“Money is better than poverty, if only for financial reasons,”

1. “Money is better than poverty, if only for financial reasons,” Woody Allen Saunders & Cornett, Financial Institutions Management, 4th ed.

2. Market Risk • The impact of unanticipated changes in market conditions (interest rates, exchange rates, securities prices) on the market value and earnings of the FI. • Widespread adoption of Value at Risk (VaR) methodologies. • VaR is the minimum losses incurred under adverse market conditions. That is, if tomorrow is a “bad day” measured statistically such that only 1% of all days have even worse conditions. • First commercially available VaR model was RiskMetrics. Saunders & Cornett, Financial Institutions Management, 4th ed.

3. The Concept of VAR • Example of VAR applied to market risk. • Market price of equity = $80 with estimated daily standard deviation = $10. • If tomorrow is a “bad day” (1 in 100 worst) then what is the value at risk? • If normally distributed, then the cutoff is 2.33 below the mean = $80 – 2.33(10) = $56.70. 99% VAR = $23.30 Figure 6.1. Saunders & Cornett, Financial Institutions Management, 4th ed.

4. Saunders & Cornett, Financial Institutions Management, 4th ed.

5. Appendix 1.1A Brief Overview of Key VAR Concepts • Banks hold capital as a cushion against losses. What is the acceptable level of risk? • Losses = change in the asset’s value over a fixed credit horizon period (1 year) due to credit events. • Figure 1.1- normal loss distribution. Figure 1.2 – skewed loss distribution. Mean of distribution = expected losses (reserves). • Unexpected Losses (UL) = %tile VAR. Losses exceed UL with probability = %. • Definition of credit event: • Default Mode: only default • Mark-to-market: all credit upgrades, downgrades & default. Saunders & Cornett, Financial Institutions Management, 4th ed.

6. FIGURE 1.1 Saunders & Cornett, Financial Institutions Management, 4th ed.

7. Saunders & Cornett, Financial Institutions Management, 4th ed.

8. Saunders & Cornett, Financial Institutions Management, 4th ed.

9. RiskMetrics • Daily Earnings at Risk (DEAR) = (Dollar MV of position) x (Price sensitivity of position) x (Potential adverse move) = (Dollar MV of position) x (Price volatility) • DEAR calculated for each source of market volatility: interest rates, security prices, exchange rates. RiskMetrics uses a 95th percentile VAR. BIS uses a 99th percentile for capital requirements. • The VaR is calculated over an N-day period VAR = DEAR x N • Finally, aggregate VAR over the entire portfolio using correlation coefficients. Saunders & Cornett, Financial Institutions Management, 4th ed.

10. DEAR for Interest Rate Risk • Use duration model: • DEAR = -MD(R)/(1+R) • FI has a $10m long position in a bond with MD=12.5 yrs. Exposed to interest rate increases. Only a 1% chance that rates will increase more than 10 bp per day. • DEAR = -12.5($10m)(.0010) = -$125,000 • 5 day VaR = 125,000 x 5 = $279,508 Saunders & Cornett, Financial Institutions Management, 4th ed.

11. DEAR for Exchange Rate Risk • US FI has $100m short position in euros. Exposed to increases in euro/$ FX rate. • There is only a 1% chance that the euro will go up more than 50 bp per day. • DEAR = ($100m) x (.0050) = $500,000 • 5 day VaR = $500,000 x 5 = $1,118,034 Saunders & Cornett, Financial Institutions Management, 4th ed.

12. Portfolio DEAR • For the 2 risk example: • DEAR = [DEAR2intrate + DEAR2FXrate + 2int,FXDEARintrateDEARFXrate]0.5 • Correlation coeff. int,FX = -.05 • DEAR = [125,0002 + 500,0002 + 2(-.05)(125,000)(500,000)]0.5 = $509,289 • Portfolio DEAR is NOT the sum of the individual DEARs if correlations are < 1. • 5 day Portfolio VAR = $509,289 x 5 = $1,138,804 Saunders & Cornett, Financial Institutions Management, 4th ed.

13. Backtesting Using the Historic Approach • Actual security distributions are not normal. Exhibit skewness and fat tails. • Use current positions. • Apply to observed market fluctuations over the past 500 days. • For a 1% VAR, the 5th worst day out of 500. For a 5% VAR, the 25th worst day of 500. Saunders & Cornett, Financial Institutions Management, 4th ed.

14. Example of Back Simulation Using a Bond Portfolio • $50 million bond portfolio with MD=4.5 yrs • 20 days of actual rate changes • DEAR=$50m x MD x R • The 5th worst day is day 3 for a Loss of $900,000. If this were 500 observations, then the 1% VaR=$900,000 Saunders & Cornett, Financial Institutions Management, 4th ed.

15. Advantages & Disadvantages of Back Simulation • Non-parametric. • Uses available data. But insufficient no. of observations. • But, past data may not be indicative of the future. • Monte Carlo simulation generates additional observations that conform with historical distribution by multiplying the var/covariance matrix by a random number generator. Typically constructs from 10,000 to 100,000 observations. Saunders & Cornett, Financial Institutions Management, 4th ed.

16. The BIS Standardized Market Risk Framework • Can use the standardized framework or internal models. • Capital Charge = 99th %-DEAR x 3 x 10 • If use internal models, must be approved and back-tested. Traffic light system: If underestimates risk < 4 days out of 250, then green light and multiplier=3 If between 4-9 days of underestimates of risk, then yellow light and multiplier > 3. If 10 days or more underestimated risk, then red light and multiplier is set at 4. Saunders & Cornett, Financial Institutions Management, 4th ed.

17. BIS Standardized Model for Fixed Income Securities • Specific Risk Charge = measures risk of liquidity or credit event. Multiply risk weight x position amount. • Risk weights: 0% (US Treasuries), .25%-1.6% for investment grade (qual) corporate of varying maturities, 4%-8% for junk (non qual) corporate of varying maturities. • General Market Risk Charge = MD x interest rate shock expected for each maturity • Vertical Offsets = disallowance factors limiting hedging of long and short positions in the same maturity bucket. 10% disallowance. • Horizontal Offsets within Time Zones: Zone 1 (1 mo-12mos) 40% disallowance, Zone 2 (>1yr-4yrs) 30% disallowance, Zone 3 (>4yrs) 30% disallowance. • Horizontal Offsets between Time Zones: Zone 1&2 40% disall., Nonadjacent Zone 1& 3 150% disallowance. Saunders & Cornett, Financial Institutions Management, 4th ed.

18. Saunders & Cornett, Financial Institutions Management, 4th ed.

19. BIS Standardized Model for Equities • For each stock: the long positions are totalled (ex: $200m) and the short positions are totalled (ex: $125m). • X Factor = 4% of sum of long and short positions = .04 x 325 = $13 million • Y Factor = 8% of net of long and short positions = .08 x 75 = $6 million • Total Capital Required = x factor + y factor = 13 + 6 = $19 million for one stock. Saunders & Cornett, Financial Institutions Management, 4th ed.

20. BIS Standardized Model of Foreign Exchange • Long Currency Positions Totalled • Short Currency Positions Totalled • Capital Charge = 8% of the higher of the longs or the shorts. • If Long $125m yen + $500m euros = +$625m and Short $75m British pound + $100m Canadian dollar = -$175m then capital charge = .08 x 625m = $50 million. Saunders & Cornett, Financial Institutions Management, 4th ed.