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

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

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

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

Appendix 1.1 A 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.

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

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

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

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

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.

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.

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

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.

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.

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.

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.

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.

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

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.

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.