Applied Monte Carlo Simulation

(This is Part 1 of 2)

Most of us have faced the pain of learning probability in statistics courses that were too theoretical and far from applicable.

Practical probability principles will be presented, based on a common-sense understanding of probability. This would be followed by 5 rules and practices to be used when we need to evaluate the probability of 2 or more events happening at the same time, a case that can happen frequently in MCS models.

Part 1 covers the Fundamentals of Probability. It then starts with the first two of the calculations of probability for 2 or more events:

A) Complement of an Event

B) Intersection of Independent Events (Multiplication Rule)

Part 2 continues with the calculations for the . . .

C) Union of Events (Inclusive OR) (Addition Rule)

D) Union of Events (Exclusive XOR) (Addition Rule)

E) Intersection of Independent Events (Multiplication Rule)

(This is Part 2 of 2)

Most of us have faced the pain of learning probability in statistics courses that were too theoretical and far from applicable.

Practical probability principles will be presented, based on a common-sense understanding of probability. This would be followed by 5 rules and practices to be used when we need to evaluate the probability of 2 or more events happening at the same time, a case that can happen frequently in MCS models.

Part 1 covers the Fundamentals of Probability. It then starts with the first two of the calculations of probability for 2 or more events:

A) Complement of an Event

B) Intersection of Independent Events (Multiplication Rule)

Part 2 continues with the calculations for the . . .

C) Union of Events (Inclusive OR) (Addition Rule)

D) Union of Events (Exclusive XOR) (Addition Rule)

E) Intersection of Independent Events (Multiplication Rule)

Random Numbers are at the heart of MCS. This lecture will show you how you can generate pseudo-random numbers in Excel (since true random numbers do not exist). We then relate random numbers to various Probability Distributions, to be used in later Lectures. Finally, I will show you a few applications of random numbers to be used when designing models. These cover shuffling items, selecting items at random or assigning items to several groups.

(This is Part 1 of 2)

The basic practice of MCS is to randomize the input variables in a formulation using the techniques presented in this Lecture. Here, we will define “random variables”. We will establish the difference between discrete and continuous variables. Based on these definitions, we will discuss the critical practice of preparing Frequency Tables. A procedure will show you how to develop the Cumulative Frequency % (or the Percentiles). This is the basis of the output analysis in MCS. The Lecture ends by presenting the logic of probability and inverse functions in Excel based on the Frequency, Relative Frequency and the Cumulative Frequency %.

Part 1 covers these topics:

A) What are Random Variables?

B) Defining the Frequency Table and Chart

C) Defining the Cumulative Frequency %

Part 2 covers these topics

D) Defining the Cumulative Frequency % (Continued from Part 1)

E) What are the Probability and Inverse Functions in Excel?

(This is Part 2 of 2)

The basic practice of MCS is to randomize the input variables in a formulation using the techniques presented in this Lecture. Here, we will define “random variables”. We will establish the difference between discrete and continuous variables. Based on these definitions, we will discuss the critical practice of preparing Frequency Tables. A procedure will show you how to develop the Cumulative Frequency % (or the Percentiles). This is the basis of the output analysis in MCS. The Lecture ends by presenting the logic of probability and inverse functions in Excel based on the Frequency, Relative Frequency and the Cumulative Frequency %.

Part 1 covers these topics:

A) What are Random Variables?

B) Defining the Frequency Table and Chart

C) Defining the Cumulative Frequency %

Part 2 covers these topics

D) Defining the Cumulative Frequency % (Continued from Part 1)

E) What are the Probability and Inverse Functions in Excel?

(This is Part 1 of 2)

The Normal Distribution is one of the most widely used distributions in statistics. It represents the behavior of a wide variety of variables such as industrial measurements, client behavior, sales demand and is also used as the basis of Six Sigma. We first cover the basic definition of the Normal Distribution (its mean and standard deviation). We then develop 4 useful applications of the Normal Distribution:

Application 1: To measure the spread of data with the Standard Deviation

Application 2: To standardize measurements with Z-scores for comparative purposes

Application 3: To ask for the value of the probability p of finding random variables below a specific value of X.

Application 4: To ask for the value of a random variable X given a specific probability p such that a proportion p of all variables is equal to or less than the cutoff variable X.

The last two are widely used when analyzing distributions of all types.

Part 1 covers these topics

A) Application 1: to Measure the Spread with the Standard Deviation

B) Application 2: to Standardize Measurements for Comparative Purposes

Part 2 covers these topics

C) Application 3: to use Area under the Curve to find Probabilities of X

D) Application 4: to find out if given a Probability, what the X Corresponding to it would be

E) Application 5: to use Excel Functions to generate Normally Distributed Random Variables

The Normal Distribution is one of the most widely used distributions in statistics. It represents the behavior of a wide variety of variables such as industrial measurements, client behavior, sales demand and is also used as the basis of Six Sigma. We first cover the basic definition of the Normal Distribution (its mean and standard deviation). We then develop 4 useful applications of the Normal Distribution:

Application 1: To measure the spread of data with the Standard Deviation

Application 2: To standardize measurements with Z-scores for comparative purposes

Application 3: To ask for the value of the probability p of finding random variables below a specific value of X.

Application 4: To ask for the value of a random variable X given a specific probability p such that a proportion p of all variables is equal to or less than the cutoff variable X.

The last two are widely used when analyzing distributions of all types.

Part 1 covers these topics

A) Application 1: to Measure the Spread with the Standard Deviation

B) Application 2: to Standardize Measurements for Comparative Purposes

Part 2 covers these topics

C) Application 3: to use Area under the Curve to find Probabilities of X

D) Application 4: to find out if given a Probability, what the X Corresponding to it would be

E) Application 5: to use Excel Functions to generate Normally Distributed Random Variables

This lecture justifies the use of a standardized 8-Step Process for Monte Carlo Simulation. We will then present the problem statement of a Case Model to be used in subsequent Lectures: the Route from Home to your Office going through a set of traffic lights.

Here, we will summarize lessons learned through spreadsheet and simulation modeling. The talk recommends some good practices to follow and warns you about some bad practices to avoid.

This Step uses the Case Model to show you how you should prepare your problem statement, the explanation of why you are setting up a model. It then shows you what information is required in the model.

Finally, it presents the first Step in simulation, namely the development of a static model. This model uses fixed estimates and is useful for two purposes. First, it allows you to test your formulation. Secondly, it makes it easier for you to migrate into the Dynamic Model to be used in Step 3.

(This is Part 1 of 2)

This Step is the heart of Monte Carlo Simulation and possibly the most difficult. First, you need to identify the input variables that you wish to randomize (simulate). Then you have to select a probability distribution that best represents the behavior of each input variable. Thirdly, given the information you collected in Step 1, you can define the parameters to use in the randomizing functions that extract values from these distributions.

Part 1 covers these topics

A) Input Variable 1: Section 1 of the Route

B) The Uniform Distribution (for Route Section 1)

C) Bernoulli Trials

Input Variable 2: The Wait at the Traffic Lights

Part 2 covers these topics

D) Input Variable 3: Section 2 of the Route

E) The Discrete Probability Distribution (for Route Section 2)

(This is Part 2 of 2)

This Step is the heart of Monte Carlo Simulation and possibly the most difficult. First, you need to identify the input variables that you wish to randomize (simulate). Then you have to select a probability distribution that best represents the behavior of each input variable. Thirdly, given the information you collected in Step 1, you can define the parameters to use in the randomizing functions that extract values from these distributions.

Part 1 covers these topics

A) Input Variable 1: Section 1 of the Route

B) The Uniform Distribution (for Route Section 1)

C) Bernoulli Trials

Input Variable 2: The Wait at the Traffic Lights

Part 2 covers these topics

D) Input Variable 3: Section 2 of the Route

E) The Discrete Probability Distribution (for Route Section 2)

Using the results of Steps 1 and 2, this lecture will show you how to set up the Dynamic Model or the model that contains all the random variable generating functions. We can then replicate the dynamic formation over 1000s of scenarios. Two different ways of replicating scenarios will be shown (copying and using the What IF feature in Excel).

This is the first of several analytic methods. Once the Dynamic Model provides us with a column of 1000s of results, the Frequency Table groups the 1000s of results in the required brackets (or bins). To ensure procedural standardization, this Lecture will show you how to decide on the size of the brackets (or bins) and how to establish their number.

It will then show you how the bins can be used to calculate the Frequency column (resulting in a histogram or a bar chart). Finally, the Lecture will show you how to calculate the Cumulative Frequency Percentage column which is really a Cumulative Probability Distribution (CPD). This table will be used in the coming Combo Chart of Step 5. It will also be used in case Inverse Functions for specific distributions are not available in Excel.

The Combo Chart is a chart that has two components: 1) The Frequency Chart (or the Bar Chart or Histogram). This contains the count for each bracket or bin. 2) The Cumulative Frequency % curve (containing the accumulated probability for each bracket or bin).

Both charts have the Random Variable X of the model plotted on the horizontal axis with the Frequency and Cumulative Frequency % plotting on the two vertical axes. Using the Combo chart will help you answer most of the questions in your Problem Statement. The whole discussion is standardized in such a manner that you can re-use this worksheet and the coming two (in Steps 6 and 7). This will save you time and avoid modeling errors. The lecture will also focus on how to read the Combo Chart.

(This is Part 1 of 2)

Continuing with the standardization of analytic results, this lecture will present 3 such analyses. First, we will present a dynamic set of descriptive statistics.

Secondly, we will explain what Percentiles are and how they are the mathematical (and more accurate) equivalent of the Combo Chart of Step 5.

Using the Excel function for Percentiles, we will prepare a table of right-tail, left-tail and interval values based on confidence levels 90%, 95% and 99%. Finally, using the percentile values, this Lecture will show you how to develop a Tornado (or Funnel) Chart.

Part 1 covers these topics

A) Step 6a: The Descriptive Statistics of our Results

B) Step 6b: Using Percentiles on our Dataset

Part 2 covers these topics

C) Step 6b: Using Percentiles on our Dataset (Cont.)

D) Step 6c: Goodness of Fit of Results with Known Distributions

(This is Part 2 of 2)

Continuing with the standardization of analytic results, this lecture will present 3 such analyses. First, we will present a dynamic set of descriptive statistics.

Secondly, we will explain what Percentiles are and how they are the mathematical (and more accurate) equivalent of the Combo Chart of Step 5.

Using the Excel function for Percentiles, we will prepare a table of right-tail, left-tail and interval values based on confidence levels 90%, 95% and 99%. Finally, using the percentile values, this Lecture will show you how to develop a Tornado (or Funnel) Chart.

Part 1 covers these topics

A) Step 6a: The Descriptive Statistics of our Results

B) Step 6b: Using Percentiles on our Dataset

Part 2 covers these topics

C) Step 6b: Using Percentiles on our Dataset (Cont.)

D) Step 6c: Goodness of Fit of Results with Known Distributions

This is the fourth Lecture on analytics. Having arrived at conclusions about how your changes in input variables affect the output, Sensitivity Analysis allows you to investigate what happens if some of your “constants” change.

Influence Analysis proceeds by setting each of the input variables to zero and noting the resulting output. A table is then prepared that shows the difference between the original output and the resulting output after such a change.

A table and a chart can then allow you to identify which of your input variables has the largest influence on the output result you are interested in. Such variables can then be given more attention. they will also show which variables have a negligible influence on the output, so they can possibly be set as fixed values without being simulated.

This Lecture concludes the modeling process by presenting your findings: numeric or qualitative results. (This will be given for the Case Model). The questions asked earlier in Step 1 (the Problem Statement) will be calculated and answered.

Now that you have a good idea of what the model gave you, you would have the chance to suggest extensions or improvements to the model using new formulations, different variables and parameters and new model components.

(This is Part 1 of 2)

This model uses the Binomial Distribution. It shows you how a showroom that sells 10 products can analyze the number of products purchased by each customer. This is our Random Variable.

Once a pattern is recognized, the Sales Department can then decide on discount and promotional schemes that will encourage customers to purchase more products.

Part 1 covers these topics

A) The Binomial Distribution

B) The Parameters of the Binomial Distribution

Part 2 covers these topics

C) The Excel Functions for the Binomial Distribution

D) The Showroom Discount Analysis Model using the Binomial Distribution

(This is Part 2 of 2)

This model uses the Binomial Distribution. It shows you how a showroom that sells 10 products can analyze the number of products purchased by each customer.

This is our Random Variable. Once a pattern is recognized, the Sales Department can then decide on discount and promotional schemes that will encourage customers to purchase more products.

Part 1 covers these topics

A) The Binomial Distribution

B) The Parameters of the Binomial Distribution

Part 2 covers these topics

C) The Excel Functions for the Binomial Distribution

D) The Showroom Discount Analysis Model using the Binomial Distribution

(This is Part 1 of 2)

This model uses the Geometric Distribution which is a special case of the Negative Binomial Distribution. The Geometric Distribution presents a Random Variable X which counts the number of failures in an experiment that are met before the first success is reached.

The model analyzes how many interviews a fieldworker can complete in one day. Given that she has been offered a rate per interview and that she has a specific goal as to how much she should earn per day, this model will help her find out if her goal can be reached or not.

Part 1 covers these topics

A) The Geometric and the Negative Binomial Distributions

Part 2 covers these topics

B) Interviewing Passengers Model using the Geometric Distribution

(This is Part 2 of 2)

This model uses the Geometric Distribution which is a special case of the Negative Binomial Distribution. The Geometric Distribution presents a Random Variable X which counts the number of failures in an experiment that are met before the first success is reached.

The model analyzes how many interviews a fieldworker can complete in one day. Given that she has been offered a rate per interview and that she has a specific goal as to how much she should earn per day, this model will help her find out if her goal can be reached or not.

Part 1 covers these topics

A) The Geometric and the Negative Binomial Distributions

Part 2 covers these topics

B) Interviewing Passengers Model using the Geometric Distribution

The purpose of this model is to show you how to develop a variety of formulation techniques that increase the validity of the model and improve its analysis. A minimarket chain called ABC has many outlets throughout the region. They all have limited shelf space.

Having never stocked pomegranate juice and seeing that it is coming up in the world of health food culture, they decided to stock only one brand of pomegranate juice. Our company is one of 13 producers of pomegranate juice in the region. We are interested in placing our pomegranate juice on the shelves of the minimarket because of the large number of outlets they have.

(This is Part 1 of 2)

This model has two aims. The first is to introduce you to the Beta Distribution. This is a powerful distribution that has many applications, depending on its shape. The two shape parameters, alpha and beta can be defined in several ways: manually, depending on the shape of the Beta Distribution needed for the model, calculated from the Mean and Standard Deviation of the raw data in the model and calculated from the 3-point PERT estimates for each task. (A Health Claim model is presented to clarify how a and b are calculated from the raw data’s Mean and Standard Deviation).

The second purpose is to simulate a 14-task project with several networking nodes. Each one of these tasks is presented with 3-point PERT estimates used to calculate the a and b of the Beta from which the duration is sampled. The end result of the model would be to provide a confidence based estimate of the Critical Path (or the total duration) of the Project.

Part 1 covers these topics

A) Introducing the Beta Distribution

B) Handling the Parameters of the Beta Distribution over different models
(Covered in Parts 1 and 2)

Part 2 covers these topics

C) Introducing a Typical Beta Model (Health Claims)

D) Introducing the Simulation of the Project’s Critical Path

(This is Part 2 of 2)

This model has two aims. The first is to introduce you to the Beta Distribution. This is a powerful distribution that has many applications, depending on its shape. The two shape parameters, alpha and beta can be defined in several ways: manually, depending on the shape of the Beta Distribution needed for the model, calculated from the Mean and Standard Deviation of the raw data in the model and calculated from the 3-point PERT estimates for each task. (A Health Claim model is presented to clarify how a and b are calculated from the raw data’s Mean and Standard Deviation).

The second purpose is to simulate a 14-task project with several networking nodes. Each one of these tasks is presented with 3-point PERT estimates used to calculate the a and b of the Beta from which the duration is sampled. The end result of the model would be to provide a confidence based estimate of the Critical Path (or the total duration) of the Project.

Part 1 covers these topics

A) Introducing the Beta Distribution

B) Handling the Parameters of the Beta Distribution over different models
(Covered in Parts 1 and 2)

Part 2 covers these topics

C) Introducing a Typical Beta Model (Health Claims)

D) Introducing the Simulation of the Project’s Critical Path

This model introduces a client applying for a bank loan by presenting an income statement projected over 4 years. For each of 8 rows in the Income statement, the client used a specified growth rate to arrive at a Net Profit Margin of 18.67% at the end of 4 years.

The bank finds that the NPM too optimistic and decides to conduct a simulation by randomizing the 8 growth rates using various distributions. The result is not good for the client as it shows that 94% of the 4000 scenarios gave a Net Profit Margin lower than that proposed by the client.

Although these courses focus on business models, I thought it would be interesting to show you how MCS can be used to calculate the value of PI.

This model has the important objective of introducing “dual level simulation”. This technique will also be used in the Batch Production model in Lecture 5.14. The reason we use Dual Level simulation is that some of the variables in the 1000s of scenarios require simulation on their own. For example, if we have 1000 rows signifying the total sales of 5 showrooms, we need a secondary simulation to run through 100s of rows that simulate the different types of sales in each showroom. To achieve this, the model requires a very short VBA model that allows Excel to loop through the Primary Table by conducting a secondary simulation in another table and picking up its summary data placing it in a specific row in the Primary table.

The model simulates 1000s of lab tests given their mean and standard deviations are known. As each day’s tests are simulated in the secondary table, the summary of results is moved to the primary table. The end objective would be to answer this question: given that the hospital is outsourcing X tests over 1000 days, how does that compare with the simulated 1000 days.

This model uses the Normal Distribution to randomize the sales in the summer season. The seller usually orders one quantity to be available at the start of the season, in May. This is used to supply demand throughout the summer. The model analyzes sales by randomizing the monthly demands. It analyzes the cost of lost sales (if quantities are not available) and completes the model by analyzing the returns from the end of summer discounts of unsold quantities. The quantities sold under discounts are extracted from a BetaPERT distribution.

This model introduces you to the Poisson Distribution, another very commonly used distribution in Monte Carlo Simulation. This is a discrete variable distribution. The model simulates the production of fabric that is delivered in rolls of 50 meters. The company has 3 policies for quality management. One consists of testing all rolls. The second consists of refunding the cost of any faulty roll when the client reports it. The third policy consists of replacing any faulty roll.

The POISSON distribution is fully explained with various examples and is then applied to randomly generated the number of defects in 1000s of rolls, applying the above 3 policies, hence establishing which policy is most feasible.

NOTE: we have added a new Workout that is not covered in the video of the lecture.

It is a modification of the workout:
L5.10--W03 Truck Loading (Single Server Queue).xlsx

and is called:

L5.10--W03a Single Server Queue - Truck Loading with BALKING.xlsx

It is accompanied by a WORD document describing the modifications.

Another important distribution is the Exponential Distribution. This is a “cousin” of the POISSON distribution but is a continuous distribution. This distribution can be sampled to generate a variable announcing the time of arrival of the next event. It is used in a variety of queuing (or waiting list) models.

This lecture covers the details of the Exponential Distribution and shows how it is related to the POISSON distribution since they share the same parameter (expressed in a reciprocal manner). The model covers a single server, being a forklift. This server awaits trucks coming into a single queue and services them by loading them with goods. The model simulates arrivals and service times resulting in such “system” data as the time trucks wait in the system, the utilization ratio of the forklift and other indicators.

Having covered the Geometric Distribution in Lecture 5.2, we continue with its “mother” distribution here. This is the Negative Binomial which predicts the probability of r successes having gone through X failures. (In the Geometric Distribution, r = 1).

A salesman knows that if he scores 12 sales a day, it would be worth his while. Therefore, we can simulate the salesman’s visits until we get 12 successes. The time it takes to locate a prospect, the time it takes to try to sell the product and the time it takes to complete a sale are all randomized. This would give the salesman a final ratio of how many sales were completed in one day. He can then decide if these timings and this objective (12 sales) are suitable or not.

One of the key indicators in evaluating investments or projects (or new companies) is the Net Present Value procedure. This is carried out by discounting (or finding the present value) of all cash flows of a project over a specific period. Once the cash flows are brought down to one date, they can be added resulting in the Net Present Value. If this is positive, the project would be feasible.

Traditional ways of calculating NPV do not provide sufficient information about the related indicator: the Internal Rate of Return (IRR). This is often calculated using Excel’s formula. However, this model shows several issues with this calculation. It uses the What IF table to allow the financial analyst to chart the NPV values as the discounting rate changes. The analyst can then identify the discounting rates where the NPV curve crosses the line (i.e., = 0). This would be the IRR.

The model simulates a set of 8 costs and revenues as well as the discounting rate to provide a confidence interval for the value of NPV.

Risk analysis is often required as a section in a project plan, a proposal or any study of investments. Analysts often take short cuts are present such risks in a qualitative manner. This lecture covers the analytic way of assessing risk exposures. It includes the analysis of probability and impact of an event which results in the damaging exposure of this event. The lecture adds a third factor, that of detectability. How easily can this event be detected, in advance?

Various Risk Analysis Tables are shown and are then simulated whereby probability, impacts or detectability estimates are simulated to result in an overall assessment of project or investment risk.

This is the second Dual Level Simulation model (the first presented in Lecture 5.7 that deals with the model of Lab Tests in a Hospital). Batches of tea arrive at the production line. Each batch would have a different weight, depending on the way its supplier packages it. The receiver inspects the batches and rejects part or all of the batches. The accepted part is placed in a Pallet with a known maximum weight. This is the secondary simulation which has as many rows as needed for filling up the pallet. The weight and other indicators are then stored in a row in the Primary Table.

We revert to the Binomial distribution in this model to simulate a hotel that has two types of rooms: Regular and King Size. WE have constants that allow us to get samples of bookings and arrivals, hence calculating “no-shows”. Depending on availability in the King Size rooms, any guest arriving and having no regular room available for him or her, will get upgraded to a King Size room, if available. Any guest who cannot be upgraded will get compensated.

A variety of financial constants will be applied to calculate the profit and loss of the two types of rooms and the underperformance of the hotel (which is the difference between the actual P/L and the maximum possible P/L.

(This is Part 1 of 2)

This lecture covers the methods needed to calculate the expected and unexpected credit losses in banks. Once calculated, banks can then cover expected losses through loss provisions (liabilities) and unexpected losses through capital or equity. An initial model is given that calculates the expected and unexpected losses. Three other models (elaborated below) represent extensions that improve the accuracy of EL and UL

The lecture starts by detailing the functioning of the LogNormal Distribution which is used to estimate the Exposure at Default (EAD).

Model 1 calculates the Expected Losses (EL) as the product of the expected exposure (EAD), the probability of default (PD) and the LGD, or the portion of EAD that is actually not paid back. The popular Michael Ong formula is used to calculate Sigma (which is also calculated using a direct evaluation of the Sigma of the losses). Moreover, using Var(99.9%), the simulation can give us an estimation of the expected and the unexpected loss.

Model 2 incorporates possible recovery of exposed amounts by suitable adjustments to the Exposure.

Model 3 applies Beta to the LGD instead of the Normal Distribution used in Model 1.

Model 4 simulates the case where PD and LGD might be correlated and presents an elaborate modification to the model that shows how the expected and the unexpected losses in such a case will increase.

Part 1

A) Introducing the LOGNORMAL Distribution

B) Plain Vanilla Model for Expected and Unexpected Losses

Part 2

B) Plain Vanilla Model for Expected and Unexpected Losses (Continued)

C) Credit Adjusted Exposure model

D) Loss given Default (LGD) is drawn from a Beta

E) Model using Correlation between Probability of Default and LGD

(This is Part 2 of 2)

This lecture (in two parts) covers the methods needed to calculate the expected and unexpected credit losses in banks. Once calculated, banks can then cover expected losses through loss provisions (liabilities) and unexpected losses through capital or equity. An initial model is given that calculates the expected and unexpected losses. Three other models (elaborated below) represent extensions that improve the accuracy of EL and UL

The lecture starts by detailing the functioning of the LogNormal Distribution which is used to estimate the Exposure at Default (EAD).

Model 1 calculates the Expected Losses (EL) as the product of the expected exposure (EAD), the probability of default (PD) and the LGD, or the portion of EAD that is actually not paid back. The popular Michael Ong formula is used to calculate Sigma (which is also calculated using a direct evaluation of the Sigma of the losses). Moreover, using Var(99.9%), the simulation can give us an estimation of the expected and the unexpected loss.

Model 2 incorporates possible recovery of exposed amounts by suitable adjustments to the Exposure.

Model 3 applies Beta to the LGD instead of the Normal Distribution used in Model 1.

Model 4 simulates the case where PD and LGD might be correlated and presents an elaborate modification to the model that shows how the expected and the unexpected losses in such a case will increase.

Part 1

A) Introducing the LOGNORMAL Distribution

B) Plain Vanilla Model for Expected and Unexpected Losses

Part 2

B) Plain Vanilla Model for Expected and Unexpected Losses (Continued)

C) Credit Adjusted Exposure model

D) Loss given Default (LGD) is drawn from a Beta

E) Model using Correlation between Probability of Default and LGD

This is a numeric method that allows businesses to select the best scoring item out of M possible alternatives. These can be recruits, projects, processes, equipment, etc. Each item will be scored out of N different criteria.

These criteria will also have weights, so the analyst can indicate which criterion is more important in the overall score. Criteria are also defined as having “high means best” such as reliability or quality or “high means worst” such as cost or duration. Formulas are presented to find the weighted index of the scores that will establish the best item in the set of M options. Monte Carlo Simulation will be applied to randomize several of the scores.

A static turnover analysis model was adapted and expanded to be a comprehensive calculation of the costs of turnover. This covers the cost during the period when the employee is absent, followed by the cost of recruiting, then the cost of training and finally the cost of the learning curve period.

Various distributions will be applied to such parameters as salaries, turnover rates, timings and such.