FRM 2016 PART 2Revision Course

MARKET RISKFRM 2016 Part 2 Revision Course

ESTIMATING MARKET RISK MEASURESReading: Estimating Market Risk Measures (Chapter 3, Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex,

England: John Wiley & Sons, 2005))

1. Definitions:

a. Arithmetic Return: and Geometric Return: ln

b. Geometric return assumes that all money received is continuously reinvested at the same rate of return.

Also, it ensures that asset prices can never become negative

2. VaR using Historical Simulation: Order all daily return observations from largest to smallest. The observation

that comes after the threshold limit is the VaR (α.n)+1

3. Parametric Estimation of VaR:

a. Delta-Normal VaR: -µ + zσ [For 5% significance, Z is 1.65 and for 1% is 2.33]

b. Lognormal VaR: 1 – e (µ - zσ)

4. Q-Q Plots: It plots both the empirical and hypothesized distribution. If the two distributions are very

similar, then the plot will be linear

5. Standard Error: Used to assess the precision of the risk measure. The simplest method is to create a confidence

interval around the quantile in question.

a. Confidence Interval: z + (z. Std Error) > VaR > z - (z. Std Error)

b. f(q) is the area of a bin width

c. Std. Error =( )/( )

6. Note:

a. Concepts like ES(Expected Shortfall) are carried forward from Part 1

b. Remember that VaR is one tailed and Confidence intervals are 2 tailed

NON-PARAMETRIC APPROACHESReading: Estimating Market Risk Measures (Chapter 4, Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex,

England: John Wiley & Sons, 2005))

1. Definitions:

a. Surrogate Density Function: Curve obtained by connecting mid-points of successive histograms. Helps

calculate VaR at any percentage point.

2. Bootstrap Historical Simulation:

a. Draw a sample from the data set and estimate VaR

b. Put the data back in the data set.

c. Repeat step a and b multiple times. Best estimate of VaR is the average VaR of the simulation runs

3. Weighted Historical Simulation Approaches

a. Age-weighted: More recent observations have more weight. Weight is given by w = ( )b. Volatility-weighted: ,∗ = , ,,c. Correlation-weighted: Incorporates updated correlations between asset pairs

d. Filtered historical simulation: Volatility is forecast for each day in the sample period and bootstrapping

used for returns

4. Advantages of non-parametric approaches:

a. Computationally simple

b. Not hindered by parametric violations of skewness and fat tails

c. Can accommodate more complex analysis

5. Disadvantages of non-parametric approaches:

a. Analysis depends critically on historical data

b. Difficult to detect structural shifts

c. Need sufficient data

PARAMETRIC APPROACHES-EXTREME VALUEReading: Parametric Approaches (II): Extreme Value (Chapter 7, Kevin Dowd, Measuring Market Risk, 2nd Edition (West

Sussex, England: John Wiley & Sons, 2005))

1. Extreme Values: The challenge of analyzing and modelling extreme values is that there are only a few

observations for which to build a model and there are ranges of extreme values that are yet to occur.

a. Extreme value theory is a branch of statistics developed to address problems associated with extreme

outcomes

2. Fisher-Tippet: As sample size n gets large, the distribution of extremes converges to the following know GEV

(Generalized Extreme Value) distribution.

a. The symbol ξ is called the tail index and indicates the shape or heaviness of the tail

i. ξ > 0, tails are heavy as in t-distribution or Pareto Distribution

ii. ξ = 0, tails are light, as in Normal and Lognormal distributions

iii. ξ < 0, tails are lighter than Normal as in the Weibull Distribution

b. Risk Management focuses only on ξ > 0 and ξ = 0

c. We apply a statistical test for hypothesis ξ = 0 and if we cannot reject the hypothesis, then we assume

that ξ = 0

3. POT(Peaks over Threshold): It is an application of EVT to the distribution of excess losses over a high threshold

a. VaR = µ + − 1i. Where β is scale parameter, ξ is tail index, α is significance level, µ is threshold (as %)

ii. n is total number of observations, Nu is no. of observations above threshold

b. ES =

4. Generalized Pareto Distribution (GPD): As µ gets large, the distribution converges into a GPD. The GPD exhibits

a curve that dips below the Normal Distribution prior to the tail and it then moves above the normal distribution

until it reaches the extreme tail

5. Issues:

a. Choosing a threshold requires a trade-off that it needs to be high enough for GPD to apply and low

enough so that there are sufficient observations

b. GEV requires one more variable (σ) which POT does not require. POT requires a threshold

c. EVT is used to measure extreme events and compute VaR. Both β and ξ can be computed using

maximum-likelihood techniques

BACK TESTING VARReading: Backtesting VaR (Chapter 6, Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk,

3rd Edition(New York: McGraw Hill, 2007))

1. Backtesting: It is the process of comparing losses predicted by the VaR model to those actually experienced over

the testing period. An unbiased measure of the number of exceptions as a proportion of the number of samples

is called failure rate

a. Failure Rate = where N is no. of exception and T is no. of samples

2. Error Types:

a. Type 1 Error: Rejecting an accurate model

b. Type 2 Error: Accepting an inaccurate model

3. Log-likelihood Ratio: LRuc is a test statistic to determine the hypothesis that model is accurate. If LRuc > 3.84, we

reject the hypothesis that the model is correct

a. As VaR confidence level increases, extreme values decrease. Thus, it becomes difficult to test for the

accuracy of the model

4. VaR to measure potential losses: To decide on the holding period, we have two theories.

a. Holding period should be equal to the amount of time required to either liquidate or hedge the portfolio

b. It should match the period over which the portfolio is not expected to change

5. Basel Committee on Backtesting: Basel requires that Market VaR be computed at 99% confidence interval and

backtested for past 1 year.

a. We expect to have 2.5 exceptions (250x0.01) each year.

b. Depending on the exceptions observed, the capital multiplier (amount a bank must hold) increases and

this lowers the bank performance if model used is incorrect

i. Multiplier is 3 for Green zones (0-4 observations)

ii. Multiplier increases from 3-4 for yellow zone(5-9 observations)

iii. Multiplier is 4 for Red zone(more than 10 observations)

c. Multiplier is based on the type of model error

i. Basic Integrity lacking/ Model Inaccuracy then penalty applies

ii. Intraday trading then penalty may be considered

iii. Bad luck due to significant market conditions may be condoned

d. Reducing confidence interval reduces the probability of type 2 errors. Also, using longer backtesting

periods can help here

6. Conditional Coverage: Unconditional coverage does not test for timing of exceptions and assumes that

exceptions are fairly equally distributed across time. Conditional coverage includes a measure of independence

of the events i.e. LRcc = LRuc+ LRind thus, if LRcc > 5.99, we reject the model

a. If exceptions are determined to be serially dependent, then model needs to be revised to incorporate

the correlations that are evident in current conditions.

VAR MAPPINGReading: VaR Mapping (Chapter 11, Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd

Edition (New York: McGraw Hill, 2007))

1. Mapping a Portfolio:

a. Market risk is measured by noting all the current positions within a portfolio. These positions are then

mapped to risk factors using factor exposures

b. Mapping involves finding common risk factors among positions in a given portfolio. This system is

position based and differs from the traditional return analysis

2. Factor Exposures:

Type Risk Factor Factor Exposure

Fixed Income Change in Interest rate Modified Duration

Equities Change in equity index prices Beta

a. If all positions in a portfolio are exposed to the same risk factors, the portfolio factor exposure can

be found as weighted average of position factor exposures

3. General and Specific Risks: One or two risk factors are appropriate to capture General or primitive risks. The

type and no. of risk factors will have an effect on the size of the residual or specific risks. Specific risks arise from

unsystematic risks of various positions in the portfolio. Diversification of the portfolio reduces specific risk and

only market risk remains (Systematic Risk or Beta)

4. Mapping Fixed Income Securities:

a. Principal Mapping: Risk of repayment of principal amounts. Average maturity of portfolio is mapped to

the coupon bond

b. Duration Mapping: Risk of bond is mapped to a zero coupon bond of the same duration. Risk level of

zero coupon bond equals the duration of the portfolio

c. Cash Flow Mapping: Risk of bond is decomposed into the risk of each cash flow of bond

d. If we assume perfect correlation between the maturity of the zeros, the portfolio VaR would be equal to

the undiversified VaR

5. Tracking error VaR: It is the deviation between the benchmark VaR and the portfolio VaR

6. Mapping for Linear Derivatives: The Delta-Normal method provides accurate estimates of VaR for portfolio and

assets that can be expressed as linear combinations of normally distributed risk factors e.g. Forwards.

7. Mapping for non-linear derivatives: Delta-Normal cannot be expected to provide as accurate estimate of the

VaR where Deltas are not stable

a. Deep out of money and in the money options have stable deltas

RISK FOR TRADING BOOKReading: Messages from the Academic Literature on Risk Measurement for the Trading Book,” Basel Committee on

Banking Supervision, Working Paper, No. 19, Jan 2011

1. VaR Implementation: Time varying volatility results from volatility fluctuation over time. As time horizon

increases, the effect of time varying volatility decreases.

2. Integrating liquidity risk:

a. Exogenous Liquidity: Refers to transaction costs for trades of average size. Its calculation is handled

thorough LVaR (Liquidity adjusted VaR). The LVaR incorporates bid-ask spread as a risk factor.

b. Endogenous Liquidity: It is related to the cost of unwinding portfolios large enough that the bid-ask

spread cannot be taken as given, but is affected by the trades themselves

3. Stress testing:

a. Historical Scenarios: Examine historical data

b. Predefined scenarios: Assess impact on profit by changes in predetermined risk factors

c. Mechanical-search stress: Automated routines to cover possible changes in risk factors

4. Risk Aggregation:

a. A compartmentalized approach sums up the risks measured separately. A unified approach considers

the interaction among the risk factors.

b. A top-down approach assumes that a bank’s portfolio can be cleanly sub-divided into Market, Credit and

Operational Risk measures. To better account for risk factors, a bottom up approach should be used

5. Balance Sheet Management: The amount of leverage on the balance sheet is pro-cyclical. Leverage is inversely

related to net worth. This results in a feedback loop (Asset prices increase in a boom and decrease in a bust,

increasing leverage). Thus, institutions economic capital tends to amplify boom and bust cycles

CORRELATION BASICSReading: Chapter 1, Gunter Meissner, Correlation Risk Modeling and Management (New York: John Wiley & Sons, 2014)

1. Definitions:

a. Correlation Risk: Measure risk of financial loss resulting from adverse changes in correlations

b. Static Correlations: Do not change over a period of time. E.g. VaR

c. Dynamic Correlations: Measure co-movement of assets over time. E.g. pairs trading

d. Wrong way risk: E.g. Positive correlation between CDS Issuer and Asset

e. Concentration Risk: Loss due to higher exposures to certain counterparties. Measured by concentration

ratio

2. Correlation Options: Prices are sensitive to correlation between assets often referred to as multi-asset options

3. Quanto Options: Used to protect from foreign currency risks

4. Correlation Swap: A fixed correlation is swapped for the actual correlation that occurs.

a. Realized Correlation is calculated as:ρ = ∑ ρ

EMPIRICAL PROPERTIES OF CORRELATIONReading: Chapter 2, Gunter Meissner, Correlation Risk Modeling and Management (New York: John Wiley & Sons, 2014)

1. Definitions:

a. Correlation between Equities: Is high during recession and low during expansionary phase of economy

b. Correlation Volatilities: Highest during normal times and lower during recession and expansion phases

c. Mean reversion: Variables return to their average value over a period of time. Δ = a(µ − S )d. Autocorrelation measures current variable with respect to past values

2. Empirical Findings for Equity, Bond and Default Correlation

STATISTICAL CORRELATION MODELSReading: Chapter 3, Gunter Meissner, Correlation Risk Modeling and Management (New York: John Wiley & Sons, 2014)

1. Limitations of Financial Models:

a. Inaccurate inputs (In times of stress, correlation increase significantly and can't use normal correlations)

b. Erroneous assumptions regarding distributions (BSM assumes constant volatility and not a smile)

c. Mathematical inconsistency (Certain inputs to BSM make models insensitive to implied volatility)

2. Pearson Correlation: Used to measure linear relationships between two variables

a. ρ , = , where Cov , = ∑ ( )( )b. The formula ensures that correlation is always between -1 and 1

3. Spearman Rank Correlation: It does not require the knowledge of distribution of the variables

a. ρ = 1 − ∑( )b. Rank all variables in X as 1 to n in order they appear. Then sort all variables from smallest to largest in Y

and rank them 1 to n

c. Calculate difference between ranks and square the difference (this is di2)

4. Kendal τ: Another ordinal measure like Spearman

5. Disadvantages of Ordinal Measures:

a. Only show rank of variables and problems arise when cardinal observations likes quantity or value of

observations are used

FINANCIAL CORRELATION MODELING

Reading: Chapter 4, Gunter Meissner, Correlation Risk Modeling and Management (New York: John Wiley & Sons, 2014)

1. Definitions:

a. Copula: Creates a joint probability distribution between two or more variables

2. Gaussian Copula: Maps distribution of each variable into a Normal distribution

a. Mapping is done on a percentile basis. First, X distribution is mapped to a standard Normal distribution

and then Y distribution is mapped

b. Helps calculate correlation between variables

EMPIRICAL APPROACHESReading: Empirical Approaches to Risk Metrics and Hedging (Chapter 6, Bruce Tuckman, Fixed Income Securities, 3rd

Edition (Hoboken, NJ: John Wiley & Sons, 2011))

1. Issues with DV01 Hedging:

a. DV01 hedge assumes that there is no basis risk i.e. yield on bond and hedging instrument rise and fall by

the same amount

2. One variable regression hedge: We plot a regression line with nominal yield as dependent variable and the real

yield as the independent variable. We get an equation of the form Δynominal = α + β Δyreal + ε. From this equation,

we take the value of β and adjust the DV01 hedge as

a. Hedge Value = β x [ DV01Nominal / DV01Real ] x Value of Portfolio

b. Regression hedge assumes that β is constant over time which is not the case

3. PCA (Principal Component Analysis): It provides a single empirical description of term structure behavior, which

can be applied to all bonds. The advantage is that we need to describe the volatility and structure of a small

number of principal components which approximate all movements in term structure.

TERM STRUCTURE MODELSReading: The Science of Term Structure Models, (Chapter 7, Bruce Tuckman, Fixed Income Securities, 3rd Edition

(Hoboken, NJ: John Wiley & Sons, 2011))

1. Binomial Rate Model: The model assumes that interest rates can only take one of two possible values in the

next period

a. The values for the interest rate tree should prohibit arbitrage i.e. the current value should be the same

as market value

b.

2. Recombining and Non-recombining: If the interest rate in the middle node is the same irrespective of up or

down move, then the tree is recombining else its non-recombining

3. Constant Maturity Treasury Swap: It is an agreement to swap a floating rate for a treasury rate such as 10-year

rate

a. E.g., , × [ ]

where ycmt is the semiannual yield of a predetermined maturity at

payment date (Do not forget to add the payoff amount at every node to the discounted value)

4. Black-Scholes-Merton: We cannot use BSM for valuation of Fixed income securities due to assumptions like:

If q = 0.5, then it is called realworld probability. If q ≠ 0, thenthe probability is called risk-neutral (ie. It equates the currentprice with market price)

Do not forget to adda coupon/payoff inevery node valuederived

If current value equalsmarket observed value, wecall it risk neutral pricing.

a. No upper price bound

b. Risk free rate is constant

c. Bond volatility is constant

5. Fixed Income with Options: Embedded options change the price-yield relationship and hence affect the price

volatility characteristics of the issue

TERM STRUCTURE MODELSReading: The Evolution of Short Rates and the Shape of the Term Structure (Chapter 8, Bruce Tuckman, Fixed Income

Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011))

1. Expected Rates: If the expected 1 year spot rates for the next three years are r1, r2, r3 then the two year spot

rate is given as ȓ (2) = (1 + r )(1 + r ) – 1 and 3 year sport rate ȓ (3) = (1 + r )(1 + r )(1 + r ) – 12. Convexity effect: The difference between the risk neutral spot rate and the middle node rate of the tree is the

convexity effect i.e. when there is uncertainty regarding the future rate, the volatility of expected rates causes

future spot rates to be lower.

3. Jensen’s Inequality: The convexity effect can be measure using a special case of Jensen’s inequality

a. ( . × )( . × ) > (0.5 ( )) + (0.5 ( )) i.e. E 1(1+r) > 1E[1+r]b. All else held equal, the value of convexity increases with maturity

4. Risk premium: Risk averse investors will price bonds with a risk premium to compensate them for taking interest

rate risk. This risk premium is added to all interest rates after current spot rate for a year

Risk neutral rate is9.952% (Derived bydiscounting and thencalculating 3 year spotrate)

TERM STRUCTURE MODELS - DRIFTReading: The Art of Term Structure Models: Drift (Chapter 9, Bruce Tuckman, Fixed Income Securities, 3rd Edition

(Hoboken, NJ: John Wiley & Sons, 2011))

1. Model 1(No Drift): It assumes no drift and that interest rates are normally distributed. The continuously

compounded rate rt will change as dr = σ dw where dr is the change in rate over small period of time, dt is small

time interval (measured in years i.e. 1 month will be 1/12), σ is annual basis point volatility of rate change and

dw is normally distributed random variable with mean 0 and standard deviation as da. Limitations: Volatility is predicted to be flat, only one factor, the short term rate; and any change in

short term rate would lead to a parallel shift in the curve

2. Model 2(Constant Drift): It adds a constant positive drift λdt (positive risk premium) to the model 1 equation,

thus dr = σ dw + λ dt where the drift combines the rate change with a risk premium. The tree is recombining as in

Model 1 but the middle node value dos not equal the first node value

a. Limitations: Calibrated values of drift are often too high, requires forecasting of risk premiums

3. Ho-Lee Model (Time dependent drift): Drift can be negative and is time dependent i.e. drift in time 1 can be

different from drift in time 2. Thus in time 1, dr = σ dw + λ1 dt and in time 2, dr = 2 σ dw + ( λ1 + λ2 )dt

4. Vasicek Model: It assumes a mean reverting process for short term rates. Thus, dr = σ dw + k (θ – r) dt where k

is the speed of mean reversion, θ is the long run value. Also, θ ≈ rLong +

a. Limitations: Breaks down during period of hyperinflation or similar structural breaks

b. Rate in T years: (θ – r)e and half-life is calculated as (θ – r)e = (θ – r)

TERM STRUCTURE –VOLATILITY & DISTRIBUTIONReading: The Art of Term Structure Models: Volatility and Distribution (Chapter 10, Bruce Tuckman, Fixed Income

Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011))

1. Model 3(Time dependent drift and volatility): It augments the Ho-Lee model with time dependent volatility.

Thus, dr = λ(t)+σ e–αt dw where e–αt decreases to 0 exponentiallya. It adds flexibility to models of future short term rates and is useful for pricing multi-period derivatives

like interest rate caps and floors

b. Limitation: Basis point volatility is determined independently of the current short term rate

2. Cox-Ingersoll-Ross (CIR): The annual basis point volatility increases as square root of current short term rate.

Thus, dr = k (θ – r) dt + σ √r dw3. Lognormal Model (Model 4): The volatility of basis points increases with rate. Thus, dr = ar dt + σ r dw where ar

is the drift

a. Deterministic Drift: dr= r e( ) or dr = r e[( ) ]b. Mean reversion: r e[ ( ) ] It is also known as Black-Karasinki model

4. Terminal Distributions of Sort Term Rate after 10 years

OIS DISCOUNTINGReading: OIS Discounting, Credit Issues, and Funding Costs (Chapter 9, John Hull, Options, Futures, and Other Derivatives,

9th Edition (New York: Pearson, 2014))

1. Definitions:

a. LIBOR: Short term interest rate that creditworthy banks (AA or better) charge each other

b. Federal Funds Rate: rate at which large financial institutions borrow from each other in US

c. OIS (Overnight Indexed Swap): Interest rate swap where fixed(OIS Rate) is exchanged for floating where

floating rate is geometric mean of federal funds rate during the period

2. Disadvantages of Treasury Rates:

a. T-bills and T-Bonds must be purchased by financial institutions and thus increase ind demand drops yield

down

b. Capital required to support investments in T-bills and T-bonds is smaller

c. They get favourable tax treatment in US

3. Disadvantages of LIBOR:

a. LIBOR is volatile in stressed conditions (Spread between LIBOR-OIS during recent financial crisis was 364

basis points)

b. LIBOR incorporates some credit risk. Thus, credit risk may be counted twice

VOLATILITY SMILESReading: Reading: Volatility Smiles (Chapter 20, John Hull, Options, Futures, and Other Derivatives, 9th Edition (New

York: Pearson, 2014))

1. Implied Volatility: Implied volatility of a call and put option will be equal for the same strike price and time to

expiration. i.e. PMkt - PBSM = CMkt - CBSM2. Volatility Smiles: Actual option prices in conjunction with BSM model can be used to derive Implied Volatility.

Implied volatility as a function of strike price generates a volatility smile curve (Options in Currency).

a. Implied volatility is higher for deep in-the-money (ITM)

and out-of-money (OTM) options.

b. This tendency results in greater chance of extreme price

movements than predicted by lognormal distribution

c. Also, long dated options tend to exhibit less of a

volatility smile than shorter dated options.

3. Volatility Skew: The smile is more of a skew for equity options.

a. There is higher implied volatility for low strike price options

(i.e. in-the-money call and out-of-money puts)

b. Probability of large down movements in price is greater than

large up movements

4. Volatility Term Structure: It is a listing of implied volatilities as a function of time to expiration for at-the-money

option contracts

5. Volatility Surface: Combination of volatility smiles with volatility term structure

6. Greeks:

a. Sticky Strike: Implied volatility is the same over short periods of time and greeks are unaffected

b. Sticky Delta: Relationship between options price and ratio of underlying to strike price remains same

7. Price Jumps: Due to price jumps, the volatility smile turns into volatility frown i.e. at-the-money options exhibit

greater implied volatility

CREDIT RISKFRM 2016 Part 2 Revision Course

CREDIT DECISIONReading: The Credit Decision (Chapter 1, Jonathan Golin and Philippe Delhaise, The Bank Credit Analysis Handbook

(Hoboken, NJ: John Wiley & Sons, 2013))

1. Credit Risk: It is the probability that the borrower will not repay the loan in accordance to the terms of

agreement

2. Components of Credit Risk:

a. The capacity and willingness to repay of obligor

b. External environment (Operating conditions, country risk, etc.)

c. Characteristic of relevant credit instrument (Product, facility, issue etc.)

d. Quality and sufficiency of any credit risk mitigants (Collateral, Guarantees, Credit enhancements etc.)

3. Qualitative & Quantitative Techniques:

a. Qualitative technique are primarily used to assess the borrowers willingness to repay the loan and

quantitative techniques are used to assess the ability to repay

b. Gathering information from different sources, face to face interviews, past loan information etc. are

used as some qualitative techniques

c. Analyzing financial statements is the primary quantitative technique

4. Measures to evaluate credit risk:

a. PD (Probability of default): Likelihood that borrower will default

b. LGD (Loss Given default): Likely percentage loss in case of default

c. EAD(Exposure at Default): Amount outstanding at time of default

d. EL (Expected Loss): PD x LGD x EAD

5. Bank Solvency: Bank insolvency does not mean that bank failure. A bank maybe insolvent but avoid failure as

long as it has sources of liquidity like the Federal Reserve.

CREDIT ANALYSTReading: The Credit Analyst (Chapter 2, Jonathan Golin and Philippe Delhaise, The Bank Credit Analysis Handbook

(Hoboken, NJ: John Wiley & Sons, 2013))

1. Credit Analyst Roles:

a. Consumer Credit Analyst: Works with individual consumer mortgages, with key objective being detailed

documentation

b. Credit Modelling Analyst: Focused on electronic scoring system, roles include developing, testing,

implementing and updating various credit scoring systems

c. Corporate Credit Analyst: Scope of analyst is limited to corporations.

d. Counterparty Credit Analyst: Analyze two-way counterparties, performs credit reviews, approves limits,

develops/ updates credit policies and procedures

2. Functions:

a. Counterparty Credit Analyst: Perform risk evaluation of a given entity on a transaction by transaction

basis or through annual review. Additionally, she may be required for compliance tasks related to Basel

2 and 3

b. Fixed Income and Equity Analyst: Provide recommendations whether to buy, sell or hold securities.

Fixed income analysts focus on determining relative value while equity analyst focus on return on equity

3. Basic Skills:

a. Able to read and interpret financial statements

b. Background in statistical concepts and macroeconomics

4. Sources of Information:

a. Corporation websites, internet, rating agencies report, regulatory filings etc.

DEFAULT RISK: QUANTITATIVE METHODSReading: Default Risk: Quantitative Methodologies (Chapter 3, de Servigny and Renault, Measuring and Managing Credit

Risk)

1. Merton Model: Structural models estimate default risk as a function of the value of the firm. Such models are

also sometimes called as value-based models.

a. Merton model assumes that Debt (D) of a firm consists only of a single zero-coupon bond issue, value of

firm(V) and equity is (E)

b. If value of firm is less than value of the debt, then the firm defaults. Payoff = D – max(D-V, 0)

c. Payment to stockholders happens only if value of firm is more than the debt. Payoff = max(V-D, 0)

d. Merton model assumes that Value (V) follows a Geometric Brownian motion and thus, payment to

stockholders is like the payoff on a long call option. The debt holder’s payoff resembles that of a short

put and a risk free bond. Value of Debt is taken a strike price and

e. Other assumptions: Bondholders cannot force bankruptcy prior to maturity, value of firm is observable.

f. As per Merton’s Model: E = V N(d ) − Be ( ) N(d )i. N(d ) = ( )√ + σ √T − t and = d − σ √T − t

ii. Note: We replace S with V and X with B in the BSM equation we learnt earlier

g. To calculate Debt, we use the simple formula: V = E + D i.e. Value of Firm is Value of equity + value of

Debt or we can calculate D as D = Be ( ) − P where Pt is value of put option calculate using BSM2. KMV Model: It builds on the Merton model and removes restrictions like all debt matures at same time. It

assumes that there are two kinds of debt, Long term (LT) and Short term (ST). The default threshold is given as

a. If LT/ST < 1.5, then Default Point = ST+ (0.5 LT)

b. If LT/ST > 1.5, then Default Point = (ST + LT) 0.7

c. Distance to Default (DD): It considers the firms asset returns and calculates the no. of standard deviation

between mean and the default threshold.

i. DD = .3. Credit Scoring Models:

a. Fisher-Linear Discriminant: A process that segregates a larger group into homogenous subgroup(Z score)

b. Parametric Discrimination: It uses a score function to determine the members of the subgroup

c. K Nearest neighbor: A non-parametric technique. Uses properties of firms into categories of interest and

categorizes a new entrant by how closely it resembles the members already in the group

d. Support vector Machines: Creates an equation by observing the characteristics of the firm

4. Decision Rules:

a. Minimum Error: Forms a conditional probability of a firm being in one group or another

b. Minimum Risk: Rules try to minimize misclassification or to minimize loss associated with error

c. Neyman-Pearson: Type 1 error is lending to a risk firm as it was incorrectly accepted as non-risky. Uses

equations to minimize type 1 error

d. Minimax: Minimizing the maximum error or risk

5. Measures of Performance of Models:

a. Receiver Operating Characteristics(ROC): Evaluates credit decision rules by computing the proportion of

correctly predicted results(Y) and incorrect predictions(X)

i. = . . and = . .ii. Cumulative Accuracy profile(CAP): Compares probability of default computed by classification

system to ranking of observed defaults

CREDIT RISK AND DERIVATIVESReading: Default Risk: Credit Risks and Credit Derivatives (Chapter 18, René Stulz, Risk Management & Derivatives

(Florence, KY: Thomson South-Western, 2002))

1. Merton Model: Refer previous chapter for notes

2. Credit Spreads: It is the difference between the yield on risk bond and risk free bond. As the time to maturity

increases credit spreads tend to widen. As risk free rate increases, value of firm increases, which in turn

decreases risk of default

3. Firm Volatility: Delta is the rate of change of the call option relative to change in value of the underlying asset.

Changes in Delta indicate the value of equity volatility is not constant ad I referred to as volatility smirk. The non-

constant volatility is a violation of BSM

4. Subordinate Debt: In distress (low firm value), volatility of financial firm will increase, value of subordinate debt

will increase while value of senior debt will decline. This is because subordinate debt behaves like equity when

the firm has low value and behaves like senior debt when the firm is not in financial distress

5. Interest rate Dynamics: Increases in interest rate will decrease the value of debt. To hedge debt, we need to

account for the interactions between changing interest rate and firm value.

6. Difficulties with Merton Model:

a. Firms capital structure is more complex than assumed

b. Merton model does not allow for jumps in the firm value (Defaults are surprises)

c. PD using Merton Model: PD = N ( ) ( ) ( ) . ( )√ andLGD = F × PD − Ve ( ) × N ( ) ( ) ( ) . ( )√ wherei. F is face value of zero coupon bond,

ii. V is value of firm,iii. T is maturity date of bond,iv. σ is volatility of firm value,v. μ is expected return on value of firm

7. Credit Risk Portfolio Models:

Model Name Explanation

Credit Risk+ Measures credit risk using common risk factors. There are only two outcomes: Default or no-default.

The PD is dependent on the credit ratings and sensitivity to each risk factor. All risk factors have a mean

value of +1. The risk factors are assumed to follow a gamma distribution. If the value of risk factor

increases, the probability of default increases

Credit Metrics It is used to calculate credit VaR of large portfolios. Calculate PV of all debt flows using forward rates

obtained from the spot rate curve for each rating category. Multiply the probability of rating change

with the mean value obtained. IN cumulative probability, look at significance level and the value is VaR

Moody’s KMV It calculates EDF(Expected Default Frequency) for each obligor. It solves for firm value and volatility. The

primary advantage is that it uses current equity values

Credit Portfolio

View

It models the rating transition matrix using macroeconomic cycle data. Macroeconomic factors are

considered the prime moving factors in default rates.

8. Credit Derivatives:

a. Credit Default Put: It pays on maturity on the default of the debt.

b. Credit Default Swap: The purchaser of CDS seeks credit protection. The purchaser will make fixed

payments to the seller of CDS for the life of the swap or until a credit event occurs

c. Total Rate of Return Swaps (TORR): The exchange of total return on a bond for a floating rate (e.g.LIBOR)

plus a specified spread. The total return also includes both capital gains and cash flows (e.g. Coupons)

over the life of the swap

d. Vulnerable Options: An option holder receives the option payment only if the seller of the option is able

to make the payments. The correlation between the value of the firm and the underlying asset value is

important for valuation of the vulnerable options.

CREDIT AND COUNTERPARTY RISKReading: Credit and Counterparty Risk (Chapter 6, Allan Malz, Financial Risk Management: Models, History, and

Institutions (Hoboken, NJ: John Wiley & Sons, 2011))

1. Credit Risk: It is either the risk of loss from default or changes in credit events or ratings. Credit risky securities

include corporate or sovereign debt, credit derivatives(CDS) and structured credit products(MBS)

2. Book and Market Value:

a. Book Value: Refers to accounting balance sheet of the firm where assets, debt and equity are typically at

book value.

b. Market Value (Economic Balance Sheet): Components are valued at Market prices.

3. Debt Seniority: Senior debt is paid first, while subordinated or junior debt is repaid only if and when the senior

debt is paid. Unsecured obligations have a general claim on the firm’s assets in bankruptcy. Secured obligations

have a claim on specific assets. A claim on collateral is called a lien on the property. Secured debt is said to have

priority over unsecured debt in the event of bankruptcy. Secured claims may have a first, second, or even third

lien on the collateral

4. Credit contract frictions:

a. Asymmetric Information: Borrower often has better information than the creditor

b. Principal-Agent problems: Interests of banks depositors are different from banks managers

c. Risk Shifting: Equity investors benefit from increased leverage whereas bondholders risk increases

d. Moral Hazard: Buying insurance or some protection reduces the incentive to avoid insured event

5. Expected Loss (EL): EL = PD × LGD × EAD or EL = PD × (1 − RR) × EAD6. Counterparty Risk:

a. Double default risk: Party that sold the default protection will default at the same time as the third

party.

b. Custodial Risk: Many brokers perform custodial as well as credit intermediation services for their clients.

During the Lehman bankruptcy in September 2008, customers of the firm’s U.K. subsidiary were

particularly badly situated, as even their unpledged assets were typically not segregated, but might be

subject to rehypothecation. If the customer’s securities are rehypothecated by the broker, the customer

becomes a creditor of the broker

7. Jump to default risk: Jump-to-default risk is an estimate of the loss that would be realized if a position, were to

default instantly.

SPREAD RISK AND DEFAULT INTENSITYReading: Spread Risk and Default Intensity Models (Chapter 7, Allan Malz, Financial Risk Management: Models, History,

and Institutions (Hoboken, NJ: John Wiley & Sons, 2011))

1. Credit Spreads: Difference in yields between the security and a reference security of the same maturity

a. Yield Spread: YTM Risky Bond – YTM of govt. Bond

b. i-spread: YTM Risky Bond – Linearly interpolated YTM of govt. bond

c. z-spread(zero coupon): spread that must be added to the Libor spot curve to arrive at the market price

d. asset-swap spread: spread on the floating leg of an asset swap on a bond

e. credit default swap spread: is the market premium of a CDS on similar bonds of the same issuer

f. Option adjusted spread: version of the z-spread that takes account of options embedded in the bonds

2. Spread’01: Change in the bond price from a 1 basis point change in the z spread

3. Hazard Rate: The hazard rate, also called the default intensity, denoted λ, is the parameter driving default

a. Cumulative probability of default is given as 1 − e and that of survival is eb. As t grows large, default probability converges to 1 and survival probability to 0

4. Risk neutral hazard rates: λ ≈5. Advantages of Using CDS for Hazard Rate: Primary advantage is that CDS rates are observable. CDS has large

liquid contracts for longer maturities.

6. Spread Risk: Change in the value of securities from changing spreads. Entire CDS curve is shocked p and down by

0.5 basis points to compute the CDS mark to market value. Spread risk can also be measured by the historical or

forward looking standard deviation of credit spreads.

PORTFOLIO CREDIT RISKReading: Portfolio Credit Risk (Chapter 8, Allan Malz, Financial Risk Management: Models, History, and Institutions

(Hoboken, NJ: John Wiley & Sons, 2011))

1. Default Correlation: the likelihood of having multiple defaults in a portfolio of debt issued by several obligors.

a. ρ = ( ) ( )2. Credit VaR: Defined as the quantile of the credit loss less the expected loss

a. If default correlation in a portfolio of credits is equal to 1, then the portfolio behaves as if it consisted of

just one credit. No credit diversification is achieved

b. If default correlation is equal to 0, then the number of defaults in the portfolio is a binomially distributed

random variable

c. Credit VaR is higher for higher probability of default but decreases as credit portfolio becomes more

granular, that is, contains more independent credits, each of which is a smaller fraction of the portfolio

3. Single Factor Model (Conditional Default Model): Used to examine impact of varying default correlation based

on a credit position. Each firm i, has a default correlation βi with market return m. The firms asset return is

defined as: a = β m + 1 − β ε where mean is β m and standard deviation is 1 − β4. Credit VaR with Single Factor Model (Unconditional Distribution): ( ) = Φ where m is realized

market return, β2 is default correlation and Φ means standard normal value. The probability of reaching the

default threshold is the same as the probability that market return is m or lower i.e.Φ(m).5. Credit VaR using Copula: Define the copula function, simulate default times, obtain market values and profit

and loss data for each scenario, compute portfolio distribution statistics

STRUCTURED CREDIT RISKReading: Portfolio Credit Risk (Chapter 9, Allan Malz, Financial Risk Management: Models, History, and Institutions

(Hoboken, NJ: John Wiley & Sons, 2011))

1. Definitions:

a. Securitization: Pooling of credit sensitive assets and creation of new securities

b. Capital Structure: Refers to the priority assigned to the tranches of a securitized asset

c. Credit Enhancements: can be external or internal

i. External: Credit protection is through swaps or insurance.

ii. Internal: Over-collaterlization or excess spread provide credit protection

d. Waterfall Structure: Outlines rules that govern distribution of cash flows to different tranches

e. Default 01: PD is shocked by 10 bps and tranches are revalued using simulations

2. Three-tiered Securitization Structure:

a. Has three tranches (Equity, Mezzanine and Senior)

b. Equity tranche has the lowest priority

3. Simulation of Credit losses

a. Estimate parameters like Default rate, pair-wise correlations and generate simulation

b. Compute losses for each simulation run

4. Effects on Tranche Values

a. Senior Tranche

i. As PD or Correlations increase, value of Senior tranche declines

b. Equity Tranche

i. As Correlation increases, value of equity tranche increases

ii. As PD increases, value of Equity tranche decreases

c. Mezzanine Tranche

i. When PD and correlations are low, it resembles a Senior tranche

ii. When PD and correlation are high, it resembles a equity tranche

DEFINING COUNTERPARTY CREDIT RISKReading: Defining Counterparty Credit Risk (Chapter 3, Jon Gregory, Counterparty Credit Risk and Credit Value adjustment:

A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012).

1. Definitions:

a. Counterparty Credit Risk: Counterparty is unable or unwilling to fulfill contractual obligations

b. Repos: Short term lending agreements usually secured by collateral.

c. Credit Exposure: Loss that is conditional on counterparty defaulting

2. Methods to manage counterparty risk:

a. Cross Product netting: Netting agreement allows counter parties to net cross-product payments

b. Close-out: Immediate closing of all contracts with a counter party

c. Collateralization: Collateral to support net exposure between counter parties

d. Walk-away: Allows party to cancel all transactions if a counterparty defaults

e. Central Counterparties: Routing transactions through exchanges

NETTING, COMPRESSION, RESETS AND TERMINATIONReading: (Chapter 4, Jon Gregory, Counterparty Credit Risk and Credit Value adjustment: A Continuing Challenge for Global

Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012).

1. Definitions:

a. ISDA Agreement: International Swaps and Derivative Association (ISDA)Master agreement standardizes

OTC agreements to reduce legal certainties and mitigate credit risk

b. Acceleration Clause: Allows acceleration of future payments on some credit events

c. Reset agreement: readjusts parameters that are heavily in the money by resetting the trade to be at the

money

d. Trade Compression: Reduction in net exposure by removing portfolio redundancies among trade with

multiple counterparties

2. Netting and Close out:

a. Netting refers to combining cash flows from different contracts with the same counterparty into a single

net amount

b. Close out netting: netting of contract values in the event of counterparties default

COLLATERALReading: (Chapter 5, Jon Gregory, Counterparty Credit Risk and Credit Value adjustment: A Continuing Challenge for Global

Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012).

1. Definitions:

a. Collateral: An asset supporting a risk in legally enforceable way

b. Valuation Agent: Calculate exposure, credit support amounts, delivery or return of collateral

c. Credit Support Annex: Incorporated into ISDA agreement allows parties to mitigate credit risk through

posting of collateral

d. Threshold: Level of exposure below which collateral will not be called

e. Rehypothecation: refers to posting of collateral to other counterparties

2. Types of Collateral Used: Cash, Government Securities. Can also include MBS, Corporate Bonds, and Commercial

Paper

CENTRAL COUNTERPARTIESReading: Central Counterparties (Chapter 7, Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A

Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012))

1. Objective of CCP: To reduce counterparty risks and provide a safety net for systemic risks

2. Functions of CCP:

a. CCP positions itself between two parties of a transaction, this is called novation

b. Requires initial as well as variation margins

c. Maintains a fund called default fund or reserve fund

3. Weakness of CCP:

a. OTC derivatives are illiquid, long-dated and complex compared to exchange traded derivatives and

hence are a challenge

b. CCP’s clearing OTC products will become systemically important themselves creating a moral hazard

during times of distress

c. CCP’s introduce more costs

d. Mutualisation means all members are treated in the same way. Most credit-worthy members may see

less advantage of their stronger credit quality.

4. Loss Waterfall Model:

Example: Current Annual profits

CREDIT EXPOSUREReading: Credit Exposure (Chapter 8, Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing

Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012))

1. Definitions:

a. Expected Exposure(EE): Amount that is

expected to be lost in case of positive MtM

b. Potential Future Exposure(PFE): Estimate of

MtM value at some point in the future or the

worst exposure at a given time interval in the

future for a given confidence level

c. Expected Positive Exposure(EPE): It is the

average EE through time

d. Effective EE: Non-decreasing EE. Used to capture risk for roll-over transactions

e. Effective EPE: Average of Effective EE

f. Re-margin Period: Period from which a collateral call takes place to when the collateral is actually

delivered

2. Calculating EE and PFE

a. EE: 0.4 × σ × T2 where σ is volatility of collateralized exposure and T2 is re-margin frequencyin years

b. PFE: k × σ × T2 where k is a constant depending on the confidence level (e.g. for 99% k=2.33)c. Volatility if there are non-cash collateral: σ + σ − 2σ σ ρ2 where σ and σ are volatilities of

underlying and collateral

3. Disadvantages of PFE:

a. It assumes a strongly collateralized position

b. It fails to account for collateral volatility

c. Liquidity and liquidation risks are not considered

d. Wrong way risk is not considered

DEFAULT PROBABILITY, CREDIT SPREADSReading: Default Probability, Credit Spreads, and Credit Derivatives (Chapter 10, Jon Gregory, Counterparty Credit Riskand Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John

Wiley & Sons, 2012))

1. Definitions:

a. Cumulative Default Probability: Represents the likelihood of counterparty default from current time to a

future date

b. Marginal Default Probability: Likelihood of counterparty default between two future points in time

c. Risk neutral default probability: Calculated from market information. They represent parameter value

from observed market price

d. Real world default probability: Calculated from historical data

2. Estimation approaches:

a. Historical data approach: Use historical default data to forecast future default probabilities

b. Equity based: Merton model, KMV are examples. It allows for dynamic approach to calculation

i. Merton Model: Equity value is call option with strike price as debt level. All debt is considered as

a single coupon payable at maturity.

ii. KMV: Relaxes certain assumptions in the Merton model

3. Index Tranches:

a. They create a capital structure for credit index whereby the loss is divided into mutually exclusive

ranges. The losses are absorbed sequentially by equity, mezzanine, senior and super-senior tranches

CREDIT VALUE ADJUSTMENTReading: Credit Value Adjustment (Chapter 12, Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A

Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012))

1. Definitions:

a. Credit Value: It is the price of counterparty credit risk. A positive CVA increases the costs of the

counterparty. It is calculated as CVA = LGD × ∑ d(t ) × EE(t ) × PD(t , t )i. d(t ) are discount factors for future losses

b. Incremental CVA: it is the change in CVA that a new trade will create

c. Marginal CVA: Breaks down netted trades into trade level contributions to the sum total of CVA

2. CVA as running spread

a. To calculate a running spread, the following formula is used Spread = EPE × Credit Spreadb. This is the amount a trader adds or subtracts from a trade leg as CVA

3. Impact of changes of Credit Spread/ Recovery rates on CVA

a. CVA increases with increase in Credit Spread

b. Increase in Recovery rate will reduce the CVA

WRONG WAY RISKReading: Wrong Way Risk (Chapter 15, Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing

Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012))

1. Definitions:

a. Wrong way Risk: Outcome of an association, dependence or linkage between exposure and

counterparty creditworthiness that generates an increase in counterparty risk.

CREDIT SCORINGReading: Credit Scoring and Retail Credit Risk Management (Chapter 9, Michel Crouhy, Dan Galai and Robert Mark, The

Essentials of Risk Management, 2nd Edition (New York: McGraw-Hill, 2014))

1. Definitions:

a. Retail Banking: Large number of small value loans where incremental exposure of any single loan is small

b. Dark Side of Retail Credit: During economic troubles, there are sudden upward movements in default

rates and unexpected falls in collateral values

c. Characteristics: Information items/ Questions in credit applications

d. Attributes: Answers to the characteristics given

2. Credit Scoring Models:

a. Credit Bureau Scores: Known as FICO scores (350-800). They are provided by an agency like Fair Isaac

Corporation/ Equifax

b. Pooled Models: Models built by outside vendors by collecting data from various sources. More

expensive than generic scores like FICO

c. Custom Models: Models are developed in-house by collecting the data on internal customers. Most

expensive but are tailored and can offer the best risk adjusted pricing

d. Key Variables: DTI (Debt to Income), LTV (Loan to Value), PMT (Payment type like ARM’s)

3. Model/ Scorecard Performance

AR = Actual DefaultsAP = Model predicted defaults

CREDIT TRANSFER MARKETSReading: The Credit Transfer Markets-and Their Implications (Chapter 12, Michel Crouhy, Dan Galai and Robert Mark,

The Essentials of Risk Management, 2nd Edition (New York: McGraw-Hill, 2014))

1. Flaws in subprime securitization

a. OTD (Originate to Distribute) model reduced the incentives for the bank to monitor the creditworthinessof the borrower. Banks held many MBS in place of transferring risk.

b. Growth in CDS markets made credit risk easier to trade enhancing the perceived liquidity of creditinstruments

c. Low risk premiums and rising asset prices contributed to low default rates reinforcing perception of lowlevels of risk

2. Techniques for Credit Risk Mitigation: Bond Insurance, Guarantees, Collateral, Early Termination(After a credit

event), Reassignment(Transfer to 3rd party after a credit event), Netting, Mark to Market, Loan Syndication,

Credit Default Swaps(CDS)

3. Credit Derivatives:

Credit Default

Swaps (CDS)

Total Return Swap

(TRS)

Credit Linked Note

(CLN)

INTRODUCTION TO SECURITIZATIONReading: An Introduction to Securitization (Moorad Choudhry, Structured Credit Products: Credit Derivatives & Synthetic

Securitization, 2nd Edition (John Wiley & Sons, 2010))

1. Definitions:

a. Securitization refers to the process of creation of asset backed securities from loan assets

b. First loss piece/ equity tranche: The most junior tranche because it is impacted by losses first.

c. Credit Enhancement: Measures that improve the rating of the ABS (Asset Backed Securities) e.g. Over

collateralization, Senior/ Junior tranches, excess spread

2. Structures of SPV used for securitization:

a. Amortizing: pay principal and interest on a coupon basis throughout the life

b. Revolving: During the revolving period, principal repayments are used to purchase new receivables

c. Master: Allows multiple securitization to be issued form same SPV

3. Performance Analysis:

a. DSCR (Debt Service Coverage Ratio): Net Operating Income/ Debt Payments. Needs to be more than 1

b. WAC (Weighted Average Coupon): Weighted coupon rate of the MBS pool

c. WAM (Weighted Average Maturity): Term to maturity of the underlying pool of MBS in months

d. WAL (Weighted Average Life): = ∑ . ( ) where PF(s) = Pool factor and t = actual/365e. CPR (Constant Payment Rate): = 1 − (1 − ) where SMM is Single Monthly Mortalityf. Public Securities Association (PSA): Standard value of CPR of 0.2% per month up to 30 months i.e. 6%.

This is called 100% PSA. It assumes mortgages prepay slower during the first 30 months

g. Default Ratio: Total credit card receivables written-off/ total credit card receivables

h. Delinquency Ratio: Credit card receivables for more than 90 days/ total credit card receivables.

i. MPR (Monthly Payment Rate): Reflects proportion of principal and interest that is repaid in a period

SUBPRIME MORTGAGE CREDITReading: Adam Ashcraft and Til Schuermann, “Understanding the Securitization of Subprime Mortgage Credit,” Federal

Reserve Bank of New York Staff Reports, No. 318 (March 2008)

1. Friction in Subprime Mortgage Securitization:

a. Mortgagor vs. originator: Typical mortgagor is not financially sophisticated

b. Originator vs. Arranger: The arranger(Issuer) is at an information disadvantage compared to the

originator

c. Arranger vs. Third Parties: Arranger has more information than third parties

d. Servicer vs. Mortgagor: Conflict arises for delinquent loans

e. Servicer vs. Third Parties: Moral hazard as servicer has incentive to show higher recovery rates

f. Asset Manager vs. Investor: Investors rely on asset managers

g. Investor vs. Credit rating Agencies: rating agencies are compensated by arranger and not the end user.

OPERATIONAL RISKFRM 2016 Part 2 Revision Course

SOUND OPERATIONAL RISK MANAGEMENTReading: Principles for the Sound Management of Operational Risk,” (Basel Committee on Banking Supervision

Publication, June 2011)

1. Definition:

a. Operational Risk: Risk of loss resulting from inadequate or failed internal processes, people, systems or

from external events. It excludes strategic or reputational risk but includes legal risks

b. CORF (Corporate Operational Risk Function): Functionally independent group that complements the

business lines risk management functions

2. 11 principles of Operational Risk management:

a. Maintenance of strong risk culture, risk framework must be fully developed, Board should review and

approve the framework, board must identify the types and levels of risks, governance structure for risks

to be in line with appetite and tolerance,

b. Risks to be identified by managers, new business should assess potential risks, process for monitoring

operational risks,

c. Strong internal controls, business contingency plans, disclosures to external stakeholders about risk

management

3. Control Environment:

a. A control environment, risk assessment, control activities, information and communication, monitoring

activities

ENTERPRISE RISK MANAGEMENTReading: Brian Nocco and René Stulz, “Enterprise Risk Management: Theory and Practice,” Journal of Applied

Corporate Finance 18, No. 4 (2006)

1. Definition:

a. ERM: Process of managing all of corporations risk within an integrated framework. Objective is to

optimize and not eliminate total risk by optimizing risk and return tradeoffs

2. Benefits of ERM:

a. Macro: Hedging diversifiable risks improves management’s ability to invest in value creating projects

b. Micro: Benefit is decentralizing risk management to ensure that each projects total risk is adequately

assessed by project planners during initial evaluation. Components include marginal risk assessment and

unit contribution to firm risk

3. ERM Framework:

a. Determine firms risk appetite

b. Estimate amount of capital needed to support desired level of risk

c. Determine optimal level of capital and risk that achieves the target rating

d. Decentralize the management of risk

4. Diversification benefits: Aggregation of market, credit and operational risks results in VaR which is less than the

sum of all VaR’s from each category

DEVELOPMENTS IN RISK APPETITE FRAMEWORKReading: Observations on Developments in Risk Appetite Frameworks and IT Infrastructure,” Senior Supervisors

Group, December 2010

1. RAF:

a. It represents the firms core risk strategy

b. It sets in place a clear, future oriented perspective of firms target profile in a number of scenarios

c. Specifies what risks a firm is willing to take and their limits

2. Risk reporting Requirements:

a. Specific Metrics (liquidity Ratios, Capital Adequacy, Risk Concentrations etc.)

b. Data Accuracy and Collection infrastructure

c. Regulatory limits

d. Supervisory expectations

OP RISK DATA AND GOVERNANCEReading: OpRisk Data and Governance (Marcelo G. Cruz, Gareth W. Peters, and Pavel V. Shevchenko, Fundamental

aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk (Hoboken, NJ: John Wiley & Sons)

1. Basel 2 Even driven Op Risk Classification:

Risk Event ExplanationExecution, Delivery &process Management

What: Failed transaction processing, problems with counterparties and vendors.Reasons: Human errors, miscommunication etc.

Clients, Products & BusinessPractices

What: Disputes with clients/ counterparties, Regulatory fines for improper practicesReasons: Human Errors

Business Disruption &Business Failures

What: System crashReason: Systems

External Frauds What: Third party or outsiders attempting fraud against the firmInternal Frauds What: Frauds committed or attempted by own employeesEmployment Practices &Workplace safety

What: Stringent labour and safety laws

Damage to Physical Assets What: Natural disasters or other events causing loss from external sources

2. Elements of Op Risk framework:

a. Internal Loss Data: All expenses associated with Operational loss except for opportunity costs, foregone

revenue and costs related to risk management to prevent future occurrence. Need to be collected for at

least 5 years as per Basel 2

i. Collection Threshold: Different threshold will result in different risk appetite

ii. Completeness of Database: Data from disparate sources needs to be complete, employees need

to send all data to a central database

iii. Recoveries and Near Misses: Gross loss to be considered, no recoveries to be considered.

However, reserves need to be included as losses

iv. Time for Resolution: Need a clear procedure to handle large and long duration losses (cases

which decide whose fault it was may take very long time for resolution)

3. Risk Control Self Assessment (RSCA)

a. Firms ask experts to conduct reviews on status of each process/ sub-process. Requires documentation

and assessment of risks

b. Universe of risks, mitigation measures and control are identified.

EXTERNAL LOSS DATAReading: External Loss Data (Chapter 8, Philippa X. Girling, Operational Risk Management: A Complete Guide to a

Successful Operational Risk Framework (Hoboken: John Wiley & Sons, 2013))

1. External Loss databases:

a. Primary goal of external databases is to collect information on tail losses and examples of large risk

events

b. Databases are of two types:

i. Subscription based: IBM Algo FIRST which collects data from the press and publicly declared

events

ii. Consortium Data: Operational Riskdata eXchange Association (ORX) where member firms

upload anonymous data events

CAPITAL MODELINGReading: Capital Modeling (Chapter 12, Philippa X. Girling, Operational Risk Management: A Complete Guide to a

Successful Operational Risk Framework (Hoboken: John Wiley & Sons, 2013))

1. Operational Modeling:

a. Basic Indicator Approach: Operational Risk capital is based on 15% of the banks gross annual income. It

is calculated as K = (∑ × ) where GI is gross income, α is 15% as set by Basel 2 and n isnumber of years in which gross income was positive years

b. Standardized Approach: The approach uses separate factors for each of the business lines as against the

standard 15% used above. The weights and factors are as below

Business Line Weight Business Line Weight The risk capital is calculated

as:K =∑ ( ×α , )IB (Corp Finance) 18% Settlement & Payment 18%IB (Trading and Sales) 18% Agency & Custody 15%Retail banking 12% Asset Management 12%

Commercial Banking 15% Retail Brokerage 12%

c. Advanced Management Approach: banks are allowed to construct their own models for calculation of

risks. Following 3 conditions should be met:

i. Demonstrate ability to capture potential fat tails (99.9% confidence interval with 1 year interval)

ii. Include loss data, external data, scenario analysis and internal control factors

iii. Allocate capital that incentivizes good behavior

d. Loss Distribution Approach: It relies on internal data as the basis of design. Issues remain with the

amount of time for which data is available

2. Modeling:

a. Frequency: Poisson distribution is used which requires mean, variance and λ (avg. number of events in a

given year)

b. Severity Distribution: Generally lognormal distributions are used. But low frequency events may make

Gamma, Pareto and Weibull distributions better. Regulators are interested in goodness of fit

c. Monte Carlo simulations are then used to generate a loss distribution

SUPERVISORY GUIDELINES FOR AMAReading: Operational Risk—Supervisory Guidelines for the Advanced Measurement Approaches,” (Basel

Committee on Banking Supervision Publication, June 2011)

1. Definitions:

a. ORMF: Operational Risk Management

Framework is the umbrella under which all

operational risk management falls

b. ORMS: Operational Risk Management Systems

include all factors that are components of risk

measurement and modeling systems used to

estimate capital charges

c. Validation: Provides assurance to integrity of

the inputs to AMA

d. Verification: Conducted by internal/ external

Audits. It is concerned with overall effectiveness of the ORMF

2. Operational Risk categories: The capital required is significantly influenced by the number of operational risk

categories. The Basel Committee requires that an AMA banks risk system sufficiently captures operational risk

factors

MODEL RISKReading: Model Risk (Chapter 15, Michel Crouhy, Dan Galai and Robert Mark, The Essentials of Risk Management, 2nd

Edition (New York: McGraw- Hill, 2014))

1. Model Risk Examples:

a. JP Morgan Chase(London Whale):

i. Prices of synthetic derivatives were reported in a favourable range instead of mid-price on a

daily basis to show more profits/ lower losses

ii. Different valuations for same products by Investment banking group and Synthetic Credit group

iii. To lower RWA, instead to trimming positions, Synthetic Credit group added more long positions

to offset short positions. This increased the RWA and risks

iv. Risk limit breaches in key metrics were reported but never acted upon

v. New model for VaR was adopted by Synthetic Credit group which grossly underreported VaR

limits as compared to banks model due to various formula errors and manual entries

b. LTCM:

i. Implemented a strategy based on the empirical fact that spreads between corporate bonds and

government bonds would converge

ii. This was true during normal market conditions but due to the financial crisis of 1998, the

spreads increased causing huge losses due to a leverage ratio of 25 to 1

iii. Most losses at LTCM were due to breakdown of correlation and volatility patterns observed in

the past

2. Model Assumptions/ Errors:

a. To assume that distribution of the underlying asset is stationary when in fact it changes over time

b. Oversimplification of models e,g, assuming rate of returns are normally distributed, volatility is constant

c. OTC products are illiquid and usually cannot be perfectly hedged

d. Same models applied to different situations

e. Incorrect inputs to a correct model

3. Mitigation of Model Risks

a. Independent vetting of process to establish how models are selected and construed

b. Invest in research to improve models

RISK-ADJUSTED PERFORMANCE MEASUREMENTReading: Risk Capital Attribution and Risk-Adjusted Performance Measurement (Chapter 17, Michel Crouhy, Dan Galai

and Robert Mark, The Essentials of Risk Management, 2nd Edition (New York: McGraw-Hill, 2014))

1. Definitions:

a. Risk Capital: Provides protection against various risks inherent in the business

b. Economic Capital: Risk Capital plus strategic reserve

c. Regulatory Capital: Regulatory capital is mandatory capital required to be maintained as per laws

2. RAROC (Risk Adjusted Return on Capital)

a. Generic Equation: RAROC = ±where economic capital is used as proxy for risk, Return on risk capital is return on the risk capital

allocated to the activity and is generally assumed that it is invested in government securities

b. RORAC (Return on Risk Adjusted Capital): RORAC =c. Sharpe Ratio: S = –d. Adjusted RAROC: Adjusted RAROC = RAROC − β (R − R ) where β is the beta of the equity

firm. The Adjusted RARCO takes into account the systemic risks of returns.

ECONOMIC CAPITAL FRAMEWORKSReading: Range of Practices and Issues in Economic Capital Frameworks,” (Basel Committee on Banking

Supervision Publication, March 2009)

1. Definitions:

a. Risk Aggregation: Involves making choices in aggregating certain types of risks.

2. Making Risks Comparable:

a. Risk Metric: Metrics used for quantification need to be sub-additive for aggregation

b. Confidence Interval: Loss distributions for different types of risk are different

c. Time Horizon: Risks measurements can have different time horizons

3. Aggregation Methodologies:

a. Simple Summation: Adding together individual capital components

b. Constant Diversification: Subtracts a fixed diversification percentage from the overall amount

c. Variance-Covariance Matrix: Summarizes interdependencies and provides framework for recognizing

diversification benefits

d. Copulas: Combines marginal distributions into a joint probability distribution

e. Full Modeling or Simulation: Simulate impact of risk drivers on all types of risks and construct a joint

distribution

LARGE BANK HOLDING COMPANIESReading: Capital Planning at Large Bank Holding Companies: Supervisory Expectations and Range of Current

Practice,” Board of Governors of the Federal Reserve System, August 2013

1. Capital Plan Rule: It is how Federal Reserve maintains interest in survivability and smooth functioning of

BHC(Bank Holding Company). The guidelines apply to all US domiciled BHC with assets equal to or greater than

$50 billion

a. Risk management foundation, Resource estimation methods, Loss estimation methods, Impact on

capital adequacy, Capital planning policy, Internal controls, Effective oversight are the 7 principles for

Capital Adequacy Process(CAP)

2. Practices for CAP:

a. Develop plans to effectively identify all risk exposures on firm wide basis

b. Establish a mechanism for review of all models used for Capital Adequacy

c. Develop a capital policy that defines principles and guidelines for capital goals and usage

d. Stress testing scenario must be based on risk factors faced by BHC

e. Attention should be paid to interrelationships between variables within a given scenario

REPURCHASE AGREEMENTS AND FINANCINGReading: Repurchase Agreements and Financing (Chapter 12, Bruce Tuckman, Angel Serrat, Fixed Income

Securities: Tools for Today’s Markets, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011))

1. Definitions:

a. Repo: One party sells a security with a commitment to buy it back at a future date at a higher price. The

difference between current price and future price is implied interest. Repo rates are always annualized

and are quoted in actual/360 format

b. Open Repos: Contracts that renew each day until cancelled

c. GC rate (General Collateral): Repo trades secured with general collateral (acceptable securities are

defined) are called GC rate

d. Federal Funds Rate: Interest rate that institutions charge each other for lending funds maintained at

Federal Reserve

2. Repo Trades: They can be secured with either general collateral or with specific collateral. Lenders in special

collateral repo trades receive a particular security as collateral and hence charge a lower rate than GC. The

collateral received can be used to finance purchase of a bond or finance.

3. Special Spread: Difference between GC and special rate is called a special spread. Spreads generally move within

0 to GC rate band

ESTIMATING LIQUIDITY RISKSReading: Estimating Liquidity Risks (Chapter 14, Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex,

England: John Wiley & Sons, 2005))

1. Definitions:

a. Liquidity Risk: Degree to which a trader cannot trade a position without excess cost, risk or

inconvenience

b. Bid-Ask spread: It is the cost of liquidity. A wider spread indicates lower liquidity and higher risk

c. Exogenous Liquidity: refers to bid-ask spread not being affected by individual trades

d. Endogenous Liquidity: refers to when a trade can affect the bid-ask spread

2. Liquidity adjusted VaR:

a. Constant Approach Spread: It calculates LVaR assuming the bid-ask spread is constant. LC = 0.5 × V ×spread where Spread = ( )/the VaR is given as VaR = V × Z × σ thus LVaR = VaR + LC

i. If the return distribution is Lognormal then, VaR = 1 − e ( × )b. Exogenous Spread Approach: It replaces the Spread as μ + (σ × Z) in place of standard formula abovec. Endogenous Spread: We estimate elasticity as E = ∆ /∆ / and use this elasticity as LVaR = VaR ×1 − E ∆

3. Liquidity at Risk: It is also known as Cash Flow at Risk and is the maximum likely cash outflow over the horizon

period specified confidence level

ASSESSING QUALITY OF RISK MEASURESReading: Assessing the Quality of Risk Measures (Chapter 11, Allan Malz, Financial Risk Management: Models,

History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011))

1. Definitions:

a. Mapping: Assignment of risk factors to positions

2. Data Preparation: Crucial in risk measurement systems

a. Market Data: Time series data is used in forecasting the future portfolio returns

b. Security Master Data: Descriptive data on securities including maturity dates, currency etc.

c. Position Data: It matches the firms books and records

3. Major Defects in model assumptions of 2007-09:

a. Assumption of future house price appreciation

b. Assumption of low correlations

LIQUIDITY AND LEVERAGEReading: Liquidity and Leverage (Chapter 12, Allan Malz, Financial Risk Management: Models, History, and

Institutions (Hoboken, NJ: John Wiley & Sons, 2011))

1. Definitions:

a. Liquidity: An asset is liquid if it is close to cash i.e. it can be sold quickly, cheaply an without moving the

price too much

b. Transaction Liquidity Risk: Buying or selling an asset would result in adverse price movement

c. Funding liquidity or balance sheet risk: Borrowers credit position is perceived to be deteriorating.

Balance sheet risks happen when long term assets are funded using short term liabilities

d. Leverage Effect: ROE is higher as leverage increases as long as ROA exceeds cost of borrowing funds

e. Hurdle rate: A firms required ROE

f. Gross leverage: Value of all assets/ capital.

g. Net leverage: Difference between long and short positions/ capital

2. MMMF (Money Market Mutual Funds): High credit quality instruments with short maturities. They are not

mark to market daily.

3. ROE: RoE = (Leverage Ratio x ROA) – [(Leverage Ratio – 1) x Cost of Debt]

4. Transaction Liquidity:

a. Trade Processing Costs: Finding a counterparty, clearing costs, trading costs are trade costs

b. Inventory Management: Dealers provide trade immediacy. The dealer must be compensated for this

exposure

c. Adverse Selection: Differentiate between liquidity traders and information traders. Spreads are more for

information traders as they know more.

d. Differences of Opinion: Difficult to find a counterparty when all participants agree on the price

e. Transaction Cost: P x 0.5(s + α σ) where s = expected spread i.e. (ask price- bid price)/ mid-price, α is

value of confidence interval and σ is standard deviation

5. Market Liquidity:

a. Tightness refers to cost of round trip transaction including brokers commission

b. Depth: How large the order must be to move the price adversely

c. Resiliency: Length of time for large orders to make the adverse move in prices

FAILURE MECHANISM OF DEALER BANKSReading: Darrell Duffie, 2010. “The Failure Mechanics of Dealer Banks,” Journal of Economic Perspectives

1. Definitions:

a. Dealer Banks: They provide intermediary functions for OTC markets like derivatives, swaps, repos etc.

Failure of a large dealer bank can result in increased systemic risks for the OTC market

b. Novation: Act of replacing one participating member with another

2. Mitigation of dealer banks liquidity risks:

a. Creation of Emergency banks and clearing banks to mitigate firm specific and system liquidity risks

b. US treasuries TARP (Troubled Asset Relief Program) was designed to mitigate adverse selection in toxic

asset markets by providing below market financing and absorbing losses above a pre-specified amount

STRESS TESTING BANKSReading: Stress Testing Banks,” Til Schuermann, prepared for the Committee on Capital Market Regulation,

Wharton Financial Institutions Center (April 2012)

1. Definitions:

a. Stress Testing: It stimulates financial results given various adverse scenarios

b. Macro-prudential stress tests: It focuses on systematic risks and the banking industry as a whole.

c. SCAP: Supervisory Capital Assessment Program, was the first macro-prudential stress test for banks in

US. It rested for same scenarios at all banks

d. CCAR: Comprehensive Capital Analysis and Review: It required banks to submit their own tress tests

together with SCAP stress test results. This provided micro issues at each bank

e. PPNR: Pre-provision net revenue, gains and losses on available for sale and held to maturity securities,

trading and counterparty losses for sic institutions with the largest trading portfolios

2. Challenges in designing a stress test:

a. The scenarios must be extreme but be reasonable and plausible

b. Not everything goes bad as once. If money is pulled out from one asset class, it must flow into another

c. Model Errors: Translation of macro factors like GDP, HPI(House Price Index) and Unemployment

employed in SCAP into actual models

d. Balance Sheet: A stress test is typically for 2 years. Balance sheet needs to be modeled for each quarter

assuming if assets will be sold or bought, prices etc.

BASEL 1, BASEL 2 AND SOLVENCY 2Reading: Basel I, Basel II, and Solvency II (Chapter 15, John Hull, Risk Management and Financial Institutions, 4th

Edition (Hoboken, NJ: John Wiley & Sons, 2015))

1. Definitions:

a. Basel 1: Norms for Banks. Contains only credit risk. Introduced in 1988b. Basel 2: Norms for banks. Contains market, credit and operational riskc. Solvency 2: Norms for Insurance industryd. Credit Equivalent Amount: Loan principal that is considered to have the same credit risk as that of the

off-balance sheet items2. Basel 1:

a. Capital to total assets has to be greater than 5%b. Banks on and off balance sheet items need to be used to calculate RWA(Risk Weighted Assets). Ratio of

capital to RWA must be more than 8% (Called Cooke Ratio)c. Tier 1 includes Equity minus goodwill and Tier 2 includes Subordinated debt, preferred stock.

Requirement of at least 50% tier 1 capitald. In 1996 amendment, market risk was also to be calculated at 99% confidence interval for a period of 10

days. This has to be back-tested for a period of 250 daysi. Market Risk: 12.5 x [max(VaRt-1, VaRavg x mc)+SRC]

ii. Credit Risk: RWA of on and off balance sheet itemsiii. Mc is set depending on the number of exceptions found during back testing

3. Basel 2:

a. Three approaches to measure credit risk: Standardized Approach, Foundations-Internal RatingBased(IRB) and Advanced-IRB approach

i. Standardized approach is similar to RWA approach under Basel 1 but with different weights asper ratings rather than OECD status

ii. Foundations-IRB: Required Capital = 12.5 x [EADi x LGDi x (WCDRi-PDi) x MA]. Than bank providesvalue for PD rest are provided by Basel

iii. Advanced-IRB: Banks supply their own estimates of EAD, LGD, PD and MAb. Requires banks to maintain capital for Operational Risk

i. Basic Indicator Approach: [Net Interest Income + Other Income]x0.15ii. Standardized Approach: Similar to basic indicator approach. Changes the multiplier for different

lines of businessiii. Advanced Measurement Approach: calculates risk at 99.9% confidence interval over a 1 year

time horizon4. Solvency 2: Solvency 2 was to be implemented from 2013 but is now postponed. This is applicable in EU onluy

and is not a international standard

a. Standardized Approach: Similar to Standardized approach under Basel 1

b. Internal Models: Similar to IRB approach under Basel 2

BASEL 2.5, BASEL 3 AND OTHER CHANGESReading: Basel II.5, Basel III, and Other Post-Crisis Changes (Chapter 16, John Hull, Risk Management and

Financial Institutions, 4th Edition (Hoboken, NJ: John Wiley & Sons, 2015))

1. Basel 2.5:

a. Requires calculation of a stressed VaR for a period of 250 days where the bank’s portfolio performed

poorly. Banks may choose the time period.

b. Market Risk Charge: [max(VaRt-1, VaRavg x mc)+ max(SVaRt-1,SVaRavg x mc)] where avg. VaR is for past 60

days in 10 day periods

c. Incremental risk charge (IRC): A 99.9% VaR over a 1 year horizon for instruments on the trading book

which are sensitive to credit risk (Earlier, trading book had lower capital charge as compared to

investment book)

d. Comprehensive Risk Measure: Single capital charge for correlation dependent instruments that replaces

SRC and IRC.

2. Basel 3:

a. Tier 1 equity capital must be 4.5% of RWA at all times, Tier 1 Capital must be 6% at all times and total

capital must be 8% at all times

b. Capital conservation buffer consisting of Tier 1 equity capital equal to 2.5% of RWA is to be built.

c. A counter cyclical buffer of up to 2.5% of RWA as decided by each countries individual central banks

d. A minimum leverage ratio (capital/ total exposure) of 3%. LCR (Liquidity coverage ratio) > 100% where

LCR is high quality liquid assets/ net cash outflows for 30 days. NSFR (Net stable funding ratio) for 1 year

> 100% where NSFR is amount of stable funding/ required amount of stable funding

3. Contingent Convertible Bonds: They convert to equity under conditions of stress. E.g. Conversion is triggered if

Tier 1 equity capital falls below 7%; as issued by Credit Suisse in 2011

4. Dodd-Frank Act: Became law in 2010 in US

a. It established Financial Stability Oversight Council (FSOC) to look out for systemic risks

b. Establishment of Office of Financial Research (OFR) to conduct research on economy and risks in US

c. Identification of SIFI (Systematically Important Financial Institutions) . They are required to hold

additional capital

d. Requirement of central clearing houses for standardized OTC derivatives

FUNDAMENTAL REVIEW OF TRADING BOOKReading: Fundamental Review of Trading Book (Chapter 17, John Hull, Risk Management and Financial Institutions, 4th

Edition (Hoboken, NJ: John Wiley & Sons, 2015))

1. Definitions:

a. Fundamental Review of Trading Book (FRTB): Basel committee proposed major revisions in May 2012 on

the way capital is calculated for trading book. This is called FRTB

b. Trading Book vs. Banking Book:

i. Trading book is what bank expects to trade and banking book consists of instruments expected

to be held till maturity.

ii. Instruments in the trading book are marked to market daily while in the banking book are not.

iii. Instruments in trading book are subject to market risk while instruments in banking book are

subject to credit risk

2. Changes proposed in FRTB:

a. Market Risk: In place of VaR at 99% confidence interval, ES (Expected Shortfall) with 97.5% confidence

interval is proposed. Distributions with heavy tails will have considerably higher ES

b. Liquidity Horizon: Earlier a 10-day VaR was used (1 day VaR calculated was multiplied by square root of

10), now it is proposed that five different liquid horizons be used of 10 days, 20 days, 60 days, 20 days

and 250 days.

RISK & INVESTMENTMANAGEMENTFRM 2016 Part 2 Revision Course

PORTFOLIO CONSTRUCTIONReading: Portfolio Construction (Chapter 14, Richard Grinold and Ronald Kahn, Active Portfolio Management: A

Quantitative Approach for Producing Superior Returns and Controlling Risk, 2nd Edition (New York: McGraw-Hill, 2000))

1. Definitions:

a. Information Ratio: A ratio of portfolio returns above the returns of a benchmark (usually an index) to the

volatility of those returns

b. Active Risk: Tracking error or standard deviation of the difference between the portfolio and index returns

c. Refining Alpha: It addresses constraint that each investor or manager has. Alpha can be refined by

scaling and trimming

2. Scaling and Trimming:

a. Trimming: Scrutinize large alphas and set their positions to zero. Large can be 3 times the portfolio alpha

b. Scaling: Rescaling volatility or information coefficient (correlation between actual and forecasted values)

to reduce standard deviation to within constraints

3. Neutralization: Removing biases and undesirable bets from alpha

a. Benchmark: Adjusting benchmark alpha to zero (i.e. Beta becomes 1)

b. Cash Neutral: Adjusting alphas so cash position is not active

c. Risk Factor approach: Separates return along several dimensions. Each dimension can be identified as

source of risk or value add and factors that are source of risk can be eliminated

4. Transaction Costs: Costs of moving one portfolio to another. They occur at a point in time whereas the benefits

are realized over a period.

5. Optimal Portfolio Creation: Issues that need to be taken care of are:

a. Risk Aversion: Risk Aversion = ×b. Alpha Coverage: Cases where we have forecasts for stocks not in the benchmark and not having

forecasts for stocks in the benchmark

6. No Trade Region: [(2 x Risk Aversion x Active Risk x Marginal Contribution to Active Risk) – Cost of Selling] <