Capital Adequacy Requirements (CAR)
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Portfolio Optimization with Drawdown Constraints
Implemented in Portfolio Safeguard by AOrDa.com PORTFOLIO OPTIMIZATION WITH DRAWDOWN CONSTRAINTS Alexei Chekhlov1, Stanislav Uryasev2, Michael Zabarankin2 Risk Management and Financial Engineering Lab Center for Applied Optimization Department of Industrial and Systems Engineering University of Florida, Gainesville, FL 32611 Date: January 13, 2003 Correspondence should be addressed to: Stanislav Uryasev Abstract We propose a new one-parameter family of risk functions defined on portfolio return sample -paths, which is called conditional drawdown-at-risk (CDaR). These risk functions depend on the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter a , the CDaR is defined as the mean of the worst (1-a) *100% drawdowns. The CDaR risk function contains the maximal drawdown and average drawdown as its limiting cases. For a particular example, we find optimal portfolios with constraints on the maximal drawdown, average drawdown and several intermediate cases between these two. The CDaR family of risk functions originates from the conditional value-at-risk (CVaR) measure. Some recommendations on how to select the optimal risk measure for getting practically stable portfolios are provided. We solved a real life portfolio allocation problem using the proposed risk functions. 1. Introduction Optimal portfolio allocation is a longstanding issue in both practical portfolio management and academic research on portfolio theory. Various methods have been proposed and studied (for a review, see, for example, Grinold and Kahn, 1999). All of them, as a starting point, assume some measure of portfolio risk. From a standpoint of a fund manager, who trades clients' or bank’s proprietary capital, and for whom the clients' accounts are the only source of income coming in the form of management and incentive fees, losing these accounts is equivalent to the death of his business. -
Basel III: Post-Crisis Reforms
Basel III: Post-Crisis Reforms Implementation Timeline Focus: Capital Definitions, Capital Focus: Capital Requirements Buffers and Liquidity Requirements Basel lll 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 1 January 2022 Full implementation of: 1. Revised standardised approach for credit risk; 2. Revised IRB framework; 1 January 3. Revised CVA framework; 1 January 1 January 1 January 1 January 1 January 2018 4. Revised operational risk framework; 2027 5. Revised market risk framework (Fundamental Review of 2023 2024 2025 2026 Full implementation of Leverage Trading Book); and Output 6. Leverage Ratio (revised exposure definition). Output Output Output Output Ratio (Existing exposure floor: Transitional implementation floor: 55% floor: 60% floor: 65% floor: 70% definition) Output floor: 50% 72.5% Capital Ratios 0% - 2.5% 0% - 2.5% Countercyclical 0% - 2.5% 2.5% Buffer 2.5% Conservation 2.5% Buffer 8% 6% Minimum Capital 4.5% Requirement Core Equity Tier 1 (CET 1) Tier 1 (T1) Total Capital (Tier 1 + Tier 2) Standardised Approach for Credit Risk New Categories of Revisions to the Existing Standardised Approach Exposures • Exposures to Banks • Exposure to Covered Bonds Bank exposures will be risk-weighted based on either the External Credit Risk Assessment Approach (ECRA) or Standardised Credit Risk Rated covered bonds will be risk Assessment Approach (SCRA). Banks are to apply ECRA where regulators do allow the use of external ratings for regulatory purposes and weighted based on issue SCRA for regulators that don’t. specific rating while risk weights for unrated covered bonds will • Exposures to Multilateral Development Banks (MDBs) be inferred from the issuer’s For exposures that do not fulfil the eligibility criteria, risk weights are to be determined by either SCRA or ECRA. -
Impact of Basel I, Basel II, and Basel III on Letters of Credit and Trade Finance
Impact of Basel I, Basel II, and Basel III on Letters of Credit and Trade Finance Requirement Basel I Basel II Basel III 2013 2015 2019 Common Equity 2.0% of 3.5% of RWA 4.5% of RWA 4.5% of RWA RWA Tier 1 Capital 4.0% of 4.0% of 4.5% of RWA 6.0% of RWA 6.0% of RWA RWA RWA Total Capital 8.0% of 8.0% of 8.0% of RWA 8.0% of RWA 8.0% of RWA RWA RWA Capital Conversion -0- -0- +2.5% of RWA Buffer Leverage Ratio Observation Observation (4% of direct assets) (based on Total Capital) 3% of total direct and contingent assets Counter Cyclical Buffer +Up to 2.5% of RWA Liquidity Coverage Observation 30 days 30 days Net Stable Funding Observation Observation 1 year Additional Loss +1% to 2.5% of RWA Absorbency Color Code Key (US Applicability): (Applies only in the US) In the US, applies only to “Large, Internationally-Active Banks” Not yet implemented in the US Depending on the bank and the point in the economic cycle, under Basel III, the total capital requirement for a bank in 2019 may be as much as 15.5% of Risk-Weighted Assets (“RWA”), compared with 8% under Basel I and Basel II. The amount of Risk-Weighted Assets (“RWA”) is computed by multiplying the amount of each asset and contingent asset by a risk weighting and a Credit Conversion Factor (“CCF”) Under Basel I, risk weightings are set: 0% for sovereign obligors, 20% for banks where tenors ≤ one year, 50% for municipalities and residential mortgages, 100% for all corporate obligors Under Basel II, risk weightings are based on internal or external (rating agency) risk ratings with no special distinction for banks; capital requirements for exposures to banks are increased by as much as 650% (from 20% to as much as 150%) The Credit Conversion Factor for Letters of Credit varies under Basel I vs. -
ESG Considerations for Securitized Fixed Income Notes
ESG Considerations for Securitized Fixed Neil Hohmann, PhD Managing Director Income Notes Head of Structured Products BBH Investment Management [email protected] +1.212.493.8017 Executive Summary Securitized assets make up over a quarter of the U.S. corporations since 2010, we find median price declines fixed income markets,1 yet assessments of environmental, for equity of those companies of -16%, and -3% median social, and governance (ESG) risks related to this sizable declines for their corporate bonds.3 Yet, the median price segment of the bond market are notably lacking. decline for securitized notes during these periods is 0% – securitized notes are as likely to climb in price as they are The purpose of this study is to bring securitized notes to fall in price, through these incidents. This should not be squarely into the realm of responsible investing through the surprising – securitizations are designed to insulate inves- development of a specialized ESG evaluation framework tors from corporate distress. They have a senior security for securitizations. To date, securitization has been notably interest in collateral, ring-fenced legal structures and absent from responsible investing discussions, probably further structural protections – all of which limit their owing to the variety of securitization types, their structural linkage to the originating company. However, we find that complexities and limited knowledge of the sector. Manag- a few securitization asset types, including whole business ers seem to either exclude securitizations from ESG securitizations and RMBS, can still bear substantial ESG assessment or lump them into their corporate exposures. risk. A specialized framework for securitizations is needed. -
Personal Loans 101: Understanding Your Credit Risk Loans Have Some Risk for Both the Borrower and the Lender
PERSONAL LOANS 101: Understanding YoUr credit risk Loans have some risk for both the borrower and the lender. The borrower takes on the responsibilities and terms of paying back the loan. The lender’s risk is the chance of non-payment. Consumers can choose from several types of loans. As a borrower, you need to understand the type of loan you are considering and its possible risk. This brochure provides information to help you make a smart choice before applying for a loan. 2 It is important to review your financial situation to see if you can handle another monthly payment before applying for a loan. Creating a budget will help you apply for the loan that best meets your present and future needs. For an interactive budget, visit www.afsaef.org/budgetplanner or www.afsaef.org/personalloans101. You will need to show the lender that you can repay what you borrow, with interest. After you have made a budget, consider these factors, which maY redUce or add risk to a Loan. 3 abiLitY to repaY the Loan Is the lender evaluating your ability to repay the loan based on facts such as your credit history, current and expected income, current expenses, debt-to- income ratio (your expenses compared to your income) and employment status? This assessment, often called underwriting, helps determine if you can make the monthly payment and raises your chances of getting a loan to fit your needs that you can afford to repay. It depends on you providing complete and correct information to the lender. Testing “your ability to repay” and appropriate “underwriting” reduces your risk when taking out any type of loan. -
Portfolio Optimization with Drawdown Constraints
PORTFOLIO OPTIMIZATION WITH DRAWDOWN CONSTRAINTS Alexei Chekhlov1, Stanislav Uryasev2, Michael Zabarankin2 Risk Management and Financial Engineering Lab Center for Applied Optimization Department of Industrial and Systems Engineering University of Florida, Gainesville, FL 32611 Date: January 13, 2003 Correspondence should be addressed to: Stanislav Uryasev Abstract We propose a new one-parameter family of risk functions defined on portfolio return sample -paths, which is called conditional drawdown-at-risk (CDaR). These risk functions depend on the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter a , the CDaR is defined as the mean of the worst (1-a) *100% drawdowns. The CDaR risk function contains the maximal drawdown and average drawdown as its limiting cases. For a particular example, we find optimal portfolios with constraints on the maximal drawdown, average drawdown and several intermediate cases between these two. The CDaR family of risk functions originates from the conditional value-at-risk (CVaR) measure. Some recommendations on how to select the optimal risk measure for getting practically stable portfolios are provided. We solved a real life portfolio allocation problem using the proposed risk functions. 1. Introduction Optimal portfolio allocation is a longstanding issue in both practical portfolio management and academic research on portfolio theory. Various methods have been proposed and studied (for a review, see, for example, Grinold and Kahn, 1999). All of them, as a starting point, assume some measure of portfolio risk. From a standpoint of a fund manager, who trades clients' or bank’s proprietary capital, and for whom the clients' accounts are the only source of income coming in the form of management and incentive fees, losing these accounts is equivalent to the death of his business. -
BOT Notification No 15-2555 (29 September 2017)-Check 2
Unofficial Translation This translation is for the convenience of those unfamiliar with the Thai language Please refer to Thai text for the official version -------------------------------------- Notification of the Bank of Thailand No. FPG. 15/2555 Re: Regulations on the Calculation of Credit Risk-Weighted Assets for Commercial Banks under the Standardised Approach (SA) _____________________________ 1. Rationale As the Bank of Thailand revised the Notification of the Bank of Thailand on Supervisory Guideline on Capital Requirement for Commercial Banks by referring to the Basel III framework: A global regulatory framework for more resilient banks and banking systems (Revised version: June 2011) of the Basel Committee on Banking Supervision, in order to ensure that commercial banks have high quality and adequate capital to absorb losses that may occur under normal and stress circumstance and to maintain the stability of financial system. The Basel III framework also includes improvement of the calculation of credit risk-weighted assets to better reflect credit risk of commercial banks. In this Notification, the Bank of Thailand thereby revises regulations on the calculation of credit risk-weighted assets under the Standardized Approach (SA) in order to be aligned with the revised regulations on components of capital, as certain items that are required to be deducted from capital under Basel II shall be calculated as credit risk-weighted assets instead, without any revisions made to the existing principles of the SA. For other items, commercial banks shall comply with existing regulations as prescribed by the Bank of Thailand. 2. Statutory Power By virtue of Sections 29, Section 30 and Section 32 of the Financial Institutions Businesses Act B.E. -
A Tax on Securitization
BASEL II respect to losers as regulatory capital burdens increase. Basel II losers include lower-rated A tax on bank, corporate and ABS exposures, OECD sovereign exposures rated below AA- (although banks might hold them for liquidity purposes anyway), non-bank equities, and non-core, high operating cost securitization activities such as asset management. Among its many effects on banks’ regulatory capital, Basel II Portfolio rebalancing might prove to be an additional capital tax on securitization Depending on the extent to which lending margins change to align themselves with rom January 1 2010, Basel II will be in standardized banks, capital requirements will revised regulatory capital burdens, Basel II full effect. The new rules are scheduled vary from a 20% risk weight for the most might also prompt banks to rebalance their to come into effect for all EU banks creditworthy exposures (that is, €1.60 of portfolios by shedding losers and keeping on January 1 2007. One year later, capital for each €100 of exposure) to a 150% winners. Fadditional rules for advanced banks will come risk weight for the least creditworthy Banks might be more willing to retain into effect, with a two-year transition period. exposures (€12 of capital for each €100 of high-quality corporate exposures on their These rules will make highly-rated asset classes exposure). Securitization exposures held by balance sheets because their capital costs more popular, could lead to the restructuring of standardized banks will vary from a 20% risk would be lower than the cost of securitizing many conduits and will act as an additional weight for the most creditworthy exposures to them while retaining the capital-heavy lower capital tax on securitization. -
Operational Risk Management Guide
OPERATIONAL RISK MANAGEMENT GUIDE U.S. DEPARTMENT OF AGRICULTURE FOREST SERVICE 2020 Last Updated 02/26/2020 RISK MANAGEMENT COUNCIL IN COOPERATION WITH THE OFFICE OF SAFETY & OCCUPATIONAL HEALTH and THE NATIONAL AVIATION SAFETY COUNCIL Contents Contents ....................................................................................................................................................................................... 2 Executive Summary .................................................................................................................................................................. i Introduction ............................................................................................................................................................................... 1 What is Operational Risk Management? ................................................................................................................... 1 The Terminology of ORM ................................................................................................................................................ 1 Principles of ORM Application ........................................................................................................................................... 6 The Five-Step ORM Process ................................................................................................................................................ 7 Step 1: Identify Hazards .................................................................................................................................................. -
T013 Asset Allocation Minimizing Short-Term Drawdown Risk And
Asset Allocation: Minimizing Short-Term Drawdown Risk and Long-Term Shortfall Risk An institution’s policy asset allocation is designed to provide the optimal balance between minimizing the endowment portfolio’s short-term drawdown risk and minimizing its long-term shortfall risk. Asset Allocation: Minimizing Short-Term Drawdown Risk and Long-Term Shortfall Risk In this paper, we propose an asset allocation framework for long-term institutional investors, such as endowments, that are seeking to satisfy annual spending needs while also maintaining and growing intergenerational equity. Our analysis focuses on how asset allocation contributes to two key risks faced by endowments: short-term drawdown risk and long-term shortfall risk. Before approving a long-term asset allocation, it is important for an endowment’s board of trustees and/or investment committee to consider the institution’s ability and willingness to bear two risks: short-term drawdown risk and long-term shortfall risk. We consider various asset allocations along a spectrum from a bond-heavy portfolio (typically considered “conservative”) to an equity-heavy portfolio (typically considered “risky”) and conclude that a typical policy portfolio of 60% equities, 30% bonds, and 10% real assets represents a good balance between these short-term and long-term risks. We also evaluate the impact of alpha generation and the choice of spending policy on an endowment’s expected risk and return characteristics. We demonstrate that adding alpha through manager selection, tactical asset allocation, and the illiquidity premium significantly reduces long-term shortfall risk while keeping short-term drawdown risk at a desired level. We also show that even a small change in an endowment’s spending rate can significantly impact the risk profile of the portfolio. -
A Nonlinear Optimisation Model for Constructing Minimal Drawdown Portfolios
A nonlinear optimisation model for constructing minimal drawdown portfolios C.A. Valle1 and J.E. Beasley2 1Departamento de Ci^enciada Computa¸c~ao, Universidade Federal de Minas Gerais, Belo Horizonte, MG 31270-010, Brazil [email protected] 2Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, UK [email protected] August 2019 Abstract In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate the problem (minimising average drawdown, maximum drawdown, or a weighted combination of the two) as a non- linear program and show how it can be partially linearised by replacing one of the nonlinear constraints by equivalent linear constraints. Computational results are presented (generated using the nonlinear solver SCIP) for three test instances drawn from the EURO STOXX 50, the FTSE 100 and the S&P 500 with daily price data over the period 2010-2016. We present results for long-only drawdown portfolios as well as results for portfolios with both long and short positions. These indicate that (on average) our minimal drawdown portfolios dominate the market indices in terms of return, Sharpe ratio, maximum drawdown and average drawdown over the (approximately 1800 trading day) out-of-sample period. Keywords: Index out-performance; Nonlinear optimisation; Portfolio construction; Portfo- lio drawdown; Portfolio optimisation 1 Introduction Given a portfolio of financial assets then, as time passes, the price of each asset changes and so by extension the value of the portfolio changes. -
Revised Standards for Minimum Capital Requirements for Market Risk by the Basel Committee on Banking Supervision (“The Committee”)
A revised version of this standard was published in January 2019. https://www.bis.org/bcbs/publ/d457.pdf Basel Committee on Banking Supervision STANDARDS Minimum capital requirements for market risk January 2016 A revised version of this standard was published in January 2019. https://www.bis.org/bcbs/publ/d457.pdf This publication is available on the BIS website (www.bis.org). © Bank for International Settlements 2015. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated. ISBN 978-92-9197-399-6 (print) ISBN 978-92-9197-416-0 (online) A revised version of this standard was published in January 2019. https://www.bis.org/bcbs/publ/d457.pdf Minimum capital requirements for Market Risk Contents Preamble ............................................................................................................................................................................................... 5 Minimum capital requirements for market risk ..................................................................................................................... 5 A. The boundary between the trading book and banking book and the scope of application of the minimum capital requirements for market risk ........................................................................................................... 5 1. Scope of application and methods of measuring market risk ...................................................................... 5 2. Definition of the trading book ..................................................................................................................................