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Overview

- The risks associated with financial intermediation:
- Interest rate risk, market risk, credit risk, off-balance-sheet risk, technology and operational risk, foreign exchange risk, country risk, liquidity risk, insolvency risk

Interest Risks

- The interest rate risk associated with financial intermediation:
- Federal Reserve policy
- Repricing model
- Maturity model
- Duration model
- *Term structure of interest rate risk

Repricing Model

- Repricing or funding gap model based on book value.
- Contrasts with market value-based maturity and duration models recommended by the Bank for International Settlements (BIS).
- Rate sensitivity means time to repricing.
- Repricing gap is the difference between the rate sensitivity of each asset and the rate sensitivity of each liability: RSA - RSL.

Maturity Buckets

- Commercial banks must report repricing gaps for assets and liabilities with maturities of:
- One day.
- More than one day to three months.
- More than 3 three months to six months.
- More than six months to twelve months.
- More than one year to five years.
- Over five years.

Repricing Gap Example

AssetsLiabilitiesGap Cum. Gap

1-day $ 20 $ 30 $-10 $-10

>1day-3mos. 30 40 -10 -20

>3mos.-6mos. 70 85 -15 -35

>6mos.-12mos. 90 70 +20 -15

>1yr.-5yrs. 40 30 +10 -5

>5 years 10 5 +5 0

Applying the Repricing Model

- DNIIi = (GAPi) DRi = (RSAi - RSLi) Dri

Example:

In the one day bucket, gap is -$10 million. If rates rise by 1%,

DNIIi = (-$10 million) × .01 = -$100,000.

Applying the Repricing Model

- Example II:

If we consider the cumulative 1-year gap,

DNIIi = (CGAPi) DRi = (-$15 million)(.01)

= -$150,000.

Rate-Sensitive Assets

- Examples from hypothetical balance sheet:
- Short-term consumer loans. If repriced at year-end, would just make one-year cutoff.
- Three-month T-bills repriced on maturity every 3 months.
- Six-month T-notes repriced on maturity every 6 months.
- 30-year floating-rate mortgages repriced (rate reset) every 9 months.

Rate-Sensitive Liabilities

- RSLs bucketed in same manner as RSAs.
- Demand deposits and passbook savings accounts warrant special mention.
- Generally considered rate-insensitive (act as core deposits), but there are arguments for their inclusion as rate-sensitive liabilities.

GAP Ratio

- May be useful to express GAP in ratio form as,

GAP/Assets.

- Provides direction of exposure and
- Scale of the exposure.
- Example:
- GAP/A = $15 million / $270 million = 0.56, or 5.6 percent.

Equal Changes in Rates on RSAs and RSLs

- Example: Suppose rates rise 2% for RSAs and RSLs. Expected annual change in NII,

NII = CGAP × R

= $15 million × .01

= $150,000

With positive CGAP, rates and NII move in the same direction.

Unequal Changes in Rates

- If changes in rates on RSAs and RSLs are not equal, the spread changes. In this case,

NII = (RSA × RRSA ) - (RSL × RRSL )

Unequal Rate Change Example

- Spread effect example:

RSA rate rises by 1.2% and RSL rate rises by 1.0%

NII = interest revenue - interest expense

= ($155 million × 1.2%) - ($155 million × 1.0%)

= $310,000

Restructuring Assets and Liabilities

- The FI can restructure its assets and liabilities, on or off the balance sheet, to benefit from projected interest rate changes.
- Positive gap: increase in rates increases NII
- Negative gap: decrease in rates increases NII

Weaknesses of Repricing Model

- Weaknesses:
- Ignores market value effects and off-balance sheet cash flows
- Overaggregative
- Distribution of assets & liabilities within individual buckets is not considered. Mismatches within buckets can be substantial.
- Ignores effects of runoffs
- Bank continuously originates and retires consumer and mortgage loans. Runoffs may be rate-sensitive.

The Maturity Model

- Explicitly incorporates market value effects.
- For fixed-income assets and liabilities:
- Rise (fall) in interest rates leads to fall (rise) in market price.
- The longer the maturity, the greater the effect of interest rate changes on market price.
- Fall in value of longer-term securities increases at diminishing rate for given increase in interest rates.

Maturity of Portfolio

- Maturity of portfolio of assets (liabilities) equals weighted average of maturities of individual components of the portfolio.
- Principles stated on previous slide apply to portfolio as well as to individual assets or liabilities.
- Typically, MA - ML > 0 for most banks and thrifts.

Effects of Interest Rate Changes

- Size of the gap determines the size of interest rate change that would drive net worth to zero.
- Immunization and effect of setting

MA - ML = 0.

Maturity Matching and Interest Rate Exposure

- If MA - ML = 0, is the FI immunized?
- Extreme example: Suppose liabilities consist of 1-year zero coupon bond with face value $100. Assets consist of 1-year loan, which pays back $99.99 shortly after origination, and 1¢ at the end of the year. Both have maturities of 1 year.
- Not immunized, although maturities are equal.
- Reason: Differences in duration.

Duration

- The average life of an asset or liability
- The weighted-average time to maturity using present value of the cash flows, relative to the total present value of the asset or liability as weights.

*Term Structure of Interest Rates

YTM

YTM

Time to Maturity

Time to Maturity

Time to Maturity

Time to Maturity

Overview

- 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

Market Risk:

- 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.

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
- Monte Carlo Simulation

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) × 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. (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.

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. Concern is that yields will rise. Probability of yield increases greater than 16.5 basis points is 5%.

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) (.01077) = $10,770

Confidence Intervals: Example

- 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

Foreign Exchange & Equities

- In the case of Foreign Exchange, DEAR is computed in the same fashion we employed for interest rate 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.

Aggregating DEAR Estimates

- Cannot simply sum up individual DEARs.
- In order to aggregate the DEARs from individual exposures we require the correlation matrix.
- Three-asset case:

DEAR portfolio = [DEARa2 + DEARb2 + DEARc2 + 2rab × DEARa × DEARb + 2rac × DEARa × DEARc + 2rbc × DEARb × DEARc]1/2

Historic or Back Simulation

- Advantages:
- Simplicity
- Does not require normal distribution of returns (which is a critical assumption for RiskMetrics)
- Does not need correlations or standard deviations of individual asset returns.

Historic or Back Simulation

- Basic idea: Revalue portfolio based on actual prices (returns) on the assets that existed yesterday, the day before, etc. (usually previous 500 days).
- Then calculate 5% worst-case (25th lowest value of 500 days) outcomes.
- Only 5% of the outcomes were lower.

Estimation of VAR: Example

- Convert today’s FX positions into dollar equivalents at today’s FX rates.
- Measure sensitivity of each position
- Calculate its delta.
- Measure risk
- Actual percentage changes in FX rates for each of past 500 days.
- Rank days by risk from worst to best.

Weaknesses

- Disadvantage: 500 observations is not very many from statistical standpoint.
- Increasing number of observations by going back further in time is not desirable.
- Could weight recent observations more heavily and go further back.

Regulatory Models

- BIS (including Federal Reserve) approach:
- Market risk may be calculated using standard BIS model.
- Specific risk charge.
- General market risk charge.
- Offsets.
- Subject to regulatory permission, large banks may be allowed to use their internal models as the basis for determining capital requirements.

BIS Model

- 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
- Vertical offsets:
- Adjust for basis risk
- Horizontal offsets within/between time zones

Credit Risk

- Risk that promised cash flows are not paid in full.
- Firm specific credit risk
- Systematic credit risk
- High rate of charge-offs of credit card debt in the 80s and 90s
- Obvious need for credit screening and monitoring
- Diversification of credit risk

Overview

- This section discusses types of loans, and the analysis and measurement of credit risk on individual loans. This is important for purposes of:
- Pricing loans and bonds
- Setting limits on credit risk exposure

Credit Quality Problems

- Problems with junk bonds, residential and farm mortgage loans.
- Credit card loans and auto loans.
- Crises in Asian countries such as Korea, Indonesia, Thailand, and Malaysia.
- Over the 90s, improvements in NPLs for large banks and overall credit quality.
- Increased emphasis on credit risk evaluation.

Return on a Loan:

- Factors: interest payments, fees, credit risk premium, collateral, other requirements such as compensating balances and reserve requirements.
- Return = inflow/outflow

k = (f + (L + M ))/(1-[b(1-R)])

- Expected return: E(r) = p(1+k)

Measuring Credit Risk

- Qualitative models: borrower specific factors are considered as well as market or systematic factors.
- Specific factors include: reputation, leverage, volatility of earnings, covenants and collateral.
- Market specific factors include: business cycle and interest rate levels.

Credit Scoring Models

- Linear probability models:

Zi =

- Statistically unsound since the Z’s obtained are not probabilities at all.
- *Since superior statistical techniques are readily available, little justification for employing linear probability models.

Other Credit Scoring Models

- Logit models: overcome weakness of the linear probability models using a transformation (logistic function) that restricts the probabilities to the zero-one interval.
- Other alternatives include Probit and other variants with nonlinear indicator functions.

Altman’s Linear Discriminant Model:

- Z=1.2X1+ 1.4X2 +3.3X3 + 0.6X4 + 1.0X5

Critical value of Z = 1.81.

- X1 = Working capital/total assets.
- X2 = Retained earnings/total assets.
- X3 = EBIT/total assets.
- X4 = Market value equity/ book value LT debt.
- X5 = Sales/total assets.

Mortality Rate Models

- Similar to the process employed by insurance companies to price policies. The probability of default is estimated from past data on defaults.
- Marginal Mortality Rates:

MMR1 = (Value Grade B default in year 1) (Value Grade B outstanding yr.1)

MMR2 = (Value Grade B default in year 2) (Value Grade B outstanding yr.2)

RAROC Models

- Risk adjusted return on capital. This is one of the more widely used models.
- Incorporates duration approach to estimate worst case loss in value of the loan:
- DL = -DL x L x (DR/(1+R)) where DR is an estimate of the worst change in credit risk premiums for the loan class over the past year.
- RAROC = one-year income on loan/DL

Option Models:

- Employ option pricing methods to evaluate the option to default.
- Used by many of the largest banks to monitor credit risk.
- KMV Corporation markets this model quite widely.

Applying Option Valuation Model

- Merton showed value of a risky loan

F(t) = Be-it[(1/d)N(h1) +N(h2)]

- Written as a yield spread

k(t) - i = (-1/t)ln[N(h2) +(1/d)N(h1)]

where k(t) = Required yield on risky debt

ln = Natural logarithm

i = Risk-free rate on debt of equivalent maturity.

*CreditMetrics

- “If next year is a bad year, how much will I lose on my loans and loan portfolio?”

VAR = P × 1.65 × s

- Neither P, nor s observed.

Calculated using:

- (i)Data on borrower’s credit rating; (ii) Rating transition matrix; (iii) Recovery rates on defaulted loans; (iv) Yield spreads.

* Credit Risk+

- Developed by Credit Suisse Financial Products.
- Based on insurance literature:
- Losses reflect frequency of event and severity of loss.
- Loan default is random.
- Loan default probabilities are independent.
- Appropriate for large portfolios of small loans.
- Modeled by a Poisson distribution.

Off-Balance-Sheet Risk

- Increased importance of off-balance-sheet activities
- Letters of credit
- Loan commitments
- Derivative positions
- Speculative activities using off-balance-sheet items create considerable risk

Technology and Operational Risk

- Risk of direct or indirect loss resulting form inadequate or failed internal processes, people, and systems or from external events.
- Some include reputational and strategic risk
- Technological innovation has seen rapid growth
- Automated clearing houses
- CHIPS

Technology and Operational Risk

- Risk that technology investment fails to produce anticipated cost savings.
- Risk that technology may break down.
- Bank of New York
- Well’s Fargo
- Economies of scale.
- Economies of scope.

Foreign Exchange Risk

- Returns on foreign and domestic investment are not perfectly correlated.
- FX rates may not be correlated.
- Example: $/DM may be increasing while $/¥ decreasing.
- Undiversified foreign expansion creates FX risk.

Foreign Exchange Risk

- Note that hedging foreign exposure by matching foreign assets and liabilities requires matching the maturities as well*.
- Otherwise, exposure to foreign interest rate risk is created.

Country or Sovereign Risk

- Result of exposure to foreign government which may impose restrictions on repayments to foreigners.
- Lack usual recourse via court system.
- Examples: South Korea, Indonesia, Thailand.
- More recently, Argentina.

Liquidity Risk

- Risk of being forced to borrow, or sell assets in a very short period of time.
- Low prices result.
- May generate runs.
- Runs may turn liquidity problem into solvency problem.
- Risk of systematic bank panics.

Insolvency Risk

- Risk of insufficient capital to offset sudden decline in value of assets to liabilities.
- Continental Illinois National Bank and Trust
- Original cause may be excessive interest rate, market, credit, off-balance-sheet, technological, FX, sovereign, and liquidity risks.

Risks of Financial Intermediation

- Other Risks and Interaction of Risks
- Interdependencies among risks.
- Example: Interest rates and credit risk.
- Discrete Risks
- Example: Tax Reform Act of 1986.
- Other examples include effects of war, market crashes, theft, malfeasance.

Macroeconomic Risks

- Increased inflation or increase in its volatility.
- Affects interest rates as well.
- Increases in unemployment
- Affects credit risk as one example.

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