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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:

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[R-R_f]>=sqrt<mathrm[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 ratio s and Jensen’s alpha s, 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<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.

Financial ratio

A financial ratio (or accounting ratio ) is a relative magnitude of two selected numerical values taken from an enterprise’s financial statement s. 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 shareholder s (owners) of a firm, and by a firm’s creditor s. Security analyst s 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 benchmark ed 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 practice s. Most public companies are required by law to use generally accepted accounting principles for their home countries, but private companies. partnership s and sole proprietorship s 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 =

Contrast ratio

The contrast ratio is a property of a display system, defined as the 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/m 2 ). 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.

Scientific calculator

A scientific calculator is a type of electronic calculator. usually but not always handheld, designed to calculate problems in science (especially physics ), engineering. and mathematics. They have almost completely replaced slide rule s in almost all traditional applications, and are widely used in both education and professional settings.

In certain contexts such as higher education, scientific calculators have been superseded by graphing calculator s, which offer a superset of scientific calculator functionality along with the ability to graph input data and write and store programs for the device. There is also some overlap with the financial calculator market.

Functions

Modern scientific calculators generally have many more features than a standard four or five-function calculator, and the feature set differs between manufacturers and models; however, the defining features of a scientific calculator include:

In addition, high-end scientific calculators will include:

While most scientific models have traditionally used a single-line display similar to traditional pocket calculators, many of them have at the very least more digits (10 to 12), sometimes with extra digits for the floating point exponent. A few have multi-line displays, with some recent models from Hewlett-Packard. Texas Instruments. Casio. Sharp. and Canon using dot matrix displays similar to those found on graphing calculator s.

Uses

Scientific calculators are used widely in any situation where quick access to certain mathematical functions is needed, especially those such as trigonometric functions that were once traditionally looked up in tables; they are also used in situations requiring back-of-the-envelope calculations of very large numbers, as in some aspects of astronomy. physics. and chemistry .

They are very often required for math classes from the junior high school level through college, and are generally either permitted or required on many standardized test s covering math and science subjects; as a result, many are sold into educational markets to cover this demand, and some high-end models include features making it easier to translate the problem on a textbook page into calculator input, from allowing explicit operator precedence using parentheses to providing a method for the user to enter an entire problem in as it is written on the page using simple formatting tools.

History

The first scientific calculator that included all of the basic features above was the programmable Hewlett-Packard HP-9100A. released in 1968, though the Wang LOCI-2 and the Mathatronics Mathatron had some features later identified with scientific calculator designs. The HP-9100 series was built entirely from discrete transistor logic with no integrated circuit s, and was one of the first uses of the CORDIC algorithm for trigonometric computation in a personal computing device, as well as the first calculator based on reverse Polish notation entry. HP became closely identified with RPN calculators from then on, and even today some of their high-end calculators (particularly the long-lived HP-12C financial calculator and the HP-48 series of graphing calculators) still offer RPN as their

From Yahoo Answers

Question: how to use calculator(sharp EL-520W) for decibel values conversion in to absolute power ratios and vise vesa ?

Answers: decibels are just a logarythmic scale. I’m pretty sure that its base ten. So, all you need to do is take you answers and take 10^x to get numbers in the normal number line.

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finance.yahoo.com/q?s=INTC then click on the Historical Pricesfinance.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 Spreadsheetwww.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.

Question: And balance equations when necessary Fe2O3 + CO —> Fe+ Co2 a. Using the above equations, if 20 mole of Fe2O3 reacts with an excess of Carbon monoxide, how many moles of carbon dioxide are formed? I don’t know how to do this, could i get some thorough explanation on how to do this so i can complete the rest of my problems

Answers: first you need to balance the equation: Fe2O3 + 3CO —> 2Fe 3CO2 then you do the mole to mole ratio. For every 1Fe2O3, there are 3 CO2 produce, so the mole to mole ratio is 1:3 so if you had 20moles of Fe2O3, you would get 60 moles of CO2

Question: Ive been asked to calculate operating ratios under ratio analysis in accounting. I think the formula is cost of sales + operating expenses / sales. Please correct me if im wrong. the problem is ive also been given number of employees for each year and my lecturer said i need to take them into consideration when calculating it. How do i calculate it? do i just stick to that formula or is it wrong? do i only take the no of employees into consideration when analysing the ratios after calculating it. A good answer will be extremely helpful. Thanks Well. ive been asked to calculate profitability, working capital, liquity etc and profitability ratios. i have done all but the operating ratios (BTW i never heard of operating ratio until i saw dis questn). ive been given operating expenses already so i dont know what the number of employees is there for. from what i heard 4rm d lecturer, it seems that the employees is part of the calculation BTW im analysing a retail companies performance over a 5 year period from a shareholder’s perspective

Answers: THE OPERATING RATIO Accountants use the information on an income statement to compute the operating ratio, which is normally used as a measure of the company’s efficiency and ability to generate income. It is used by investors to determine how worthwhile an investment may be. The operating ratio is computed by dividing the sum of the cost of the goods sold and the operating expenses by the total sales. However I think your teacher might have used the term operating ratios in the plural to mean Financial and operating ratios, such as gross profits as a percent of sales, which are derived from company financial statements. Ratios are calculated for categories such as liquidity, asset management, debt management, profitability, and market value. They are used to study changes in a company’s operations over time. If he wanted you to use the no. of employees, then he might have expected you to calculate the Average Wage and Benefit Cost per Employee over the 5 yrs. You take the wages amt and add on other personnel-related expenses like medical benefits and divide that by the no. of employees and you do that for the 5 yrs. From the trend, you can see if the cost per employee is getting more and more or less and less.

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