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P2.T5. Market Risk Measurement & Management Gunter Meissner

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P2.T5. Market Risk Measurement & Management Gunter Meissner P2.T5. Market Risk Measurement & Management Gunter Meissner, Correlation Risk Modeling and Management Bionic Turtle FRM Study Notes Meissner, Chapter 1: Some Correlation Basics DESCRIBE FINANCIAL CORRELATION RISK AND THE AREAS IN WHICH IT APPEARS IN FINANCE. ... 4 EXPLAIN HOW CORRELATION CONTRIBUTED TO THE GLOBAL FINANCIAL CRISIS OF 2007 TO 2009. ................................................................................................................................. 9 DESCRIBE THE STRUCTURE, USES, AND PAYOFFS OF A CORRELATION SWAP. ........................ 13 ESTIMATE THE IMPACT OF DIFFERENT CORRELATIONS BETWEEN ASSETS IN THE TRADING BOOK ON THE VAR CAPITAL CHARGE. .......................................................................................... 14 EXPLAIN THE ROLE OF CORRELATION RISK IN MARKET RISK AND CREDIT RISK. ....................... 16 RELATE CORRELATION RISK TO SYSTEMIC AND CONCENTRATION RISK. ................................. 17 CHAPTER 1: MEISSNER’S QUESTIONS AND ANSWERS (Q&A) ............................................... 21 Meissner, Chapter 2: Empirical Properties of Correlation: How Do Correlations Behave in the Real World? DESCRIBE HOW EQUITY CORRELATIONS AND CORRELATION VOLATILITIES BEHAVE THROUGHOUT VARIOUS ECONOMIC STATES. ............................................................................................. 26 CALCULATE A MEAN REVERSION RATE USING STANDARD REGRESSION AND CALCULATE THE CORRESPONDING AUTOCORRELATION. ............................................................................... 28 IDENTIFY THE BEST-FIT DISTRIBUTION FOR EQUITY, BOND, AND DEFAULT CORRELATIONS. ...... 32 CHAPTER 2: MEISSNER’S QUESTIONS AND ANSWERS (Q&A) ............................................... 34 Meissner, Chapter 5 :Financial Correlation Modeling – Bottom-Up Approaches (pages 126-134 only) EXPLAIN THE PURPOSE OF COPULA FUNCTIONS AND THE TRANSLATION OF THE COPULA EQUATION. ....................................................................................................................... 36 DESCRIBE THE GAUSSIAN COPULA AND EXPLAIN HOW TO USE IT TO DERIVE THE JOINT PROBABILITY OF DEFAULT OF TWO ASSETS. ........................................................................ 37 SUMMARIZE THE PROCESS OF FINDING THE DEFAULT TIME OF AN ASSET CORRELATED TO ALL OTHER ASSETS IN A PORTFOLIO USING THE GAUSSIAN COPULA. ........................................... 40 CHAPTER 5: MEISSNER’S QUESTIONS AND ANSWERS ......................................................... 41 2 Meissner, Chapter 1: Some Correlation Basics Describe financial correlation risk and the areas in which it appears in finance. Explain how correlation contributed to the global financial crisis of 2007 to 2009. Describe the structure, uses, and payoffs of a correlation swap. Estimate the impact of different correlations between assets in the trading book on the VaR capital charge. Explain the role of correlation risk in market risk and credit risk. Relate correlation risk to systemic and concentration risk. Key ideas and/or definitions in this chapter To be developed on next revision TBD-2 3 Describe financial correlation risk and the areas in which it appears in finance. Financial correlation risk is the risk of loss due to an adverse change in correlation between two or more variables. For example: Wrong-way risk is adverse correlation between a bond issuer (issued bond is the reference asset below) and the bond insurer (bond insurer is the CDS Seller below)1 Correlation risk includes co-movement between non-financial variables (e.g., economic, political, technical). For most risk measures (e.g., volatility, value at risk), an increase in correlation implies an increase in the risk of financial loss. During the global financial crisis (GFC), famously the correlations spiked. This is a typical symptom of a crisis: correlation increase, or spike, even approaching 1.0 in severe situations. Examples from Meissner2: Sovereign debt and currency value: In 2012, US exporters were hurt by a decreasing Euro currency and increasing Euro sovereign debt Geopolitical tensions: Middle East tensions can hurt demand and increase oil prices Correlated markets and economies: A slowing gross domestic product (GDP) in the United States can hurt Asian and European exporters and investors since economies and financial markets are correlated worldwide. 1 Inspired by Meissner’s Figure 1.1 (Gunter Meissner, Correlation Risk Modeling and Management, New York: Wiley, 2014) 2 Gunter Meissner, Correlation Risk Modeling and Management, New York: Wiley, 2014 4 Correlation risk via Meissner’s example3 of a credit default swap (CDS) A CDS transfers credit risk from an investor to a counterparty. For example, An investor invested $1.0 million in a bond issued by Spain (aka, the reference asset) but worries about its default. To hedge default risk, he bought a CDS from a French bank, BNP Paribas (aka, the counterparty who sells the CDS and is synthetically long the reference). o The investor is protected against default from Spain: in case of default, the CDS counterparty (BNP Paribas) will pay the originally invested $1.0 million to the investor (if we assume the recovery rate and accrued interest are zero) o The value of the CDS, the fixed CDS spread s, is determined by the default probability of the reference entity Spain. The worst-case scenario is the joint default of Spain and BNP Paribas, in which case the investor will lose his entire investment in the Spanish bond of $1.0 million. The investor is exposed to default correlation risk between the reference asset r (Spain) and the counterparty c (BNP Paribas). o The spread s is also determined by the joint default correlation of BNP Paribas and Spain. If that default correlation increases, the present value of the CDS for the investor will decrease and the investor will suffer a paper loss. o Because both Spain and BNP Paribas are in Europe, we assume that there is a positive default correlation between the two. This investor has wrong-way correlation risk (aka, short wrong-way risk). Meissner’s4 example continued: Below (our render of Meissner’s Figure 1.25), we see that above ρ = −0.30, higher correlation implies a lower CDS spread. Why? An increasing ρ indicates a higher probability that both the reference and counterparty simultaneously default. In extremis (ie, ρ = 1.0) the CDS is worthless and deserves no spread. For a correlation from −1.0 to about −0.30, the CDS spread increases slightly, which is perhaps non-intuitive. But a less negative correlation indicates a higher probability of either Spain or BNP Paribas defaulting. If only Spain defaults, the CDS buyer collects the payoff; If only BNP defaults, the CDS buyer must repurchase insurance, possibly at a higher price. The relationship is non- monotonous; the CDS spread alternates between increasing and decreasing. 3 Gunter Meissner, Correlation Risk Modeling and Management, New York: Wiley, 2014 4 Gunter Meissner, Correlation Risk Modeling and Management, New York: Wiley, 2014 5 Ibid but actual spreadsheet constructed by David Harper 5 Financial correlations are common in finance. Meissner considers five areas: (1) investments and correlation, (2) trading and correlation, (3) risk management and correlation, (4) the global financial crisis and correlation, and (5) regulation and correlation. Investments and correlation In Markowitz's portfolio theory (MPT, including CAPM), diversification is a benefit and diversification is imperfect (less than one) correlation. For given asset returns and volatilities, a lower correlation will decrease for the same level of expected return. For example: Consider a two-asset portfolio that performed as below: The simple return is given by, (St – St-1)/St-1. Over the illustrated time frame (from 2014 to 2019) the average returns are: µX= 13.70% and µY = 5.22%. The portfolio’s return depends on the weights and is given by the following (in this example, if the weights are equal, then the portfolio return is +9.46%): = + The sample standard deviation of returns (aka, volatility) is given by: = ( − ) − In this example, the volatilities for each asset are: = 17.20% and = 10.32%. 6 For example (continued): Covariance. The covariance measures how two variables “covary” or move together. The covariance measures the strength of the linear relationship between two variables. The covariance of returns for assets X and Y is derived with equation: = ( − )( − ) − In our example, CovXY = −0.0117. But the covariance is not easy to interpret. It is much more convenient to use the Pearson correlation coefficient, ρ(x,y), which returns scale-free (ie, unitless) values between −1.0 and +1.0. This correlation coefficient is: = In this example rXY = −0.6594; ie, these asset returns are negatively correlated. We can calculate the standard deviation for our two-asset portfolio P as: = + + Under equal (50/50) weights, the above portfolio volatility is , = . %. The standard deviation is probably the most common measure of risk in finance. Put simply, a higher (lower) standard deviation implies higher (lower) risk. Classical finance assumes risk-averse investors who prefer, all other things being equal (aka, ceteris paribus), lower risk and therefore lower standard deviations. But a risk-seeking investor would prefer a higher standard deviation because it provides the upside possibility of higher payoffs! This is also a criticism of standard deviation as a risk measure: it is indifferent
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