# Calculate Standard Deviation

**What is Standard Deviation?**

**How do I Calculate Standard Deviation?**

**The standard deviation formula is depicted below:**

Home Finance terms

Simplifying Statistics: How to Calculate Standard Deviation

• Standard deviation is a formula most often found in statistics, probability theory and formula. When applied to a set of data, standard deviation will calculate the variation present from the mean or expected value. For instance, a low standard deviation will indicate that the given data points are very close to the mean, while a high standard deviation denotes a large spread of data.

• In addition to expressing variables of a given population, standard deviation is also used to measure confidence in statistical conclusions or as a risk assessment in finance. For example, the margin of error in polling data is determined by calculating the standard deviation if the results had been conducted several times.

• Standard deviation is critical in finance, because the technique can elucidate on the rate of return for an investment or transaction. In essence, the standard deviation will yield the underlying investment or transaction’s volatility. An individual, in finance, will calculate standard deviation to find the percentage or level of risk for a given investment security (such as a stock or bond etc.) or the risk of actively managed bundles of securities (such as hedge funds, mutual funds, or ETFs).

• The basic concept of risk is that, as it increases, the expected rate of return for the underlying asset will increase to entice potential investors. Investors, in other words, should expect a higher return on a riskier investment to obfuscate the uncertainty latent in the purchase. In essence, standard deviation will provide a quantified estimation regarding the uncertainty of future returns.

• To calculate standard deviation, an individual must obviously know what formula to use. At first glance, the standard deviation formula may seem daunting; however, the standard deviation formula is considered fairly basic, especially when compared to other statistical equations.

• In a statistical study, a conclusion is formulated regarding a particular set of data and it’s variance from a control set. To formulate this conclusion, the standard deviation, must be applied. used is regarded as the standard deviation. As a result, the standard deviation is typically uniform to the average deviation from the mean.

• In this formula, X is the value of mean, N is the sample size and X(i) represents each data value from i=N to i=1. The large “E” symbol represents the summation function in mathematics; this symbol indicates that must add up the sum. To utilize the standard deviation formula it is suggested that the individual have a basic understanding of algebra.

Everything You Need to Know about Gross Margin:

**What is Gross Margin?**

• In economics, gross margin is the difference between the production costs (excluding payroll, taxation, interest payments, and overhead) and sales revenue. Gross margin, as a result of this ratio, can be defined as the amount of contribution to a business, after paying for all direct fixed and variable costs.

• Gross margin is simply all revenue obtained by a company minus the cost of the goods sold, divided by the revenue. When expressed in absolute terms gross margin is equal to the company’s net sales minus the cost of the goods sold plus the annual sales return. Furthermore, gross margin may also be expressed as a ratio of gross profit to the cost of goods sold, typically in the form of a percentage.

• The cost of sales, used in the gross margin calculation, will include all variable costs and fixed costs of the business operation. These costs must be linked directly to the sale of the company’s product; material costs, labor, shipping costs and supplier profits are all accounted for in the cost of sales. That being said, cost of sales does not include any indirect fixed costs, such as office expenses, administrative costs, rent etc.

• As a result of these variables, a higher gross margin (for a manufacturing company) will typically reflect a greater efficiency in regards to turning raw materials into income. For a retailer, a higher gross margin reflects the company’s markup over wholesale. A larger gross margin is generally considered ideal for the majority of business entities.

**How is Gross Margin used to Measure Profits?**

• A retailer may measure their profit by utilizing two analytical methods: markup and margin. Both methods will give a description of gross profit; the markup expresses profit as a percentage of the retailer’s cost per product, while the margin expresses profit as a percentage of the retailer’s sales price for the product.

• The equation used to calculate the markup or the monetary value of gross margin is the following: sales-cost of goods sold.

• Return on equity is a financial formula that measures the rate of return shareholders’ equity or ownership interest of the common stock owner. Return on equity also measures a firm’s efficiency at generating profits from each unit of shareholder’s equity—known as net assets.

• The return on equity formula will show how well a company uses investment funds to generate earnings growth; any company who has a return on equity between 15 and 20% is thought to be doing very well.

• The return on equity formula is simply net income after tax divided by shareholder equity. Return on equity is always equal to a fiscal year’s net income, which occurs after preferred stock dividends by before common stock dividends are paid out, divided by the total equity. As is common with a number of financial ratios, return on equity is best used to compare and contrast companies in the same industry.

• A high return on equity will yield no immediate benefits to the underlying company; stock prices are strongly influenced by earnings per share, therefore, the company will be paying more for a higher return on equity. The benefit of a high return on equity comes from the reinvesting of earnings, which in turn, leads to a high rate of growth. Furthermore, the benefit of a high return on equity can come as a dividend on common shares or as a combination of dividends and reinvestment platforms in the company.

• A sustainable growth model will show that when a firm pays dividends to its shareholders, its earnings growth rate will lower. For instance, if the dividend offered was 20%, the growth is expected will only be roughly 80% of the return on equity rate. Furthermore, the growth rate will be lower if the earnings are used to re-purchase shares; if the shares are purchased at a multiple of book value, the incremental earnings will be only a fraction of the return on equity. It is important to remember that, return on equity is calculated from the company’s individual perspective and on the company as a whole.

• The Monte Carlo Model is a system used in mathematical finance to calculate option prices. More specifically, the Monte Carlo method will calculate the value of a singular option with multiple sources of speculation and complexities.

• In regards to theory, the Monte Carlo Model utilizes risk neutral valuations; in this practice, the price of the option is shown as its discounted expected value. When applied, this technique will generate several thousand random price paths used simulate then subsequently calculate the associated exercise value or payoff of the option. These generated payoffs are then average and discounted on the specific trading day. The result of this 4-step process will yield the value of the option.

• In most cases, an option attached to an equity may be modeled with one source of uncertainty: the price of the underlying stock. For these options, the Monte Carlo is typically not utilized, for a more routine or simplistic pricing formula (Black Scholes) will suffice.

• The beauty behind the Monte Carlo model is that it allows for a compounding in the uncertainty of the underlying asset. For example, in a situation where the underlying asset is denominated in a foreign currency, an additional source of uncertainty will be found in the exchange rate. Thus, the exchange rate and the underlying price must be separately simulated and then combined to accurately determine the value of the currency. In models, such as the Monte Carlo Model, correlation between these sources of risk is incorporated.

How is the Monte Carlo Model Applied?

• The Monte Carlo Model is most useful when valuating options that contain multiple sources of uncertainty or possess complicated features. In essence, the Monte Carlo Model is particularly useful for evaluating any option that cannot be estimated using a more straightforward formula, such as a Black-Scholes or Lattice based computation. As a result of this characteristic, the Monte Carlo Model is widely used in valuing path dependent options, such as lookbacks or real option analysis.

• In traditional financial accounting, a cash flow statement is a financial document that shows how changes in a firm’s balance sheet and income will invariably affect cash and cash-like assets. Furthermore, the cash flow statement will divide the firm’s expenses and income statements into investing, operating and finance-related activities.

• In essence, a cash flow statement is concerned with the flow of cash and cash-like securities in and out of a business. The cash flow statement must capture both the firm’s current operating results and the accompanying changes of their balance sheet. When used as an analytical tool, the cash flow statement will be successful in determining the short-term viability of the underlying company. More specifically, the cash flow statement is used as a marker to indicate how well or timely a company can meet its debt obligations.

• The following people and business organizations will utilize a cash flow statement to discern the true health of a company:

o Accounting personnel who need to evaluate the organization’s ability to cover payroll and other immediate expenses

o Potential investors who need to analyze and judge whether the company is financially stable

o Potential creditors or lenders who will require a clear picture of a company’s ability to fulfill loan obligations

o Shareholders who possess a percentage ownership in the business

o Potential employees or contractors who are required to know whether the company will be able to afford compensation

• The cash flow statement will reflect a firm’s liquidity and more specifically their ability to meet short-term liabilities. The balance sheet represents a snapshot of a firm’s financial resources and obligations at a single time period, while the income statement will summarize a firm’s financial transactions over an interval of time. These two financial documents reflect the foundation of a firm’s accounting endeavor; combined, they will match a firm’s revenues with the expenses associated with generating such revenues.

• In contrast to the previously mentioned financial documents, the cash flow statement will include only inflows and outflows of cash or cash-like securities; the cash flow statement excludes transactions that do not directly alter cash payments and receipts. As a result, the cash flow statement is a cash basis report on three basic financial maneuvers: investing activities, operating activities and financial activities.

• The cash flow statement will intend to provide a firm with the following functions:

o The cash flow statement will provide information on a firm’s liquidity and its ability to alter cash flows for future obligations or circumstances

o The cash flow statement will provide additional information for evaluating changes in assets, liabilities and equity

o The cash flow statement will improve the comparability measures of different company’s operating performances through the elimination of different accounting methods

o The cash flow statement will indicate the amount, probability and timing of future cash flows

• Standard deviation is a commonly-used measurement of diversity or variability in statistics, finance and probability theory. More specifically, standard deviation will show how much variation is present from the mean or expected value. For instance, a low standard deviation will indicate that the given data points are very close to the mean, while a high standard deviation indicates that the data are spread over a large range of values.

• In addition to expressing variables of a given population, standard deviation is also used to measure confidence in statistical conclusions. For instance, the margin of error in polling data is typically determined by calculating the standard deviation in the results if the same poll were to be conducted a number of times.

• A standard deviation calculator is a free online resource that enables you to calculate the standard deviation, sum, mean and confidence range for a given set of numbers. The standard deviation calculator can be used for population measures or to assess risk for financial investments.

• Unlike other online resources (such as a mortgage or credit card calculator) the standard deviation calculator does not require the user to input variables in specific in a series of spaces provided. Instead, the standard deviation calculator is offered as a large box, where the user will input the pertinent set or series of numbers for their given problem or situation. After the numbers are entered, the user simply clicks “calculate” and the standard deviation calculator will provide a percentage range for your sub-set.

• Standard deviation is critical in finance, because the technique can elucidate on the rate of return for an investment or transaction. In essence, the standard deviation will yield the underlying investment or transaction’s volatility.

• In finance, standard deviation is used to represent the risk associated with a given investment security (such as a stock or bond etc.) or the risk of actively managed bundles of securities (such as hedge funds, mutual funds, or ETFs).

• Risk a primary factor when determining how to manage or invest in securities; risk determines the variation in returns on the investment, which in turn offers a mathematical basis for the investment decision.

• The basic concept of risk is that, as it increases, the expected rate of return for the underlying asset will increase to entice potential investors. Investors, in other words, should expect a higher return on a riskier investment to obfuscate the uncertainty latent in the purchase. In essence, standard deviation will provide a quantified estimation regarding the uncertainty of future returns.

• Standard deviation is a commonly-used measurement of diversity or variability in statistics, finance and probability theory. More specifically, standard deviation will show how much variation is present from the mean or expected value—in finance, it can be applied to transactions or maneuvers. A low standard deviation will indicate that the given data points are very close to the mean, while a high standard deviation indicates that the data are spread over a vast spectrum of values.

• In addition to expressing variables of a given population, standard deviation is also used to measure confidence in statistical conclusions. For instance, the margin of error in polling data is typically determined by calculating the standard deviation, as if the poll were conducted several times.

• Standard deviation is critical in finance, because the technique can elucidate the rate of return for an investment or transaction. In essence, the standard deviation will yield the underlying investment or transaction’s volatility.

• In finance, standard deviation is used to represent the risk associated with a given security (such as a stock or bond etc.) or the risk of actively managed bundles of securities (such as hedge funds, mutual funds, or ETFs).

• Risk is a primary factor when determining how to manage or invest in securities; risk determines the variation in returns on the investment, which in turn offers a mathematical basis for the investment decision.

• The basic concept of risk is that, as it increases, the expected rate of return for the underlying asset will increase to entice potential investors. Investors, should thus, expect a higher potential rate of return for a riskier investment to obfuscate the uncertainty latent in the purchase. In essence, standard deviation will provide a quantified estimation regarding the uncertainty of future returns.

• Let’s assume that you are choosing between two stocks: stock A and stock B. Over the past 20 years, Stock A has yielded an average return of 10% per year, with a standard deviation of 20 percentage points and Stock B, over this timeframe, has averaged 15% with a standard deviation of 30 percentage points.

• Using this example, on the basis of analyzing risk and return, an investor should decide that Stock A is the safer play because Stock B’s 10 percentage point increase in standard deviation yields a greater risk of uncertainty. As a result, Stock B is more likely to fall short of the initial investment more often than Stock A.

• In this example, Stock A is expected to earn roughly 10 percent, plus or minus 20 percentage points per year—thus the range that Stock A can yield is 30% gains to -10% losses.

• At first glance, the standard deviation formula may seem daunting; however, the standard deviation formula is considered fairly basic, especially when compared to other statistical equations.

• In the majority of statistical studies, a conclusion is formulated to evaluate (and subsequently decipher) whether a specific set of data is different from the control set. To formulate such a conclusion, the variability of the data must be known. The formula used to measure this variability is standard deviation. As a result, the standard deviation is approximately equal to the average deviation from the mean.

• The standard deviation formula is depicted below:

• In this formula, X is the value of mean, N is the sample size and X(i) represents each data value from i=N to i=1. The large “E” symbol represents the summation function in mathematics; this symbol indicates that must add up the sum. To utilize the standard deviation formula it is suggested that the individual have a basic understanding of algebra.

• Standard deviation is a commonly-used measurement of diversity or variability in statistics, finance and probability theory. More specifically, standard deviation will show how much variation is present from the mean or expected value—in finance, it can be applied to transactions or maneuvers. A low standard deviation will indicate that the given data points are very close to the mean, while a high standard deviation indicates that the data are spread over a large range of values.

• In addition to expressing variables of a given population, standard deviation is also used to measure confidence in statistical conclusions. For instance, the margin of error in polling data is typically determined by calculating the standard deviation if the same poll were to be conducted several times.

• Standard deviation is critical in finance, because the technique can elucidate on the rate of return for an investment or transaction. In essence, the standard deviation will yield the underlying investment or transaction’s volatility.

• In finance, standard deviation is used to represent the risk associated with a given investment security (such as a stock or bond etc.) or the risk of actively managed bundles of securities (such as hedge funds, mutual funds, or ETFs).

• Risk a primary factor when determining how to manage or invest in securities; risk determines the variation in returns on the investment, which in turn offers a mathematical basis for the investment decision.

• The basic concept of risk is that, as it increases, the expected rate of return for the underlying asset will increase to entice potential investors. Investors, in other words, should expect a higher return on a riskier investment to obfuscate the uncertainty latent in the purchase. In essence, standard deviation will provide a quantified estimation regarding the uncertainty of future returns.

• In regards to accounting, book value is the value of an asset according to its balance sheet. In terms of assets, the value is based on the original cost of the asset minus ant amortization, impairment costs, or depreciation on the asset. Most commonly, a company’s book value will be its total assets minus all liabilities and intangible assets. In practice; however, depending on the calculation, a book value may include intangible assets or goodwill. When these variables are excluded, the accounting term is often specified as a “tangible book value.”

• An asset’s initial book value will be its acquisition cost or its actual cash value. Over time, this book value will decrease due to the presence of depreciation, depletion and amortization. Depreciation is used to take note of the declining value of tangible assets (cars, buildings etc.) over time; amortization is used to record the declining value of intangible assets, such as patents; and depletion is used to record the consumption of the natural resources, which complement or are needed to sustain the attached asset.

• A company’s book value, which is regarded as an asset held by a separate entity, is the company’s shareholders’ equity, the market value of the shares owned by a separate entity or the acquisition cost of the underlying shares.

• A corporation’s book value is used as an analytical tool to help determine whether the market value of shares is above or below the book value. That being said, both measures (book value and market value) are somewhat biased; the underlying corporation’s accounting records will typically not reflect the market value of the entity’s assets and liabilities and the market value of the corporation’s stock is subject to wide fluctuations.

• Book value is may be used as a valuation metric to set the floor for stock prices under worst-case scenarios. For instance, when a company is liquidated, the book value is the figure left over to signify all debts owed. Furthermore, book value per share is also used to generate a measure of earnings for companies.

__Everything you need to know about Earnings per Share:__

**What are Earnings per Share?**

• Earnings per share refers to the amount of earnings per each outstanding share of a public corporation’s stock; in the United States, the Financial Accounting Standards Board requires all publicly-traded companies to produce income statements that account for earnings per share for all major categories outlined in the income statement. As a result, all publicly traded companies, in the United States of America, are required to report their earnings per share for their continuing operations, their net income, all extraordinary items on the income sheet and discontinued operations.

• Earnings per share refers to the portion of a company’s profit that is allocated to each outstanding share of common stock. When calculating a company’s earnings per share, it is better to use a weighted average number of shares outstanding because the number of outstanding shares can fluctuate over time.

**How do Companies Calculate Earnings per Share?**

• The earnings per share formula are different for each report; in general, the earnings per share formula will not include preferred dividends for variables outside of net income and continued operations.

• In a basic sense, the earnings per share formula will look as such:

o Earnings Per Share= Profit/ Weighted Average Common Shares

• For calculating the earnings per share of the firm’s net income, the formula will look as such:

o Earnings Per Share= Net Income-All dividends on Preferred Stock/ Average number of outstanding shares

• The earnings per share formula for continuing operations will look as such:

o Earnings Per Share= Income from Continuing Operations/Weighted Average of Common Shares

• The Earnings per Share formula will only include dividends that were actually declared (by shareholders) in the current year. In this case, all declared dividends are subtracted from the earnings per share formula. The exception to this rule is when preferred shares are cumulative, in which case all annual dividends are deducted regardless of their declaration status. Furthermore, dividends in arrears are not relevant when calculating earnings per share.