Portfolio 1 has a higher potential loss than Portfolio 2 based on credit risk analysis of two bond portfolios using Credit Metrics methodology. Simulations show Portfolio 1 has a 99.5% VaR of $375,306 compared to $223,956 for Portfolio 2. While Portfolio 1 has higher average credit ratings, Portfolio 2 has lower volatility, risk, and tail risk due to including less correlated C rated bonds, making it the safer portfolio.
This document discusses strategies for hedging risks faced by Muck River Plaza, a shopping center with two major anchor tenants (Best Buy and Barnes & Noble) and smaller tenants. It first evaluates the importance of the anchor tenants and models their credit risk and probability of default using the KMV-Merton model. It then values the lease obligations under different scenarios for the anchor tenants. Finally, it discusses hedging strategies and recommends specific derivatives to hedge risks, including risks from lower sales volumes impacting smaller tenants.
This document provides an overview of various credit default models, including:
- Merton's structural model, which uses Black-Scholes option pricing theory to estimate probability of default.
- Extensions to Merton's model, including the KMV model which maps "distance to default" to historical default rates.
- Ratings-based models that use credit rating migration probabilities provided by rating agencies.
- Multivariate factor models that model default dependence between firms using common factors like the economy.
The document discusses key aspects and assumptions of these different modeling approaches.
IFRS 9 Implementation : Using the Z-score approach as a KRI to identify adverse credit deterioration for Stage Transition from 1 to stages 2/3 in IFRS 9 Modeling
Credit risks are calculated based on the borrowers’ overall ability to repay. Our objective was to use optimization in order to create a tool that approves or rejects loans to borrowers. We also used optimization to establish how much interest rate/credit will be extended to borrowers who were approved for a loan.
Game Theory & Logistic Regression: Monetizing Trust in Contracts Through Bina...Kurt Schulzke
In The Speed of Trust, Steven M.R. Covey argues that trust is monetizable. This study confirms Covey's hypothesis by applying binary classification (via SAS Proc Logistic) to 10 years of data from a 3 x 3 prisoner's dilemma game.
It is not difficult to find situations of marked change in variables and with unpredictable event risk implies estimation problems. E.g.,
Credit spreads in 2008 rise to levels that could never have been forecast based upon previous history. The subprime crisis of 2007/8: credit spreads & volatility rise to unseen levels & shift in debtor behavior (delinquency patterns)
E.g., estimating the volatility from data in a calm (turbulent) period implies under (over) estimation of future realized volatility
This document is a thesis submitted by Jai Kedia for a degree in mathematics and business economics. It examines alternative risk measures to the traditional beta measure in predicting stock returns. The thesis provides an introduction and acknowledges the contributions of the advisors. It then presents an abstract that outlines the goal of analyzing if alternative risk measures such as higher moments, size, leverage, and price-to-book ratio can improve predictions of stock returns beyond just beta. Finally, it presents a table of contents that outlines the various chapters covering the return/risk relationship, modern portfolio theory, mathematical analysis of stock prices, a literature review on previous empirical studies, the empirical analysis conducted, and a conclusion.
This document summarizes a research paper that examines how financial distress affects the cross-section of equity returns. The paper develops a simple model that considers financial leverage in equity valuation and the potential for shareholder recovery during financial distress. The model shows that the possibility of shareholder recovery can reduce equity risk for highly distressed stocks. This helps explain various empirical patterns, such as lower returns for distressed stocks, stronger value effects for high default risk firms, and momentum profits concentrated in low credit quality stocks. The model predicts a hump-shaped relationship between value premiums and default probability, as well as stronger momentum profits for nearly distressed firms with higher potential recovery. Empirical tests on market data generally confirm these predictions.
This document discusses strategies for hedging risks faced by Muck River Plaza, a shopping center with two major anchor tenants (Best Buy and Barnes & Noble) and smaller tenants. It first evaluates the importance of the anchor tenants and models their credit risk and probability of default using the KMV-Merton model. It then values the lease obligations under different scenarios for the anchor tenants. Finally, it discusses hedging strategies and recommends specific derivatives to hedge risks, including risks from lower sales volumes impacting smaller tenants.
This document provides an overview of various credit default models, including:
- Merton's structural model, which uses Black-Scholes option pricing theory to estimate probability of default.
- Extensions to Merton's model, including the KMV model which maps "distance to default" to historical default rates.
- Ratings-based models that use credit rating migration probabilities provided by rating agencies.
- Multivariate factor models that model default dependence between firms using common factors like the economy.
The document discusses key aspects and assumptions of these different modeling approaches.
IFRS 9 Implementation : Using the Z-score approach as a KRI to identify adverse credit deterioration for Stage Transition from 1 to stages 2/3 in IFRS 9 Modeling
Credit risks are calculated based on the borrowers’ overall ability to repay. Our objective was to use optimization in order to create a tool that approves or rejects loans to borrowers. We also used optimization to establish how much interest rate/credit will be extended to borrowers who were approved for a loan.
Game Theory & Logistic Regression: Monetizing Trust in Contracts Through Bina...Kurt Schulzke
In The Speed of Trust, Steven M.R. Covey argues that trust is monetizable. This study confirms Covey's hypothesis by applying binary classification (via SAS Proc Logistic) to 10 years of data from a 3 x 3 prisoner's dilemma game.
It is not difficult to find situations of marked change in variables and with unpredictable event risk implies estimation problems. E.g.,
Credit spreads in 2008 rise to levels that could never have been forecast based upon previous history. The subprime crisis of 2007/8: credit spreads & volatility rise to unseen levels & shift in debtor behavior (delinquency patterns)
E.g., estimating the volatility from data in a calm (turbulent) period implies under (over) estimation of future realized volatility
This document is a thesis submitted by Jai Kedia for a degree in mathematics and business economics. It examines alternative risk measures to the traditional beta measure in predicting stock returns. The thesis provides an introduction and acknowledges the contributions of the advisors. It then presents an abstract that outlines the goal of analyzing if alternative risk measures such as higher moments, size, leverage, and price-to-book ratio can improve predictions of stock returns beyond just beta. Finally, it presents a table of contents that outlines the various chapters covering the return/risk relationship, modern portfolio theory, mathematical analysis of stock prices, a literature review on previous empirical studies, the empirical analysis conducted, and a conclusion.
This document summarizes a research paper that examines how financial distress affects the cross-section of equity returns. The paper develops a simple model that considers financial leverage in equity valuation and the potential for shareholder recovery during financial distress. The model shows that the possibility of shareholder recovery can reduce equity risk for highly distressed stocks. This helps explain various empirical patterns, such as lower returns for distressed stocks, stronger value effects for high default risk firms, and momentum profits concentrated in low credit quality stocks. The model predicts a hump-shaped relationship between value premiums and default probability, as well as stronger momentum profits for nearly distressed firms with higher potential recovery. Empirical tests on market data generally confirm these predictions.
The document discusses credit migration risk modeling for calculating the Incremental Risk Charge (IRC). It outlines the requirements for IRC models, including using a one-year capital horizon at a 99.9% confidence level. It also discusses model assumptions, such as assigning positions to liquidity buckets and using a constant level of risk trading strategy. The document then provides an initial outline for an IRC risk model and discusses considerations such as the need to model credit migration risk under both objective and risk-neutral probability measures.
CLEAN: A Patented Risk-Neutral Approach to MBS ValuationKalotayAnalytics
This document describes the CLEANTM model for valuing mortgage-backed securities (MBS). The CLEANTM model treats mortgages as callable amortizing bonds and models prepayments by dividing mortgage pools into buckets based on borrower behavior. The key risk factors in the model are interest rates, volatility, and homeowner credit spreads. The model calibrates quickly and intuitively based on observable market data. It provides realistic valuations, risk measurements, and trading opportunities without the limitations of other prepayment models.
This document discusses differences between FAS-133 and IAS 39 standards regarding the effectiveness of interest rate risk hedges. It shows that interest rate swaps intended to hedge fixed income assets will not be 100% effective as assumed, leading to problems for IAS 39 which does not allow the shortcut method of FAS-133. Several remedies are proposed, including matching swap reset dates to evaluation dates, separating hedges of each cash flow, or using cumulative effectiveness tests. However, each remedy has shortcomings and the best solution may be guidance in IAS 39 allowing treatment similar to the FAS-133 shortcut method. This inconsistency could impact bank capital requirements under Basel II.
Generic valuation framework for insurance liabilities - August 2017 editionNick Kinrade
This document proposes a generic framework for determining the market value of insurance liabilities that consists of three components: 1) the best estimate liability, which is the risk-free discounted value of expected liability cash flows, 2) a deferred tax liability for tax on temporary differences between the value of liabilities for tax purposes versus market value, and 3) a risk margin with two parts - a capital margin reflecting the cost of funding capital requirements, and a liability margin reflecting financial market risk and liquidity costs in liability cash flows. The framework allows for debt financing of capital requirements and considers tax and liability funding costs. It is consistent with several valuation standards and provides a basis for interpreting their cost-of-capital parameters.
Stress testing involves simulating the impact of exceptional but plausible risk factor changes on a bank's financial position. BASIC Bank uses stress testing techniques to quantify the effects of changes in credit, interest rate, exchange rate, equity price, liquidity, and other risks. Scenarios are developed to assess the bank's resilience under various adverse conditions, such as increases in non-performing loans, falls in collateral values, or defaults by major borrowers.
This document provides an overview of the key concepts to be covered in Chapter 5 on risk and return. It begins with learning objectives for the chapter, which include understanding the relationship between risk and return, defining and measuring risk and return, investor attitudes toward risk, risk and return in portfolio context, the capital asset pricing model, and efficient financial markets. It then covers definitions of return, examples of calculating return, definitions of risk, and how to determine expected return and standard deviation using probability distributions to measure risk. Other topics summarized are risk attitudes, risk and return for portfolios, diversification, the capital asset pricing model, and systematic versus unsystematic risk.
[EN] A detailed look at the treatment of convertible bonds under the new Solv...NN Investment Partners
NN Investment Partners takes a detailed look at the treatment of convertible bonds under the new Solvency II regulatory regime for European insurers, from November 2015.
Merger means of payment impact on analyst recommendationYiling Zhang
1) The document analyzes how the means of payment (cash vs stock) in mergers and acquisitions affects short-term analyst recommendation changes and stock returns for acquiring firms.
2) It finds that cash deals are more likely to lead to analyst upgrades of recommendations for acquiring firm stocks within 90 days of the deal announcement. Acquiring firms that use cash see higher short-term abnormal stock returns compared to stock deals.
3) The findings provide evidence that the means of payment contains information about future returns, as the market reacts to differences in analyst recommendation changes driven by the payment type.
[EN] Convertible bonds offer investors equity-like returns with a risk profil...NN Investment Partners
NN Investment Partners explains how convertible bonds offer investors equity-like returns with a risk profile comparable to that of bonds, from November 2015.
- Direct real estate outperformed other asset classes on a risk-adjusted basis based on summary statistics of returns from 1987-1999 in the UK. Bonds also outperformed equities during this period.
- Direct real estate had a negative correlation with other asset classes, providing diversification benefits, while indirect real estate was strongly positively correlated with equities.
- During an economic downturn from 1993-1995 in the UK, direct real estate increased while other asset classes declined, demonstrating its diversification properties.
- A mean variance analysis found that an optimal portfolio allocated 57% to direct real estate, 41% to bonds, 2% to equities, and 0% to indirect real estate, achieving the highest risk
This document summarizes key concepts from Chapter 5 of Principles of Managerial Finance by Lawrence J. Gitman, which focuses on risk and return. It discusses measuring risk for single and multiple assets, the benefits of diversification, and international diversification. It then introduces the Capital Asset Pricing Model (CAPM) as a tool for valuing securities based on their non-diversifiable risk relative to the market. The chapter materials include study guides, problem templates, and answers to review questions about risk measurement, diversification, beta calculation, and the security market line.
This document discusses theories of corporate capital structure and presents a regression model to test whether firms have target debt ratios. It finds that:
1) Firms appear to have target debt ratios that depend on firm characteristics, consistent with the tradeoff theory of capital structure.
2) Firms only partially adjust their debt ratios each year to close the gap between their actual and target ratios. The typical firm closes about one-third of the gap per year.
3) This partial adjustment model provides a better fit for the data than alternatives like the pecking order theory or market timing theory, which cannot explain why firms would revert to a target debt ratio. However, these theories still have some explanatory power.
The document discusses correlation in investment management. It defines correlation as a statistical measure of how investment returns move in relation to each other. Anticipating correlations correctly is key for investment decisions and risk management, as falsely predicting low correlations can result in unexpectedly high portfolio risk if correlations rise. While past or ex-post correlation can be observed, ex-ante or future correlation is difficult to predict and requires sophisticated risk models as relationships between assets may change over time.
Expected value return & standard deviationJahanzeb Memon
This document defines key concepts related to expected value, expected return, and standard deviation. It explains that expected value is the weighted average of all possible values of a random variable. Expected return is calculated by multiplying the probability and return of each possible scenario and summing the results. The document provides an example of calculating expected return using four scenarios. It also defines standard deviation as a measure of how spread out data is from the mean.
This document discusses the complex tax treatment of municipal bonds and how it affects their interest rate risk. It notes that gains and losses from municipal bond sales are subject to taxes, and taxes depress the market prices of bonds selling at a discount. Standard analytics do not account for taxes, which causes the interest rate sensitivity and effective duration of discount bonds to be underestimated. The document advocates analyzing muni bonds using a tax-neutral framework to properly assess interest rate risk and potential returns.
This document summarizes a presentation on core deposit modeling best practices. It discusses topics like rate sensitivities in a rising rate environment, valuation of core deposits, sensitivity analysis, liquidity concerns, core deposit studies and behavioral inputs. Key points covered include using historical data to model rate sensitivities, the GAAP definition of valuing core deposits as the present value of average balances discounted by alternative funding costs, and the importance of sensitivity analysis and considering different scenarios in modeling.
The ICAR Indian Institute of Water Management was established in 1988 and aims to develop improved water management technologies through research. It conducts research through five programs: rainwater management, canal water management, groundwater management, waterlogged area management, and on-farm research and technology transfer.
The document then discusses the design of creek irrigation systems. It defines tidal creeks and explains how salinity varies in creeks over tidal cycles. It also discusses factors that influence salinity changes like urbanization. The document outlines the process for designing creek irrigation systems which includes determining design discharge, selecting a cross-sectional shape based on soil type and erosion control needs, using Manning's formula to calculate dimensions, and adding freeboard
El silicio es un elemento químico común en la corteza terrestre. Es el segundo elemento más abundante en la corteza terrestre y se encuentra principalmente en forma de sílice y arena de sílice. El silicio se utiliza ampliamente en la electrónica y la industria de los semiconductores.
Senior High School Regional Conference Parallel Session A-6 dorothyjoyjalalon
The document describes the career guidance program at a school to help students choose career paths. It includes exploratory courses in grades 7-8 covering agriculture, home economics, ICT and industrial arts. Other activities are interpreting career assessments, career coaching, integrating career planning into classes, mock interviews, career expos, and discussing labor market trends. The goal is to help students discover their interests and strengths and make informed choices about senior high school tracks and careers.
Este documento resume los conceptos clave de la Web 2.0 y la nube. Define la Web 2.0 como un paradigma que permite ofrecer servicios de computación a través de una red, generalmente Internet. Explica que la Web 2.0 permite la colaboración entre usuarios y el acceso a información desde cualquier lugar. También describe algunas aplicaciones clave como blogs, wikis y redes sociales. Finalmente, destaca las ventajas de la nube como la escalabilidad, la independencia de ubicación y el menor costo en comparación con sistemas tradicional
The document discusses credit migration risk modeling for calculating the Incremental Risk Charge (IRC). It outlines the requirements for IRC models, including using a one-year capital horizon at a 99.9% confidence level. It also discusses model assumptions, such as assigning positions to liquidity buckets and using a constant level of risk trading strategy. The document then provides an initial outline for an IRC risk model and discusses considerations such as the need to model credit migration risk under both objective and risk-neutral probability measures.
CLEAN: A Patented Risk-Neutral Approach to MBS ValuationKalotayAnalytics
This document describes the CLEANTM model for valuing mortgage-backed securities (MBS). The CLEANTM model treats mortgages as callable amortizing bonds and models prepayments by dividing mortgage pools into buckets based on borrower behavior. The key risk factors in the model are interest rates, volatility, and homeowner credit spreads. The model calibrates quickly and intuitively based on observable market data. It provides realistic valuations, risk measurements, and trading opportunities without the limitations of other prepayment models.
This document discusses differences between FAS-133 and IAS 39 standards regarding the effectiveness of interest rate risk hedges. It shows that interest rate swaps intended to hedge fixed income assets will not be 100% effective as assumed, leading to problems for IAS 39 which does not allow the shortcut method of FAS-133. Several remedies are proposed, including matching swap reset dates to evaluation dates, separating hedges of each cash flow, or using cumulative effectiveness tests. However, each remedy has shortcomings and the best solution may be guidance in IAS 39 allowing treatment similar to the FAS-133 shortcut method. This inconsistency could impact bank capital requirements under Basel II.
Generic valuation framework for insurance liabilities - August 2017 editionNick Kinrade
This document proposes a generic framework for determining the market value of insurance liabilities that consists of three components: 1) the best estimate liability, which is the risk-free discounted value of expected liability cash flows, 2) a deferred tax liability for tax on temporary differences between the value of liabilities for tax purposes versus market value, and 3) a risk margin with two parts - a capital margin reflecting the cost of funding capital requirements, and a liability margin reflecting financial market risk and liquidity costs in liability cash flows. The framework allows for debt financing of capital requirements and considers tax and liability funding costs. It is consistent with several valuation standards and provides a basis for interpreting their cost-of-capital parameters.
Stress testing involves simulating the impact of exceptional but plausible risk factor changes on a bank's financial position. BASIC Bank uses stress testing techniques to quantify the effects of changes in credit, interest rate, exchange rate, equity price, liquidity, and other risks. Scenarios are developed to assess the bank's resilience under various adverse conditions, such as increases in non-performing loans, falls in collateral values, or defaults by major borrowers.
This document provides an overview of the key concepts to be covered in Chapter 5 on risk and return. It begins with learning objectives for the chapter, which include understanding the relationship between risk and return, defining and measuring risk and return, investor attitudes toward risk, risk and return in portfolio context, the capital asset pricing model, and efficient financial markets. It then covers definitions of return, examples of calculating return, definitions of risk, and how to determine expected return and standard deviation using probability distributions to measure risk. Other topics summarized are risk attitudes, risk and return for portfolios, diversification, the capital asset pricing model, and systematic versus unsystematic risk.
[EN] A detailed look at the treatment of convertible bonds under the new Solv...NN Investment Partners
NN Investment Partners takes a detailed look at the treatment of convertible bonds under the new Solvency II regulatory regime for European insurers, from November 2015.
Merger means of payment impact on analyst recommendationYiling Zhang
1) The document analyzes how the means of payment (cash vs stock) in mergers and acquisitions affects short-term analyst recommendation changes and stock returns for acquiring firms.
2) It finds that cash deals are more likely to lead to analyst upgrades of recommendations for acquiring firm stocks within 90 days of the deal announcement. Acquiring firms that use cash see higher short-term abnormal stock returns compared to stock deals.
3) The findings provide evidence that the means of payment contains information about future returns, as the market reacts to differences in analyst recommendation changes driven by the payment type.
[EN] Convertible bonds offer investors equity-like returns with a risk profil...NN Investment Partners
NN Investment Partners explains how convertible bonds offer investors equity-like returns with a risk profile comparable to that of bonds, from November 2015.
- Direct real estate outperformed other asset classes on a risk-adjusted basis based on summary statistics of returns from 1987-1999 in the UK. Bonds also outperformed equities during this period.
- Direct real estate had a negative correlation with other asset classes, providing diversification benefits, while indirect real estate was strongly positively correlated with equities.
- During an economic downturn from 1993-1995 in the UK, direct real estate increased while other asset classes declined, demonstrating its diversification properties.
- A mean variance analysis found that an optimal portfolio allocated 57% to direct real estate, 41% to bonds, 2% to equities, and 0% to indirect real estate, achieving the highest risk
This document summarizes key concepts from Chapter 5 of Principles of Managerial Finance by Lawrence J. Gitman, which focuses on risk and return. It discusses measuring risk for single and multiple assets, the benefits of diversification, and international diversification. It then introduces the Capital Asset Pricing Model (CAPM) as a tool for valuing securities based on their non-diversifiable risk relative to the market. The chapter materials include study guides, problem templates, and answers to review questions about risk measurement, diversification, beta calculation, and the security market line.
This document discusses theories of corporate capital structure and presents a regression model to test whether firms have target debt ratios. It finds that:
1) Firms appear to have target debt ratios that depend on firm characteristics, consistent with the tradeoff theory of capital structure.
2) Firms only partially adjust their debt ratios each year to close the gap between their actual and target ratios. The typical firm closes about one-third of the gap per year.
3) This partial adjustment model provides a better fit for the data than alternatives like the pecking order theory or market timing theory, which cannot explain why firms would revert to a target debt ratio. However, these theories still have some explanatory power.
The document discusses correlation in investment management. It defines correlation as a statistical measure of how investment returns move in relation to each other. Anticipating correlations correctly is key for investment decisions and risk management, as falsely predicting low correlations can result in unexpectedly high portfolio risk if correlations rise. While past or ex-post correlation can be observed, ex-ante or future correlation is difficult to predict and requires sophisticated risk models as relationships between assets may change over time.
Expected value return & standard deviationJahanzeb Memon
This document defines key concepts related to expected value, expected return, and standard deviation. It explains that expected value is the weighted average of all possible values of a random variable. Expected return is calculated by multiplying the probability and return of each possible scenario and summing the results. The document provides an example of calculating expected return using four scenarios. It also defines standard deviation as a measure of how spread out data is from the mean.
This document discusses the complex tax treatment of municipal bonds and how it affects their interest rate risk. It notes that gains and losses from municipal bond sales are subject to taxes, and taxes depress the market prices of bonds selling at a discount. Standard analytics do not account for taxes, which causes the interest rate sensitivity and effective duration of discount bonds to be underestimated. The document advocates analyzing muni bonds using a tax-neutral framework to properly assess interest rate risk and potential returns.
This document summarizes a presentation on core deposit modeling best practices. It discusses topics like rate sensitivities in a rising rate environment, valuation of core deposits, sensitivity analysis, liquidity concerns, core deposit studies and behavioral inputs. Key points covered include using historical data to model rate sensitivities, the GAAP definition of valuing core deposits as the present value of average balances discounted by alternative funding costs, and the importance of sensitivity analysis and considering different scenarios in modeling.
The ICAR Indian Institute of Water Management was established in 1988 and aims to develop improved water management technologies through research. It conducts research through five programs: rainwater management, canal water management, groundwater management, waterlogged area management, and on-farm research and technology transfer.
The document then discusses the design of creek irrigation systems. It defines tidal creeks and explains how salinity varies in creeks over tidal cycles. It also discusses factors that influence salinity changes like urbanization. The document outlines the process for designing creek irrigation systems which includes determining design discharge, selecting a cross-sectional shape based on soil type and erosion control needs, using Manning's formula to calculate dimensions, and adding freeboard
El silicio es un elemento químico común en la corteza terrestre. Es el segundo elemento más abundante en la corteza terrestre y se encuentra principalmente en forma de sílice y arena de sílice. El silicio se utiliza ampliamente en la electrónica y la industria de los semiconductores.
Senior High School Regional Conference Parallel Session A-6 dorothyjoyjalalon
The document describes the career guidance program at a school to help students choose career paths. It includes exploratory courses in grades 7-8 covering agriculture, home economics, ICT and industrial arts. Other activities are interpreting career assessments, career coaching, integrating career planning into classes, mock interviews, career expos, and discussing labor market trends. The goal is to help students discover their interests and strengths and make informed choices about senior high school tracks and careers.
Este documento resume los conceptos clave de la Web 2.0 y la nube. Define la Web 2.0 como un paradigma que permite ofrecer servicios de computación a través de una red, generalmente Internet. Explica que la Web 2.0 permite la colaboración entre usuarios y el acceso a información desde cualquier lugar. También describe algunas aplicaciones clave como blogs, wikis y redes sociales. Finalmente, destaca las ventajas de la nube como la escalabilidad, la independencia de ubicación y el menor costo en comparación con sistemas tradicional
Second Harvest Food Bank distributed nearly 7 million pounds of food to over 72,000 people through its network of 200 member agencies in the last fiscal year. This included distributing over 1.8 million pounds of fresh foods like produce, meat and dairy. The organization saw a 4% increase in individuals served compared to the previous year. Second Harvest aims to expand its operations in the coming year through a planned move to a larger facility.
Design Thinking to Design Doing: Can designers change the world?Álvaro Márquez
What are the fundamental questions you should ask yourself before engaging in any design task?
Slides from the Design Thinking Meetup hosted by Thoughtworks in Sydney - February 2016
My media product uses some conventions of real magazines but also challenges some conventions. On the front cover and contents page, I used typical layouts but challenged conventions in some ways, like only including cover lines on one side initially. My double page spread originally challenged conventions by centering the image but I changed it based on feedback. Through this process, I learned to use new technologies like Photoshop and gained experience with tools like Blogger.
The document discusses different types of pavements used for road construction including unsurfaced, surfaced, flexible, and rigid pavements. It provides details on the materials, design principles, properties, and construction procedures for various pavement types. These include earthen roads, gravel roads, water bound macadam roads, and cement concrete roads. The key components, types of joints, and construction methods for cement concrete pavements are also summarized.
Fears in business operations are known as risks. They mainly affect external and international
relations and other business relations. In the event where operational risks are prominent, the
viability of a business in the future deteriorates and is a complete failure or crippling of the entire
business system. Risk aversion also takes into consideration proper analysis of future prospect of
a specific business before even making an ideal analysis of future prospect of a specific business
before engaging in capital investment
- See more at: http://www.customwritingservice.org/blog/risks-and-returns/
Ch_05 - Risk and Return Valuation Theory.pptkemboies
This chapter discusses portfolio theory and asset pricing models. It introduces concepts such as portfolio risk and return, systematic and unsystematic risk, the efficient frontier, and the capital asset pricing model (CAPM). The chapter objectives are to discuss portfolio risk and return, examine the logic of portfolio theory, show how CAPM is used to value securities, and explain the arbitrage pricing theory (APT). Key models covered include the minimum variance portfolio, capital market line, security market line, and the arbitrage pricing theory as an alternative to CAPM.
Ch_05 - Risk and Return Valuation Theory.pptkemboies
This chapter discusses portfolio theory and asset pricing models. It introduces concepts such as portfolio risk and return, systematic and unsystematic risk, the efficient frontier, and the capital asset pricing model (CAPM). CAPM holds that the expected return of an asset is determined by its sensitivity to non-diversifiable market risk (beta) and the expected market return. The chapter also covers the arbitrage pricing theory, which attributes an asset's return to multiple systematic factors rather than just one market factor.
This document discusses risk and return concepts in finance. It defines types of risk like stand-alone risk and portfolio risk. It shows how to calculate the expected return and standard deviation of individual investments and portfolios. Lower risk can be achieved through diversification since unique investment risks offset each other in a portfolio. The Capital Asset Pricing Model suggests investors should only be compensated for systematic market risk rather than risks that can be diversified away. Beta is introduced as a measure of a security's non-diversifiable market risk relative to the overall market.
This document provides an overview of key concepts in credit risk management, including:
1) Credit risk arises from factors like a borrower's ability to repay, economic conditions, specific events, and regional factors. It is the risk of financial loss if a counterparty fails to meet contractual obligations.
2) Banks assess probability of default, exposure at default, and loss given default to measure and manage credit risk. Transition matrices track how probabilities of default change over time.
3) Credit risk arises in both a bank's trading book (exchange traded and OTC derivatives) and banking book (loans and off-balance sheet commitments). Credit ratings and market prices help estimate probability of default.
This document provides an overview of key concepts in credit risk management, including:
1) Credit risk arises from factors like a borrower's ability to repay, economic conditions, specific events, and regional factors. It is the risk of financial loss if a counterparty fails to meet contractual obligations.
2) Banks assess probability of default, exposure at default, and loss given default to measure credit risk. Transition matrices track how probabilities of default change over time.
3) Credit risk arises in a bank's banking book from loans and in its trading book from exchange traded and over-the-counter derivatives. Credit ratings and spreads between corporate bond yields and risk-free rates provide information on default probabilities.
Chapter 06 - Efficient Diversification
Chapter 06
Efficient Diversification
1. So long as the correlation coefficient is below 1.0, the portfolio will benefit from diversification because returns on component securities will not move in perfect lockstep. The portfolio standard deviation will be less than a weighted average of the standard deviations of the component securities.
2. The covariance with the other assets is more important. Diversification is accomplished via correlation with other assets. Covariance helps determine that number.
3. a and b will have the same impact of increasing the Sharpe ratio from .40 to .45.
4. The expected return of the portfolio will be impacted if the asset allocation is changed. Since the expected return of the portfolio is the first item in the numerator of the Sharpe ratio, the ratio will be changed.
5. Total variance = Systematic variance + Residual variance = β2 Var(rM) + Var(e)
When β = 1.5 and σ(e) = .3, variance = 1.52 × .22 + .32 = .18. In the other scenarios:
a. Both will have the same impact. Total variance will increase from .18 to .1989.
b. Even though the increase in the total variability of the stock is the same in either scenario, the increase in residual risk will have less impact on portfolio volatility. This is because residual risk is diversifiable. In contrast, the increase in beta increases systematic risk, which is perfectly correlated with the market-index portfolio and therefore has a greater impact on portfolio risk.
6.
a. Without doing any math, the severe recession is worse and the boom is better. Thus, there appears to be a higher variance, yet the mean is probably the same since the spread is equally large on both the high and low side. The mean return, however, should be higher since there is higher probability given to the higher returns.
b.
Calculation of mean return and variance for the stock fund:
c. Calculation of covariance:
Covariance has increased because the stock returns are more extreme in the recession and boom periods. This makes the tendency for stock returns to be poor when bond returns are good (and vice versa) even more dramatic.
7.
a. One would expect variance to increase because the probabilities of the extreme outcomes are now higher.
b.
Calculation of mean return and variance for the stock fund:
c. Calculation of covariance
Covariance has decreased because the probabilities of the more extreme returns in the recession and boom periods are now higher. This gives more weight to the extremes in the mean calculation, thus making their deviation from the mean less pronounced.
8. The parameters of the opportunity set are:
E(rS) = 15%, E(rB) = 9%, S = 32%, B = 23%, = 0.15, rf = 5.5%
From the standard deviations and the correlation coefficient we generate the covariance matrix [note that Cov(rS, rB) = SB]:
Bonds
StocksBonds
529.0
110.4Stocks
110.4
1024.0
The minimum-variance portfolio proportions are:
wMin(S) = = ...
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Credit matrics report
1. INVESTX PLC
Portfolio Risk Report
Credit Metrics analysis on bonds’ credit risk and portfolios values
M.Zhang
3/7/2015
2. Mz96 Credit Metrics Report INVESTX PLC
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Spreadsheet in Excel Page in Report
Overview P1
Method "Data Analysis", "Portfolio 1",
"Portfolio 2"
P2-4
Results "Comparison" P5-7
Recommendation P8
Limitations P9-10
Overview
This report analyses two bond portfolios’ credit risk with Credit Metrics methodology, which
considers how each bond’s credit rating changes given the correlation between them. So we
can do simulations and see the effect of upgrading/downgrading of bonds on the whole
portfolio’s value in one year and the credit risk is quantified by calculating Value at Risk for
the portfolio.
There are 4 states for the bonds: A rated, B rated, C rated and Default.
Nine bonds are available for investment: 6 B rated bonds (from companies: R, S, T, U, V, W)
and 3 C rated bonds (from companies: X, Y, Z) with 10 years’ term and 5% annual coupon.
Our client wishes to invest in B rated bonds only for his portfolio as he thinks it is safer.
However, considering the correlations between these bonds, there may be potential big losses
occurring. Therefore, this report looks at the following 2 portfolios:
A portfolio of 6 B rated bonds in same industry (R, S, T, U, V, W)
A portfolio of 3 B rated bonds in same industry (R, S, T) and 3 C rated bonds in
different industries (X, Y, Z)
Being in the same industry implies higher correlation between one bond to another.
By simulating portfolio values in one year’s time, we analyse the distribution pattern and
99.5% VaR for the 2 portfolios and make a recommendation about which portfolio is safer to
invest in.
3. Mz96 Credit Metrics Report INVESTX PLC
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Method
Credit Metrics model assesses credit risk due to changes of credit rating of bonds in a
portfolio, e.g. downgrading and upgrading’s effect on credit quality. By simulating different
scenarios considering the correlation between bonds, we can obtain the VaR for the portfolio
in one year.
Steps taken:
Obtain Covariance Matrix and Cholesky Matrix for bonds in the portfolio
Simulate multivariate Normal random variables using Cholesky Matrix
Return the simulated values back to the according credit rating states using transition
matrix
Calculate the values for a bond in each credit rating state
Obtain the simulated portfolio values in one year’s time
Obtain VaR 99.5% for the simulations for each portfolio
Correlation between the bonds in the portfolio is obtained by analysing the equity returns for
the companies for the past 3 years.
To do this, we first need to find the Covariance Matrix as seen in ‘Data Analysis’ spreadsheet.
Then the Cholesky Matrix( C ) is obtained from the Covariance Matrix ( ∑ ) by performing
Cholesky decomposition1
to the Covariance Matrix.
The result is checked by multiplying Cholesky Matrix with its transpose to fit equation:
CC’=∑
Cholesky Matrix allows us to generate multivariate Normal random variables xi with same
correlation as the equity returns between the companies, which we assume to represent the
bonds’ correlations in the portfolio.
The values in Excel is copied and pasted values for illustration. The first 10 rows contain
formula used, which can be easily reproduced if more simulations are needed. Then we
multiply the standard Normal random variables by transpose of Cholesky Matrix.
These correlated random variables would then be returned back to the credit ratings.
Since each simulation trial contains variables xi from standard Normal distribution with same
correlation as the bonds, it determines the new ratings in one year for each bond. Given the
Transition Matrix, we can return xi to the credit rating it belongs to in one year’s time by
inversing the cumulative transition probability with standard Normal function to set the
boundary for categorising the simulated values.
1
See Paul Sweeting- Enterprise Risk Management Formula 10.97
4. Mz96 Credit Metrics Report INVESTX PLC
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The following diagrams show how the simulated results can be categorised into four states:
A rated, B rated, C rated, or Default for a bond starts as B rated and C rated respectively.
We can see a B rated bond has largest probability to remain B rated.
-3 -2 -1 0 1 2 3
B Rated Bond
Bond remains
B rated
ACDefault
1.47-1.126-1.881
If xi falls
below
-1.881
If xi falls
between
-1.881
and
-1.126
If xi falls between
-1.126 and 1.476
If xi is
above 1.476
-3 -2 -1 0 1 2 3
C Rated Bond
Bond remains
C rated
ADefault B
1.641.036-1.036
If xi falls
below
-1.036
If xi falls between
-1.036 and 1.036
If xi falls
between
-1.036 and
1.644
If xi is
above 1.644
5. Mz96 Credit Metrics Report INVESTX PLC
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C rated bond is most likely to remain C rated and has larger probability to default.
The next step is to calculate the values of the bonds in different states. Recovery rate of a
defaulted bond is 30% of face value. Current risk free rate is 2.5% and credit spread for A
rated, B rated and C rated bond are 0.5%, 2%, and 6% respectively. With coupons payable
for 10 years in arrears, using discounted cash flow methods, the current bond value and
values at the end of first year for each rating can be obtained by annuity formula.
Below is a summary of implied risk discount rate for each rating and the values of the bonds:
Credit Rating Credit risk
Current value
Implied Discount
Rate
End of first
year
A High quality, low credit risk 117.06 3.0% 120.57
B
Speculative, moderate credit
risk 103.96
4.5% 108.63
C High credit risk 77.04 8.5% 83.58
D 30.00
At the start of year, 100 is invested in each bond. Both portfolios starts with same initial
value of 600. Assuming the bond is divisible and is priced as the present value, the holding at
the start is:
Portfolio 1
R S T U V W portfolio total
initial investment 100 100 100 100 100 100 600
number of bonds 0.962 0.962 0.962 0.962 0.962 0.962
Portfolio 2
R S T X Y Z portfolio total
initial investment 100 100 100 100 100 100 600
number of bonds 0.962 0.962 0.962 1.298 1.298 1.298
3,000 simulations has been performed representing different possible scenarios of portfolio
values in one year. And the losses for each simulation are calculated by taking the difference
between portfolio value at the start (600) and simulated portfolio values (sum of the 6 bond
values in one year). A negative loss indicates a gain.
The VaR at 99.5% representing the loss that we are 99.5% confident that our loss would not
exceed over one year, would be obtained from the simulations and used to compare the 2
portfolios. In this project, it is obtained by finding the highest 99.5 percentile of the losses
incurred as shown below:
VaR 99.5%
Portfolio 1 Portfolio 2
375.306 223.956
6. Mz96 Credit Metrics Report INVESTX PLC
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This means, for Portfolio 1, 99.5% of the time the loss wouldn’t exceed 375.306. For
Portfolio 2, 99.5% of the time the loss wouldn’t exceed 223.956. This result indicates that,
Portfolio 1 has a higher potential loss than Portfolio 2.
7. Mz96 Credit Metrics Report INVESTX PLC
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Results
Below is a summary statistics of the results:
Portfolio 1 Portfolio 2
Average Loss -4.39 -12.57
Average Portfolio Value 604.39 612.57
Variance 5237.32 4336.05
Max Loss 426.85 327.04
Max Gain 95.90 171.01
VaR 99.5% 375.31 223.96
Even though the average credit rating for Portfolio 1 is higher, the results show that Portfolio
2 generates a higher average return.
Also, Portfolio 2 has a lower variance, this means the portfolio values are less volatile than
Portfolio 1. The 99.5% Value at Risk for Portfolio 2 is much lower, this means at given
confidence level, the loss from Portfolio 2 is capped at a much lower level than Portfolio 1 in
one year’s time.
This is because Portfolio 2 contains 3 C rated bonds that has low correlation to each other and
to the 3 B rated bonds. The low correlation means that the portfolio is more diversified. So
when one specific market is bad, bond values would not drop together and create huge losses.
Below is a histogram of Portfolio 1:
We can see that in most case (57%) we would have a gain of 20, this is because the bonds are
relatively highly correlated, they tend to behave the same way as each other, i.e. if one bond
stays in B rating, the others are likely to stay in B rating, which causes the leptokurtic shape.
0
200
400
600
800
1000
1200
1400
1600
1800
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
420
more
Loss
Portfolio 1 Histogram
8. Mz96 Credit Metrics Report INVESTX PLC
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However, if one bond performs badly, the others are likely to behave the same way, which
causes the potential huge loss (greatest loss lies beyond 420 for a probability of 0.43%) in the
tail area. The tail is long and fat, which means there is a chance of catastrophic risk.
Below is a histogram for Portfolio 2:
Values for portfolio 2 is spreat more evenly. With four peaks at -70, -30, 40, and 110, these
may be caused by the 3 correlated B rated bonds (R, S, T) behaving in similar ways. But the
effect is offset by the 3 less correlated bonds (X, Y, Z).
It has a positive skew showing a chance of general trend of gain. The lagest loss is around
330 with a probability of 0.07% which is a much lower change for a lower loss compared to
Portfolio 1.
0
100
200
300
400
500
600
700
800
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
More
Loss
Portfolio 2 Histogram
9. Mz96 Credit Metrics Report INVESTX PLC
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The following diagram shows a comparison between loss distributions from both portfolios.
Both portfolios peak around zero, but Portfolio 1 has a fatter and longer tail than portfolio 2.
This means a higher potential loss if we invest solely in B rated correlated bonds. Also
Portfolio 2 has a higher potential gain with lower potential loss than Portfolio 1.
This diagram indicates that Portfolio 2 is a less risky choice than Portfolio 1.
0
500
1000
1500
2000
2500
-150 -100 -50 0 50 100 150 200 250 300 350 400 450 More
Loss Comparison
Portfolio 1
Portfolio 2
10. Mz96 Credit Metrics Report INVESTX PLC
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Recommendation
Depending on how much risk the client would like to take, he should consider investing in
some C rated bonds for diversification in the portfolio. This would reduce the risk of large
losses occurring due to the high correlation of B rated bonds.
According to the results above, Portfolio 2 offers a less volatile return over the year and has a
lower VaR than Portfolio 1. This means if the worst case scenario happens, our client would
lose significantly less if he chooses Portfolio 2.
Since he wants a ‘safer’ portfolio, his statement of ‘invest solely in B rated bonds’ is not an
appropriate action to take as it is more risky due to concentration risk. The safer approach
should be adding some bonds with lower correlation, i.e.the C rated bonds in this case, so that
the tail of loss distribution is not as fat and portfolio values less concentrated. In this way,
there is less chance of huge losses due to all the correlated bonds performing badly together
which is safer.
According to his actual risk appetite and preference, he should choose how many C rated
bonds to add to the portfolio, or bonds other than the 9 bonds given that has low or negative
correlation to the existing invested bonds. This can reduce credit risk by diversification
without extra costs.
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Limitations
The results should, however, be used with caution with consideration of the following
limitations:
Using equity returns’ correlation for bonds
The bonds’ credit quality’s correlation may not behave the same way as equity returns. Price
for shares can be affected by many demand and supply factors including subjective opinions
of investors while bonds may be affected by other factors. Therefore the Cholesky Matrix
may not represent the bonds’ correlations perfectly and this may lead to the inaccuracy of the
model.
Assume future performance would be the same
We used empirical data for modelling correlation and assume future behaviour to be the same,
which might not be the case. And there may be new risks or other factors effecting the credit
quality of bonds.
Difficulty to capture fat tail nature
This needs large amount of data and large number of simulations to capture the whole shape
of portfolio distribution.
Credit rating may not reflect the actual credit quality
I t is not necessary the highly rated investments have better credit quality as rating agency are
paid by the companies being rated. Therefore as the method relies on credit rating’s accuracy
to reflect credit risk, it may not be reliable.
Unavailability of rating
This method cannot be performed if a company has no credit rating available. E.g. Some
unlisted firms’ bonds would not be suitable to be used with this method.
Data quality
The quality of results depends hugely on the quality of the data given. The results would not
be reliable if there are any data errors.
Only 4 credit rating state
This is overly simplified as in reality there would be more categories for credit rating, which
leads to the only 4 values the bonds can take, giving cluster in certain values.
Limited amount of data
The data are only for the past 3 years and may not capture the whole picture for the
correlation between each bonds.
Assuming a multivariate Normal
It may not be the case in reality therefore introducing inaccuracy.
12. Mz96 Credit Metrics Report INVESTX PLC
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Simplified assumptions
Flat yield curve, all bonds starts at the same time, and other simplified assumptions may
mean that the modelling doesn’t follow reality closely and the results may not be very
accurate.