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Financial ratio

A financial ratio (or accounting ratio) is a relative magnitude of two selected numerical values taken from an enterprise's financial statements. Often used in accounting, there are many standard ratios used to try to evaluate the overall financial condition of a corporation or other organization. Financial ratios may be used by managers within a firm, by current and potential shareholders (owners) of a firm, and by a firm's creditors. Security analysts use financial ratios to compare the strengths and weaknesses in various companies. If shares in a company are traded in a financial market, the market price of the shares is used in certain financial ratios.

Ratios can be expressed as a decimal value, such as 0.10, or given as an equivalent percent value, such as 10%. Some ratios are usually quoted as percentages, especially ratios that are usually or always less than 1, such as earnings yield, while others are usually quoted as decimal numbers, especially ratios that are usually more than 1, such as P/E ratio; these latter are also called multiples. Given any ratio, one can take its reciprocal; if the ratio was above 1, the reciprocal will be below 1, and conversely. The reciprocal expresses the same information, but may be more understandable: for instance, the earnings yield can be compared with bond yields, while the P/E ratio cannot be: for example, a P/E ratio of 20 corresponds to an earnings yield of 5%.

Sources of data for financial ratios

Values used in calculating financial ratios are taken from the balance sheet, income statement, statement of cash flows or (sometimes) the statement of retained earnings. These comprise the firm's "accounting statements" or financial statements. The statements' data is based on the accounting method and accounting standards used by the organization.

Purpose and types of ratios

Financial ratios quantify many aspects of a business and are an integral part of the financial statement analysis. Financial ratios are categorized according to the financial aspect of the business which the ratio measures. Liquidity ratios measure the availability of cash to pay debt. Activity ratios measure how quickly a firm converts non-cash assets to cash assets. Debt ratios measure the firm's ability to repay long-term debt. Profitability ratios measure the firm's use of its assets and control of its expenses to generate an acceptable rate of return. Market ratios measure investor response to owning a company's stock and also the cost of issuing stock.

Financial ratios allow for comparisons

  • between companies
  • between industries
  • between different time periods for one company
  • between a single company and its industry average

Ratios generally hold no meaning unless they are benchmarked against something else, like past performance or another company. Thus, the ratios of firms in different industries, which face different risks, capital requirements, and competition are usually hard to compare.

Accounting methods and principles

Financial ratios may not be directly comparable between companies that use different accounting methods or follow various standard accounting practices. Most public companies are required by law to use generally accepted accounting principles for their home countries, but private companies, partnerships and sole proprietorships may not use accrual basis accounting. Large multi-national corporations may use International Financial Reporting Standards to produce their financial statements, or they may use the generally accepted accounting principles of their home country.

There is no international standard for calculating the summary data presented in all financial statements, and the terminology is not always consistent between companies, industries, countries and time periods.

Abbreviations and terminology

Various abbreviations may be used in financial statements, especially financial statements summarized on the Internet. Sales reported by a firm are usually net sales, which deduct returns, allowances, and early payment discounts from the charge on an invoice. Net income is always the amount after taxes, depreciation, amortization, and interest, unless otherwise stated. Otherwise, the amount would be EBIT, or EBITDA (see below).

Companies that are primarily involved in providing services with labour do not generally report "Sales" based on hours. These companies tend to report "revenue" based on the monetary value of income that the services provide.

Note that Shareholder's Equity and Owner's Equity are not the same thing, Shareholder's Equity represents the total number of shares in the company multiplied by each share's book value; Owner's Equity represents the total number of shares that an individual shareholder owns (usually the owner with controlling interest), multiplied by each share's book value. It is important to make this distinction when calculating ratios.

Other abbreviations

(Note: These are not ratios, but values in currency.)

  • COGS = Cost of goods sold, or cost of sales.
  • EBIT = ratio of the luminance of the brightest color (white) to that of the darkest color (black) that the system is capable of producing. A high contrast ratio is a desired aspect of any display.

    There is no official, standardized way to measure contrast ratio for a system or its parts, so ratings provided by different manufacturers of display devices are not necessarily comparable to each other due to differences in method of measurement, operation, and unstated variables. Manufacturers have traditionally favored measurement methods that isolate the device from the system, whereas other designers have more often taken the effect of the room into account. An ideal room would absorb all the light reflecting from a projection screen or emitted by a CRT, and the only light seen in the room would come from the display device. With such a room, the contrast ratio of the image would be the same as the contrast ratio of the device. Real rooms reflect some of the light back to the displayed image, lowering the contrast ratio seen in the image.

    Moving from a system that displays a static motionless image to a system that displays a dynamic, changing picture slightly complicates the definition of the contrast ratio, because of the need to take into account the extra temporal dimension to the measuring process. Thus the ratio of the luminosity of the brightest and the darkest color the system is capable of producing simultaneously at any instant of time is called static contrast ratio, while the ratio of the luminosity of the brightest and the darkest color the system is capable of producing over time is called dynamic contrast ratio.

    Methods of measurement

    Many display devices favor the use of the full on/full off method of measurement, as it cancels out the effect of the room and results in an ideal ratio. Equal proportions of light reflect from the display to the room and back in both "black" and "white" measurements, as long as the room stays the same. This will inflate the light levels of both measurements proportionally, leaving the black to white luminance ratio unaffected.

    Some manufacturers have gone as far as using different device parameters for the three tests, even further inflating the calculated contrast ratio. With DLP projectors, one method to do this is to enable the clear sector of the color filter wheel for the "on" part and disable it for the "off" part This practice is rather dubious, as it will be impossible to reproduce such contrast ratios with any useful image content.

    Another measure is the ANSI contrast, in which the measurement is done with a checker board patterned test image where the black and white luminosity values are measured simultaneously. This is a more realistic measure of system capability, but includes the potential of including the effects of the room into the measurement, if the test is not performed in a room that is close to ideal.

    It is useful to note that the full on/full off method effectively measures the dynamic contrast ratio of a display, while the ANSI contrast measures the static contrast ratio.

    Dynamic Contrast (DC)

    A notable recent development in the LCD technology is the so-called "dynamic contrast" (DC). When there is a need to display a dark image, the display would underpower the backlight lamp (or decrease the aperture of the projector's lens using an iris), but will proportionately amplify the transmission through the LCD panel. This gives the benefit of realizing the potential static contrast ratio of the LCD panel in dark scenes when the image is watched in a dark room. The drawback is that if a dark scene does contain small areas of superbright light, image quality may be over exposed.

    The trick for the display is to determine how much of the highlights may be unnoticeably blown out in a given image under the given ambient lighting conditions.

    Brightness, as it is most often used in marketing literature, refers to the emitted luminous intensity on screen measured in candela per square metre (cd/m2). The higher the number, the brighter the screen.

    It is also common to market only the dynamic contrast ratio capability of a display (when it is better than its static contrast ratio), which should not be directly compared to the static contrast ratio. A plasma display with a static 5000:1 contrast ratio will show superior contrast to an LCD with 5000:1 dynamic and 1000:1 static contrast ratio when the input signal contains a full range of brightnesses from 0 to 100% simultaneously. They will, however, be on-par when input signal ranges only from 0 to 20% brightness.

    Contrast ratio in a real room

    In marketing literature, contrast ratios for emissive (as opposed to reflective) displays are always measured under the optimum condition of a room in total darkness. In typical viewing situations the contrast ratio is significantly lower due to the reflection of light from the surface of the display, making it harder to distinguish between different devices with very high contrast ratios. How much the room light reduces the contrast ratio depends on the luminance of the display, as well as the amount of light reflecting off the display.

    A clean print at a typical movie theater may have a contrast ratio of 500:1 Dynamic contrast ratio is usually measured at factory with two panels (one vs another) of the same model as each panel will have an inherent Dark and Light (Hot) spot. Static is usually measured with the same screen showing half screen full bright vs half screen full dark. This usually results in a lower ratio as brightness will creep into the dark area of the screen thus giving a higher luminance.


Sharpe ratio

__NOTOC__ The Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return (or risk premium) per unit of risk in an investment asset or a trading strategy, named after William Forsyth Sharpe. Since its revision by the original author in 1994, it is defined as:

S = \frac{R-R_f}{\sigma} = \frac{E[R-R_f]}{\sqrt{\mathrm{var}[R-R_f]}},

where R is the asset return, R_f is the return on a benchmark asset, such as the risk free rate of return, E[R-R_f] is the expected value of the excess of the asset return over the benchmark return, and {\sigma} is the standard deviation of the excess of the asset return (this is often confused with the excess return over the benchmark return; the Sharpe ratio utilizes the asset standard deviation whereas the information ratio utilizes standard deviation of excess return over the benchmark, i.e. the tracking error, as the denominator.). Note, if R_f is a constant risk free return throughout the period,

\sqrt{\mathrm{var}[R-R_f]}=\sqrt{\mathrm{var}[R]}.

The Sharpe ratio is used to characterize how well the return of an asset compensates the investor for the risk taken, the higher the Sharpe ratio number the better. When comparing two assets each with the expected return E[R] against the same benchmark with return R_f, the asset with the higher Sharpe ratio gives more return for the same risk. Investors are often advised to pick investments with high Sharpe ratios. However like any mathematical model it relies on the data being correct. Pyramid schemes with a long duration of operation would typically provide a high Sharpe ratio when derived from reported returns but the inputs are false. When examining the investment performance of assets with smoothing of returns (such as with-profits funds) the Sharpe ratio should be derived from the performance of the underlying assets rather than the fund returns.

Sharpe ratios, along with Treynor ratios and Jensen's alphas, are often used to rank the performance of portfolio or mutual fund managers.

History

In 1952, Swati Goenka of Cambridge suggested maximizing the ratio "(m-d)/σ", where m is expected gross return, d is some "disaster level" (a.k.a., minimum acceptable return) and σ is standard deviation of returns. This ratio is just the Sharpe Ratio, only using minimum acceptable return instead of risk-free return in the numerator, and using standard deviation of returns instead of standard deviation of excess returns in the denominator.

In 1966, William Forsyth Sharpe developed what is now known as the Sharpe ratio. Sharpe originally called it the "reward-to-variability" ratio before it began being called the Sharpe Ratio by later academics and financial operators.

Sharpe's 1994 revision acknowledged that the risk free rate changes with time. Prior to this revision the definition was
S = \frac{E[R]-R_f}{\sigma} assuming a constant R_f .

Recently, the (original) Sharpe ratio has often been challenged with regard to its appropriateness as a fund performance measure during evaluation periods of declining markets.

Examples

Suppose the asset has an expected return of 15% in excess of the risk free rate. We typically do not know if the asset will have this return; suppose we assess the risk of the asset, defined as standard deviation of the asset's excess return, as 10%. The risk-free return is constant. Then the Sharpe ratio (using a new definition) will be 1.5 (R - R_f = 0.15 and \sigma = 0.10 ).

As a guide post, one could substitute in the longer term return of the S&P500 as 10%. Assume the risk-free return is 3.5%. And the average standard deviation of the S&P500 is about 16%. Doing the math, we get that the average, long-term Sharpe ratio of the US market is about 0.4 ((10%-3.5%)/16%). But we should note that if one were to calculate the ratio over, for example, three-year rolling periods, then the Sharpe ratio could vary dramatically.

Strengths and weaknesses

The Sharpe ratio has as its principal advantage that it is directly computable from any observed series of returns without need for additional information surrounding the source of profitability. Other ratios such as the bias ratio have recently been introduced into the literature to handle cases where the observed volatility may be an especially poor proxy for the risk inherent in a time-series of observed returns.

While the Treynor ratio works only with systematic risk of a portfolio, the Sharpe ratio observes both systematic and idiosyncratic risks.

The returns measured can be of any frequency (i.e. daily, weekly, monthly or annually), as long as they are normally distributed, as the returns can always be annualized. Herein lies the underlying weakness of the ratio - not all asset returns are normally distributed.

Abnormalities like kurtosis, fatter tails and higher peaks, or skewness on the distribution can be a problematic for the ratio, as standard deviation doesn't have the same effectiveness when these problems exist. Sometimes it can be downright dangerous to use this formula when returns are not normally distributed.

Because it is a dimensionless ratio, laypeople find it difficult to interpret Sharpe Ratios of different investments. For example, how much better is an investment with a Sharpe Ratio of 0.5 than one with a Sharpe Ratio of -0.2? This weakness was well addressed by the development of the Modigliani Risk-Adjusted Performance measure, which is in units of percent return -- universally understandable by virtually all investors.



From Yahoo Answers

Question:THE RATIO HAS TO BE A FRACTION. for example use 0.93.. and turn into a ratio in the form of a/b (a over b) also how do u turn a mixed number into a ratio? (also in form of a fraction a/b) and how do u turn 0 into a fractional ratio also??

Answers:Easy peasy if you have a scientific or graphical calculator take the decimal such as 0.93, type it in press equals or execute (which ever your calculator has) then press the fraction button (it will look like (a b/c)) Or to do it manually, for the decimal 0.93, that is 93/100. for others you might be able to simplify further for example 0.25 = 25/100 = 1/4. does that help?

Question:Write the trigonometric ratio for cos Y as a fraction and as a decimal rounded to the nearest hundredth. (the diagram is a right triangle XYZ and the side length for the legs are 9 and 12 and the hypotenuse is 15.) I am having trouble figuring this question out for homework are there any hints anyone would be willing to throw at me? Serious answers only please.

Answers:It depends on which vertex is Y. cos Y is opp side over hypotenuse. so it might be 9/15 or 12/15 then just plug those numbers into a calculator as a division problem to get a decimal answer ex: 9/15 = .60

Question:If the atom has a radius of approximately 10^-10 m, and the nucleus has a radius of approximately 10^-15 m, calculate the ratio of the nucleus volume to the volume of the atom. Please show working! All those exponents have just got me confused! Thanks in advance.

Answers:You divide 10^-15m by 10^10m. Subtract the exponent. 10^(-15m - (-10m) = 10^(-5m)

Question:The 20 day Volatility Ratio is calculated as 1 Day Implied Volatility divided by 20 Day Statistical Volatility. The 90 day Volatility Ratio is calculated as 1 Day Implied Volatility divided by 90 Day Statistical Volatility. Question: We have a Volatlity chart for 3 month ,6 month and 1 year datas only. Where can i get 1 day Implied Volatility data? Where can i get 20 day statistcal volatlity data? I think, we can can get the value of 90 day (3 month) Statstcal volatility since we have volatility view chart for 3 months. Can someone please help me in how to find out those values (1 day Implied Volatility & 20 day Statistical Volatlity)? Thank you.

Answers:<<>> Simply use the current implied volatility. <<>> The easiest way to get it is simply to calculate it. Start by getting the historical prices for the time period you want. You can do this several places, including Yahoo Finance. For example, if I wanted 20 days of historical quotes for INTC I would start at the Yahoo quotes page http://finance.yahoo.com/q?s=INTC then click on the "Historical Prices" link to get the page at http://finance.yahoo.com/q/hp?s=INTC I would then set the date range I wanted and click on the "Get Prices" button. On the page I got back I would go to the bottom of the page and click on the "Download To Spreadsheet" button to put the data into an Excel spreadsheet. I would then calculate the standard deviation of the closing prices using the STDEV function. (If you are not familiar with the STDEV function see http://www.gifted.uconn.edu/siegle/research/Normal/stdexcel.htm ) I would then annualize the standard deviation by multiplying it by the square root of (365 / N) where N is the number of calendar days worth of data I used. Finally I would convert the annualized standard deviation into the statistical volatility by multiplying it by 100 and dividing it by the price of the stock.

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