# Portfolio Loss Distribution

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Portfolo Loss Dstrbuton

2 Rsky assets n loan ortfolo hghly llqud assets hold-to-maturty n the bank s balance sheet Outstandngs The orton of the bank asset that has already been extended to borrowers. Commtment A commtment s an amount the bank has commtted to lend. Should the borrower encounter fnancal dffcultes, t would draw on ths commtted lne of credt.

3 Adjusted exosure and exected loss Let α be the amount of drawn down or usage gven default. Outstandng + α commtment, Rsky Asset value at later tme H, V H Adjusted exosure s the rsky art of V H. (1 α) commtment, Rskless Exected loss adjusted exosure loss gven default robablty of default * Normally, racttoners treat the uncertan draw-down rate as a known functon of the oblgor s end-of-horzon credt class ratng.

4 Examle calculaton of exected loss Commtment Outstandng Internal rsk ratng Maturty Tye Unused drawn-down on default (for nternal ratng 3) Adjusted exosure on default EDF for nternal ratng 3 Loss gven default for non-secured asset Exected loss \$10,000,000 \$3,000, year Non-secured 65% \$8,250, % 50% \$6,188

5 Unexected loss Unexected loss s the estmated volatlty of the otental loss n value of the asset around ts exected loss. AE EDF LGD 2 2 σ LGD + σ 2 EDF where σ EDF 2 EDF (1- EDF). Assumtons * The random rsk factors contrbutng to an oblgor s default (resultng n EDF) are statstcally ndeendent of the severty of loss (as gven by LGD). * The default rocess s two-state event.

6 Examle on unexected loss calculaton Adjusted exosure \$8,250,000 EDF 0.15% σ EDF 3.87% LGD 50% σ LGD 25% Unexected loss \$178,511 * The calculated unexected loss s 2.16% of the adjusted exosure, whle the exected loss s only 0.075%

7 Comarson between exected loss and unexected loss * The hgher the recovery rate (lower LGD), the lower s the ercentage loss for both EL and. * EL ncreases lnearly wth decreasng credt qualty (wth ncreasng EDF) * ncreases much faster than EL wth ncreasng EDF. Percentage loss er unt of adjusted loss 10% 5% 10% EL EDF

8 Assets wth varyng terms of maturty * The longer the term to maturty, the greater the varaton n asset value due to changes n credt qualty. * The two-state default rocess aradgm nherently gnores the credt losses assocated wth defaults that occur beyond the analyss horzon. * To mtgate some of the maturty effect, banks commonly adjust a rsky asset s nternal credt class ratng n accordance wth ts terms to maturty.

9 Portfolo exected loss where EL EL AE LGD EDF EL s the exected loss for the ortfolo, AE s the rsky orton of the termnal value of the th asset to whch the bank s exosed n the event of default. We may wrte EL AE w EL AE where the weghts refer to AE w AE AE AE.

10 EL AE EL AE AE AE EL AE w EL AE AE w EL EL /AE 1 \$10 M 0.5 \$ \$4 M 0.2 \$ \$6 M 0.3 \$ AE \$20M 1 w EL AE

11 Portfolo unexected loss ortfolo unexected loss j ρ j w w j j where AE EDF σ LGD + GD σ E L DF and ρ j s the correlaton of default between asset and asset j. Due to dversfcaton effect, we exect <<.

12 Rsk contrbuton The rsk contrbuton of a rsky asset to the ortfolo unexected loss s defned to be the ncremental rsk that the exosure of a sngle asset contrbutes to the ortfolo s total rsk. RC and t can be shown that RC j j ρ j.

13 Undversfable rsk The rsk contrbuton s a measure of the undversfable rsk of an asset n the ortfolo the amount of credt rsk whch cannot be dversfed away by lacng the asset n the ortfolo. RC To ncororate ndustry correlaton, usng ndustry α and j ndustry β RC (1 ) + α ραα β α k β k ρ αβ.

14 Calculaton of EL, and RC for a two-asset ortfolo ρ EL default correlaton between the two exosures ortfolo exected loss EL EL 1 + EL 2 ortfolo unexected loss RC 1 RC rsk contrbuton from Exosure 1 rsk contrbuton from Exosure 2 + ρ RC1 1(1 + ρ2) / RC2 2(2 + ρ1) / RC 1 + RC 2 << 1 + 2

15 Fttng of loss dstrbuton The two statstcal measures about the credt ortfolo are ortfolo exected loss; ortfolo unexected loss. At the smlest level, the beta dstrbuton may be chosen to ft the ortfolo loss dstrbuton. Reservaton A beta dstrbuton wth only two degrees of freedom s erhas nsuffcent to gve an adequate descrton of the tal events n the loss dstrbuton.

16 Beta dstrbuton The densty functon of a beta dstrbuton s > > < < Γ Γ + Γ otherwse 0 0 0, 1 0, ) (1 ),, ( 1 1 ) ( ) ( ) ( β α β α β α β α β α x x x x F Mean and varance β α α µ +. 1) ( ) ( β α β α αβ σ 1 x f(x, α, β)

17 Economc Catal If X T s the random varable for loss and z s the ercentage robablty (confdence level), what s the quantty v of mnmum economc catal EC needed to rotect the bank from nsolvency at the tme horzon T such that Pr[ X T v] z. Here, z s the desred debt ratng of the bank, say, 99.97% for an AA ratng.

18 frequency of loss X T EL EC

19 Catal multler Gven a desred level of z, what s EC such that Pr[ X EL EC] T z. Let CM (catal multler) be defned by EC CM then Pr X T EL CM z.

20 Monte Carol smulaton of loss dstrbuton of a ortfolo 1. Estmate default and losses 2. Estmate asset correlaton between oblgors Assgn rsk ratngs to loss facltes and determne ther default robablty + Assgn LGD and σ LGD Determne arwse asset correlaton whenever ossble OR Assgn oblgors to ndustry groungs, then determne ndustry ar correlaton

21 3. Generate random loss gven default 4. Generate correlated default events Determne stochastc loss gven default + Correlated default events + Decomoston of covarance matrx + Smulate default ont

22 5. Loss calculaton 6. Loss dstrbuton Calculate faclty loss for each scenaro and obtan ortfolo loss Construct smulated ortfolo loss dstrbuton

23 Generaton of correlated default events Generate a set of random numbers drawn from a standard normal dstrbuton. Perform a decomoston (Cholesky, SVD or egenvalue) on the asset correlaton matrx to transform the ndeendent set of random numbers (stored n the vector e ) nto a set of correlated asset values (stored n the vector e ). Here, the transformaton matrx s M, where e M e. The covarance matrx and M are related by M T M.

24 Calculaton of the default ont The default ont threshold, DP, of the th oblgor can be defned as DP N 1 (EDF, 0, 1). The crteron of default for the th oblgor s default f e < ' DP no default f e ' DP.

25 Generate loss gven default The LGD s a stochastc varable wth an unknown dstrbuton. A tycal examle may be Recovery rate (%) LGD (%) σ LGD (%) secured unsecured LGD LGD + σ s s f LGD where f s drawn from a unform dstrbuton whose range s selected so that the resultng LGD has a standard devaton that s consstent wth hstorcal observaton.

26 Calculaton of loss Summng all the smulated losses from one sngle scenaro Loss Adjusted exosure Oblgors n default LGD Smulated loss dstrbuton The smulated loss dstrbuton s obtaned by reeatng the above rocess suffcently number of tmes.

27 Features of ortfolo rsk The varablty of default rsk wthn a ortfolo s substantal. The correlaton between default rsks s generally low. The default rsk tself s dynamc and subject to large fluctuatons. Default rsks can be effectvely managed through dversfcaton. Wthn a well-dversfed ortfolo, the loss behavor s characterzed by lower than exected default credt losses for much of the tme, but very large losses whch are ncurred nfrequently.

### THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek

HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo

### Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting

Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of

### Vasicek s Model of Distribution of Losses in a Large, Homogeneous Portfolio

Vascek s Model of Dstrbuton of Losses n a Large, Homogeneous Portfolo Stephen M Schaefer London Busness School Credt Rsk Electve Summer 2012 Vascek s Model Important method for calculatng dstrbuton of

### DI Fund Sufficiency Evaluation Methodological Recommendations and DIA Russia Practice

DI Fund Suffcency Evaluaton Methodologcal Recommendatons and DIA Russa Practce Andre G. Melnkov Deputy General Drector DIA Russa THE DEPOSIT INSURANCE CONFERENCE IN THE MENA REGION AMMAN-JORDAN, 18 20

### Simon Acomb NAG Financial Mathematics Day

1 Why People Who Prce Dervatves Are Interested In Correlaton mon Acomb NAG Fnancal Mathematcs Day Correlaton Rsk What Is Correlaton No lnear relatonshp between ponts Co-movement between the ponts Postve

### Optimal Bidding Strategies for Generation Companies in a Day-Ahead Electricity Market with Risk Management Taken into Account

Amercan J. of Engneerng and Appled Scences (): 8-6, 009 ISSN 94-700 009 Scence Publcatons Optmal Bddng Strateges for Generaton Companes n a Day-Ahead Electrcty Market wth Rsk Management Taken nto Account

Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton

### I. SCOPE, APPLICABILITY AND PARAMETERS Scope

D Executve Board Annex 9 Page A/R ethodologcal Tool alculaton of the number of sample plots for measurements wthn A/R D project actvtes (Verson 0) I. SOPE, PIABIITY AD PARAETERS Scope. Ths tool s applcable

### b) The mean of the fitted (predicted) values of Y is equal to the mean of the Y values: c) The residuals of the regression line sum up to zero: = ei

Mathematcal Propertes of the Least Squares Regresson The least squares regresson lne obeys certan mathematcal propertes whch are useful to know n practce. The followng propertes can be establshed algebracally:

### ErrorPropagation.nb 1. Error Propagation

ErrorPropagaton.nb Error Propagaton Suppose that we make observatons of a quantty x that s subject to random fluctuatons or measurement errors. Our best estmate of the true value for ths quantty s then

### Measuring portfolio loss using approximation methods

Scence Journal of Appled Mathematcs and Statstcs 014; (): 4-5 Publshed onlne Aprl 0, 014 (http://www.scencepublshnggroup.com/j/sjams) do: 10.11648/j.sjams.01400.11 Measurng portfolo loss usng approxmaton

### Time Series Analysis in Studies of AGN Variability. Bradley M. Peterson The Ohio State University

Tme Seres Analyss n Studes of AGN Varablty Bradley M. Peterson The Oho State Unversty 1 Lnear Correlaton Degree to whch two parameters are lnearly correlated can be expressed n terms of the lnear correlaton

### Communication Networks II Contents

8 / 1 -- Communcaton Networs II (Görg) -- www.comnets.un-bremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP

### Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.

Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.

### Lecture 14: Implementing CAPM

Lecture 14: Implementng CAPM Queston: So, how do I apply the CAPM? Current readng: Brealey and Myers, Chapter 9 Reader, Chapter 15 M. Spegel and R. Stanton, 2000 1 Key Results So Far All nvestors should

### Risk Management and Financial Institutions

Rsk Management and Fnancal Insttutons By John C. Hull Chapter 3 How Traders manage Ther Exposures... Chapter 4 Interest Rate Rsk...3 Chapter 5 Volatlty...5 Chapter 6 Correlatons and Copulas...7 Chapter

### Portfolio Management. Summer Term Exercise 2: The Capital Asset Pricing Model (CAPM) Prof. Dr. Hans-Peter Burghof / Katharina Nau

Unversty of Hohenhem Char of ankng and Fnancal Servces Portfolo anagement Summer Term 0 Eercse : The Catal sset Prcng odel (CP) Prof. Dr. Hans-Peter urghof / Katharna Nau Sldes: c/o aron Schulz/ Robert

### Capital asset pricing model, arbitrage pricing theory and portfolio management

Captal asset prcng model, arbtrage prcng theory and portfolo management Vnod Kothar The captal asset prcng model (CAPM) s great n terms of ts understandng of rsk decomposton of rsk nto securty-specfc rsk

### THE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES

The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered

### Portfolio Risk Decomposition (and Risk Budgeting)

ortfolo Rsk Decomposton (and Rsk Budgetng) Jason MacQueen R-Squared Rsk Management Introducton to Rsk Decomposton Actve managers take rsk n the expectaton of achevng outperformance of ther benchmark Mandates

### NPAR TESTS. One-Sample Chi-Square Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6

PAR TESTS If a WEIGHT varable s specfed, t s used to replcate a case as many tmes as ndcated by the weght value rounded to the nearest nteger. If the workspace requrements are exceeded and samplng has

### benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or

### Stress test for measuring insurance risks in non-life insurance

PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n non-lfe nsurance Summary Ths memo descrbes stress testng of nsurance

### Multivariate EWMA Control Chart

Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant

### Credit Limit Optimization (CLO) for Credit Cards

Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary Agenda Background Tradtonal approaches to credt

### The Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15

The Analyss of Covarance ERSH 830 Keppel and Wckens Chapter 5 Today s Class Intal Consderatons Covarance and Lnear Regresson The Lnear Regresson Equaton TheAnalyss of Covarance Assumptons Underlyng the

### Discount Rate for Workout Recoveries: An Empirical Study*

Dscount Rate for Workout Recoveres: An Emprcal Study* Brooks Brady Amercan Express Peter Chang Standard & Poor s Peter Mu** McMaster Unversty Boge Ozdemr Standard & Poor s Davd Schwartz Federal Reserve

### Underwriting Risk. Glenn Meyers. Insurance Services Office, Inc.

Underwrtng Rsk By Glenn Meyers Insurance Servces Offce, Inc. Abstract In a compettve nsurance market, nsurers have lmted nfluence on the premum charged for an nsurance contract. hey must decde whether

### Reporting Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (including SME Corporate), Sovereign and Bank Instruction Guide

Reportng Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (ncludng SME Corporate), Soveregn and Bank Instructon Gude Ths nstructon gude s desgned to assst n the completon of the FIRB

### x f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60

BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true

### Introduction to Regression

Introducton to Regresson Regresson a means of predctng a dependent varable based one or more ndependent varables. -Ths s done by fttng a lne or surface to the data ponts that mnmzes the total error. -

### Risk Model of Long-Term Production Scheduling in Open Pit Gold Mining

Rsk Model of Long-Term Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,

### Forecasting the Direction and Strength of Stock Market Movement

Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract - Stock market s one of the most complcated systems

### Robust Design of Public Storage Warehouses. Yeming (Yale) Gong EMLYON Business School

Robust Desgn of Publc Storage Warehouses Yemng (Yale) Gong EMLYON Busness School Rene de Koster Rotterdam school of management, Erasmus Unversty Abstract We apply robust optmzaton and revenue management

### L10: Linear discriminants analysis

L0: Lnear dscrmnants analyss Lnear dscrmnant analyss, two classes Lnear dscrmnant analyss, C classes LDA vs. PCA Lmtatons of LDA Varants of LDA Other dmensonalty reducton methods CSCE 666 Pattern Analyss

### Risk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008

Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn

### Can Auto Liability Insurance Purchases Signal Risk Attitude?

Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159-164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? Chu-Shu L Department of Internatonal Busness, Asa Unversty, Tawan Sheng-Chang

### The covariance is the two variable analog to the variance. The formula for the covariance between two variables is

Regresson Lectures So far we have talked only about statstcs that descrbe one varable. What we are gong to be dscussng for much of the remander of the course s relatonshps between two or more varables.

### The OC Curve of Attribute Acceptance Plans

The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4

### The Analysis of Outliers in Statistical Data

THALES Project No. xxxx The Analyss of Outlers n Statstcal Data Research Team Chrysses Caron, Assocate Professor (P.I.) Vaslk Karot, Doctoral canddate Polychrons Economou, Chrstna Perrakou, Postgraduate

5 Fxed ncome rsk attrbuton Chthra Krshnamurth RskMetrcs Group chthra.krshnamurth@rskmetrcs.com We compare the rsk of the actve portfolo wth that of the benchmark and segment the dfference between the two

### An Alternative Way to Measure Private Equity Performance

An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate

### 1. Measuring association using correlation and regression

How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a

### CHAPTER 14 MORE ABOUT REGRESSION

CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp

### SIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA

SIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA E. LAGENDIJK Department of Appled Physcs, Delft Unversty of Technology Lorentzweg 1, 68 CJ, The Netherlands E-mal: e.lagendjk@tnw.tudelft.nl

### Copulas. Modeling dependencies in Financial Risk Management. BMI Master Thesis

Copulas Modelng dependences n Fnancal Rsk Management BMI Master Thess Modelng dependences n fnancal rsk management Modelng dependences n fnancal rsk management 3 Preface Ths paper has been wrtten as part

### Analysis of Covariance

Chapter 551 Analyss of Covarance Introducton A common tas n research s to compare the averages of two or more populatons (groups). We mght want to compare the ncome level of two regons, the ntrogen content

### Kiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1120

Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel (Germany) Kel Workng Paper No. Path Dependences n enture Captal Markets by Andrea Schertler July The responsblty for the contents of the workng

### arxiv:1109.1256v1 [q-fin.pm] 6 Sep 2011

WORKING PAPER December 2010 Fnancal Analysts Journal Volume 67, No. 4 July/August 2011, p. 42-49 arxv:1109.1256v1 [q-fn.pm] 6 Sep 2011 Dversfcaton Return, Portfolo Rebalancng, and the Commodty Return Puzzle

### The impact of hard discount control mechanism on the discount volatility of UK closed-end funds

Investment Management and Fnancal Innovatons, Volume 10, Issue 3, 2013 Ahmed F. Salhn (Egypt) The mpact of hard dscount control mechansm on the dscount volatlty of UK closed-end funds Abstract The mpact

### Outline. Investment Opportunity Set with Many Assets. Portfolio Selection with Multiple Risky Securities. Professor Lasse H.

Portfolo Selecton wth Multple Rsky Securtes. Professor Lasse H. Pedersen Prof. Lasse H. Pedersen Outlne Investment opportunty set wth many rsky assets wth many rsky assets and a rsk-free securty Optmal

### A Simplified Method for Calculating the Credit Risk of Lending Portfolios

A Smplfed Method MOETARY for Calculatng AD ECOOMIC the Credt STUDIES/DECEMBER Rsk of Lendng Portfolos 000 A Smplfed Method for Calculatng the Credt Rsk of Lendng Portfolos Akra Ieda, Kohe Marumo, and Toshnao

### Method for assessment of companies' credit rating (AJPES S.BON model) Short description of the methodology

Method for assessment of companes' credt ratng (AJPES S.BON model) Short descrpton of the methodology Ljubljana, May 2011 ABSTRACT Assessng Slovenan companes' credt ratng scores usng the AJPES S.BON model

### On the computation of the capital multiplier in the Fortis Credit Economic Capital model

On the computaton of the captal multpler n the Forts Cret Economc Captal moel Jan Dhaene 1, Steven Vuffel 2, Marc Goovaerts 1, Ruben Oleslagers 3 Robert Koch 3 Abstract One of the key parameters n the

### Questions that we may have about the variables

Antono Olmos, 01 Multple Regresson Problem: we want to determne the effect of Desre for control, Famly support, Number of frends, and Score on the BDI test on Perceved Support of Latno women. Dependent

### Efficient Project Portfolio as a tool for Enterprise Risk Management

Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse

### Characterization of Assembly. Variation Analysis Methods. A Thesis. Presented to the. Department of Mechanical Engineering. Brigham Young University

Characterzaton of Assembly Varaton Analyss Methods A Thess Presented to the Department of Mechancal Engneerng Brgham Young Unversty In Partal Fulfllment of the Requrements for the Degree Master of Scence

### CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL

### Chapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT

Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the

### Applied Research Laboratory. Decision Theory and Receiver Design

Decson Theor and Recever Desgn Sgnal Detecton and Performance Estmaton Sgnal Processor Decde Sgnal s resent or Sgnal s not resent Nose Nose Sgnal? Problem: How should receved sgnals be rocessed n order

### The impact of bank capital requirements on bank risk: an econometric puzzle and a proposed solution

Banks and Bank Systems, Volume 4, Issue 1, 009 Robert L. Porter (USA) The mpact of bank captal requrements on bank rsk: an econometrc puzzle and a proposed soluton Abstract The relatonshp between bank

### SDN: Systemic Risks due to Dynamic Load Balancing

SDN: Systemc Rsks due to Dynamc Load Balancng Vladmr Marbukh IRTF SDN Abstract SDN acltates dynamc load balancng Systemc benets o dynamc load balancng: - economc: hgher resource utlzaton, hgher revenue,..

### Descriptive Statistics (60 points)

Economcs 30330: Statstcs for Economcs Problem Set 2 Unversty of otre Dame Instructor: Julo Garín Sprng 2012 Descrptve Statstcs (60 ponts) 1. Followng a recent government shutdown, Mnnesota Governor Mark

### Débats économiques et financiers N 1

Débats économques et fnancers N 1 How dfferent s the regulatory captal from the economc captal: the case of busness loans portfolos held by the major bankng groups n France Mchel Detsch * et Henr Frasse

### Face Verification Problem. Face Recognition Problem. Application: Access Control. Biometric Authentication. Face Verification (1:1 matching)

Face Recognton Problem Face Verfcaton Problem Face Verfcaton (1:1 matchng) Querymage face query Face Recognton (1:N matchng) database Applcaton: Access Control www.vsage.com www.vsoncs.com Bometrc Authentcaton

### A Simplified Framework for Return Accountability

Reprnted wth permsson from Fnancal Analysts Journal, May/June 1991. Copyrght 1991. Assocaton for Investment Management and Research, Charlottesvlle, VA. All rghts reserved. by Gary P. Brnson, Bran D. Snger

### ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management

ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C Whte Emerson Process Management Abstract Energy prces have exhbted sgnfcant volatlty n recent years. For example, natural gas prces

### 9.1 The Cumulative Sum Control Chart

Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s

### The Choice of Direct Dealing or Electronic Brokerage in Foreign Exchange Trading

The Choce of Drect Dealng or Electronc Brokerage n Foregn Exchange Tradng Mchael Melvn & Ln Wen Arzona State Unversty Introducton Electronc Brokerage n Foregn Exchange Start from a base of zero n 1992

### Chapter 7. Random-Variate Generation 7.1. Prof. Dr. Mesut Güneş Ch. 7 Random-Variate Generation

Chapter 7 Random-Varate Generaton 7. Contents Inverse-transform Technque Acceptance-Rejecton Technque Specal Propertes 7. Purpose & Overvew Develop understandng of generatng samples from a specfed dstrbuton

### Mean Molecular Weight

Mean Molecular Weght The thermodynamc relatons between P, ρ, and T, as well as the calculaton of stellar opacty requres knowledge of the system s mean molecular weght defned as the mass per unt mole of

### Abstract. 260 Business Intelligence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING

260 Busness Intellgence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING Murphy Choy Mchelle L.F. Cheong School of Informaton Systems, Sngapore

### ENTERPRISE RISK MANAGEMENT IN INSURANCE GROUPS: MEASURING RISK CONCENTRATION AND DEFAULT RISK

ETERPRISE RISK MAAGEMET I ISURACE GROUPS: MEASURIG RISK COCETRATIO AD DEFAULT RISK ADIE GATZERT HATO SCHMEISER STEFA SCHUCKMA WORKIG PAPERS O RISK MAAGEMET AD ISURACE O. 35 EDITED BY HATO SCHMEISER CHAIR

### THE TITANIC SHIPWRECK: WHO WAS

THE TITANIC SHIPWRECK: WHO WAS MOST LIKELY TO SURVIVE? A STATISTICAL ANALYSIS Ths paper examnes the probablty of survvng the Ttanc shpwreck usng lmted dependent varable regresson analyss. Ths appled analyss

### Chapter 7: Answers to Questions and Problems

19. Based on the nformaton contaned n Table 7-3 of the text, the food and apparel ndustres are most compettve and therefore probably represent the best match for the expertse of these managers. Chapter

### Marginal Benefit Incidence Analysis Using a Single Cross-section of Data. Mohamed Ihsan Ajwad and Quentin Wodon 1. World Bank.

Margnal Beneft Incdence Analyss Usng a Sngle Cross-secton of Data Mohamed Ihsan Ajwad and uentn Wodon World Bank August 200 Abstract In a recent paper, Lanjouw and Ravallon proposed an attractve and smple

### CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES

CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable

### Control Charts for Means (Simulation)

Chapter 290 Control Charts for Means (Smulaton) Introducton Ths procedure allows you to study the run length dstrbuton of Shewhart (Xbar), Cusum, FIR Cusum, and EWMA process control charts for means usng

### Clustering Gene Expression Data. (Slides thanks to Dr. Mark Craven)

Clusterng Gene Epresson Data Sldes thanks to Dr. Mark Craven Gene Epresson Proles we ll assume we have a D matr o gene epresson measurements rows represent genes columns represent derent eperments tme

### Exchange rate volatility and its impact on risk management with internal models in commercial banks

Banks and Bank Systems, Volume, Issue 4, 007 Devjak Sreko (Slovena), Andraž Grum (Slovena) Exchange rate volatlty and ts mpact on rsk management wth nternal models n commercal banks Abstract Fnancal markets

### A Model of Private Equity Fund Compensation

A Model of Prvate Equty Fund Compensaton Wonho Wlson Cho Andrew Metrck Ayako Yasuda KAIST Yale School of Management Unversty of Calforna at Davs June 26, 2011 Abstract: Ths paper analyzes the economcs

### STATISTICAL DATA ANALYSIS IN EXCEL

Mcroarray Center STATISTICAL DATA ANALYSIS IN EXCEL Lecture 6 Some Advanced Topcs Dr. Petr Nazarov 14-01-013 petr.nazarov@crp-sante.lu Statstcal data analyss n Ecel. 6. Some advanced topcs Correcton for

### Lecture 3. 1 Largest singular value The Behavior of Algorithms in Practice 2/14/2

18.409 The Behavor of Algorthms n Practce 2/14/2 Lecturer: Dan Spelman Lecture 3 Scrbe: Arvnd Sankar 1 Largest sngular value In order to bound the condton number, we need an upper bound on the largest

### 1 De nitions and Censoring

De ntons and Censorng. Survval Analyss We begn by consderng smple analyses but we wll lead up to and take a look at regresson on explanatory factors., as n lnear regresson part A. The mportant d erence

### Macro Factors and Volatility of Treasury Bond Returns

Macro Factors and Volatlty of Treasury Bond Returns Jngzh Huang Department of Fnance Smeal Colleage of Busness Pennsylvana State Unversty Unversty Park, PA 16802, U.S.A. Le Lu School of Fnance Shangha

### Outline. CAPM: Introduction. The Capital Asset Pricing Model (CAPM) Professor Lasse H. Pedersen. Key questions: Answer: CAPM

The Catal Asset Prcng odel (CAP) Proessor Lasse H. Pedersen Pro. Lasse H. Pedersen 1 Key questons: Outlne What s the equlbrum requred return, E(R), o a stock? What s the equlbrum rce o a stock? Whch ortolos

THE USE OF RISK ADJUSTED CAPITAL TO SUPPORT BUSINESS DECISION-MAKING By Gary Patrk Stefan Bernegger Marcel Beat Rüegg Swss Rensurance Company Casualty Actuaral Socety and Casualty Actuares n Rensurance

### CEIOPS-DOC-42/09. (former CP 49) October 2009

CEIOPS-DOC-42/09 CEIOPS Advce for Level 2 Imlementng Measures on Solvency II: Standard formula SCR - Artcle 109 c Lfe underwrtng rsk (former CP 49) October 2009 CEIOPS e.v. Westhafenlatz 1-60327 Frankfurt

### An Analysis of Pricing Methods for Baskets Options

An Analyss of Prcng Methods for Baskets Optons Martn Krekel, Johan de Kock, Ralf Korn, Tn-Kwa Man Fraunhofer ITWM, Department of Fnancal Mathematcs, 67653 Kaserslautern, Germany, emal: krekel@twm.fhg.de

### Fragility Based Rehabilitation Decision Analysis

.171. Fraglty Based Rehabltaton Decson Analyss Cagdas Kafal Graduate Student, School of Cvl and Envronmental Engneerng, Cornell Unversty Research Supervsor: rcea Grgoru, Professor Summary A method s presented

### Economic Interpretation of Regression. Theory and Applications

Economc Interpretaton of Regresson Theor and Applcatons Classcal and Baesan Econometrc Methods Applcaton of mathematcal statstcs to economc data for emprcal support Economc theor postulates a qualtatve

### Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits

Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.

### Construction Rules for Morningstar Canada Target Dividend Index SM

Constructon Rules for Mornngstar Canada Target Dvdend Index SM Mornngstar Methodology Paper October 2014 Verson 1.2 2014 Mornngstar, Inc. All rghts reserved. The nformaton n ths document s the property

### Transition Matrix Models of Consumer Credit Ratings

Transton Matrx Models of Consumer Credt Ratngs Abstract Although the corporate credt rsk lterature has many studes modellng the change n the credt rsk of corporate bonds over tme, there s far less analyss

### Statistical Methods to Develop Rating Models

Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and

### Imperial College London

F. Fang 1, C.C. Pan 1, I.M. Navon 2, M.D. Pggott 1, G.J. Gorman 1, P.A. Allson 1 and A.J.H. Goddard 1 1 Appled Modellng and Computaton Group Department of Earth Scence and Engneerng Imperal College London,

### Measurement of Farm Credit Risk: SUR Model and Simulation Approach

Measurement of Farm Credt Rsk: SUR Model and Smulaton Approach Yan Yan, Peter Barry, Ncholas Paulson, Gary Schntkey Contact Author Yan Yan Unversty of Illnos at Urbana-Champagn Department of Agrcultural

### Exhibit 1 Index breakdown by region, industrial sector and credit rating. Investment Grade index High Yield index weight issuers weight issuers

The art of trackng corporate bond ndces Laurent Gouzlh, Marelle de Jong, Therry Lebeaupan and Hongwen Wu 1 Abstract The corporate bond ndces, bult by market ndex provders to serve as nvestment benchmarks,

### RELIABILITY, RISK AND AVAILABILITY ANLYSIS OF A CONTAINER GANTRY CRANE ABSTRACT

Kolowrock Krzysztof Joanna oszynska MODELLING ENVIRONMENT AND INFRATRUCTURE INFLUENCE ON RELIABILITY AND OPERATION RT&A # () (Vol.) March RELIABILITY RIK AND AVAILABILITY ANLYI OF A CONTAINER GANTRY CRANE

### INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS

21 22 September 2007, BULGARIA 119 Proceedngs of the Internatonal Conference on Informaton Technologes (InfoTech-2007) 21 st 22 nd September 2007, Bulgara vol. 2 INVESTIGATION OF VEHICULAR USERS FAIRNESS