In Book 1: Novel Six Sigma Approaches to Risk Assessment and Management

ISBN: 9781522527039

Author: Vojo Bubevski (Independent Researcher)

Abstract: The proposed method is applied to Investment Management for portfolio selection to achieve investment objectives by controlling risk. DMAIC framework applies proven stochastic techniques to investment management: i) Define: Optimisation constructs an Efficient Frontier of optimal portfolios with an expected return in a predefined range with a determined increment; ii) Measure: Simulation calculates and measures the portfolio return, Variance, Standard Deviation, Value at Risk (VAR), Sharpe Ratio, and Beta of Efficient Frontier portfolios; Six Sigma capability metrics of the investment process are calculated versus specified limits; iii) Analyse: Analysis allows for selection of the best Efficient Frontier portfolio with maximum Sharpe Ratio. Simulation sensitivity analysis identifies the riskiest asset; iv) Improve: Portfolio revision considers options to improve the portfolio and replaces the asset with an option to reduce risk. Portfolio execution implements the revised portfolio; v) Control: Ongoing portfolio management evaluates portfolio performance on a regular basis and if required, revises the portfolio considering changes in the market and investor’s position.                      Keywords: Investment Management; Portfolio Analysis; Asset & Liability Management; Six Sigma; DMAIC; Stochastic optimisation; Monte Carlo simulation.

The Results: The complete results of the Efficient Frontier portfolios are as follows. Table 1 shows the Mean Return (µ) and the investment fractions of total funds invested in each asset.

Table 1: The Efficient Frontier Portfolios’ Investment Fractions

µ	Fund 1	Fund 2	Fund 3	Fund 4
0.091	0.29440	0.40323	0.30237	0
0.092	0.30565	0.37249	0.32186	0
0.093	0.31689	0.34175	0.34136	0
0.094	0.32814	0.31101	0.36085	0
0.095	0.33938	0.28027	0.38035	0

Table 2 shows the Mean Return (µ), Variance (V), Standard Deviation (σ), VAR, Sharpe Ratio (SR), and Beta (β).

Table 2: The Efficient Frontier Portfolios’ Details

µ	V	σ	VAR	SR	β
0.091	0.233	0.473	-0.188	0.0776	0.723
0.092	0.242	0.491	-0.225	0.0784	0.730
0.093	0.252	0.502	-0.291	0.0787	0.740
0.094	0.267	0.517	-0.375	0.0784	0.756
0.095	0.293	0.541	-0.491	0.0767	0.777

The Efficient Frontier of the optimal portfolios is as follows. The Efficient Frontier curve shows that an increase in the expected return of the portfolio causes an increase in the portfolio Standard Deviation. To emphasise, the Efficient Frontier gets flattered as expected. This shows that each additional unit of Standard Deviation (i.e., risk) allowed, increases the portfolio Mean Return by less and less.

 

Chapter 3: Measuring and Analysisng Credit RiskIn Book 2: Six Sigma Improvements for Basel III and Solvency II in Risk Management

ISBN: 9781522572800

Author: Vojo Bubevski (Independent Researcher) 

Abstract: This chapter discusses the measurement and analysis of credit risk. A factory plans to accomplish a project and applies for credit to a bank to finance the project. The bank considers a loan to finance the factory project and assesses the credit risk. The chapter presents the analysis and measurement of different aspects of credit risk to answer how much should be lent to the factory project and for how long considering the risk inherent in the transaction. Credit risk is assessed considering: 1. Cash flow projection; 2. Count of negative cash flow; 3. Maximum negative cash flow; 4. Net Present Value (NPV) based on dividends; 5. Internal Rate of Return (IRR) based on dividends; 6. Capital asset NPV and IRR; 7. Solvency loan; 8. Risk of bankruptcy; and 9. Financial Analysis Measures: i) Gross Margin; ii) Interest Coverage; iii) Financial Coverage; iv) Return on Investment; v) Return on Assets; vi) Net Worth. Keywords: Financial Risk Management, Credit Risk, Basel III, Six Sigma DMAIC, Monte Carlo Simulation. 

The Results: Monte Carlo simulation was run to measure and analyse the credit risk. In this section, the Cash Flow Projections are only presented and then discussed for credit risk assessment. The Cash Flow Projection in US$M is showing Cash Flow Mean, Cash Flow Mean +/- One Standard Deviation, and Cash Flow Mean Probability Distribution from 5% to 95%. The Minimum Cash Flow Mean is in Year 5, which is negative; and the Maximum Cash Flow Mean is in Year 16, which is positive. The Cash Flow Mean is negative from Year 4 to Year 6.

 

In Book 2: Six Sigma Improvements for Basel III and Solvency II in Risk Management

ISBN: 9781522572800

Author: Vojo Bubevski (Independent Researcher)

Abstract: Market risk management in a portfolio selection of correlated assets is considered in this chapter. The chapter elaborates on how to construct and select an optimal portfolio of correlated assets to control VAR considering the risk-associated limits. Stochastic Optimisation is used to construct the Efficient Frontier of minimal mean-variance investment portfolios with maximal return and minimal acceptable risk. Monte Carlo simulation is utilised to stochastically calculate and measure the portfolio return, Variance, Standard Deviation, VAR, and Sharpe Ratio of the Efficient Frontier portfolios. Six Sigma process capability metrics are also stochastically calculated against desired specified target limits for VAR and Sharpe Ratio of the Efficient Frontier portfolios. Simulation results are analysed and the optimal portfolio is selected from the Efficient Frontier based on the criteria of maximum Sharpe Ratio.                                                                          Keywords: Financial Risk Management, Market Risk, Basel III, Six Sigma DMAIC, Stochastic Optimisation, Monte Carlo Simulation.

The Results: To select technically the best portfolio, the two optimal portfolios are compared as presented in Table 4. Table 4: The Optimal Portfolios’ Results

Portfolio	µ	σ	VAR	SR	Cp	Cpk	σ-L
1	0.26076	0.45993	-0.3248	0.26877	0.23543	0.23543	0.70629
2	0.15018	0.19305	-0.1364	0.39980	0.23550	0.23550	0.70642

The comparison involves Mean Return (µ), Standard Deviation (σ), Value at Risk (VAR), Sharpe Ratio (SR), Process Capability (Cp), Process Capability Index (Cpk), and Sigma Level (σ-L). Considering the results in Table 3, the Optimal Portfolio 2 risk measures, as well as Six Sigma performance metrics, are better compared to the respective parameters of Optimal Portfolio 1, even though Optimal Portfolio 1 gains greater Mean Return. The summary is as follows:

Mean Return (µ) decreased by 0.11058;

Standard Deviation (σ), i.e., a risk factor, decreased by 0.26688;

Value at Risk (VAR), e., a risk factor, decreased by 0.1884;

Sharpe Ratio (SR), i.e., a risk-adjusted measure, increased by 0.13103;

Process Capability (Cp), i.e. Six Sigma performance measure, increased by 0.00007;

Process Capability Index (Cpk), i.e., Six Sigma performance measure, increased by 0.00007; and

Sigma Level (σ-L), i.e., Six Sigma performance measure, increased by 0.00013.

In conclusion, Optimal Portfolio 2 is technically better than Optimal Portfolio 1. So, Optimal Portfolio 2 is selected and recommended for implementation. This was the key goal of the method. Therefore, the ultimate objective of the method has been met and the method’s results are satisfactorily verified. 

 

Chapter 5: Managing Liquidity RiskIn Book 2: Six Sigma Improvements for Basel III and Solvency II in Risk Management

ISBN: 9781522572800

Author: Vojo Bubevski (Independent Researcher) 

Abstract: This chapter describes liquidity risk management in retail banking. The chapter elaborates on how to determine an optimal cash management strategy to provide for liquidity of a retail bank which maximises profit by using the Miller-Orr Cash Management Model: 1. Stochastic Optimisation is used to construct the Efficient Frontier of optimal cash management policies with maximal profit determining the Daily Target Cash Balance and Daily Upper Cash Limit to maintain liquidity; 2. Monte Carlo simulation is used to stochastically calculate and measure the Profit, Variance, Standard Deviation, and VAR of the cash management policies; 3. Six Sigma process capability metrics are also stochastically calculated, against the bank’s specified target limits, for Profit and VAR of the Efficient Frontier cash management policies; and 4. Simulation results are analysed and the optimal cash management strategy is selected from the Efficient Frontier based on the criteria of minimal VAR.                    Keywords: Financial Risk Management, Liquidity Risk, Basel III, Six Sigma DMAIC, Stochastic Optimisation, Monte Carlo Simulation.

The Results: To select technically the best strategy, the two optimal strategies are compared in Table 3. The comparison involves Mean Profit (µ), Standard Deviation (σ), Value at Risk (VAR), Process Capability (Cp), Process Capability Index (Cpk), and Sigma Level (σ-L). Considering the values in Table 3, the Optimal Cash Management Strategy 2 results, including the Mean Profit (µ), risk measures, as well as Six Sigma performance metrics are slightly better compared to the respective parameters of Optimal Cash Management Strategy 1. 

Table 3: The Optimal Cash Management Strategies’ Results

Strategy	µ	σ	VAR	Cp	Cpk	σ-L
1	$2,021.80	$1,539.33	-$510.16	0.2189	0.2189	0.6567
2	$2,041.99	$1,528.97	-$472.96	0.2226	0.2226	0.6678

The summary is as follows: Mean Profit (µ) increased by $20.19; Standard Deviation (σ), i.e., a risk factor, decreased by $10.36; Value at Risk (VAR), e., a risk factor, decreased by $37.20; Process Capability (Cp), i.e., Six Sigma performance measure, increased by 0.0037; Process Capability Index (Cpk), i.e., Six Sigma performance measure, increased by 0.0037; and Sigma Level (σ-L), i.e., Six Sigma performance measure, increased by 0.0111.

To conclude, Optimal Cash Management Strategy 2 is technically slightly better than Optimal Cash Management Strategy 1. So, Optimal Cash Management Strategy 2 is selected and recommended for implementation. This was the key goal of the method. Therefore, the ultimate objective of the method has been met and the method’s results are satisfactorily verified. 

Chapter 6: Managing Interest Rate Risk

In Book 2: Six Sigma Improvements for Basel III and Solvency II in Risk Management

ISBN: 9781522572800Author: Vojo Bubevski (Independent Researcher)

Abstract: This chapter discusses the method’s application to interest rate risk. The method is using interest rate derivatives elaborating how to value the two-year Inverse Floater Derivative to manage interest rate risk. The chapter presents a model for the interest rate risk associated with a two-year Inverse Floater Derivative as follows. Monte Carlo simulation is used to stochastically calculate the total Net Present Value (NPV) of the two-year Inverse Floater Derivative, the associated Variance, Standard Deviation, and VAR. Six Sigma process capability metrics are also stochastically calculated against desired specified target limits for the total NPV, as well as relating VAR of two-year Inverse Floater Derivative. Simulation results are presented and analysed.

Keywords: Financial Risk Management, Interest Rate Risk, Basel III, Six Sigma DMAIC, Stochastic Optimisation, Monte Carlo Simulation.

The Results: Simulation calculated the Total Present Value (TotalPV), Total Present Value Mean (TotalPVµ), Standard Deviation, and VAR for the two-year Inverse Floater derivative. The Inverse Floater’s Total Present Value is $32.708(M) with a Minimum of $17.363(M), Maximum of $44.544(M), Standard Deviation of $3.441(M), and VAR of $26.7924(M). The probability that the Total Present Value will be below $26.79(M) is 5%. There is a 90% probability that it will be in the range of $26.79(M) – $38.13(M), and a 5% probability that it will be more than $38.13(M). The previous step predicted Inverse Floater’s Total Present Value Mean as $32.708(M) with a Minimum of $17.363(M), a Maximum of $44.544(M), and a Standard Deviation of $3.441(M). These figures are appreciated, but not sufficient for appropriate risk analysis particularly because the Standard Deviation is $3.441(M) (i.e., reasonable). So, the Six Sigma process capability measurement will be performed to add additional valuable information for decision-making. Therefore, the Total Present Value is simulated using Normal Distribution with a Mean of $32.708(M) and a Standard Deviation of $3.441(M). The Normal Distribution is used for simplicity, but other distributions can be used if more appropriate. The Total Present Value distribution around the Six Sigma target limits is shown in Figure 2. The target parameters are LSL, TV-15%; TV, $32.708(M); and USL, TV+15%. The predicted Total Present Value Mean is $32.708(M) with a Standard Deviation of $3.441(M). The Total Present Value minimum is $15.764(M); and the maximum, is $48.385(M). The Six Sigma process capability metrics are Cp, 0.4753; Cpk, 0.4753; and σ-L, 1.4260. The probability that the Total Present Value will be less than $27.05(M) is 5%; 90.0% probability that it will be in the range of $27.05(M) – $38.37(M); and a 5.0% probability that it will be above $38.37(M). The Standard Deviation and Six Sigma capability metrics are reasonable.  This shows the risk and the performance are acceptable. 

Chapter 7: Managing Foreign Exchange RiskIn Book 2: Six Sigma Improvements for Basel III and Solvency II in Risk Management

ISBN: 9781522572800

Author: Vojo Bubevski (Independent Researcher)

Abstract: This chapter discusses the method’s application to foreign exchange risk management by elaborating on how to use foreign exchange options for hedging the interest rate risk. The problem is to determine how many European Put options to purchase for optimal hedging of the foreign exchange risk. Stochastic Optimisation is used to construct an Efficient Frontier of optimal hedging strategies of the foreign exchange risk with minimal Standard Deviation. Monte Carlo simulation is utilised to stochastically calculate and measure the Total Amount Hedged (US $), Variance, Standard Deviation, and VAR of Efficient Frontier optimal hedging strategies. Six Sigma process capability metrics are also stochastically calculated against desired specified target limits for the Total Amount Hedged and associated VAR of Efficient Frontier optimal hedging strategies. Simulation results are analysed and the optimal hedging strategy is selected based on the criteria of minimal VAR.

Keywords: Financial Risk Management, Foreign Exchange Risk, Basel III, Six Sigma DMAIC, Stochastic Optimisation, Monte Carlo Simulation

The Results: To select technically the best strategy, the two optimal strategies are compared in Table 2.

Table 2: The Optimal Forex Hedging Strategies’ Results

Strategy	µ	σ	VAR	Cp	Cpk	σ-L
1	$270,715.85	$7,728.20	$258,003.31	0.2335	0.2335	0.7006
2	$270,426.25	$7,709.21	$257,745.22	0.2339	0.2339	0.7016

The comparison involves Mean Profit (µ), Standard Deviation (σ), Value at Risk (VAR), Process Capability (Cp), Process Capability Index (Cpk), and Sigma Level (σ-L). Considering the values in Table 2, the Optimal Forex Hedging Strategy 2 results, including risk measures, as well as Six Sigma performance metrics are slightly better compared to the respective parameters of Optimal Forex Hedging Strategy 1. Only the Mean Profit (µ) is less for Strategy 2. The summary is as follows. Mean Profit (µ) was reduced by $289.60; Standard Deviation (σ), i.e., a risk factor, decreased by $18.99; Value at Risk (VAR), e., a risk factor, decreased by $258.09; Process Capability (Cp), i.e., Six Sigma performance measure, increased by 0.0004; Process Capability Index (Cpk), i.e., Six Sigma performance measure, increased by 0.0004; and Sigma Level (σ-L), i.e., Six Sigma performance measure, increased by 0.0010.

To conclude, Optimal Forex Hedging Strategy 2 is technically slightly better than Optimal Forex Hedging Strategy 1. So, Optimal Forex Hedging Strategy 2 is selected and recommended for implementation. This was the key goal of the method. Therefore, the ultimate objective of the method has been met and the method’s results are satisfactorily verified.  

Chapter 4: Predicting Financial Statements

In Book 4: Risk Management for Businesses with Stochastic Six Sigma DMAIC Method

ISBN: 978-620-2-67095-1

Author: Vojo Bubevski (Independent Researcher)

Abstract: This chapter presents an example of modelling financial statements for businesses. The model is created for general forecasting purposes, including financing needs and credit analysis. In this example, a company has a fairly healthy forecasted cash flow for 2020 but also aims to reduce its long-term debt in 2020 to a desired amount from the known debt in 2019. The company is forecasting that, in the base case, its financial position will be sufficient to do this. However, it wishes to analyse the probability that a short-term financing facility will be needed. The short-term debt could be zero, therefore, the probability that it is non-zero is thoroughly analysed.                                    Keywords: Business Risk Management, Risk Assessment, Finance, Financial Statements, Stochastic Model, Six Sigma DMAIC, Stochastic Optimisation, Monte Carlo Simulation.

The Results: The five simulations are presented in Table 7 below.

Table 7: Financial Statements Key Aspects Prediction ($MM)

Statements Data	Sim 1	Sim 2	Sim 3	Sim 4	Sim 5
Operating Profit	179.6975	131.9745	83.9478	35.7868	-12.6826
Net Income	122.8338	89.4089	55.7711	22.0392	-11.9085
Total Assets	639.6657	596.5495	553.1597	567.9356	596.5498
Short-term Debt	0	0	0	58.2902	130.6966
Total Liability & Equity	639.6657	596.5495	553.1597	567.9356	596.5498
Operating sub-Total	207.2136	156.8350	106.0567	55.1653	3.8686
Investing sub-Total	28.1371	47.6405	67.2710	86.9713	106.8004
Financing sub-Total	-182.3953	-111.2520	-39.5475	32.2902	104.6966
Net Increase in Cash CFS	-3.3188	-2.0575	-0.7619	0.4843	1.7649

The Operating Profit, Net Income, and Operating Total predictions start with $179.6975 MM, $122.8338 MM, and $207.2136 MM respectively in Simulation 1. Then they continuously decline to -$12.6826 MM, -$11.9085 MM, and $3.8686 MM in Simulation 5. The Total Assets and Total Liability & Equity both start at $639.6657 MM in Simulation 1 and continuously decline to a minimum of $553.1597 MM in Simulation 3. Then they both increase again to $596.5498 MM in Simulation 5. It should be noted that they overlay in the graph (Figure 1). The Short-term Debt is predicted to be zero in Simulations 1, 2 & 3. Then it increases to $58.2902 MM and $130.6966 MM in Simulation 4 & 5 respectively. The Investing Total, Financing Total, and Net Increase in Cash predictions start with $28.1371 MM, -$182.3953 MM, and -$3.3188 MM respectively in Simulation 1. Then they continuously increase to $106.8004 MM, $104.6966 MM, and $1.7649 MM in Simulation 5. 

Chapter 2: Financial Forecasting for BusinessesIn Book 8: Business Risk Analysis and Prediction

ISBN: 978-620-3-19675-7

Author: Vojo Bubevski (Independent Researcher)  

Abstract: In this chapter, a stochastic model for a typical business financial forecast is presented. The forecast is for nine years, i.e., from 2020 to 2028. The model’s financial inputs are Price Increase with Entry & no Entry, Volume Increase with Entry & no Entry, Unit Production Cost Increase, Overhead Percent of Sales Revenue, Tax Rate, and Discount Rate. It is assumed that the Competitor Entry is zero, i.e., No. The Financial Calculations include Capital Investment, Price variables, Volume variables, Sales variables, Unit Production Cost, Overhead, Cost of Goods Sold, Gross Margin, Operating Expense variables, Net Before Tax, Depreciation Over 5 Years, Tax variables, and Net After Tax. The model outputs are Net Cash Flow, Total Net Cash, and Net Present Value (NPV).  The financial inputs are modelled with the Normal probability distributions and Financial Calculations use the Variability functions. Sensitivity and What-If Analysis is applied to find which of the key inputs are most influential to the NPV output.

Keywords: Risk & Decision Analysis, Business Financial Forecast, Financial Risk, Sensitivity Analysis, What-If Analysis, Monte Carlo simulation, Stochastic model. 

The Results: Calculated Net Cash Flow per Year graph is presented with values given in dollars ($). The Net Cash Flow starts at -$200,000 in the Year 2020 and exponentially increases to $18,020,751 in the Year 2028.The Net Cash Flow Per Year Mean, i.e., the Summary Trend, is showing the values. The Net Cash Flow Mean Summary Trend, which involves is a probability distribution calculation, is equal to the calculated results, which also use the Normal Distribution to calculate the financial variables from which the Net Cash Flow per Year is calculated (Ref. Formulas (2 – 9)). However, the Summary Trend presents the Net Cash Flow Mean, the probability of the Net Cash Flow Mean changes from 25% to 75%, the probability of changes from 5% to 95%, and the Simulation path.Similarly, the Net Cash Flow starts with circa -$200,000 in the Year 2020 and increases exponentially reaching circa $18,000,000 in the Year 2028.