Chapter 12 Market Risk

Overview This chapter discusses how market risk arises and how it can threaten the solvency of FIs. We discuss the importance of market risk. We learn how to measure market risk. We learn about the concepts of the RiskMetrics model, the back simulation approach and the Monte Carlo simulation approach. We discuss how regulators measure market risk exposures for capital adequacy purposes. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

Introduction Market risk is the uncertainty resulting from changes in market prices. It can be measured over periods as short as one day. Usually measured in terms of dollar exposure amount or as a relative amount against some benchmark. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

Market Risk Measurement Why is Market Risk Measurement (MRM) Important? Management information, Setting risk limits, Resource allocation, Performance evaluation, Regulation. Calculating Market Risk Exposure RiskMetrics, Historic or back simulation, Monte Carlo simulation. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

The RiskMetrics Model Developed after a former chairman of JPMorgan requested a single dollar number at close of business from his team regarding the firm’s market risk exposure. Market risk = Estimated potential loss under adverse circumstances. Daily earnings at risk = Dollar market value of the position × Price volatility. RiskMetrics calculates daily earnings at risk for: Fixed income, Foreign exchange, Equities. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

The Market Risk of Fixed-Income Securities Daily price volatility can be stated as: (-MD) × adverse daily yield move where MD = D/(1+R) Modified duration = MacAulay duration/(1+R) Confidence intervals: If we assume that changes in the yield are normally distributed, we can construct confidence intervals around the projected DEAR. Assuming normality, 90% of the time the disturbance will be within 1.65 standard deviations of the mean. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

The Market Risk of Fixed-Income Securities Confidence intervals (example): Suppose that we are long in 7-year zero-coupon bonds and we define ‘bad’ yield changes such that there is only 5% chance of the yield change being exceeded in either direction. Assuming normality, 90% of the time yield changes will be within 1.65 standard deviations of the mean. If the standard deviation is 10 basis points, this corresponds to 16.5 basis points. The concern is that yields will rise. Probability of yield increases greater than 16.5 basis points is 5%. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

The Market Risk of Fixed-Income Securities Confidence intervals (example): Price volatility = (-MD) × (Potential adverse change in yield) = (-6.527) × (0.00165) = -1.077% DEAR = Market value of position × (Price volatility) = ($1,000,000) × (0.01077) = $10,770 To calculate the potential loss for more than one day: Market value at risk (VAR) = DEAR × N Example: For a five-day period, VAR = $10,770 × 5 = $24,082 Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

Foreign Exchange In the case of foreign exchange, DEAR is computed in the same way as interest rate risk. Dollar equivalent value of position = FX position × spot exchange rate DEAR = dollar value of position × FX volatility Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

Equities CAPM states that: Total risk = systematic risk + unsystematic risk. For equities, if the portfolio is well-diversified then DEAR = dollar value of position × stock market return volatility where the market return volatility is taken as 1.65 sM. For less well-diversified FIs, the effect of unsystematic risk on the value of the trading position would need to be added. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

Portfolio Aggregation Assume three individual DEARs: Seven-year zero coupon bonds = $10,770, CHF spot: $9,320, Australian equities: $33,000. DEARs are not additive, i.e. total DEAR ≠ $53,090. Simple addition ignores correlations. Portfolio DEAR calculated using a correlation matrix. Three asset case: DEAR portfolio = [DEARa2 + DEARb2 + DEARc2 + 2rab × DEARa *× DEARb + 2rac × DEARa × DEARc + 2rbc × DEARb × DEARc]1/2 Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

The Historic or Back Simulation Approach Advantages of back simulation: Simplicity, No normal distribution assumption, No necessity to calculate correlations or standard deviations of asset returns. Essential idea: Revaluation of current asset portfolio on basis of past actual prices (usually previous 500 days). Then calculate 5% worst-case (25th lowest value of 500 days) outcomes. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

The Historic or Back Simulation Approach Calculation of value at risk (VAR): Measure exposure, Measure sensitivity: calculate its delta, Measure risk, Measure risk again, Rank days by risk from worst to best, VAR. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

The Historic or Back Simulation Approach Weaknesses: Disadvantage: 500 observations is not very many from a statistical standpoint. Increasing the number of observations by going back further in time is not desirable. (Could weight recent observations more heavily and go further back.) Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

The Monte Carlo Simulation Approach Addresses potential problem of limited observation by adding additional observations. Steps involved: Calculation of historic variance–covariance matrix, Decomposition of matrix into two matrices, Decomposition allows us to set up scenarios, Calculation of VAR. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

Regulatory Models: The BIS Standardised Framework Two major ways of calculating market risk exposures: Simple standardised framework, Use of internal models (to be approved by regulatory supervisor). See: www.bis.org Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

Fixed Income and BIS Distinction between: Further distinction between: Specific risk charge: risk weights × absolute dollar values of long and short positions General market risk charge: reflect modified durations × expected interest rate shocks for each maturity. Further distinction between: Vertical offsets: adjust for basis risk, Horizontal offsets: either within time zones or between time zones. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

Foreign Exchange and BIS Standardised model requires calculation of net exposure. Net exposure to be converted into $ at current spot exchange rate. Capital requirement equal to 8% of the total long position of the FI. Model involves partial offsetting of currency risk. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

Equities and BIS Remember the major sources of risk inherent in equities: Unsystematic risk, Systematic risk. BIS and unsystematic risk: 4% × gross position in an equity. BIS and systematic risk: reflected in the net long or net short position (BIS and unsystematic risk: 4% × gross position in an equity). BIS and systematic risk: reflected in the net long or net short position (y factor). Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher

The BIS Regulations and Large Bank Internal Models In calculating DEAR, adverse change in rates defined as 99th percentile (rather than 95th under RiskMetrics). Minimum holding period is 10 days (means that RiskMetrics’ daily DEAR is multiplied by 10). Capital charge will be the higher of: Previous day’s VAR (or DEAR  10), Average Daily VAR over previous 60 days times a multiplication factor  3. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett Slides prepared by Maike Sundmacher