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Three aims of RM:

- Identify, assess and prioritize risks
- Minimize, monitor and control the probability of unfortunate events
- Maximize business opportunities



probability that an actual return on an investment will be lower than the exp. return


Efficient Frontier

represents the set of all the portfolios that maximize the expected return for a given volatility, thus dominating all other portfolios



can be calculated by Systematic Risk (beta * Rm) (not diversified) and Idiosyncratic Risk (e) (diversified) with alpha as extra return and beta obtained by OLS


Difference Exchange Traded & OTC

standard contracts versus computer/telephone network


Difference Forward and Future contract

OTC and Exchange respectively


Net Interest Income

excess of interest received over interest paid


Net Interest Margin

The ratio between Net Interest Income and income producing assets



weighted average of the times in which payments are made, where the weights are given by the proportions of the bond’s total present value at different times (can be negative by going short on a bond)



- Monotonicity  allows for an ordering of risks. If Z1 < Z2 then f(Z1) < f(Z2)
- Sub-additivity  Incentives to diversification. f(Z1 + Z2) ≤ f(Z1) + f(Z2)
- Positive Homogeneity  proportional to risk. f(aZ) = af(Z)
- Translation Invariance  neutral risk w.r.t. liquidity. f(Z + b) = f(Z)


Coherency Variance and Std Dev

Variance not coherent because of positive homogeneity and sub-additivity. Std. Dev. always


Value at Risk

VaR is the loss value for which the probability of observing a larger loss, given the available information is equal to 1 minus alpha


Expected Shortfall

average value of all the values exceeding the threshold (VaR)


Credit Risk

the potential that a bank borrower or counterparty will fail to meet its obligations in accordance with agreed terms
- Default Risk (EAD * LGD)
- Migration Risk (downgrade risk related to deterioration in the counterparty’s creditworthiness)
- Spread Risk (rise in the spreads required by the market from borrowers)
- Recovery Risk (recovery rate actually recorded after liquidation of counterparty’s assets will be smaller than original estimates.


3 approaches to Credit Risk (Basel II-III)

1. Standardized Approach (risk weights provided by regulator)
2. Foundation Internal Rating Based (can compute PD of their counterparty’s)
3. Advanced Internal Rating Based (free to calculate all risk parameters)



Loss rate experienced on a credit exposure if the counterparty defaults


Basel Framework

1. Minimum Capital Requirements (Credit Risk, Market Risk, Operational Risk)
2. Supervisory Review Process
3. Market Discipline


Moody’s KMV

IMPORTANT is the Distance to Default. Overcomes weaknesses of Merton:
1. Gaussianity
2. Default may only happen in T


Market Risk

the risk of losses in on-and off-balance sheet positions arising from movements in market prices (VaR and ES)
- Historical-simulation Approach
- Model-building Approach


Operational risk

risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. Includes legal risk, excludes strategic and reputational risk. Four sources:
1. Process Risk
2. People Risk
3. System Risk
4. External Risk


3 approaches to asses operational risk under Basel II-III

1. Basic Indicator
2. Standardized Approach
3. Advanced Measurement Approach


Difference Basel:

- Basel 1, no model of default correlation
- Basel 2 has the three pillars and the three approaches to Credit Risk
- Basel 2 has the three approaches to Operational Risk
- Basel 2.5 has three changes
o Calculation of Stressed VaR
o New incremental risk charge
o Comprehensive risk measure for instruments dependent on credit correlation
- Basel 3 states that a bank’s total capital consists of:
o Tier 1 equity capital
o Additional Tier 1 capital
o Tier 2 capital