FRM 考试知识点总结 |

FRM

Part 1

foundation of risk management

overview

what is risk

expected loss

unexpected loss

risk manager's job

uncover the source of risk and measure its impact: help make risk management decision

balance risk and reward

make risk transparent to key decision makers and stakeholders

find the right relationship between business leaders and the specialist risk managment functions

topology of risk

market risk

equity price risk

interest rate risk

tranding risk

gap risk

foreign exchange risk

commodity price risk

credit risk

default risk

bankruptcy risk

downgrade risk

settlement risk

liquidity risk

funding liquidity risk

trading liquidity risk

operational risk

potential losses resulting from operational weaknesses including inadquate sysetms, management failure, faulty controls, fraud and human errors

human factor risk

technology risk

legal and regulatory risk

business risk

strategic risk

reputation risk

systematic risk

putting risk management into practice

determining the objective

mapping the risks

instruments for risk management

constructing and implementing a strategy

performance evaluation

ERM

comprehensive and integrated framework for managing key risks in order to achieve business objectives, minimise unexpected earnings volatility and maximise firm value

Markowitz portfolio theory

effective frontier

CML

CAPM

SML

Sharpe ratio $\frac{E[R_p] - R_f}{\sigma(R_p)}$

Treynor ratio $\frac{E[R_p] - R_f}{\beta_p}$

Sortino ratio $\frac{E[R_p] - MAR}{\sqrt{\frac{1}{N-1}\sum_{t=1}^N \left( R_{p_t} - MAR\right)^2 } }$

MAR: minimum acceptable return

Jensen's alpha

information ratio $\frac{E[R_p] - E[R_B]}{\sigma(R_p-R_B) }$

$\sigma(R_p-R_B)$ is called tracking error

APT

factor model

Fama-French Three-Factor model

SMB: small minus big

HML: high minus low

market

examples of financial disasters

quantitative analysis

probability

statistics

moment, central moment, expected value, variance, skewness, kurtosis, covariance, correlation

sample mean, variance $s^2 = \sum_{i=1}^n \frac{(X_i-\overline{X})^2}{n-1}$

best linear unbiased estimator(BLUE)

linearity

unbiased

has minimum variance

Chebyshev's inequality

$P(|X-\mu|\leq k\sigma) \geq 1 - \frac{1}{k^2}$#### $P(|X-\mu|\leq k\sigma) \geq 1 - \frac{1}{k^2}$

distribution

binomial

poisson

uniform

normal

$1 \sigma: 68\% 1.65 \sigma: 90\%, 1.96\sigma:95\%, 2.58\sigma,99\%$ $1 \sigma: 68\%, 1.65 \sigma: 90\%, 1.96\sigma:95\%, 2.58\sigma: 99\%$

logmormal

Chi-Square distribution

t-distribution

F-distribution

hypothesis test

sampling and estimation

CLT: central limit theorem

large sample $n \geq 30la$ , assume approximately normal

standard error of mean: $\overline{X}$$SE(X) = \frac{s}{\sqrt{n}}$

steps

state null and alternative hypothesis

identify the test statistic

select a level of significance

formulate a decision rule

take a sample, arrive at decision

do not reject / reject the hypothesis

selecting test statistics

mean

normally distributed, known variance

$z = \frac{\tilde{X}-\mu_0}{\sigma/\sqrt{n}} \sim N(0,1)$

normally distributed, unknown variance

$t = \frac{\tilde{X}-\mu_0}{s/\sqrt{n}} \sim t(n-1)$

variance

normally distributed

$\chi^2 = \frac{(n-1)s^2}{\sigma_0^2} \sim \chi^2(n-1)$

two independent normally distributed

$F = \frac{s_1^2}{s_2^2} \sim F(n_1-1,n_2-1)$

errors

type 1

reject the null hypothesis when it is actually true

significance level

the probability of making type 1 error

= P(type 1 error)

type 2

fail to reject the null hypothesis when it is actually false

power of a test

the probability of correctly rejecting the null hypothesis when it is false

= 1 - P(type 2 error)

linear regression

standard error of regression

measure the fit of the regression line

$SER = \sqrt{\frac{\sum (Y_i-\hat{Y}_i)^2}{n-2}}$

analysis of variance(ANOVA) table

$R^2$the coefficient of determination $R^2 = \frac{ESS}{TSS} = 1 - \frac{SSR}{TSS}$

$R^2 = \frac{ESS}{TSS} = 1 - \frac{SSR}{TSS}$

ESS: explained sum of squares $= \sum (\hat{Y}_i-\overline{Y})^2$

SSR: sum of square residuals $= \sum (Y_i - \hat{Y}_i)^2$

TSS: total sum of squares

confidence interval for the regression coefficient

$\hat{b} \pm (t_c \times s_{\hat{b}})$

$s_{\hat{b}}$ : standard error of the regression coefficient

regression coefficient hypothesis testing

test if the true slop is b

use t-test $t = \frac{\hat{b} - b}{s_{\hat{b}}} \sim t(n-2)$

multiple regression

adjusted $R^2 = 1 - \frac{SSR/n-k-1}{TSS/n-1}$

$= 1 - \frac{SSR/n-k-1}{TSS/n-1}$

does not increase when a new independent variable is added

homoskedasticity and heteroskedasticity

the standard errors are usually not reliable estimate

serial correlation

multicolinearity

omitted variable bias

bias arises when one or more regressors are correlated with an omitted variable

forecasting trends

measure of model fitness

mean squared error(MSE)

adjusted MSE

$S^2 = \frac{\sum e_t^2}{T-k}$

deduct the degree of freedom to reduce MSE bias

Aksikr information criterion(AIC)

deal with trade-off between the goodness of fit of the model and the complexity of the model

AIC = $e^{\frac{2k}{T}} \times MSE$

Schwarz information criterion(SIC)

lower SIC implies either fewer explanatory variables, better fit, or both

the only consistency criterion

cycle

Wold's representation

estimating volatilities and correlation

ARCH model

EWMA model

GARCH(1,1) model

copula

nonlinear relationship

tail dependence

simulation methods

Monte Carlo simulation

price increments are assumed to have a normal distribution

select other distributions

bootstrapping

draw from historical scenarios

ineffective situations

outliers in the data

non-independent data

find a distribution using historical data

variance reduction techniques

antithetic variables

control variates

random number generation

financial market and products

Bond markets

interest rate

treasury rates, LIBOR, repo rates

overnight indexed swap(OIS) rates, riskfree rate

spot rates, forward rates

simple interest, compounding interest

major theories of term structure

expection theory

market segmentation theory

liquidity preference theory

bond valuation

= sum of discounted cash flow

risk metrics

Maculay duration

average period of cash flow returning weighted by discounted cash flow

modified duration

$= -\frac{\Delta P}{\Delta y} \times \frac{1}{P} = \frac{D_{Macaulay}}{1+y}$

DV01

= modified duration * bond value * 0.0001

convexity

$P = P_0 - DP_0\Delta y + \frac{1}{2}CP_0(\Delta y)^2$

reinvestment risk

treasury market

treasury bills

maturity of one year or less

cash price = 100 $\left(1- \text{discount rate} \times \frac{n}{360} \right)$

treasury notes and treasury bonds

make interest payments semi-annually

clean price

not including any accrued interest

dirty price

= clean price + accrued interest

day convention

treasury bond: actual / actual

corporate and municipal bonds: 30 / 360

money market instruments: actual / 360

corporate bond

credit risk

credit default risk

credit spread risk

loss resulting from changes in the level of credit spreads

MBS

derivatives markets

forward and futures

futures

traded on an exchange

standardized contracts

settled daily

high liquidity

guaranteed by clearinghours

margin required and adjusted

pricing

hedging strategies using forward

swap

main types

interest rate swap

currency swap

option

trading strategies involving options

bull spread

bear spread

butterfly

canlendar

straddle

strangle

strip

strap

call option

without dividend, European = American

#### $D > K(1-e^{-r(T-t)})$ shuld exercise at time when dividend is paid

greeks

MBS(mortgage-backed securities)

prepayment of mortgage loans

SMM(single monthly mortality rate)

CPR(conditional prepayment rate)

$CPR_n = 1 - (1-SMM_n)^{12}$

central conterparties

exchanges

OTC

main risk

counterparty risk

systemic risk

investment banks

IPO

insurance companies

mutual funds and hedge funds

valuation and risk model

fixed income

valuation

sum of discounted cash flow

bond replication

law of one price

risk metrics

key rate shifts

option

binomial trees

Black-Scholes-Merton model

Greek letters

risk models

market risk

types of risk measures

mean-variance framework

value at risk(VaR)

conditional VaR / expected shortfall

spectral risk measures

Putting VaR to work

credit risk

external and internal ratings

capital structure in banks

country risk

loss distribution approach

operational risk

operational risk management

risk control and self-assessment(RCSA)

key risk indicators(KRIs)

regulatory capital requirement

capital requirement

basic indicator approach(BIA)

standardized approach(SA)

advanced measurement approach(AMA)

data requirement

insurance in mitigating operational risk

moral hazard

adverse selection

stress testing

Part 2

investment management and risk management

factor investing

factor theory

CAPM

assumptions

make decisions solely in terms of expected values and standard deviations

plan for the same single holding period

have homogeneous expectations or beliefs

An individual cannot affect the asset price by buying or selling action

All assets are tradable, infinitely divisible

Markets are frictionless, including no transaction cost and no taxes

Short sale is allowed unlimitedly

Unlimited lending and borrowing at the riskless rate

only market factor

all risky assets have risk premiums determined only by their exposure to the market portfolio

Lessons

hold the factors not the assets

risk is factor exposure

generalization of CAPM

multi-factor

factors

Macro factors

economic growth

inflation

volatility

productivity, demographic, political

dynamic factors

size

The SMB factor was designed to capture the

outperformance of small firms relative to large firms

value

value investing: long value stocks and short growth stocks

negative feedback strategy

momentum

trend investing

positive feedback strategy

Fama-French three factor model

market index, firm size, book-to-market ratio

A shock to a factor matters more than the level of the factor.

can use data mining to find new factors

efficient market hypothesis

weak

market data

semi-strong

all publicly known and available information

passive investing

strong

all information

Alpha

excess return w.r.t a benchmark

tracking error

standard error of excess return

information ratio

$IR = \frac{active \ return }{tracking \ error} = \frac{\alpha}{\sigma}$

Ideal benchmark

Well defined, Tradable , Replicable, Adjusted for risk

Grinold fundamental law

IR = IC $\times \sqrt{BR}$

IC: the correlation of the manager's forecast with the actual returnd

BR(the breadth of the strategy): how many bets are taken

assumption

each active return is independent from the other active forecasts for that period and independent from the forecast for the security in subsequent periods

low-risk anomaly

stocks with low betas and low volatility have high returns

explanation

data mining

leverage constraints

agency problems

eg. long only

preference

illiquid assets

characteristics

infrequent trading, small amounts being traded, low turnover

source of illiquidity

due to market imperfections

participation costs

transaction costs

search frictions

asymmetric information

price impact

large trade will move markets

funding constraints

biases on reported returns

survivorship bias

infrequent sampling

smoothed price curve, underestimated volatility

selection bias

illiquidity risk premiums

allocation across asset classes

illiquidity premiums may not be true

illiquidity biases

reported data cannot be trusted

ignored risk

no market index for inliquid assets

no comparison

factor risk cannot be separated from manager skill

investing in illiquid markets is always a bet on management talent

choose securities within an asset class that are more illiquid

assets from different classes are rarely treated consistently as a whole

eg: treasuries on the run / off the run

act as market maker at the individual security level

supply liquidity by acting as an intermediary

rebalancing

force asset owners to buy at low prices when others want to sell

counter-cyclical

portfolio risk management

inputs for construction

Tasks

assess the impact of practical issues in portfolio construction, such as determination of risk aversion, incorporation of specific risk aversion, proper alpha coverage

describe portfolio revisions and reblancing, evaluate the tradeoff between alpha, risk, transaction costs and time horizon

determine the optimal no-trade region for rebalancing with transaction costs

alphas

refining alphas

motivation

most active managers construct portfolio subject to certain constraints

eg. no short, cash limit, liquidity

scales the alphas

$\alpha = volatility * IC * Score$

score has mean 0 and standrad deviation 1

volatility = residual risk

$std(\alpha) = volatility * IC$

trim alpha outliers

very large positive or negative alphas can have undue influence

closely examine all stocks with alphas greater in magnitude than three times the scale of the alphas

neutralization

remove alpha of benchmark

active risk aversion

general risk aversion

$= \frac{IR}{2\sigma_{\alpha}}$

utility function

$= \alpha_p - \lambda_A \sigma_{\alpha}^2$

#### $\alpha_p = IR * \sigma_{\alpha}$

specific factor risk

transaction costs

marginal contribution to value added(MCVA)

construction techniques

objective

maximize active returns minus an active risk penalty

screen

steps

rank the assets by alpha

choose the top performing assets

equal-weight or capitalization-weight

advantage

simple, easy to understand

robust

enhance alphas by concentrating the portfolio in the high-alpha stocks

risk control

include a sufficient number of stocks to avoid concentation in any single stock

transaction costs are limited by controlling turnover

disadvantage

ignore all informations in the alphas except for the rankings

exclude assets with lower alpha

straification

steps

split the list of assets into mutually exclusive categories

screen

linear programming

advantage

take all information into consideration

disadvantage

hard to produce portfolios with a prescribed number of stocks

quadratic programming

VaR measures

assumptions

Delta-normal model

all individual security returns are assumed normally distributed

traditional portfolio analysis

based on variances and covariances

individual VaR

$= z \times \sigma \times V$

z : z-score associated with the level of confidence

$\sigma$ : the standard deviation of stock returns

V : the market value of the stock

VaR for several stocks

correlation matters in large portfolio

marginal VaR

$= z \frac{cov(R_i,R_p)}{\sigma_p} = z \times \beta_i \times \sigma_p = z \times \rho_{ip} \times \sigma_i$

incremental VaR

the change of VaR owing to a new position

$= VaR_{p+a} -VaR_{p}$

or $\approx MVaR_i \times amount$

component VaR

indicate how much the portfolio VaR would change approximately if the given component is deleted

= MVaR * component value

portfolio risk

analytic methods

only consider risk

when the portfolio risk has reached a global minimum, all MVaRs or all betas must be equal

consider risk and return

maximize the Shape ratio with VaR

$\frac{R_p-F_f}{VaR_p}$

all ratios of excess return to marginal VaR(beta) $\frac{R_i-F_f}{MVaR_i}$ must be equal

VaR and risk budgeting

DB vs DC

surplus at risk(SaR)

risk monitering

liquidity duration

protfolio performance measurement

risk-adjusted performance measures

Sharpe ratio

$= \frac{R_p-R_f}{\sigma_p}$

Treynor ratio

$= \frac{R_p-R_f}{\beta_p}$

for well diversified portfolio, Shaper ratio and Treynor ratio give the same ranking

Jensen's alpha

information ratio

statistical significance of alpha

Modiglinai-square measure

$M^2 = \frac{\sigma_m}{\sigma_p}(R_p-R_f) - (R_m-R_f)$

market timing

include high(low) beta stocks if expect an up(down) market

style analysis

Regress fund returns on indexes reprensenting a range of asset classes. The regression coefficient on each index measures the fund's implicit allocation to that 'style'

performance attribution

asset allocation

equity / bond

selection

sector selection

security selection

hedge fund

strategies

agency problem

due diligence

market risk management and measurement

VaR and other risk measures

methods of VaR estimation

parametric approach

requires to explicitly specify the statistical distribution from which our data observations are drawn

normal VaR

$VaR_{\alpha} = - (\mu - z_{\alpha}\times \sigma)$

lognormal VaR

$VaR_{\alpha} = (1-e^{\mu - z_{\alpha}\times \sigma}) \times P$

nonparametric approach

see coherent risk measures

standard errors of quantile estimators

$SE(q) = \left[ \frac{p(1-p)}{nf(q)^2} \right]^{1/2}$

p: the proportion for the quantile

f(q): the corresponding probability density function

coherent risk measures

Def

weighted average of the quantiles of the loss distribution, where the weighting function is specified by the user

expected shortfall(ES)

probability-weighted average of tail losses

Quantile-Quantile(QQ) plot

a plot of the quantiles of the empirical distribution against those of some specified distribution and can be used to identify the distribution of our data by its shape

non-parametric historical simulation

basic historical simulation

bootstrap historical simulation

steps

create a large number of new samples at random from our original sample with replacement

each new 'resampled' sample gives a new VaR or ES estimate

take the best estimate to be mean of these resample-based estimates

non-parametric density estimation

use histograms to simulate the probability density function

weighted historical simulation

semi-prametric

age-weighted historical simulation(BRW)

discount the older observations in favor of newer ones

$w_i = \frac{\lambda^{i-1}(1-\lambda)}{1-\lambda^n}$

volatility-weighted historical simulation(HW)

correlation-weighted historical simulation

filtered historical simulation

backtesting VaR

difficulties

the trading portfolio evolves dynamically in practice

testing framework

test statistic

$z = \frac{x-pT}{\sqrt{p(1-p)T}}$

x: number of exceptions

the exceptions are assumed to be independent

model verification

unconditional coverage model

ignore time variation in the data, so the exceptions should be evenly spread over time

reject if $LR_{uc} > 3.84$ (95% confidence level)

conditional coverage model

$LR_{cc}=LR_{uc} + LR_{ind}$

reject if $LR_{cc} > 5.991$

type 1 and type 2 errors

Basel rules

daily exceptions of 99% VaR over the last year

Basel penalty zones

number of exceptions

multiplicative factor k

penalty

green

<= 4

3

no

yellow

5

3.4

model integrity or accuracy: should apply

6

3.5

intraday trading: should be considered

7

3.65

bad luck: no guidance

8

3.75

9

3.85

red

>=10

4

automatic penalty

VaR mapping

similar to PCA

choice of the set of general risk factors should reflect the tradeoff between better quality of the approximation and faster processing

mapping process

making all positions to market in current dollars

the market value for each instrument is then allocated to the risk factors

positions are summed for each risk factor

applications

mapping fixed-income portfolio

modelling dependence: correlation and copulas

financial correlation risk

the risk of financial loss due to adverse movements in correlation between two or more variables

eg

during 2008 financial crisis, the correlation between default of bonds increases substantially, thus decrease the value of senior tranche

statistical correlation models

Pearson correlation

$\rho_{XY} = \frac{cov(X,Y)}{\sigma_X\sigma_Y}$

limitations

financial relationship are typically nonlinear

zero correlation does not imply independence

not invariant to tranformations

Spearman rank correlation

$\rho_{S} = 1 - \frac{6\sum d_i^2}{n(n^2-1)}$

n: number of observations

$d_i$ :the difference between the ranking for period i

Kendall’s $\tau$

$\tau = \frac{n_c-n_d}{n(n-1)/2}$

$n_c$: number of concordant pairs

concordanct pairs: $sgn(X_i-X_j) = sgn(Y_i-Y_j), i\neq j$

$n_d$ : number of discordant pairs

discondant pairs: $sgn(X_i-X_j) = -sgn(Y_i-Y_j), i\neq j$

$X_i=X_j \text{ or } Y_i=Y_j$ : neither concordant nor discordant

limitation of ordinal risk measures

less sensitive to outliers

financial correlation modeling

Def

create a joint probability distribution between two or more variables while maintaining their individual marginal distributions

Gaussian copula

term structure models of interest rate

binomial interest rate tree model

backward induction valuation

steps

find the risk-neutral probabilities that equate the price of the underlying securities with their expected discounted values

price the contingent claim by expected discounted

value under these risk-neutral probabilities

issues

recombining vs non-recombining

option-adjusted spread(OAS)

size of time steps

models

drift

no drift

constant drift

Ho-Lee model: time-dependent drift

$dr =\lambda_tdt + \sigma dW$

Vasicek model: mean-reverting drift

$dr =\kappa(\theta - r)dt + \sigma dW$

volatility

CIR model

$dr = \kappa(\theta - \alpha r)dt + \sigma \sqrt{r} dW$

Courtadon model

$dr = \kappa(\theta - \alpha r)dt + \sigma r dW$

other related topics

empirical approaches to risk metrics and hedges

DV01

drawback

the changes in yields on hedged portfolio and

hedging instrument may not be one-for-one

partial solution

regression analysis based on historical data

volatility smiles

credit risk management and measurement

identification of credit risk

tasks

define and explain credit risk

explain the components of credit risk evaluation

describe, compare and contrast various credit risk mitigants and their role in credit risk

four componets of credit risk

obligor's capacity and willingness to repay

external conditions

attributes of bligation from which credit risk arises

credit risk mitigants

collateral

guarantees promised by a third party to accept liability

quantitative measures of credit risk

probability of default (PD)

loss given default (LGD)

exposure at default (EAD)

expected loss(EL)

= EAD * PD * LGD

use cash to cover

unexpected losses(UL)

= credit VaR

use capital to cover

concentration risk

sum of individual risks does not equal the portfolio risk

measurement

marginal contribution to portfolio UL

classifications of credit risk

default-mode(loss-based) valuation

default risk

recovery risk

exposure risk

value-based valuation

migration risk

spread risk

liquidity risk

measurement of credit risk

estimate probability of default (PD)

experts-based approach

agencies' rating

migration matrix

change on PD

investment-grade credits, increase more than proportional with the horizion

speculative-grade credits, increase less than proportional with the horizion

internal credit rating

infer from corporate bond prices

risk-neutral measure

$P= \frac{100}{1+YTM} = (1-PD)\frac{100}{1+R_f} + PD\frac{100(1-LGD)}{1+R_f}$

credit spread: $YTM-R_f \approx PD\times LGD$

real world

$YTM-R_f - \text{risk premium} \approx PD\times LGD$

different kinds of credit spread

nominal spread

$YTM_{\text{risky bond}}-YTM_{\text{benckmark government bond}}$

i-spread (interpolated)

linearly interpolated YTM on benchmark government bond or swap rate

Z-spread (Zero volatility spread)

Option adjusted spread (OAS)

Z-spread adjusted for optionality of embedded options

Z-spread = OAS if no option

spread01(DVCS)

Increase and decrease the z-spread by 0.5 basis points, reprice the bond for each of these shocks, and compute the difference

infer from equity prices

credit risk as option

Equity: Long call option on firm value V, strike price= F

Merton model

$S_t = V_tN(d_1) -Fe^{-r(T-t)}N(d_2)$

$d_1 = \frac{\ln(V/Fe^{-r(T-t)})}{\sigma\sqrt{T-t}}+\frac{\sigma\sqrt{T-t}}{2}, d_2 = d_1-\sigma\sqrt{T-t}$

$N(d_2)$

probability of exercising the call option = 1-PD = $1- N(-d_2)$

credit spread

$= -\frac{1}{T-t} \ln\left(\frac{D}{F}\right) -r_f$

distance to default (DtD)

$= -\frac{\ln(V/F)+(\mu-0.5\sigma^2)(T-t)-\text{ other payouts} } {\sigma\sqrt{T-t}}$

limitations

applicable only to liquid, publicly traded names

subordinated debt

firm value low

like equity

long call

firm value high

like senior debt

short call

KMV model

overcome two shortcoming of Merton model

all the debt matures at the same time

the value of the firm follows a lognormal diffusion process

default intensity models

distributions

Poisson distribution

exponential distribution

Hazard rate (or default intensity)

survival probability

$P(t^*>t) = 1-F(t) = e^{-\lambda t}$

memoryless

recovery rate (RR)

$\lambda \approx \frac{z}{1-RR}$

the spread is approximately equal to the default probability times the LGD

credit scoring model

retail credit risk

three types

credit bureau scores

pooled models

custom model

cost: credit bureau scores < pooled Models < custom models

other methods

structural Approaches

reduced Form Approaches

statistical-based models

supervised model

LDA

logistic regression

unsupervised model

clustering

PCA

heuristic approaches

mimic human decision

numerical approaches

neural network

estimate LGD and EAD

LGD

the seniority of the OTC derivative claim

timing of recovery

credit exposure

metrics

Expected MtM

the expected value of a transaction at a given point in the future

Expected exposure (EE)

the amount that is expected to be lost (positive MtM only) if the counterparty defaults

Expected exposure is larger than expected MtM.

Potential future exposure (PFE)

the worst exposure that could occur at a given time in the future at a given confidence level

Maximum PFE

highest PFE value over a given time interval

Expected positive exposure (EPE)

the average exposure across all time horizons——the weighted average of the EE across time

Negative Exposure

#### represented by negative future values, from a counterparty’s point of view

effective EE (EEE)

#### a non-decreasing version of the EE profile

Effective Expected Positive Exposure (EEPE)

#### introduced for regulatory capital. It is the average of the effective EE (EEE)

deal with two problems

#### EPE neglect very large exposures

EPE may underestimate exposure for short-dated transactions and not properly capture “rollover risk”

factors

future uncertainty

bond and loan

interest rate swap

optionality

credit derivative

risk migrants

netting

#### netting benefit improves for a large number of exposures and low correlation

netting factor

$= \frac{\sqrt{n+n(n-1)\rho}}{n}$

collateral

counterparty risk

migrants

netting

create legal risk in cases where a netting agreement cannot be legally enforced

expose other creditors to more significant losses

collateral

hedging

central counterparties

#### potentially create operational and liquidity risks, and also systemic risk

credit limits and CVA

credit limits

counterparty risk can be diversified by limiting exposure to any given counterparty.

credit value adjustment (CVA)

price counterparty risk

assume no wrong-way risk

sum of discounted expected exposure

as a spread

= EPE * spread

wrong-way risk and right-way risk

stress test

portfolio credit risk

default correlation

single-factor model

unconditional default distribution

conditional default distribution

credit risk portfolio models

CreditRisk+(credit suisse)

CreditRiskTM (JPMorgan)

KMV model (Moody)

Credit Portfolio View (McKinsey)

management of credit risk

credit derivative swap

#### First-to-Default CDS

#### Total Return Swap (TRS)

#### Asset-Backed Credit-Linked Notes

#### Vulnerable Option

#### Swap with Credit Risk

#### Collateralized Debt Obligations (CDOs)

structured products

PD and correlation effect

convexity effect

securitization

seven frictions

operation risk management and measurement

OpRisk management framework

def

risk of loss resulting from inadequate or failed internal processes, people and systems or from eternal events

include legal risk, but exclude strategic and reputational risk

three common lines of defense

business line management

independent corporate operational risk management function

independent review

principles for sound management of operational risk

summary

人和流程

general principle

1. The board of directors should take the lead in establishing a strong risk management culture

2. Banks should develop, implement and maintain a Framework that is fully integrated into the bank’s overall risk management processes

governance

board of directors

3. The board of directors should establish, approve and periodically review the Framework

4. The board of directors should approve and review a risk appetite and tolerance statement for operational risk that articulates the nature, types, and levels of operational risk that the bank is willing to assume

senior management

5. Senior management should develop for approval by the board of directors a clear, effective and robust governance structure with well defined, transparent and consistent lines of responsibility

risk management enviroment

indentification and assessment

6. Senior management should ensure the identification and assessment of the operational risk inherent in all material products, activities, processes and systems to make sure the inherent risks and incentives are well understood

tools for assessing operating risks

audit findings

focus on control weaknesses and vulnerabilities

internal loss data collection and analysis

provide meaningful information for assessing exposure to operational risk and effectiveness of internal controls

external data collection and analysis

risk self assessment(RSA)

assess the processes underlying its operations against potential threats, vulnerabilities, and consider their potential impact

risk control self assessment(RCSA)

evaluate inherent risk before controls are considered

business process mapping

risk and performance indicators

key risk indicators(KRIs)

key performance indicators(KPIs)

scenario analysis

measurement

use the output of the risk assessment tools as inputs into a model that estimates operational risk exposure

comparative analysis

7. Senior management should ensure that there is an approval process for all new products, activities, processes and systems that fully assesses operational risk

monitoring and reporting

8. Senior management should ensure that there is an approval process for all new products, activities, processes and systems that fully assesses operational risk

control and mitigation

9. Banks should have a strong control environment that utilizes policies, processes and systems; appropriate internal controls; and appropriate risk mitigation and transfer strategies

five components of strong control enviroment

control enviroment

risk assessment

control activities

information and communication

monitoring activities

business resiliency and continuity

10. Banks should have business resiliency and continuity plans in place to ensure an ability to operate on an ongoing basis and limit losses in the event of severe business disruption

role of disclosure

11. A bank’s public disclosures should allow stakeholders to assess its approach to operational risk management

enterprise risk management

def

all risks viewed together within a coordinated and strategic framework

macro level

#### more strategic risks and opportunities should be put into core business

micro level

focus on decentralizing the risk-return trade-off in a company

four-step conceptual framework

management begins by determining the firm's appetite

given the firm's target rating, management estimates the amount of capital it requires to support the risk of its operations

management determines the optimal combination of capital and risk that is expected to yield its target rating

top management decentralizes the risk-capital trade-off and makes investment and operating decisions optimize their trade-off

technology risk

risk appetite framework

#### help strategic decisions and risk management

articulate a clearly defined risk appetite for the firm: not only about risk management but also about their firms’ forward-looking business strategies

The board of directors sets overarching expectations for the risk profile, while CEO, CRO, and CFO translate those expectations into incentives and constraints for business lines

data aggregation

data quality

accuracy, completeness, consistency, reasonableness, currency, uniqueness

OpRisk data

scenario analysis

common biases

prentation bias

context bias

anchoring bias

hundle bias or anxiety bias

gaming

参与者利益与整体利益有冲突，不肯暴露真实意图，却努力影响结果

availablity bias

over / under confidence bias

inexpert opinion

modelling approaches

data features

low frequency

#### discrete

development

people are not reliable

little research of operational risk

Basel 3

return to basic approach

basic approach

standardized approach

advanced measurement approach

extreme value

generalized extreme-value theory (GEV)

peaks-over-threshold approach (POT)

model risk

sources

distribution of the underlying asset is stationary

rates of return are normally distributed

oversimplify a model

assume perfect capital market exists

liquidity is assumed to be ample

misapplied to a given situation

risk capital attribution and risk-adjusted performance

capital planning and framework

effective capital adequacy process

框架，方法论，流程，人

sound foundational risk management

effective loss-estimation methodologies

solid source-estimation methodologies

sufficient capital adequacy impact assessment

comprehensive capital policy and capital planning

robust internal controls

effective governance

financing: liquidity and leverage

Repo rate

GC rate

special rate

liquidity risk

constant spread approach

exogenous spread approach

endogenous price approach

liquidity discount approach

liquidity-at-risk (LaR) or cash-flow-at-risk (CFaR)

5 factors affecting cash flow and LaR

source of liquidity risk

transaction liquidity risk

balance sheet risk

systemic risk

banks failure

Basel Accords

current issues