Rate of return - Knowledge (XXG)

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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

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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. 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. 3599: 36: 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 Unless the interest is withdrawn at the end of each quarter, it will earn more interest in the next quarter. 6081: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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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.)

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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

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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

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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

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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.

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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%.

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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.

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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

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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

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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

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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.

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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%.

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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.

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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.

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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

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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).

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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.

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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

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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.

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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:

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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%.

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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

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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%

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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,

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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%

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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:

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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.

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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

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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.

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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%.

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Hudson, Robert; Gregoriou, Andros (2010-02-07). "Calculating and Comparing Security Returns is Harder than you Think: A Comparison between Logarithmic and Simple Returns".

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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.

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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.

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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.

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Ratios typically used by financial analysts to compare a company's performance over time or compare performance between companies include return on investment (ROI),

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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.

6996: 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: 7197: 5542:

percentage yield, compound interest) is higher than for simple interest because the interest is reinvested as capital and then itself earns interest. The

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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).

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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

7048: 6116: 6065: 4536: 3386: 1129: 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} 7277: 6916: 6891: 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

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contracts, and bank-sponsored commingled funds, collective benefit funds or common trust funds, all derive their value from an underlying

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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: 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: 7140: 7130: 7116: 7078: 6980: 6049: 3646: 3038: 119: 5969: 7348: 7099: 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 3620: 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: 53: 6860: 7423: 7165: 7092: 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.

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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: 57: 2525: 1565: 7024: 72: 7428: 6124: 5959:

The final investment value of $ 103.02 compared with the initial investment of $ 100 means the return is $ 3.02 or 3.02%.

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either longer or shorter than one year, such as a month, or two years, annualized for comparison with a one-year return.

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The geometric average return over the 4-year period was −1.64%. Over 4 years, this translates into an overall return of:

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with no information provided about the timing of the installments. The rate of return is 4,000 / 100,000 = 4% per year.

6532: 79: 6060:. Investors and other parties are interested to know how the investment has performed over various periods of time. 3609: 2423: 285: 7408: 7330: 216: 5332:

Factors that investors may use to determine the rate of return at which they are willing to invest money include:

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For example, assuming reinvestment, the cumulative return for four annual returns of 50%, -20%, 30%, and −40% is:

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

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period return over the overall period can be calculated by combining the returns within each of the subperiods.

86: 5052: 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:

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For a return of +20%, followed by −20%, this again has an average return of 0%, but an overall return of −4%.

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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: 7433: 7376: 6572: 6557: 6516: 5395: 5338: 5219: 3677: 2029: 1829: 949: 68: 5617: 5444: 4460: 4419: 1115: 7301: 5549: 207:(ROI) is return per dollar invested. It is a measure of investment performance, as opposed to size (c.f. 7283: 7226: 6657: 6577: 6567: 6552: 6542: 5368: 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: 169: 165: 4636: 5310:

include ROI in a player's tracked statistics, assisting users in evaluating an opponent's performance.

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The geometric average rate of return was 5%. Over 4 years, this translates into an overall return of:

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shares, totalling a final value of 1,030. The change in value is 1,030 − 1,000 = 30, so the return is

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This formula can be used on a sequence of logarithmic rates of return over equal successive periods.

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Carl Bacon. Practical Portfolio Performance Measurement and Attribution. West Sussex: Wiley, 2003.

6622: 6617: 6612: 6057: 5326: 5320: 5227: 3016:{\displaystyle {\bar {r}}={\frac {1}{n}}\sum _{i=1}^{n}{r_{i}}={\frac {1}{n}}(r_{1}+\cdots +r_{n})} 761: 141: 3686:(IRR) (which is a variety of money-weighted rate of return) is the rate of return which makes the 6990: 6945: 6831:"rate of return: definition of rate of return in Oxford dictionary (British & World English)" 4237: 7354: 7324: 7192: 7136: 7126: 7112: 7088: 7074: 6976: 6957: 6953: 6912: 6887: 6883: 6816: 6607: 6597: 6582: 6537: 6527: 5437: 5433: 5426: 5417:, the higher the discount rate (rate of return) the investor will demand from the investment. 5223: 5215: 3687: 1120: 692: 6739: 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 " 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

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The use of logarithmic returns prevents investment prices in models from becoming negative.

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The appropriate method of annualization depends on whether returns are reinvested or not.

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Comparison of ordinary returns and logarithmic returns for an initial investment of $ 100

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The rate of return which an investor requires from a particular investment is called the

3855: 1957: 235:, can be calculated over a single period. The single period may last any length of time. 7231: 7221: 6592: 5784:

The return between the beginning of 2015 and the end of January 2016 in US dollars is:

5414: 5355: 5296: 4302: 4052: 3997: 3693: 3049: 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.

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is the return on the investment in the first currency (US dollars in our example), and

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are logarithmic returns in successive periods, then the overall logarithmic return

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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

6813:"return: definition of return in Oxford dictionary (British & World English)" 1082:

According to the CFA Institute's Global Investment Performance Standards (GIPS),

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Return measures the increase in size of an asset or liability or short position.

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US mutual funds are to compute average annual total return as prescribed by the

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Example: Stock with low volatility and a regular quarterly dividend, reinvested

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invested for the next period (or reduces it, in the case of a negative return).

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Investments generate returns to the investor to compensate the investor for the

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an arithmetic return of −50% is equivalent to a logarithmic return of −69.31%.

5813:". If the price often changes a great deal, the stock has "high volatility". 149: 145: 5956:

The number of shares purchased each quarter = ($ Dividend)/($ Stock Price).

7295: 7271: 7237: 5346: 5280: 4615:{\displaystyle R_{\mathrm {log} }=R_{\mathrm {log} ,1}+R_{\mathrm {log} ,2}} 3849: 161: 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)} 7249: 6941: 153: 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:

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If the returns are logarithmic returns, however, the logarithmic return

6521: 133: 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:

7243: 5953:

The quarterly dividend is reinvested at the quarter-end stock price.

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." 7209: 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 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}}} 5387: 472:

If the initial value is zero, then no return can be calculated.

7154: 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\%} 6086: 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%

5234: 4959:

Example #3 Highly volatile rates of return, including losses

3592: 2400:

periods, assuming returns are reinvested, if the returns over

691:

Assuming returns are reinvested however, due to the effect of

29: 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)

4630:

Comparing geometric with arithmetic average rates of return

1687:

is the annualized logarithmic rate of return for a return

7097:

Richard A. Brealey, Stewart C. Myers and Franklin Allen.

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 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. 5820: 5374:

whether or not the investors want the money available

5295:(i.e., unadjusted annual return) less than the annual 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} 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

5218:process, companies would traditionally compare the 60:. Unsourced material may be challenged and removed. 6909:Portfolio construction, management, and protection 6783: 6757: 6728: 6264: 6173: 6008: 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 6064:performance returns of one fund to another, the 5546:or annualized return on the above investment is 3047:, the appropriate average rate of return is the 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. 4643:the performance, the greater the difference. 1105:Logarithmic or continuously compounded return 175:A loss instead of a profit is described as a 8: 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). 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: 7151: 6995:: CS1 maint: location missing publisher ( 6037:Mutual fund and investment company returns 7083:Zvi Bodie, Alex Kane and Alan J. Marcus. 6770: 6741: 6717: 6704: 6665: 6245: 6241: 6219: 6207: 6205: 6152: 6128: 6126: 5983: 5971: 5727: 5721: 5698: 5692: 5656: 5634: 5619: 5572: 5551: 5099:{\displaystyle (1-0.4274)^{4}-1=-89.25\%} 5072: 5054: 4921: 4903: 4773: 4767: 4593: 4592: 4566: 4565: 4545: 4544: 4538: 4510: 4509: 4503: 4469: 4468: 4462: 4428: 4427: 4421: 4356: 4355: 4349: 4304: 4258: 4245: 4239: 4193: 4187: 4141: 4135: 4095: 4086: 4080: 4074: 4054: 4026: 4025: 4019: 3999: 3954: 3952: 3915: 3910: 3908: 3886: 3881: 3879: 3859: 3857: 3831: 3826: 3824: 3780: 3757: 3751: 3745: 3734: 3720: 3718: 3695: 3647:Learn how and when to remove this message 3524: 3511: 3509: 3454: 3390: 3388: 3278: 3236: 3226: 3207: 3196: 3189: 3169: 3155: 3136: 3125: 3081: 3080: 3069: 3068: 3065: 3004: 2985: 2968: 2958: 2953: 2947: 2936: 2922: 2908: 2907: 2905: 2882: 2829: 2828: 2796: 2795: 2769: 2768: 2742: 2741: 2715: 2714: 2704: 2693: 2673: 2672: 2666: 2635: 2634: 2628: 2601: 2576: 2554: 2527: 2504: 2476: 2457: 2444: 2431: 2425: 2405: 2385: 2341: 2322: 2304: 2282: 2267: 2239: 2222: 2204: 2188: 2166: 2151: 2127: 2115: 2094: 2082: 2046: 2037: 2031: 2008: 1985: 1959: 1950:is the growth factor in the first period. 1930: 1909: 1894: 1882: 1846: 1837: 1831: 1807: 1801: 1781: 1761: 1727: 1699: 1698: 1692: 1659: 1658: 1652: 1636: 1635: 1629: 1595: 1594: 1574: 1573: 1567: 1544: 1516: 1515: 1509: 1481: 1480: 1474: 1441: 1409: 1408: 1402: 1363: 1362: 1357: 1347: 1334: 1328: 1305: 1269: 1259: 1253: 1240: 1224: 1223: 1217: 1180: 1170: 1164: 1138: 1137: 1131: 1064: 1044: 1024: 1004: 958: 953: 951: 917: 904: 884: 860: 837: 817: 793: 763: 740: 720: 700: 664: 656: 633: 610: 590: 498: 496: 420: 418: 392: 386: 361: 355: 326: 315: 302: 295: 287: 264: 120:Learn how and when to remove this message 6287: 5449: 5134:Cash flow example on $ 1,000 investment 5132: 4957: 4806: 4670: 4123: 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 6804: 6729:{\displaystyle (x+y)(x-y)=x^{2}-y^{2}.} 6649: 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\%} 7087:. New York: McGraw-Hill/Irwin, 2004. 7085:Essentials of Investments, 5th Edition 6988: 6882:. Cambridge University Press. p. 6275:Mutual fund capital gain distributions 6048:and related variable products such as 6025:Cost Basis = $ 100 + $ 4.06 = $ 104.06 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 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 7: 7244:Enterprise value/gross cash invested 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 58:adding citations to reliable sources 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 7123:Investment Performance Measurement 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: 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 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 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}}} 34: 7349:Risk-adjusted return on capital 7100:Principles of Corporate Finance 5793:Returns when capital is at risk 2420:successive time subperiods are 45:needs additional citations for 6975:. New York. pp. 442–456. 6859:John Simpson (6 August 2012). 6694: 6682: 6679: 6667: 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: 1: 7071:Barron's Finance, 4th Edition 6973:Barron's Finance, 4th Edition 6861:"CIPM Exam Tips & Tricks" 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 1432:= logarithmic rate of return 1019:to an annual rate of return 7029:Corporate Finance Institute 6533:Compound annual growth rate 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}} 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% 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 7296:Price-earnings to growth 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 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 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:Annualized 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: 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: 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: 5392:deposit accounts 5289:purchasing power 5209:return on assets 5205:return on equity 5136: 5105: 5103: 5102: 5097: 5077: 5076: 4961: 4954: 4952: 4951: 4946: 4926: 4925: 4810: 4803: 4801: 4800: 4795: 4778: 4777: 4674: 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: 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: 7047: 7046: 7042: 7033: 7031: 7023: 7022: 7018: 7009: 7008: 7004: 6987: 6983: 6970: 6969: 6965: 6931: 6930: 6926: 6919: 6906: 6905: 6901: 6894: 6873: 6872: 6868: 6858: 6857: 6853: 6844: 6842: 6838: 6829: 6828: 6824: 6811: 6810: 6806: 6801: 6796: 6795: 6767: 6766: 6738: 6737: 6713: 6700: 6662: 6661: 6655: 6651: 6646: 6633:Value investing 6563:Expected return 6513: 6286: 6277: 6221: 6215: 6214: 6202: 6201: 6137: 6133: 6132: 6123: 6122: 6113: 6100: 6092:net asset value 6039: 5979: 5968: 5967: 5819: 5806: 5800: 5795: 5763: 5754: 5723: 5718: 5717: 5694: 5689: 5688: 5652: 5630: 5616: 5615: 5600: 5568: 5548: 5547: 5429: 5423: 5411:cost of capital 5378:for other uses. 5323: 5317: 5193: 5112: 5068: 5051: 5050: 4980:Rate of return 4917: 4900: 4899: 4829:Rate of return 4769: 4764: 4763: 4693:Rate of return 4666: 4632: 4588: 4561: 4540: 4535: 4534: 4505: 4500: 4499: 4464: 4459: 4458: 4423: 4418: 4417: 4351: 4346: 4345: 4301: 4300: 4254: 4241: 4236: 4235: 4189: 4184: 4183: 4137: 4132: 4131: 4091: 4076: 4071: 4070: 4051: 4050: 4021: 4016: 4015: 3996: 3995: 3992: 3983: 3949: 3948: 3938:cost of capital 3911: 3905: 3904: 3882: 3876: 3875: 3854: 3853: 3827: 3821: 3820: 3776: 3763: 3753: 3715: 3714: 3692: 3691: 3680: 3674: 3653: 3642: 3636: 3633: 3618: 3602: 3591: 3582: 3567: 3562: 3513: 3506: 3505: 3392: 3385: 3384: 3275: 3274: 3222: 3191: 3151: 3120: 3116: 3115: 3067: 3062: 3061: 3041: 3035: 3000: 2981: 2954: 2902: 2901: 2879: 2878: 2871: 2824: 2791: 2764: 2737: 2710: 2668: 2663: 2662: 2630: 2625: 2624: 2597: 2572: 2550: 2524: 2523: 2501: 2500: 2472: 2453: 2440: 2427: 2422: 2421: 2402: 2401: 2382: 2381: 2343: 2300: 2278: 2264: 2263: 2218: 2200: 2184: 2162: 2148: 2147: 2123: 2112: 2111: 2090: 2079: 2078: 2048: 2033: 2028: 2027: 2005: 2004: 1982: 1981: 1956: 1955: 1911: 1890: 1879: 1878: 1848: 1833: 1828: 1827: 1803: 1798: 1797: 1778: 1777: 1758: 1757: 1751: 1724: 1723: 1694: 1689: 1688: 1654: 1631: 1626: 1625: 1590: 1569: 1564: 1563: 1541: 1540: 1511: 1506: 1505: 1476: 1471: 1470: 1467: 1438: 1437: 1404: 1399: 1398: 1358: 1353: 1343: 1330: 1325: 1324: 1302: 1301: 1265: 1255: 1249: 1242: 1219: 1214: 1213: 1176: 1166: 1160: 1133: 1128: 1127: 1107: 1061: 1060: 1041: 1040: 1021: 1020: 1001: 1000: 948: 947: 906: 880: 857: 856: 834: 833: 814: 813: 789: 760: 759: 737: 736: 717: 716: 715:, and a return 697: 696: 653: 652: 630: 629: 607: 606: 587: 586: 583: 535: 500: 493: 492: 478: 463: 425: 415: 414: 408:= initial value 388: 383: 382: 357: 352: 351: 322: 311: 298: 297: 284: 283: 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: 7445: 7437: 7436: 7434:Temporal rates 7431: 7426: 7421: 7416: 7411: 7406: 7396: 7395: 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: 7180: 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: 24: 14: 13: 10: 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: 7146: 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: 7063: 7054: 7050: 7044: 7041: 7030: 7026: 7020: 7017: 7012: 7006: 7003: 6998: 6992: 6984: 6982:0-7641-1275-9 6978: 6974: 6967: 6964: 6959: 6955: 6951: 6947: 6943: 6939: 6935: 6928: 6925: 6920: 6914: 6910: 6903: 6900: 6895: 6889: 6885: 6880: 6879: 6870: 6867: 6862: 6855: 6852: 6847: 6840: 6837: 6832: 6826: 6823: 6818: 6814: 6808: 6805: 6798: 6778: 6775: 6772: 6749: 6746: 6743: 6723: 6718: 6714: 6710: 6705: 6701: 6697: 6691: 6688: 6685: 6676: 6673: 6670: 6659: 6656:Consider the 6653: 6650: 6643: 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: 6510: 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: 6283: 6281: 6274: 6272: 6258: 6255: 6246: 6242: 6237: 6216: 6211: 6199: 6196: 6193: 6190: 6187: 6184: 6181: 6158: 6148: 6141: 6138: 6134: 6120: 6118: 6110: 6108: 6107:each period. 6105: 6104:total returns 6098:Total returns 6097: 6095: 6093: 6088: 6082: 6078: 6075: 6069: 6067: 6061: 6059: 6055: 6052:policies and 6051: 6047: 6043: 6036: 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: 5816: 5814: 5812: 5805: 5797: 5792: 5787: 5786: 5785: 5779: 5778: 5777: 5773: 5770: 5767: 5760: 5758: 5751: 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: 5597: 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: 5420: 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: 5314: 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: 5190: 5183: 5180: 5177: 5174: 5171: 5170: 5166: 5163: 5160: 5157: 5154: 5153: 5149: 5146: 5143: 5140: 5138: 5137: 5131: 5127: 5123: 5119: 5116: 5109: 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: 4663: 4661: 4657: 4654: 4651: 4648: 4644: 4642: 4638: 4629: 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: 3989: 3987: 3980: 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: 3671: 3669: 3666: 3662: 3651: 3648: 3640: 3637:February 2020 3630: 3626: 3622: 3616: 3615: 3611: 3606:This section 3604: 3600: 3595: 3594: 3588: 3586: 3579: 3577: 3575: 3574: 3564: 3559: 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: 3032: 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: 2868: 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: 1748: 1746: 1743: 1729: 1695: 1672: 1655: 1649: 1632: 1608: 1591: 1587: 1570: 1562: 1561: 1560: 1546: 1512: 1477: 1464: 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: 1104: 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 580: 578: 557: 554: 548: 545: 542: 539: 536: 531: 528: 525: 522: 519: 516: 513: 510: 507: 504: 501: 491: 490: 489: 486: 482: 475: 473: 470: 466: 460: 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: 247: 243:Single-period 242: 240: 236: 234: 230: 222: 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:)

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Index