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58-398: The price–earnings ratio , also known as P/E ratio , P/E , or PER , is the ratio of a company's share (stock) price to the company's earnings per share . The ratio is used for valuing companies and to find out whether they are overvalued or undervalued. As an example, if share A is trading at $ 24 and the earnings per share for the most recent 12-month period is $ 3 , then share A has

116-432: A 2 , … , a n } {\textstyle \left\{a_{1},a_{2},\,\ldots ,\,a_{n}\right\}} is given by: That is, the n th root of the product of the elements. For example, for 1 , 2 , 3 , 4 {\textstyle 1,2,3,4} , the product 1 ⋅ 2 ⋅ 3 ⋅ 4 {\textstyle 1\cdot 2\cdot 3\cdot 4}

174-393: A 2 , … , a n > 0 {\displaystyle a_{1},a_{2},\dots ,a_{n}>0} since | ln ⁡ a 1 a 2 ⋯ a n t n = 1 n ln ⁡ ( a 1 a 2 ⋯

232-537: A k {\displaystyle a_{k}} and a k + 1 {\displaystyle a_{k+1}} is a k + 1 / a k {\displaystyle a_{k+1}/a_{k}} . The geometric mean of these growth rates is then just: The fundamental property of the geometric mean, which does not hold for any other mean, is that for two sequences X {\displaystyle X} and Y {\displaystyle Y} of equal length, This makes

290-419: A n ) = 1 n ( ln ⁡ a 1 + ln ⁡ a 2 + ⋯ + ln ⁡ a n ) . {\displaystyle \textstyle {\vphantom {\Big |}}\ln {\sqrt[{n}]{a_{1}a_{2}\cdots a_{n}{\vphantom {t}}}}={\frac {1}{n}}\ln(a_{1}a_{2}\cdots a_{n})={\frac {1}{n}}(\ln a_{1}+\ln a_{2}+\cdots +\ln a_{n}).} This

348-419: A , b ] → ( 0 , ∞ ) {\displaystyle f:[a,b]\to (0,\infty )} is a positive continuous real-valued function, its geometric mean over this interval is For instance, taking the identity function f ( x ) = x {\displaystyle f(x)=x} over the unit interval shows that the geometric mean of the positive numbers between 0 and 1

406-449: A "primary" P/E can be used instead, based on the earnings projections made for the next years to which a discount calculation is applied. As the ratio of a stock (share price) to a flow (earnings per share), the P/E ratio has the units of time. It can be interpreted as the amount of time over which the company would need to sustain its current earnings in order to make enough money to pay back

464-437: A P/E ratio of ⁠ $ 24 / $ 3/year ⁠ = 8 years. Put another way, the purchaser of the share is investing $ 8 for every dollar of annual earnings; or, if earnings stayed constant it would take 8 years to recoup the share price. Companies with losses (negative earnings) or no profit have an undefined P/E ratio (usually shown as "not applicable" or " N/A "); sometimes, however, a negative P/E ratio may be shown. There

522-399: A financial investment. Suppose for example a person invests $ 1000 and achieves annual returns of +10%, −12%, +90%, −30% and +25%, giving a final value of $ 1609. The average percentage growth is the geometric mean of the annual growth ratios (1.10, 0.88, 1.90, 0.70, 1.25), namely 1.0998, an annual average growth of 9.98%. The arithmetic mean of these annual returns – 16.6% per annum –

580-536: A given earnings per share and P/E's fall. The average U.S. equity P/E ratio from 1900 to 2005 is 14 (or 16, depending on whether the geometric mean or the arithmetic mean , respectively, is used to average). Jeremy Siegel has suggested that the average P/E ratio of about 15 (or earnings yield of about 6.6%) arises due to the long-term returns for stocks of about 6.8%. In Stocks for the Long Run , (2002 edition) he had argued that with favorable developments like

638-515: A given sample of points a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} , the geometric mean is the minimizer of whereas the arithmetic mean is the minimizer of Thus, the geometric mean provides a summary of the samples whose exponent best matches the exponents of the samples (in the least squares sense). In computer implementations, naïvely multiplying many numbers together can cause arithmetic overflow or underflow . Calculating

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696-481: A period of several years, one could formulate something of a standardized P/E ratio, which could then be seen as a benchmark and used to indicate whether or not a stock is worth buying. In private equity , the extrapolation of past performance is driven by stale investments. State and local governments that are more fiscally stressed by higher unfunded pension liabilities assume higher portfolio returns through higher inflation assumptions, but this factor does not attenuate

754-399: Is 24 {\textstyle 24} , and the geometric mean is the fourth root of 24, approximately 2.213. The geometric mean can also be expressed as the exponential of the arithmetic mean of logarithms. By using logarithmic identities to transform the formula, the multiplications can be expressed as a sum and the power as a multiplication: When a 1 ,

812-505: Is a general consensus among most investors that a P/E ratio of around 20 is 'fairly valued'. There are multiple versions of the P/E ratio, depending on whether earnings are projected or realized, and the type of earnings. Some people mistakenly use the formula ⁠ market capitalization / net income ⁠ to calculate the P/E ratio. This formula often gives the same answer as ⁠ market price / earnings per share ⁠ , but if new capital has been issued it gives

870-516: Is also the arithmetic-harmonic mean in the sense that if two sequences ( a n {\textstyle a_{n}} ) and ( h n {\textstyle h_{n}} ) are defined: and where h n + 1 {\textstyle h_{n+1}} is the harmonic mean of the previous values of the two sequences, then a n {\textstyle a_{n}} and h n {\textstyle h_{n}} will converge to

928-410: Is equal to 1 e {\displaystyle {\frac {1}{e}}} . In many cases the geometric mean is the best measure to determine the average growth rate of some quantity. For instance, if sales increases by 80% in one year and the next year by 25%, the result is the same as that of a constant growth rate of 50%, since the geometric mean of 1.80 and 1.25 is 1.50. In order to determine

986-405: Is greater than the par value, as in a rights issue, the shares are said to be sold at a premium (variously called share premium , additional paid-in capital or paid-in capital in excess of par). This equation shows the constituents that make up a company's real share capital: This is differentiated from share capital in the accounting sense, as it presents nominal share capital and does not take

1044-496: Is maintained, and that dividends are not paid when a company is not showing a profit above the level of historically recorded legal capital. Geometric mean When the collection of numbers and their geometric mean are plotted in logarithmic scale , the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm ⁠ ln {\displaystyle \ln } ⁠ of each number, finding

1102-489: Is not a meaningful average because growth rates do not combine additively. The geometric mean can be understood in terms of geometry . The geometric mean of two numbers, a {\displaystyle a} and b {\displaystyle b} , is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths a {\displaystyle a} and b {\displaystyle b} . Similarly,

1160-482: Is only obtained when all numbers in the data set are equal; otherwise, the geometric mean is smaller. For example, the geometric mean of 2 and 3 is 2.45, while their arithmetic mean is 2.5. In particular, this means that when a set of non-identical numbers is subjected to a mean-preserving spread — that is, the elements of the set are "spread apart" more from each other while leaving the arithmetic mean unchanged — their geometric mean decreases. If f : [

1218-428: Is possible for the weighted geometric mean. The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound annual growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant growth rate that would yield

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1276-524: Is sometimes called the log-average (not to be confused with the logarithmic average ). It is simply the arithmetic mean of the logarithm-transformed values of a i {\displaystyle a_{i}} (i.e., the arithmetic mean on the log scale), using the exponentiation to return to the original scale, i.e., it is the generalised f-mean with f ( x ) = log ⁡ x {\displaystyle f(x)=\log x} . A logarithm of any base can be used in place of

1334-507: Is the geometric mean of the maximum and minimum distances of the ellipse from a focus ; it is also the geometric mean of the semi-major axis and the semi-latus rectum . The semi-major axis of an ellipse is the geometric mean of the distance from the center to either focus and the distance from the center to either directrix . Another way to think about it is as follows: Consider a circle with radius r {\displaystyle r} . Now take two diametrically opposite points on

1392-462: The Dot-com bubble P/E had risen to 32. The collapse in earnings caused P/E to rise to 46.50 in 2001. It has declined to a more sustainable region of 17. Its decline in recent years has been due to higher earnings growth . Due to the collapse in earnings and rapid stock market recovery following the 2020 Coronavirus Crash , the trailing P/E ratio reached 38.3 on October 12, 2020. This elevated level

1450-545: The "average" growth per year is 44.2249%. If we start with 100 oranges and let the number grow with 44.2249% each year, the result is 300 oranges. The geometric mean has from time to time been used to calculate financial indices (the averaging is over the components of the index). For example, in the past the FT 30 index used a geometric mean. It is also used in the CPI calculation and recently introduced " RPIJ " measure of inflation in

1508-458: The PER does not in itself indicate whether the share is a bargain. The PER depends on the market's perception of the risk and future growth in earnings. A company with a low PER indicates that the market perceives it as higher risk or lower growth or both as compared to a company with a higher PER. The PER of a listed company's share is the result of the collective perception of the market as to how risky

1566-631: The United Kingdom and in the European Union. This has the effect of understating movements in the index compared to using the arithmetic mean. Although the geometric mean has been relatively rare in computing social statistics, starting from 2010 the United Nations Human Development Index did switch to this mode of calculation, on the grounds that it better reflected the non-substitutable nature of

1624-412: The arithmetic mean and the harmonic mean . For all positive data sets containing at least one pair of unequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between (see Inequality of arithmetic and geometric means .) The geometric mean of a data set { a 1 ,

1682-413: The arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function ⁠ exp {\displaystyle \exp } ⁠ , The geometric mean of two numbers is the square root of their product, for example with numbers ⁠ 2 {\displaystyle 2} ⁠ and ⁠ 8 {\displaystyle 8} ⁠

1740-459: The arithmetic mean), and then normalize that result to one of the computers. The three tables above just give a different weight to each of the programs, explaining the inconsistent results of the arithmetic and harmonic means (Table 4 gives equal weight to both programs, the Table 2 gives a weight of 1/1000 to the second program, and the Table 3 gives a weight of 1/100 to the second program and 1/10 to

1798-427: The arithmetic or harmonic mean would change the ranking of the results depending on what is used as a reference. For example, take the following comparison of execution time of computer programs: Table 1 The arithmetic and geometric means "agree" that computer C is the fastest. However, by presenting appropriately normalized values and using the arithmetic mean, we can show either of the other two computers to be

Price–earnings ratio - Misplaced Pages Continue

1856-589: The average P/E ratio for the S&;P 500 index has ranged from 4.78 in Dec 1920 to 44.20 in Dec 1999. However, except for some brief periods, during 1920–1990 the market P/E ratio was mostly between 10 and 20. The average P/E of the market varies in relation with, among other factors, expected growth of earnings, expected stability of earnings, expected inflation, and yields of competing investments. For example, when U.S. treasury bonds yield high returns, investors pay less for

1914-452: The average growth rate, it is not necessary to take the product of the measured growth rates at every step. Let the quantity be given as the sequence a 0 , a 1 , . . . , a n {\displaystyle a_{0},a_{1},...,a_{n}} , where n {\displaystyle n} is the number of steps from the initial to final state. The growth rate between successive measurements

1972-403: The choice of the geometric mean less obvious than one would expect from the "Properties" section above. The equally distributed welfare equivalent income associated with an Atkinson Index with an inequality aversion parameter of 1.0 is simply the geometric mean of incomes. For values other than one, the equivalent value is an Lp norm divided by the number of elements, with p equal to one minus

2030-433: The company is and what its earnings growth prospects are in relation to that of other companies. Investors use the PER to compare their own perception of the risk and growth of a company against the market's collective perception of the risk and growth as reflected in the current PER. If investors believe that their perception is superior to that of the market, they can make the decision to buy or sell accordingly. Since 1900,

2088-420: The current share price. While the P/E ratio can in principle be given in terms of any time unit, in practice it is essentially always implicitly reported in years, with the unit of "years" rarely indicated explicitly. (This is the convention followed in this article.) The price/earnings ratio (PER) is the most widely used method for determining whether shares are "correctly" valued in relation to one another. But

2146-483: The extrapolative effects of past returns. When a company has no earnings or is posting losses, in both cases P/E will be expressed as "N/A." Though it is possible to calculate a negative P/E, this is not the common convention. Share capital A corporation 's share capital , commonly referred to as capital stock in the United States, is the portion of a corporation's equity that has been derived by

2204-412: The fastest. Normalizing by A's result gives A as the fastest computer according to the arithmetic mean: Table 2 while normalizing by B's result gives B as the fastest computer according to the arithmetic mean but A as the fastest according to the harmonic mean: Table 3 and normalizing by C's result gives C as the fastest computer according to the arithmetic mean but A as the fastest according to

2262-494: The first one). The use of the geometric mean for aggregating performance numbers should be avoided if possible, because multiplying execution times has no physical meaning, in contrast to adding times as in the arithmetic mean. Metrics that are inversely proportional to time (speedup, IPC ) should be averaged using the harmonic mean. The geometric mean can be derived from the generalized mean as its limit as p {\displaystyle p} goes to zero. Similarly, this

2320-422: The future compared to companies with a lower price–earning ratio. A low price–earning ratio may indicate either that a company may currently be undervalued or that the company is doing exceptionally well relative to its past trends. The price-to-earnings ratio can also be seen as a means of standardizing the value of one dollar of earnings throughout the stock market. In theory, by taking the median of P/E ratios over

2378-443: The geometric mean is 1 ⋅ 12 ⋅ 18 3 = {\displaystyle \textstyle {\sqrt[{3}]{1\cdot 12\cdot 18}}={}} 216 3 = 6 {\displaystyle \textstyle {\sqrt[{3}]{216}}=6} . The geometric mean is useful whenever the quantities to be averaged combine multiplicatively, such as population growth rates or interest rates of

Price–earnings ratio - Misplaced Pages Continue

2436-530: The geometric mean is 2 ⋅ 8 = {\displaystyle \textstyle {\sqrt {2\cdot 8}}={}} 16 = 4 {\displaystyle \textstyle {\sqrt {16}}=4} . The geometric mean of the three numbers is the cube root of their product, for example with numbers ⁠ 1 {\displaystyle 1} ⁠ , ⁠ 12 {\displaystyle 12} ⁠ , and ⁠ 18 {\displaystyle 18} ⁠ ,

2494-438: The geometric mean of x {\textstyle x} and y {\textstyle y} . The sequences converge to a common limit, and the geometric mean is preserved: Replacing the arithmetic and harmonic mean by a pair of generalized means of opposite, finite exponents yields the same result. The geometric mean of a non-empty data set of positive numbers is always at most their arithmetic mean. Equality

2552-415: The geometric mean of three numbers, a {\displaystyle a} , b {\displaystyle b} , and c {\displaystyle c} , is the length of one edge of a cube whose volume is the same as that of a cuboid with sides whose lengths are equal to the three given numbers. The geometric mean is one of the three classical Pythagorean means , together with

2610-410: The geometric mean the only correct mean when averaging normalized results; that is, results that are presented as ratios to reference values. This is the case when presenting computer performance with respect to a reference computer, or when computing a single average index from several heterogeneous sources (for example, life expectancy, education years, and infant mortality). In this scenario, using

2668-399: The geometric mean using logarithms is one way to avoid this problem. The geometric mean of a data set is less than the data set's arithmetic mean unless all members of the data set are equal, in which case the geometric and arithmetic means are equal. This allows the definition of the arithmetic-geometric mean , an intersection of the two which always lies in between. The geometric mean

2726-400: The harmonic mean: Table 4 In all cases, the ranking given by the geometric mean stays the same as the one obtained with unnormalized values. However, this reasoning has been questioned. Giving consistent results is not always equal to giving the correct results. In general, it is more rigorous to assign weights to each of the programs, calculate the average weighted execution time (using

2784-410: The inequality aversion parameter. In the case of a right triangle , its altitude is the length of a line extending perpendicularly from the hypotenuse to its 90° vertex. Imagining that this line splits the hypotenuse into two segments, the geometric mean of these segment lengths is the length of the altitude. This property is known as the geometric mean theorem . In an ellipse , the semi-minor axis

2842-400: The issue of shares in the corporation to a shareholder, usually for cash . Share capital may also denote the number and types of shares that compose a corporation's share structure. In accounting , the share capital of a corporation is the nominal value of issued shares (that is, the sum of their par values , sometimes indicated on share certificates). If the allocation price of shares

2900-456: The lower capital gains tax rates and transaction costs, P/E ratio in "low twenties" is sustainable, despite being higher than the historic average. Set out below are the recent year end values of the S&;P 500 index and the associated P/E as reported. For a list of recent contractions ( recessions ) and expansions see U.S. Business Cycle Expansions and Contractions . Note that at the height of

2958-476: The market assigns to those earnings. In turn, the primary drivers for multiples such as the P/E ratio is through higher and more sustained earnings growth rates. Consequently, managers have strong incentives to boost earnings per share, even in the short term, and/or improve long-term growth rates. This can influence business decisions in several ways: In general, a high price–earning ratio indicates that investors are expecting higher growth of company's earnings in

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3016-405: The natural logarithm. For example, the geometric mean of ⁠ 1 {\displaystyle 1} ⁠ , ⁠ 2 {\displaystyle 2} ⁠ , ⁠ 8 {\displaystyle 8} ⁠ , and ⁠ 16 {\displaystyle 16} ⁠ can be calculated using logarithms base 2: Related to the above, it can be seen that for

3074-454: The premium value of shares into account, which instead is reported as additional paid-in capital. Legal capital is a concept used in European corporate and foundation law , United Kingdom company law , and various other corporate law jurisdictions to refer to the sum of assets contributed to a company by shareholders when they are issued shares. The law often requires that this capital

3132-474: The result is 314 oranges, not 300, so the linear average over -states the year-on-year growth. Instead, we can use the geometric mean. Growing with 80% corresponds to multiplying with 1.80, so we take the geometric mean of 1.80, 1.166666 and 1.428571, i.e. 1.80 × 1.166666 × 1.428571 3 ≈ 1.442249 {\displaystyle {\sqrt[{3}]{1.80\times 1.166666\times 1.428571}}\approx 1.442249} ; thus

3190-402: The same final amount. Suppose an orange tree yields 100 oranges one year and then 180, 210 and 300 the following years, so the growth is 80%, 16.6666% and 42.8571% for each year respectively. Using the arithmetic mean calculates a (linear) average growth of 46.5079% (80% + 16.6666% + 42.8571%, that sum then divided by 3). However, if we start with 100 oranges and let it grow 46.5079% each year,

3248-473: The statistics being compiled and compared: Not all values used to compute the HDI (Human Development Index) are normalized; some of them instead have the form ( X − X min ) / ( X norm − X min ) {\displaystyle \left(X-X_{\text{min}}\right)/\left(X_{\text{norm}}-X_{\text{min}}\right)} . This makes

3306-711: The wrong answer, as market capitalization = ( market price ) × ( current number of shares), whereas earnings per share = ⁠ net income / weighted average number of shares ⁠ . Variations on the standard trailing and forward P/E ratios are common. Generally, alternative P/E measures substitute different measures of earnings, such as rolling averages over longer periods of time (to attempt to "smooth" volatile or cyclical earnings, for example), or "corrected" earnings figures that exclude certain extraordinary events or one-off gains or losses. The definitions may not be standardized. For companies that are loss-making, or whose earnings are expected to change dramatically,

3364-436: Was only attained twice in history, 2001-2002 and 2008-2009. The P/E ratio of a company is a major focus for many managers. They are usually paid in company stock or options on their company's stock (a form of payment that is supposed to align the interests of management with the interests of other stock holders). The stock price can increase in one of two ways: either through improved earnings or through an improved multiple that

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