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Breaking Down Risk Modeling Cheat Sheet by


Equations | Formulas

Linear Regression Analysis
y = mx + b

y = dependent variable; m = slope;
x = dependent variable; b = y-inte­rcept
Shareh­olders' Equity
= Total Assets­−Total Liabil­ities ​
Balanced Sheet
Assets = Liabil­ities + Shareh­olders Equity
Working Capital
= (Current Assets - Current Liabil­ities)
Current Ratio
= (Current Assets / Current Liabil­ities)
Acid Test (Quick) Ratio
= (cash + accounts receivable + market securi­ties) / Current Liabil­ities
Debt to Equity Ratio
= (Long Term Debt / Shareh­olders Equity)
Debt to Assets Ratio
= (Total Liabil­ities / Total Assets)
Coeffi­cient of Variation
= Standard Deviation / Mean
= (sum of the values / the number of values)
Expected Value
= (proba­bility x possibe outcomes)
Expected Loss Ratio
= Probab­ility of Default (PD) x Loss Given Default (LGD) x Exposure at Default (EAD)

Financial Ratios

Shareh­olders' Equity: represents the net worth of a company, which is the dollar amount that would be returned to shareh­olders if a company's total assets were liquid­ated, and all of its debts were repaid. Typically listed on a company's balance sheet, this financial metric is commonly used by analysts to determine a company's overall fiscal health.
Shareh­olders' equity is also used to determine the value of ratios, such as the debt-t­o-e­quity ratio (D/E), return on equity (ROE), and the book value of equity per share (BVPS).
Standard Deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

*A volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low.
*the smaller the degree of disper­sion, the lesser the volati­lity, and the greater the accuracy of predicitions.
*As a downside, the standard deviation calculates all uncert­ainty as risk, even when it’s in the investor's favor - such as above average returns.
Variance: The term variance refers to a statis­tical measur­ement of the spread between numbers in a data set. Variance measures how far each number in the set is from the mean and thus from every other number in the set.
The square root of the variance is the standard deviation (σ), which helps determine the consis­tency of an invest­ment's returns over a period of time

Investors use variance to see how much risk an investment carries and whether it will be profit­able.
Value at Risk (VaR): measures and quantifies the level of financial risk within a firm, portfolio or position over a specific time frame. This metric is most commonly used by investment and commercial banks to determine the extent and occurrence ratio of potential losses in their instit­utional portfolios.
Risk managers use VaR to measure and control the level of risk exposure. One can apply VaR calcul­ations to specific positions or whole portfolios or to measure firm-wide risk exposure.
Capital Asset Pricing Model (CAPM): describes the relati­onship between systematic risk and expected return for assets, partic­ularly stocks.

Securi­tie­s|I­nve­stment Risks

Derivative: A derivative is a financial security with a value that is reliant upon or derived from, an underlying asset or group of assets—a benchmark. The derivative itself is a contract between two or more parties, and the derivative derives its price from fluctu­ations in the underlying asset.
Securities: "­sec­uri­ty" refers to a fungible, negotiable financial instrument that holds some type of monetary value. It represents an ownership position in a public­ly-­traded corpor­ation via stock; a creditor relati­onship with a govern­mental body or a corpor­ation repres­ented by owning that entity's bond; or rights to ownership as repres­ented by an option.
There are primarily three types of securi­ties: equity­—which provides ownership rights to holders; debt—e­sse­ntially loans repaid with periodic payments; and hybrid­s—which combine aspects of debt and equity.

Technical Analysis

Skewness: refers to a distortion or asymmetry that deviates from the symmet­rical bell curve, or normal distri­bution, in a set of data. If the curve is shifted to the left or to the right, it is said to be skewed. Skewness can be quantified as a repres­ent­ation of the extent to which a given distri­bution varies from a normal distri­bution. A normal distri­bution has a skew of zero, while a lognormal distri­bution, for ex, would exhibit some degree of right-­skew.

Guide to Volatility

Volati­lity: a statis­tical measure of the dispersion of returns for a given security or market index. In most cases, the higher the volati­lity, the riskier the security. Volatility is often measured as either the standard deviation or variance between returns from that same security or market index.
Calculate Volati­lity: Volatility is often calculated using variance and standard deviation. The standard deviation is the square root of the Variance.
1. Find the mean of the data set.
2. Calculate the difference between each data value and the mean. This is often called deviation.
3. Square the deviat­ions.
4. Add the squared deviations together.
5. Divide the sum of the squared deviations by the number of data values.
Implied volatility: the parameter component of an option pricing model, such as the Black-­Scholes model, which gives the market price of an option. Implied volatility shows how the market­place views where volatility should be in the future.
Since implied volatility is forwar­d-l­ooking, it helps us gauge the sentiment about the volatility of a stock or the market. However, implied volatility does not forecast the direction in which an option is headed.
Implied Volatility vs. Historical Volatility:
Implied, or projected, volatility is a forwar­d-l­ooking metric used by options traders to calculate probab­ility.
Implied volati­lity, as its name suggests, uses supply and demand, and represents the expected fluctu­ations of an underlying stock or index over a specific time frame.
With Historical Volati­lity, traders use past trading ranges of underlying securities and indexes to calculate price changes.
Calcul­ations for historical volatility are generally based on the change from one closing price to the next.
Black Scholes Model: also known as the Black-­Sch­ole­s-M­erton (BSM) model, is a mathem­atical model for pricing an options contract. In partic­ular, the model estimates the variation over time of financial instru­ments. It assumes these instru­ments (such as stocks or futures) will have a lognormal distri­bution of prices. Using this assumption and factoring in other important variables, the equation derives the price of a call option.
Volatility is a metric that measures the magnitude of the change in prices in a security. Generally speaking, the higher the volati­lit­y—and, therefore, the risk—the greater the reward. If volatility is low, the premium is low as well.

Financial Analysis

Monte Carlo Simulation: used to model the probab­ility of different outcomes in a process that cannot easily be predicted due to the interv­ention of random variables.
It is a technique used to understand the impact of risk and uncert­ainty in prediction and foreca­sting models.
Correl­ation: a statistic that measures the degree to which two variables move in relation to each other.
Correl­ation measures associ­ation, but doesn't show if x causes y or vice versa, or if the associ­ation is caused by a third–­perhaps unseen­–fa­ctor.
Correl­ation Coeffi­cient: a statis­tical measure of the strength of the relati­onship between the relative movements of two variables. The values range between -1.0 and 1.0. A calculated number greater than 1.0 or less than -1.0 means that there was an error in the correl­ation measur­ement. A correl­ation of -1.0 shows a perfect negative correl­ation, while a correl­ation of 1.0 shows a perfect positive correl­ation. A correl­ation of 0.0 shows no linear relati­onship between the movement of the two variables.
Linear Relati­onship: a statis­tical term used to describe a straig­ht-line relati­onship between two variables. Linear relati­onships can be expressed either in a graphical format where the variable and the constant are connected via a straight line or in a mathem­atical format where the indepe­ndent variable is multiplied by the slope coeffi­cient, added by a constant, which determines the dependent variable.
Linear relati­onships can be expressed either in a graphical format or as a mathem­atical equation of the form y = mx + b.
Expected Value: A weighted average of the values of the random variable, for which the probab­ility function provides the weights, based on its Theore­tical Probab­ility.
If an experiment can be repeated a large number of times, the expected value can be interp­reted as long-run average

Statis­tical Measures

Dispersion: that describes the size of the distri­bution of values expected for a particular variable. Dispersion can be measured by several different statis­tics, such as range, variance, and standard deviation. In finance and investing, dispersion usually refers to the range of possible returns on an invest­ment, but it can also be used to measure the risk inherent in a particular security or investment portfolio. It is often interp­reted as a measure of the degree of uncert­ainty, and thus, risk, associated with a particular security or investment portfolio. {{nl} Generally speaking, the higher the disper­sion, the riskier an investment is, and vice versa.
Random Variable: a variable whose value is unknown or a function that assigns values to each of an experi­ment's outcomes. Random variables are often designated by letters and can be classified as discrete, which are variables that have specific values, or contin­uous, which are variables that can have any values within a continuous range.
The use of random variables is most common in probab­ility and statis­tics, where they are used to quantify outcomes of random occurr­ences.
Regression: a statis­tical method used in finance, investing, and other discip­lines that attempts to determine the strength and character of the relati­onship between one dependent variable (usually denoted by Y) and a series of other variables (known as indepe­ndent variab­les).
Regression helps investment and financial managers to value assets and understand the relati­onships between variables, such as commodity prices and the stocks of businesses dealing in those commod­ities.
Coeffi­cient of Variation (CV): is a statis­tical measure of the dispersion of data points in a data series around the mean. The coeffi­cient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drasti­cally different from one another.
*The lower the ratio of the standard deviation to mean return, the better risk-r­eturn trade-off.


Probab­ility Analysis: A technique for foreca­sting events, such as accidental and business losses, on the assumption that they are governed by an unchanging probab­ility distri­bution.
Theore­tical Probab­ility: Probab­ility that is based on theore­tical principles rather than real experi­ences.
Empirical Probab­ility (Poste­riori Probab­ility): Probab­ility measure that is based on actual experience through historical data or observ­ation of facts.
What is Empirical Probab­ility? Empirical probab­ility uses the number of occurr­ences of an outcome within a sample set as a basis for determ­ining the probab­ility of that outcome. The number of times "­event X" happens out of 100 trials will be the probab­ility of event X happening. An empirical probab­ility is closely related to the relative frequency of an event.
Probab­ility Distri­bution: A presen­tation (table, chart, or graph) of probab­ility estimates of a particular set of circum­stances and of probab­ility of each possible outcome.
Normal Distri­bution: A balanced probab­ility distri­bution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distri­bution will appear as a bell curve.
Discreet Probab­ility Distri­bution: Consists of the values a random variable can assume and the corres­ponding probab­ilities of the values.
Continuous Probab­ility Distri­bution: repres­ented as either graphs or by dividing the distri­bution into a finite # of bins and calcul­ating the probab­ility of an outcome failing within the range repres­ented by each bin; shows all the possible outcomes and associated probab­ilities for a given event.


Probab­ility Analysis: A technique for foreca­sting events, such as accidental and business losses, on the assumption that they are governed by an unchanging probab­ility distri­bution.
Probab­ility Distri­bution: A presen­tation (table, chart, or graph) of probab­ility estimates of a particular set of circum­stances and of probab­ility of each possible outcome.
Theore­tical Probab­ility: Probab­ility that is based on theore­tical principles rather than real experi­ences (Coin Toss/R­olling Dice)
Empirical Probab­ility: Probab­ility measure that is based on actual experience through historical data or observ­ation of facts – this method is most often used by insurance profes­sionals
Law of Large Numbers: A mathematic principle stating that as the number of similar but indepe­ndent exposure units increase, the relative accuracy or predic­tions about future outcomes (losses) also increase.
Earnings at Risk (EaR): A technique used to assess earnings by measuring the likelihood that earnings will be below a specific dollar amount over a specific period of time.
Value at Risk (VaR): A technique to quantify financial risk by measuring the likelihood of losing more than a specific dollar amount over a specific period of time.
Condit­ional Value at Risk (cVaR): A technique to quantify the likelihood of losing a specific dollar amount that exceeds the VaR threshold.
Trend Analysis: An analysis that identifies patterns in past data and then projects these patterns into the future.
Regression Analysis: A statis­tical technique that is used to estimate relati­onships between variables.
Linear Regression Analysis: A form of regression analysis that assumes that the change in the dependent variable is constant for each unit of change in the indepe­ndent variable.


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