Wikipedia

Financial risk management

Institutions

Certifications

Financial risk management is the practice of protecting economic value in a firm by managing exposure to financial risk - principally credit risk and market risk, with more specific variants as listed aside - as well as some aspects of operational risk. As for risk management more generally, financial risk management requires identifying the sources of risk, measuring these, and crafting plans to mitigate them.[1][2] See Finance § Risk management for an overview.

Financial risk management as a "science" can be said to have been born[3] with modern portfolio theory, particularly as initiated by Professor Harry Markowitz in 1952 with his article, "Portfolio Selection";[4] see Mathematical finance § Risk and portfolio management: the P world.

The discipline can be qualitative and quantitative; as a specialization of risk management, however, financial risk management focuses more on when and how to hedge,[5] often using financial instruments to manage costly exposures to risk.[6]

  • In the banking sector worldwide, the Basel Accords are generally adopted by internationally active banks for tracking, reporting and exposing operational, credit and market risks.[7][8]
  • Within non-financial corporates,[9][10] the scope is broadened to overlap enterprise risk management, and financial risk management then addresses risks to the firm's overall strategic objectives.
  • In investment management[11] risk is managed through diversification and related optimization; while further specific techniques are then applied to the portfolio or to individual stocks as appropriate.

In all cases, the last "line of defence" against risk is capital, "as it ensures that a firm can continue as a going concern even if substantial and unexpected losses are incurred".[12]

Economic perspective

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Neoclassical finance theory prescribes that (1) a firm should take on a project only if it increases shareholder value.[13] Further, the theory suggests that (2) firm managers cannot create value for shareholders or investors by taking on projects that shareholders could do for themselves at the same cost; see Theory of the firm and Fisher separation theorem.

Given these, there is therefore a fundamental debate relating to "Risk Management" and shareholder value.[5][14][15] The discussion essentially weighs the value of risk management in a market versus the cost of bankruptcy in that market: per the Modigliani and Miller framework, hedging is irrelevant since diversified shareholders are assumed to not care about firm-specific risks, whereas, on the other hand hedging is seen to create value in that it reduces the probability of financial distress.

When applied to financial risk management, this implies that firm managers should not hedge risks that investors can hedge for themselves at the same cost.[5] This notion is captured in the so-called "hedging irrelevance proposition":[16] "In a perfect market, the firm cannot create value by hedging a risk when the price of bearing that risk within the firm is the same as the price of bearing it outside of the firm."

In practice, however, financial markets are not likely to be perfect markets.[17][18][19][20] This suggests that firm managers likely have many opportunities to create value for shareholders using financial risk management, wherein they are able to determine which risks are cheaper for the firm to manage than for shareholders. Here, market risks that result in unique risks for the firm are commonly the best candidates for financial risk management.[21]

Application

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As outlined, businesses are exposed, in the main, to market, credit and operational risk. A broad distinction[12] exists though, between financial institutions and non-financial firms - and correspondingly, the application of risk management will differ. Respectively:[12] For Banks and Fund Managers, "credit and market risks are taken intentionally with the objective of earning returns, while operational risks are a byproduct to be controlled". For non-financial firms, the priorities are reversed, as "the focus is on the risks associated with the business" - ie the production and marketing of the services and products in which expertise is held - and their impact on revenue, costs and cash flow, "while market and credit risks are usually of secondary importance as they are a byproduct of the main business agenda". (See related discussion re valuing financial services firms as compared to other firms.) In all cases, as above, risk capital is the last "line of defence".

Banking

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The 5% Value at Risk of a hypothetical profit-and-loss probability density function
Further information: Bank § Capital and risk, Investment banking § Risk management, and Shadow banking system § Risks or vulnerability
See also: Derivative (finance) § Risks, Interest rate swap § Risks, Option (finance) § Risks, Value at risk § VaR risk management, and Corporate bond § Risk analysis

Banks and other wholesale institutions face various financial risks in conducting their business, and how well these risks are managed and understood is a key driver [22] behind profitability, as well as of the quantum of capital they are required to hold.[23] Financial risk management in banking has thus grown markedly in importance since the Financial crisis of 2007–2008.[24] (This has given rise[24] to dedicated degrees and professional certifications.)

The major focus here is on credit and market risk, and especially through regulatory capital, includes operational risk. Credit risk is inherent in the business of banking, but additionally, these institutions are exposed to counterparty credit risk. Both are to some extent offset by margining and collateral; and the management is of the net-position. Large banks are also exposed to Macroeconomic systematic risk - risks related to the aggregate economy the bank is operating in[25] (see Too big to fail).

The discipline[26][27][7][8] is, as outlined, simultaneously concerned with (i) managing, and as necessary hedging, the various positions held by the institution - both trading positions and long term exposures; and (ii) calculating and monitoring the resultant economic capital, as well as the regulatory capital under Basel III — which covers also leverage and liquidity — with regulatory capital as a floor.

Correspondingly, and broadly, the analytics [27][26] are based as follows: For (i) on the "Greeks", the sensitivity of the price of a derivative to a change in its underlying factors; as well as on the various other measures of sensitivity, such as DV01 for the sensitivity of a bond or swap to interest rates, and CS01 or JTD for exposure to credit spread. For (ii) on value at risk, or "VaR", an estimate of how much the investment or area in question might lose with a given probability in a set time period, with the bank holding "economic"- or “risk capital” correspondingly; common parameters are 99% and 95% worst-case losses - i.e. 1% and 5% - and one day and two week (10 day) horizons.[28] These calculations are mathematically sophisticated, and within the domain of quantitative finance.

The regulatory capital quantum is calculated via specified formulae: risk weighting the exposures per highly standardized asset-categorizations, applying the aside frameworks, and the resultant capital — at least 12.9%[29] of these Risk-weighted assets (RWA) — must then be held in specific "tiers" and is measured correspondingly via the various capital ratios. In certain cases, banks are allowed to use their own estimated risk parameters here; these "internal ratings-based models" typically result in less required capital, but at the same time are subject to strict minimum conditions and disclosure requirements. As mentioned, additional to the capital covering RWA, the aggregate balance sheet will require capital for leverage and liquidity; this is monitored via[30] the LR, LCR, and NSFR ratios.

The financial crisis exposed holes in the mechanisms used for hedging (see Fundamental Review of the Trading Book § Background, Tail risk § Role of the global financial crisis (2007-2008), Value at risk § Criticism, and Basel III § Criticism). As such, the methodologies employed have had to evolve, both from a modelling point of view, and in parallel, from a regulatory point of view.

Regarding the modelling, changes corresponding to the above are: (i) For the daily direct analysis of the positions at the desk level, as a standard, measurement of the Greeks now inheres the volatility surface — through local- or stochastic volatility models — while re interest rates, discounting and analytics are under a "multi-curve framework". Derivative pricing now embeds considerations re counterparty risk and funding risk, amongst others,[31] through the CVA and XVA "valuation adjustments"; these also carry regulatory capital. (ii) For Value at Risk, the traditional parametric and "Historical" approaches, are now supplemented[32][27] with the more sophisticated Conditional value at risk / expected shortfall, Tail value at risk, and Extreme value theory. For the underlying mathematics, these may utilize mixture models, PCA, volatility clustering, copulas, and other techniques.[33] Extensions to VaR include Margin-, Liquidity-, Earnings- and Cash flow at risk, as well as Liquidity-adjusted VaR. For both (i) and (ii), model risk is addressed[34] through regular validation of the models used by the bank's various divisions; for VaR models, backtesting is especially employed.

Regulatory changes, are also twofold. The first change, entails an increased emphasis[35] on bank stress tests.[36] These tests, essentially a simulation of the balance sheet for a given scenario, are typically linked to the macroeconomics, and provide an indicator of how sensitive the bank is to changes in economic conditions, whether it is sufficiently capitalized, and of its ability to respond to market events. The second set of changes, sometimes called "Basel IV", entails the modification of several regulatory capital standards (CRR III is the EU implementation). In particular FRTB addresses market risk, and SA-CCR addresses counterparty risk; other modifications are being phased in from 2023.

To operationalize the above, Investment banks, particularly, employ dedicated "Risk Groups", i.e. Middle Office teams monitoring the firm's risk-exposure to, and the profitability and structure of, its various businesses, products, asset classes, desks, and / or geographies.[37] By increasing order of aggregation:

  1. Financial institutions will set[38][26][39] limit values for each of the Greeks, or other sensitivities, that their traders must not exceed, and traders will then hedge, offset, or reduce periodically if not daily; see the techniques listed below. These limits are set given a range [40] of plausible changes in prices and rates, coupled with the board-specified risk appetite[41] re overnight-losses.[42]
  2. Desks, or areas, will similarly be limited as to their VaR quantum (total or incremental, and under various calculation regimes), corresponding to their allocated [43] economic capital; a loss which exceeds the VaR threshold is termed a "VaR breach". RWA is correspondingly monitored from desk level[38] and upward.
  3. Each area's (or desk's) concentration risk will be checked[44][37][45] against thresholds set for various types of risk, and / or re a single counterparty, sector or geography.
  4. Leverage will be monitored, at very least re regulatory requirements via LR, the Leverage Ratio, as leveraged positions could lose large amounts for a relatively small move in the price of the underlying.
  5. Relatedly,[30] liquidity risk is monitored: LCR, the Liquidity Coverage Ratio, measures the ability of the bank to survive a short-term stress, covering its total net cash outflows over the next 30 days with "high quality liquid assets"; NSFR, the Net Stable Funding Ratio, assesses its ability to finance assets and commitments within a year. Any "gaps", also, must be managed.[46]
  6. Systemically Important Banks hold additional capital such that their total loss absorbency capacity, TLAC, is sufficient[47] given both RWA and leverage. (See also "MREL"[48] for EU institutions.)

Periodically,[49] these all are estimated under a given stress scenario — regulatory and,[50] often, internal — and risk capital,[22] together with these limits if indicated,[22][51] is correspondingly revisited (or optimized[52]). Here, more generally, these tests provide estimates for scenarios beyond the VaR thresholds, thus “preparing for anything that might happen, rather than worrying about precise likelihoods".[53] The approaches taken center either on a hypothetical or historical scenario,[35][27] and may apply increasingly sophisticated mathematics[54][27] to the analysis.

A key practice,[55] incorporating and assimilating the above, is to assess the Risk-adjusted return on capital, RAROC, of each area (or product). Here,[56] "economic profit" is divided by allocated-capital; and this result is then compared[56][23] to the target-return for the area — usually, at least the equity holders' expected returns on the bank stock[56] — and identified under-performance can then be addressed. (See similar below re. DuPont analysis.) The numerator, risk-adjusted return, is realized trading-return less a term and risk appropriate funding cost as charged by Treasury to the business-unit under the bank's funds transfer pricing (FTP) framework;[57] direct costs are (sometimes) also subtracted.[55] The denominator is the area's allocated capital, as above, increasing as a function of position risk;[58][59][55] several allocation techniques exist.[43] RAROC is calculated both ex post as discussed, used for performance evaluation (and related bonus calculations), and ex ante - i.e. expected return less expected loss - to decide whether a particular business unit should be expanded or contracted.[60]

Other teams, overlapping the above Groups, are then also involved in risk management. Corporate Treasury is responsible for monitoring overall funding and capital structure; it shares responsibility for monitoring liquidity risk, and for maintaining the FTP framework. Middle Office maintains the following functions also: Product Control is primarily responsible for insuring traders mark their books to fair value — a key protection against rogue traders — and for "explaining" the daily P&L; with the "unexplained" component, of particular interest to risk managers. Credit Risk monitors the bank's debt-clients on an ongoing basis, re both exposure and performance. In the Front Office — since counterparty and funding-risks span assets, products, and desks — specialized XVA-desks are tasked with centrally monitoring and managing overall CVA and XVA exposure and capital, typically with oversight from the appropriate Group.[31]

Performing the above tasks — while simultaneously ensuring that computations are consistent[61] over the various areas, products, teams, and measures — requires that banks maintain a significant investment[62] in sophisticated infrastructure, finance / risk software, and dedicated staff. Risk software often deployed is from FIS, Kamakura, Murex, Numerix and Refinitiv. Large institutions may prefer systems developed entirely "in house" - notably[63] Goldman Sachs ("SecDB"), JP Morgan ("Athena"), Jane Street, Barclays ("BARX"), BofA ("Quartz") - while, more commonly, the pricing library will be developed internally, especially as this allows for currency re new products or market features.

Corporate finance

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Contribution analytics: Profit and Loss for units sold at current fixed costs.
 
The same, for varying (scenario-based) Revenue levels, at current Fixed and Total costs.
Further information: Corporate finance § Financial risk management
See also: Asset and liability management, Treasury management, Strategic financial management, and Managerial risk accounting

In corporate finance, and financial management more generally,[64][10] financial risk management, as above, is concerned with business risk - risks to the business’ value, within the context of its business strategy and capital structure.[65] The scope here - ie in non-financial firms[12] - is thus broadened[9][66][67] (re banking) to overlap enterprise risk management, and financial risk management then addresses risks to the firm's overall strategic objectives, incorporating various (all) financial aspects[68] of the exposures and opportunities arising from business decisions, and their link to the firm’s appetite for risk, as well as their impact on share price. In many organizations, risk executives are therefore involved in strategy formulation: "the choice of which risks to undertake through the allocation of its scarce resources is the key tool available to management."[69]

Re the standard framework,[68] then, the discipline largely focuses on operations, i.e. business risk, as outlined. Here, the management is ongoing[10] — see following description — and is coupled with the use of insurance,[70] managing the net-exposure as above: credit risk is usually addressed via provisioning and credit insurance; likewise, where this treatment is deemed appropriate, specifically identified operational risks are also insured.[67] Market risk, in this context,[12] is concerned mainly with changes in commodity prices, interest rates, and foreign exchange rates, and any adverse impact due to these on cash flow and profitability, and hence share price.

Correspondingly, the practice here covers two perspectives; these are shared with corporate finance more generally:

  1. Both risk management and corporate finance share the goal of enhancing, or at least preserving, firm value.[64] Here,[9][68] businesses devote much time and effort to (short term) liquidity-, cash flow- and performance monitoring, and Risk Management then also overlaps cash- and treasury management, especially as impacted by capital and funding as above. More specifically re business-operations, management emphasizes their break even dynamics, contribution margin and operating leverage, and the corresponding monitoring and management of revenue, of costs, and of other budget elements. The DuPont analysis entails a "decomposition" of the firm's return on equity, ROE, allowing management to identify and address specific areas of concern,[71] preempting any underperformance vs shareholders' required return.[72] In larger firms, specialist Risk Analysts complement this work with model-based analytics more broadly;[73][74] in some cases, employing sophisticated stochastic models,[74][75] in, for example, financing activity prediction problems, and for risk analysis ahead of a major investment.
  2. Firm exposure to long term market (and business) risk is a direct result of previous capital investment decisions. Where applicable here[12][68][64] — usually in large corporates and under guidance from[76] their investment bankers — risk analysts will manage and hedge[70] their exposures using traded financial instruments to create commodity-,[77][78] interest rate-[79][80] and foreign exchange hedges[81][82] (see further below). Because company specific, "over-the-counter" (OTC) contracts tend to be costly to create and monitor — i.e. using financial engineering and / or structured products — ”standard” derivatives that trade on well-established exchanges are often preferred.[14][68] These comprise options, futures, forwards, and swaps; the "second generation" exotic derivatives usually trade OTC. Complementary to this hedging, periodically, Treasury may also adjust the capital structure, reducing financial leverage - i.e. repaying debt-funding - so as to accommodate increased business risk; they may also suspend dividends.[83]

Multinational corporations are faced with additional challenges, particularly as relates to foreign exchange risk, and the scope of financial risk management modifies significantly in the international realm.[81] Here, dependent on time horizon and risk sub-type — transactions exposure[84] (essentially that discussed above), accounting exposure,[85] and economic exposure[86] — so the corporate will manage its risk differently. The forex risk-management discussed here and above, is additional to the per transaction "forward cover" that importers and exporters purchase from their bank (alongside other trade finance mechanisms).

Hedging-related transactions will attract their own accounting treatment, and corporates (and banks) may then require changes to systems, processes and documentation;[87][88] see Hedge accounting, Mark-to-market accounting, Hedge relationship, Cash flow hedge, IFRS 7, IFRS 9, IFRS 13, FASB 133, IAS 39, FAS 130.

It is common for large corporations to have dedicated risk management teams — typically within FP&A or corporate treasury — reporting to the CRO; often these overlap the internal audit function (see Three lines of defence). For small firms, it is impractical to have a formal risk management function, but these typically apply the above practices, at least the first set, informally, as part of the financial management function; see discussion under Financial analyst.

The discipline relies on a range of software,[89] correspondingly, from spreadsheets (invariably as a starting point, and frequently in total[90]) through commercial EPM and BI tools, often BusinessObjects (SAP), OBI EE (Oracle), Cognos (IBM), and Power BI (Microsoft). [91]

Investment management

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Further information: Portfolio optimization, Active management, and Passive management
See also: Post-modern portfolio theory and Financial economics § Portfolio theory
 
Efficient Frontier. The hyperbola is sometimes referred to as the "Markowitz bullet", and its upward sloped portion is the efficient frontier if no risk-free asset is available. With a risk-free asset, the straight capital allocation line is the efficient frontier.
 
Here maximizing return and minimizing risk such that the portfolio is Pareto efficient (Pareto-optimal points in red).

Fund managers, classically,[92] define the risk of a portfolio as its variance[11] (or standard deviation), and through diversification the portfolio is optimized so as to achieve the lowest risk for a given targeted return, or equivalently the highest return for a given level of risk; these risk-efficient portfolios form the "Efficient frontier" (see Markowitz model). The logic here is that returns from different assets are highly unlikely to be perfectly correlated, and in fact the correlation may sometimes be negative. In this way, market risk particularly, and other financial risks such as inflation risk (see below) can at least partially be moderated by forms of diversification.

A key issue, however, is that the (assumed) relationships are (implicitly) forward looking. As observed in the late-2000s recession, historic relationships can break down, resulting in losses to market participants believing that diversification would provide sufficient protection (in that market, including funds that had been explicitly set up to avoid being affected in this way[93]). A related issue is that diversification has costs: as correlations are not constant it may be necessary to regularly rebalance the portfolio, incurring transaction costs, negatively impacting investment performance;[94] and as the fund manager diversifies, so this problem compounds (and a large fund may also exert market impact). See Modern portfolio theory § Criticisms.

Addressing these issues, more sophisticated approaches have been developed, both to defining risk, and to the optimization itself. (Respective examples: (tail) risk parity, focuses on allocation of risk, rather than allocation of capital; the Black–Litterman model modifies the "Markowitz optimization", to incorporate the views of the portfolio manager.[95]) Relatedly, modern financial risk modeling employs a variety of techniques — including value at risk, [96] historical simulation, stress tests, and extreme value theory — to analyze the portfolio and to forecast the likely losses incurred for a variety of risks and scenarios.

Here, guided by the analytics, Fund Managers (and traders) will apply specific risk hedging techniques.[92][11] As appropriate, these may relate to the portfolio as a whole or to individual holdings:

Further, and more generally, various safety-criteria may guide overall portfolio construction. The Kelly criterion[108] will suggest - i.e. limit - the size of a position that an investor should hold in her portfolio. Roy's safety-first criterion[109] minimizes the probability of the portfolio's return falling below a minimum desired threshold. Chance-constrained portfolio selection similarly seeks to ensure that the probability of final wealth falling below a given "safety level" is acceptable.

Managers may also employ factor models[110] (generically APT) to measure exposure to macroeconomic and market risk factors[111] using time series regression. Ahead of an anticipated movement in any of these factors, the Manager may then, as indicated, reduce holdings, hedge, or purchase offsetting exposure. Inflation for example, although impacting all securities,[112] can be managed [113][114] at the portfolio level by appropriately [115] increasing exposure to inflation-sensitive stocks, and / or by investing in tangible assets, commodities and inflation-linked bonds; the latter may also provide a direct hedge.[116]

In parallel with all above,[117][118] managers — active and passive — periodically monitor and manage tracking error, i.e. underperformance vs a "benchmark". Here, they will use attribution analysis preemptively so as to diagnose the source early, and to take corrective action: realigning, often factor-wise, on the basis of this "feedback". [118] [119] As relevant, they will similarly use style analysis to address style drift. See also Fixed-income attribution.

Given the complexity of these analyses and techniques, Fund Managers typically rely on sophisticated software (as do banks, above). Widely used platforms are provided by BlackRock (Aladdin), Refinitiv (Eikon), Finastra, Murex, Numerix, MPI and Morningstar.

See also

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Articles
Discussion
Lists

Bibliography

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Financial institutions

  • Allen, Steve L. (2012). Financial Risk Management: A Practitioner's Guide to Managing Market and Credit Risk (2 ed.). John Wiley. ISBN 978-1118175453.
  • Coleman, Thomas (2011). A Practical Guide to Risk Management (PDF). CFA Institute. ISBN 978-1-934667-41-5.
  • Crockford, Neil (1986). An Introduction to Risk Management (2 ed.). Woodhead-Faulkner. ISBN 0-85941-332-2.
  • Crouhy, Michel; Galai, Dan; Mark, Robert (2013). The Essentials of Risk Management (2 ed.). McGraw-Hill Professional. ISBN 9780071818513.
  • Christoffersen, Peter (2011). Elements of Financial Risk Management (2 ed.). Academic Press. ISBN 978-0-12-374448-7.
  • Farid, Jawwad Ahmed (2013). Models at Work: A Practitioner's Guide to Risk Management. Palgrave Macmillan. ISBN 978-1137371638.
  • Hull, John (2023). Risk Management and Financial Institutions (6 ed.). John Wiley. ISBN 978-1-119-93248-2.
  • McNeil, Alexander J.; Frey, Rüdiger; Embrechts, Paul (2015), Quantitative Risk Management. Concepts, Techniques and Tools, Princeton Series in Finance (revised ed.), Princeton, NJ: Princeton University Press, ISBN 9780691166278, MR 2175089, Zbl 1089.91037
  • Miller, Michael B. (2019). Quantitative Financial Risk Management. John Wiley. ISBN 9781119522201.
  • Roncalli, Thierry (2020). Handbook of Financial Risk Management. Chapman & Hall. ISBN 9781138501874.
  • Tapiero, Charles (2004). Risk and Financial Management: Mathematical and Computational Methods. John Wiley & Son. ISBN 0-470-84908-8.
  • van Deventer; Donald R.; Kenji Imai; Mark Mesler (2004). Advanced Financial Risk Management: Tools and Techniques for Integrated Credit Risk and Interest Rate Risk Management. John Wiley. ISBN 978-0-470-82126-8.
  • Wernz, Johannes (2021). Bank Management and Control: Strategy, Pricing, Capital and Risk Management (2 ed.). Springer. ISBN 978-3030428686.

Corporations

Portfolios

References

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  1. ^ Peter F. Christoffersen (22 November 2011). Elements of Financial Risk Management. Academic Press. ISBN 978-0-12-374448-7.
  2. ^ Financial Risk Management, Finance Glossary. Gartnergartner.com
  3. ^ W. Kenton (2021). "Harry Markowitz", investopedia.com
  4. ^ Markowitz, H.M. (March 1952). "Portfolio Selection". The Journal of Finance. 7 (1): 77–91. doi:10.2307/2975974. JSTOR 2975974.
  5. ^ a b c See § "Does Corporate Risk Management Create Value?" in Capital Budgeting Applications and Pitfalls. Ch 13 of Ivo Welch (2022). Corporate Finance, 5 Ed. IAW Publishers. ISBN 978-0984004904
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  12. ^ a b c d e f See "Market Risk Management in Non-financial Firms", in Carol Alexander, Elizabeth Sheedy eds. (2015). The Professional Risk Managers’ Handbook 2015 Edition. PRMIA. ISBN 978-0976609704
  13. ^ See for example, "Corporate Finance: First Principles", in Aswath Damodaran (2014). Applied Corporate Finance. Wiley. ISBN 978-1118808931
  14. ^ a b Jonathan Lewellen (2003). Financial Management - Risk Management. MIT OCW
  15. ^ Why Corporations Hedge; Ch 3.7 in Baranoff et. al.
  16. ^ KRISHNAMURTI CHANDRASEKHAR; Krishnamurti & Viswanath (eds.) "; Vishwanath S. R. (2010-01-30). Advanced Corporate Finance. PHI Learning Pvt. Ltd. pp. 178–. ISBN 978-81-203-3611-7.
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  28. ^ Pearson, Neil (2002). Risk Budgeting: Portfolio Problem Solving with Value-at-Risk. John Wiley & Sons. ISBN 978-0-471-40556-6.
  29. ^ Steven Nickolas (2023). "Tier 1 Capital vs. Tier 2 Capital", Investopedia
  30. ^ a b PwC (2016). An overview of the LCR, NSFR and LR
  31. ^ a b International Association of Credit Portfolio Managers (2018). "The Evolution of XVA Desk Management"
  32. ^ Saunders, Anthony; Allen, Linda (2010). Credit Risk Management In and Out of the Financial Crisis: New Approaches to Value at Risk and Other Paradigms. Hoboken, NJ: John Wiley & Sons. ISBN 978-0-470-62236-0.
  33. ^ See for example III.A.3, in Carol Alexander, ed. (January 2005). The Professional Risk Managers' Handbook. PRMIA Publications. ISBN 978-0976609704
  34. ^ Riccardo Rebonato (N.D.). Theory and Practice of Model Risk Management.
  35. ^ a b Troy Segal (2021). "What Is a Bank Stress Test? How It Works, Benefits, and Criticism", Investopedia
  36. ^ Basel Committee on Banking Supervision (2009). "Principles for sound stress testing practices and supervision"
  37. ^ a b International Association of Credit Portfolio Managers (2022). "Risk mitigation techniques in credit portfolio management"
  38. ^ a b Bank for International Settlements (2019). MAR12 - Definition of trading desk
  39. ^ Open Risk Manual (2021). "Risk Limit"
  40. ^ Bank for International Settlements (2001). Principles for the Management and Supervision of Interest Rate Risk
  41. ^ Open Risk Manual (2021). "Limit framework"
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  44. ^ Basel Committee on Banking Supervision (1999). "Risk Concentrations Principles"
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  46. ^ Bank for International Settlements (2016). Interest rate risk in the banking book
  47. ^ Bank for International Settlements (2017). TLAC – Executive Summary
  48. ^ "Minimum Requirement for own funds and Eligible Liabilities"; see MREL, treasurers.org
  49. ^ Basel Committee on Banking Supervision (2009). "Range of practices and issues in economic capital frameworks"
  50. ^ KPMG (2016)."Stress testing - A benchmark analysis of systemically important financial institutions"
  51. ^ Financial Stability Board (2013). "Principles for An Effective Risk Appetite Framework"
  52. ^ KPMG (2017). "Balance sheet optimisation:the returns dilemma for banks"
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  75. ^ See for example this problem (from John Hull's Options, Futures, and Other Derivatives), discussing cash position modeled stochastically.
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  97. ^ a b c d e f g For discussion and examples re calculating the appropriate "optimal hedge ratio" - based on beta, delta, or duration - and then executing, see: Roger G . Clarke (1992). "Options and Futures: A Tutorial". CFA Institute Research Foundation
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