4966:Year 1
4915:0.0164
4858:−1.6%
4821:Year 3
4818:Year 2
4815:Year 1
4685:Year 3
4682:Year 2
4679:Year 1
4396:40.55%
4393:0.995%
4294:$ 100
4276:−$ 100
4229:$ 200
4177:$ 100
3848:= net
3544:0.0164
3521:0.0640
3474:0.0164
3353:0.0640
1123:, is:
254:return
248:Return
229:return
144:on an
142:profit
138:return
96:
89:
82:
75:
67:
7379:(SGR)
7368:(SIR)
7357:(RRR)
7339:(ROE)
7327:(ROC)
7315:(ROA)
7304:(P/S)
7298:(PEG)
7292:(P/E)
7274:(P/B)
7262:Omega
7258:(LTV)
7234:(E/P)
7218:(D/E)
6946:S2CID
6644:Notes
6638:Yield
6506:year.
6467:7.893
6464:2.734
6461:2.449
6458:1.303
5940:1.98%
5937:4.08%
5873:$ 99
5870:$ 102
5867:$ 101
5544:yield
5349:rates
5306:Many
5235:taxes
5167:$ 50
5158:$ 100
5091:89.25
4992:115%
4841:−40%
4789:21.55
4339:100%
4321:−100%
4279:−$ 50
4226:$ 150
4223:$ 101
4220:$ 100
4174:$ 100
4171:$ 100
4168:$ 100
4165:$ 100
4162:$ 100
4159:$ 100
2877:over
2110:and
1722:, if
956:1.331
140:is a
101:JSTOR
87:books
7137:ISBN
7127:ISBN
7113:ISBN
7089:ISBN
7075:ISBN
6997:link
6977:ISBN
6954:SSRN
6934:SSRN
6913:ISBN
6888:ISBN
6736:For
6001:2.98
5915:$ 99
5887:0.01
5884:0.01
5864:$ 98
5566:1.01
5554:4.06
5492:$ 10
5415:risk
5388:bank
5356:risk
5191:Uses
5178:5.5%
5172:ROI
5164:$ 60
5161:$ 55
5000:−95%
4983:−95%
4852:9.5%
4835:−20%
4771:1.05
4457:and
4324:−50%
4291:$ 50
4282:−$ 1
4217:$ 99
4214:$ 50
4102:>
3816:and
3682:The
3612:any
3610:cite
3580:Fees
3483:1.64
3448:0.40
3433:0.30
3418:0.20
3403:0.50
3362:6.40
3335:0.40
3320:0.30
3305:0.20
3290:0.50
2873:The
1559:is:
1209:is:
1109:The
755:is:
558:12.2
227:The
203:The
164:and
73:news
6938:doi
6750:100
6087:IRS
5989:100
5934:−1%
5847:$ 1
5535:1%
5184:5%
5175:10%
4940:6.4
4855:16%
4849:50%
4838:30%
4832:50%
4722:5%
4705:5%
4336:50%
4327:−1%
4288:$ 1
4285:$ 0
4211:$ 0
3957:NPV
3723:NPV
3623:by
2496:or
1624:so
1113:or
549:000
543:200
532:000
526:200
514:400
508:346
433:000
219:).
132:In
56:by
7400::
7027:.
6993:}}
6989:{{
6952:.
6944:.
6936:.
6886:.
5974:ln
5594:.
5532:1%
5529:1%
5526:1%
5329:.
5181:6%
4989:0%
4986:0%
4719:5%
4716:5%
4713:5%
4702:5%
4699:5%
4696:5%
4390:0%
4381:−∞
4333:1%
4330:0%
4117:.
2143::
1244:ln
1155:ln
975:10
852::
648::
457:.
423:30
215:,
211:,
200:.
189:.
172:.
160:,
136:,
7174:e
7167:t
7160:v
7055:.
7037:.
6999:)
6985:.
6960:.
6940::
6921:.
6896:.
6884:8
6863:.
6848:.
6833:.
6779:1
6776:=
6773:x
6747:=
6744:x
6724:.
6719:2
6715:y
6706:2
6702:x
6698:=
6695:)
6692:y
6686:x
6683:(
6680:)
6677:y
6674:+
6671:x
6668:(
6259:1
6251:n
6247:/
6243:1
6238:)
6233:P
6229:V
6226:R
6223:E
6217:(
6212:=
6209:T
6168:V
6165:R
6162:E
6159:=
6154:n
6149:)
6145:T
6142:+
6139:1
6135:(
6130:P
6016:.
5998:=
5994:)
5981:(
5729:c
5725:r
5700:i
5696:r
5669:1
5663:)
5658:c
5654:r
5650:+
5647:1
5644:(
5641:)
5636:i
5632:r
5628:+
5625:1
5622:(
5582:1
5574:4
5570:)
5563:(
5560:=
5364:)
5230:.
5211:.
5085:=
5082:1
5074:4
5070:)
5060:1
5057:(
4934:=
4931:1
4923:4
4919:)
4909:1
4906:(
4786:=
4783:1
4775:4
4622:.
4608:2
4605:,
4601:g
4598:o
4595:l
4590:R
4586:+
4581:1
4578:,
4574:g
4571:o
4568:l
4563:R
4559:=
4553:g
4550:o
4547:l
4542:R
4518:g
4515:o
4512:l
4507:R
4484:2
4481:,
4477:g
4474:o
4471:l
4466:R
4443:1
4440:,
4436:g
4433:o
4430:l
4425:R
4364:g
4361:o
4358:l
4353:r
4307:r
4260:i
4256:V
4247:f
4243:V
4195:f
4191:V
4143:i
4139:V
4105:0
4097:i
4093:V
4088:/
4082:f
4078:V
4057:r
4034:g
4031:o
4028:l
4023:r
4002:r
3965:0
3962:=
3917:n
3913:C
3888:0
3884:C
3861:t
3833:t
3829:C
3793:0
3790:=
3782:t
3778:)
3774:r
3771:+
3768:1
3765:(
3759:t
3755:C
3747:n
3742:0
3739:=
3736:t
3728:=
3698:r
3650:)
3644:(
3639:)
3635:(
3631:.
3617:.
3538:=
3535:1
3526:4
3515:1
3477:=
3468:=
3465:1
3456:4
3451:)
3442:1
3439:(
3436:)
3430:+
3427:1
3424:(
3421:)
3412:1
3409:(
3406:)
3400:+
3397:1
3394:(
3356:=
3347:=
3344:1
3338:)
3329:1
3326:(
3323:)
3317:+
3314:1
3311:(
3308:)
3299:1
3296:(
3293:)
3287:+
3284:1
3281:(
3264:n
3247:1
3238:n
3233:)
3228:i
3224:r
3220:+
3217:1
3214:(
3209:n
3204:1
3201:=
3198:i
3187:=
3184:1
3175:n
3172:1
3166:)
3162:)
3157:i
3153:r
3149:+
3146:1
3143:(
3138:n
3133:1
3130:=
3127:i
3118:(
3113:=
3107:c
3104:i
3101:r
3098:t
3095:e
3092:m
3089:o
3086:e
3083:g
3072:r
3055:n
3011:)
3006:n
3002:r
2998:+
2992:+
2987:1
2983:r
2979:(
2974:n
2971:1
2966:=
2960:i
2956:r
2949:n
2944:1
2941:=
2938:i
2928:n
2925:1
2920:=
2911:r
2885:n
2844:n
2841:,
2837:g
2834:o
2831:l
2826:R
2822:+
2816:+
2811:3
2808:,
2804:g
2801:o
2798:l
2793:R
2789:+
2784:2
2781:,
2777:g
2774:o
2771:l
2766:R
2762:+
2757:1
2754:,
2750:g
2747:o
2744:l
2739:R
2735:=
2730:i
2727:,
2723:g
2720:o
2717:l
2712:R
2706:n
2701:1
2698:=
2695:i
2687:=
2681:g
2678:o
2675:l
2670:R
2643:g
2640:o
2637:l
2632:R
2608:)
2603:n
2599:R
2595:+
2592:1
2589:(
2583:)
2578:2
2574:R
2570:+
2567:1
2564:(
2561:)
2556:1
2552:R
2548:+
2545:1
2542:(
2539:=
2536:R
2533:+
2530:1
2507:R
2478:n
2474:R
2470:,
2464:,
2459:3
2455:R
2451:,
2446:2
2442:R
2438:,
2433:1
2429:R
2408:n
2388:n
2355:A
2351:A
2345:C
2339:=
2336:1
2328:A
2325:C
2320:=
2317:1
2311:)
2306:2
2302:R
2298:+
2295:1
2292:(
2289:)
2284:1
2280:R
2276:+
2273:1
2270:(
2245:A
2242:C
2237:=
2233:)
2228:B
2225:C
2220:(
2215:)
2210:A
2207:B
2202:(
2198:=
2195:)
2190:2
2186:R
2182:+
2179:1
2176:(
2173:)
2168:1
2164:R
2160:+
2157:1
2154:(
2129:2
2125:R
2121:+
2118:1
2096:1
2092:R
2088:+
2085:1
2060:B
2056:B
2050:C
2044:=
2039:2
2035:R
2011:C
1988:B
1968:A
1962:B
1936:A
1933:B
1928:=
1923:A
1919:A
1913:B
1907:+
1904:1
1901:=
1896:1
1892:R
1888:+
1885:1
1860:A
1856:A
1850:B
1844:=
1839:1
1835:R
1809:1
1805:R
1784:B
1764:A
1730:t
1707:g
1704:o
1701:l
1696:R
1673:t
1667:g
1664:o
1661:l
1656:R
1650:=
1644:g
1641:o
1638:l
1633:r
1609:t
1603:g
1600:o
1597:l
1592:r
1588:=
1582:g
1579:o
1576:l
1571:R
1547:t
1524:g
1521:o
1518:l
1513:r
1489:g
1486:o
1483:l
1478:R
1444:t
1417:g
1414:o
1411:l
1406:r
1377:t
1371:g
1368:o
1365:l
1360:r
1355:e
1349:i
1345:V
1341:=
1336:f
1332:V
1308:r
1283:t
1278:)
1271:i
1267:V
1261:f
1257:V
1251:(
1238:=
1232:g
1229:o
1226:l
1221:r
1189:)
1182:i
1178:V
1172:f
1168:V
1162:(
1152:=
1146:g
1143:o
1140:l
1135:R
1067:r
1047:t
1027:r
1007:R
972:=
969:1
960:3
928:1
919:t
914:R
911:+
908:1
902:=
899:1
890:t
887:1
882:)
878:R
875:+
872:1
869:(
866:=
863:r
840:r
820:R
795:t
791:)
787:r
784:+
781:1
778:(
775:=
772:R
769:+
766:1
743:t
723:R
703:r
670:t
667:R
662:=
659:r
636:r
613:t
593:R
555:=
546:,
540:,
537:1
529:,
523:,
520:1
511:,
505:,
502:1
442:3
439:=
430:,
427:1
394:i
390:V
363:f
359:V
328:i
324:V
317:i
313:V
304:f
300:V
293:=
290:R
267:R
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.