1. Market Risk Chapter 10 © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. McGraw-Hill/Irwin Part A http://davidmlane.com/hyperstat/z_table.html http://www.statsoft.com/textbook/sttable.htmlhttp://www.statsoft.com/textbook/sttable.html for 50% table OR http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htmhttp://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm for 100% table

2. 10-2 Overview  This chapter discusses the nature of market risk and appropriate measures Dollar exposure RiskMetrics Historic or back simulation Monte Carlo simulation Links between market risk and capital requirements

3. 10-3 Bank Asset Categories  Classification of bank assets determines how they are reported: Trading  Mark-to-market gains/losses flow to Income statement and on to SE Held For Sale  Mark-to-market gains/losses bypass income statement, but flow directly to SE Held For Investment  Market value is ignored  Text breaks into two categories Banking Book (Held for Investment) Trading Book (Trading and Held for Sale)

4. 10-4 Bank Asset Categories  Trading accounts are small  Held for Sale category is usually very limited  Vast majority of assets are Held for Investment (Banking Book) Market risk is not measured  Severely limits scope of any mark-to-market reporting

5. 10-5 Trading Book vs “Banking Book”

6. 10-6 Trading Risks  Trading exposes banks to risks 1995 Barings Bank 1996 Sumitomo Corp. lost $2.6 billion in commodity futures trading AllFirst/ Allied Irish $691 million loss  Allfirst eventually sold to Buffalo based M&T Bank due to dissatisfaction among stockholders of Allied Irish Untold trading position losses at Merrill Lynch, Lehman et al in 2008

7. 10-7 Implications  Emphasizes importance of: Measurement of exposure Control mechanisms for direct market risk—and employee created risks Hedging mechanisms  Of interest to regulators

8. 10-8 Market Risk  Market risk is the uncertainty resulting from changes in market prices. Affected by other risks such as interest rate risk and FX risk (factors) 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.

9. 10-9 Market Risk Measurement  Important in terms of: Management information Setting limits Resource allocation (risk/return tradeoff) Performance evaluation Regulation  BIS and Fed regulate market risk via capital requirements leading to potential for overpricing of risks  Allowances for use of internal models to calculate capital requirements

10. 10-10 Calculating Market Risk Exposure  Generally concerned with estimated potential loss under adverse circumstances.  Three major approaches of measurement JPM RiskMetrics (or variance/covariance approach) Historic or Back Simulation (later) Monte Carlo Simulation (later)

11. 10-11 JP Morgan RiskMetrics Model Idea is to determine the daily earnings at risk = dollar value of position × price sensitivity × potential adverse move in yield or, DEAR = Dollar market value of position × Price volatility. Can be stated as (MD) × (potential adverse daily yield move) where, MD = D/(1+R) Modified duration = MacAulay duration/(1+R)

12. 10-12 JP Morgan RiskMetrics Model Idea is to determine the daily earnings at risk = dollar value of position × price sensitivity × potential adverse move in yield or, DEAR = Dollar loss on what we define as a bad day in the market A bad day of interest rate movements is measuring interest rate risk A bad day in the exchange rate if measuring currency risk A bad day of credit spread movements if measuring credit risk

13. 10-13 DEAR  Simplified: Dollar Sensitivity of portfolio x estimated adverse move in factor  For fixed income securities, dollar sensitivity of portfolio = MD% x $PV  For Treasury securities, the risk factor we measure against is market interest rate changes

14. 10-14 DEAR Denomination  The prices sensitivity% in the first term must be consistent with the measure used for the adverse move  For fixed income, if you use MD% as the base measure, that means you are suing 1% as a base You must sue s consistent measure for the factor. In this case, use 1.0 stated as a whole number

15. 10-15 An Example  $100,000 portfolio of fixed income securities with MD% of 5%.  Estimated adverse interest rate move for one day is.30%  DEAR = $100,000 x.05 x.30 = $1,500.  DEAR is a product of how much you own, how volatile it is and how much you think rates might go against you on a bad day.

16. 10-16 An Example – What is New?  You know hw to find the PV of the position Calculate price  You know how find %MD Calculate modified duration  How do you define “a bad day”? Riskmetrics variance/covariance approach Historic or back simulation Monte Carlo analysis

17. 10-17 Riskmetrics variance/covariance approach  Steps to define “a bad period” Select the measurement period – we use a period of one day for DEAR Compile data on past “one-period” changes in the risk factor (interest rate?) Calculate SD and mean to create a normal distribution  Note that SD will be a one-day SD for DEAR Select how bad you think “bad” is  The worst 5% of days?  The worst 1% of days  The worst.01% of days?

18. 10-18 Confidence Intervals If we assume that changes in the yield are normally distributed, we can construct confidence intervals around the projected DEAR. (Other distributions can be accommodated but normal is generally sufficient). Assuming normality, 90% of the time the disturbance will be within 1.65 standard deviations of the mean.  (5% of the extreme values greater than +1.65 standard deviations and 5% of the extreme values less than -1.65 standard deviations)

19. 10-19 Adverse 7-Year Rate Move Computed: http://davidmlane.com/hyperstat/z_table.htmlhttp://davidmlane.com/hyperstat/z_table.html Table: http://www.statsoft.com/textbook/sttable.html

20. 10-20 Confidence Intervals: Example p271 Suppose that we are long in 7-year zero-coupon bonds and the market rate is 7.24682 %. 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. Concern is that yields will rise. Probability of yield increases greater than 16.5 basis points is 5%.

21. 10-21 Confidence Intervals: Example  MD = 7/(1+.072468) = 6.527  Price volatility = (MD)  (Potential adverse change in yield) = (6.527)  (0.00165) = 1.077% DEAR = Market value of position  (Price volatility) = ($1,000,000)  (.01077) = $10,770

22. 10-22 Confidence Intervals: Example  To calculate the potential loss for more than one day: Market value at risk (VAR N ) = DEAR ×  Example: For a five-day period, VAR 5 = $10,770 × = $24,082  Note that DEAR is nothing more than a VAR with one day as the period

23. 10-23 Foreign Exchange  In the case of Foreign Exchange, DEAR is computed in the same fashion we employed for interest rate risk.  We can skip the step of converting yield changes to price changes because we directly measure price change.  DEAR = dollar value of position × FX rate volatility volatility where the FX rate volatility is taken as 1.65  FX http://www.oanda.com/convert/fxhistory

24. 10-24 Foreign Exchange Example in Text p273  Have position of E1,600,000  Exchange rate = 1.6E per $ or 1E=$.625  $PV of position = $1,000,000  You find that daily SD of exchange rate= 55.5 BP  You want a “worst 5% of bad days” level, so you choose a confidence interval of 90%  For a 90% confidence interval, Z= 1.65  1.65 x 55.5BP =1.65x.00555 =.00932  $PV x price volatility = $1,000,000 =.00932 = $9,320