FRM 2 Exam Questions and answers 2025
Netting .Factor .- .ANS✓✓-sqrt(n .+ .n .(n .- .1) .p) ./ .n
Ho-Lee .Model .- .ANS✓✓-dr .= .lambda(t)*dt .+ .sigma*dw
Vasicek .Model .- .ANS✓✓-dr .= .k*(theta .- .r)*dt .+ .sigma*dw
Half-life .= .ln(2)/k
Cox-Ingersoll-Ross .Model .(CIR) .- .ANS✓✓-dr .= .k*(theta .- .r)*dt .+
.sigma*sqrt(r)*dw
Friction .1: .Mortgagor .and .Originator .- .ANS✓✓-The .borrower .may .not .even .be
.aware .of .the .financing .options .available. .On .the .other .hand, .the .lender .may
.steer .the .borrower .to .products .that .are .not .suitable.
Friction .2: .Originator .and .Arranger .- .ANS✓✓-The .arranger .(issuer) .purchases
.the .loans .from .the .originators .for .the .purpose .of .resale .through .securitized
.products. .The .originator .has .superior .knowledge .about .the .borrower .(adverse
.selection .problem).
Friction .3: .Arranger .and .third-parties .- .ANS✓✓-The .arranger .of .the .pool .of
.mortgages .will .possess .better .information .about .the .borrower .than .third
.parties .including .rating .agencies, .asset .managers, .and .warehouse .lenders.
Friction .4: .Servicer .and .Mortgagor .- .ANS✓✓-The .servicer's .role .is .to .manage
.the .cash .flows .of .the .pool .and .follow .up .on .delinquencies .and .foreclosures. .A
.conflict .of .interest .arises .for .delinquent .loans.
Friction .5: .Servicer .and .third-parties .- .ANS✓✓-The .servicer .faces .a .moral
.hazard .problem .because .their .(lack .of) .effort .can .impact .the .asset .manager
.and .credit .rating .agencies .without .directly .affecting .their .own .cash .flow
.distribution.
Friction .6: .Asset .manger .and .investor .- .ANS✓✓-The .investor .relies .on .the
.asset .manager's .expertise .to .identify .and .analyze .potential .investments
Friction .7: .Investor .and .credit .rating .agencies .- .ANS✓✓-Rating .agencies .are
.compensated .by .the .arranger .and .not .the .end .user, .the .investor.
,Default .time .distribution .- .ANS✓✓-F(t) .= .1 .- .e^(-lambda*t)
Coherent .Risk .Measure: .Monotonicity .- .ANS✓✓-If .X .< .Y, .then .p(Y) .< .p(X)
If .the .expected .value .of .Y .is .greater .than .X, .then .the .risk .of .Y .is .less .than .the
.risk .of .X
Coherent .Risk .Measure: .Sub-additivity .- .ANS✓✓-p(X .+ .Y) .< .p(X) .+ .p(Y)
The .portfolio's .risk .should .not .be .greater .than .the .sum .of .its .parts
Coherent .Risk .Measure: .Positive .Homogenity .- .ANS✓✓-p(lambda*X) .=
.lambda*p(X)
Double .portfolio, .double .the .risk
Coherent .Risk .Measure: .Translation .Invariance .- .ANS✓✓-p(X .+ .c) .= .p(X) .- .c
Like .adding .cash
Operational .Risk .Management: .3 .Lines .of .Defense .- .ANS✓✓-1. .Business .Line
.Management
2. .Independent .Corporate .operation .RM .function
3. .Independent .review/audit
Basel .Suggestions .for .Sound .Operational .Risk .Managemnet .- .ANS✓✓-1.
.Strong .risk .management .culture
2. .Fully .integrated .with .overall .RM .process
3. .Board .of .directors .reviews .OR .framework
4. .Board .approves .risk .appetite/tolerance
5. .Well .defined .governance .structure
6. .Incentives .incorporate .risks .taken
7. .Approval .for .new .line .of .business
8. .Constant .monitoring .of .OR
9. .Internal .controls .to .mitigate/transfer .risk
10. .Major .business .disruption .plans
11. .Disclosure
Risk .Capacity .- .ANS✓✓-Max .level .of .risk .an .institution .can .take
Risk .Appetitte .- .ANS✓✓-Aggregate .level .and .types .of .risks .willing .to .take
.given .risk .capacity
Operational .Risk .Taxonomy .- .ANS✓✓-Process .of .identifying .and .classifying
.operational .risks.
1. .System .Failures
2. .Natural .Disasters
, 3. .Employee .practices .& .workplace .safety .(HR .Function)
4. .External .Fraud .(system .hacking)
5. .Internal .Fraud .(internal .employee .fraud)
Operation .Risk .Capital: .Basic .Indicator .Approach .- .ANS✓✓-Operation .risk
.capital .is .15% .of .annual .gross .income .over .last .3 .years
Operation .Risk .Capital: .Standardization .Approach .- .ANS✓✓-Assigns .a .different
.beta .factor .to .each .business .line. .
Operational .risk .capital .=average_3(sum(GI(1-8) .* .B(1-8)) .)
IB .and .settlement: .18%
Commercial .banking, .Agency/custody .services: .15%
Retail .banking .and .brokerage, .AM: .12%
Operation .Risk .Capital: .Advanced .Measurement .Approach .- .ANS✓✓-Banks .can
.use .their .own .models .if .they .show:
1. .Can .capture .fat .tail .losses .(99.9th .percentile .over .1-year .horizon)
2. .Include .internal .loss .data, .external .loss .data, .scenario .analysis .and .business
.environment .control .factors
3. .Allocate .capital .in .a .way .that .incentivizes .good .behavior
Basel .1: .Capital .Requirements .- .ANS✓✓-1. .Total .Assets .to .Capital .< .20
2. .Total .Capital .to .RWA .< .8%
3. .Equity .Capital .> .2% .RWA
4. .Tier .1 .capital .> .4% .RWA
Basel .1996 .Amendment .- .ANS✓✓-Requires .banks .to .measure .market .risks
.associated .with .trading .activities .and .have .capital .to .back .them.
1. .Standardized .Measurement .Approach .- .assigns .a .capital .charge .to .each
.element .in .trading .book .separately. .Ignores .correlations.
2. .Internal .Models .Approach .- .max(Var[10], .m_c*Var[60]) .+ .SRC
SRC .is .a .specific .risk .charge .that .captures .company .risks
Basel .2: .3 .Pillers .- .ANS✓✓-1. .Minimum .Capital .- .0.8 .* .(credit .RWA .+ .market
.RWA .+ .operation .RWA)
2. .Supervisory .Review
3. .Market .Discipline .- .More .disclosure .of .risks .taken .and .capital .to .cover .those
.risks
Solvency .I .and .II .- .ANS✓✓-Establishes .capital .requirements .for .insurance
.companies.
Solvency .capital .ratio .(less .severe .consequences) .- .firm .must .submit .plan .to
.restore .capital
Netting .Factor .- .ANS✓✓-sqrt(n .+ .n .(n .- .1) .p) ./ .n
Ho-Lee .Model .- .ANS✓✓-dr .= .lambda(t)*dt .+ .sigma*dw
Vasicek .Model .- .ANS✓✓-dr .= .k*(theta .- .r)*dt .+ .sigma*dw
Half-life .= .ln(2)/k
Cox-Ingersoll-Ross .Model .(CIR) .- .ANS✓✓-dr .= .k*(theta .- .r)*dt .+
.sigma*sqrt(r)*dw
Friction .1: .Mortgagor .and .Originator .- .ANS✓✓-The .borrower .may .not .even .be
.aware .of .the .financing .options .available. .On .the .other .hand, .the .lender .may
.steer .the .borrower .to .products .that .are .not .suitable.
Friction .2: .Originator .and .Arranger .- .ANS✓✓-The .arranger .(issuer) .purchases
.the .loans .from .the .originators .for .the .purpose .of .resale .through .securitized
.products. .The .originator .has .superior .knowledge .about .the .borrower .(adverse
.selection .problem).
Friction .3: .Arranger .and .third-parties .- .ANS✓✓-The .arranger .of .the .pool .of
.mortgages .will .possess .better .information .about .the .borrower .than .third
.parties .including .rating .agencies, .asset .managers, .and .warehouse .lenders.
Friction .4: .Servicer .and .Mortgagor .- .ANS✓✓-The .servicer's .role .is .to .manage
.the .cash .flows .of .the .pool .and .follow .up .on .delinquencies .and .foreclosures. .A
.conflict .of .interest .arises .for .delinquent .loans.
Friction .5: .Servicer .and .third-parties .- .ANS✓✓-The .servicer .faces .a .moral
.hazard .problem .because .their .(lack .of) .effort .can .impact .the .asset .manager
.and .credit .rating .agencies .without .directly .affecting .their .own .cash .flow
.distribution.
Friction .6: .Asset .manger .and .investor .- .ANS✓✓-The .investor .relies .on .the
.asset .manager's .expertise .to .identify .and .analyze .potential .investments
Friction .7: .Investor .and .credit .rating .agencies .- .ANS✓✓-Rating .agencies .are
.compensated .by .the .arranger .and .not .the .end .user, .the .investor.
,Default .time .distribution .- .ANS✓✓-F(t) .= .1 .- .e^(-lambda*t)
Coherent .Risk .Measure: .Monotonicity .- .ANS✓✓-If .X .< .Y, .then .p(Y) .< .p(X)
If .the .expected .value .of .Y .is .greater .than .X, .then .the .risk .of .Y .is .less .than .the
.risk .of .X
Coherent .Risk .Measure: .Sub-additivity .- .ANS✓✓-p(X .+ .Y) .< .p(X) .+ .p(Y)
The .portfolio's .risk .should .not .be .greater .than .the .sum .of .its .parts
Coherent .Risk .Measure: .Positive .Homogenity .- .ANS✓✓-p(lambda*X) .=
.lambda*p(X)
Double .portfolio, .double .the .risk
Coherent .Risk .Measure: .Translation .Invariance .- .ANS✓✓-p(X .+ .c) .= .p(X) .- .c
Like .adding .cash
Operational .Risk .Management: .3 .Lines .of .Defense .- .ANS✓✓-1. .Business .Line
.Management
2. .Independent .Corporate .operation .RM .function
3. .Independent .review/audit
Basel .Suggestions .for .Sound .Operational .Risk .Managemnet .- .ANS✓✓-1.
.Strong .risk .management .culture
2. .Fully .integrated .with .overall .RM .process
3. .Board .of .directors .reviews .OR .framework
4. .Board .approves .risk .appetite/tolerance
5. .Well .defined .governance .structure
6. .Incentives .incorporate .risks .taken
7. .Approval .for .new .line .of .business
8. .Constant .monitoring .of .OR
9. .Internal .controls .to .mitigate/transfer .risk
10. .Major .business .disruption .plans
11. .Disclosure
Risk .Capacity .- .ANS✓✓-Max .level .of .risk .an .institution .can .take
Risk .Appetitte .- .ANS✓✓-Aggregate .level .and .types .of .risks .willing .to .take
.given .risk .capacity
Operational .Risk .Taxonomy .- .ANS✓✓-Process .of .identifying .and .classifying
.operational .risks.
1. .System .Failures
2. .Natural .Disasters
, 3. .Employee .practices .& .workplace .safety .(HR .Function)
4. .External .Fraud .(system .hacking)
5. .Internal .Fraud .(internal .employee .fraud)
Operation .Risk .Capital: .Basic .Indicator .Approach .- .ANS✓✓-Operation .risk
.capital .is .15% .of .annual .gross .income .over .last .3 .years
Operation .Risk .Capital: .Standardization .Approach .- .ANS✓✓-Assigns .a .different
.beta .factor .to .each .business .line. .
Operational .risk .capital .=average_3(sum(GI(1-8) .* .B(1-8)) .)
IB .and .settlement: .18%
Commercial .banking, .Agency/custody .services: .15%
Retail .banking .and .brokerage, .AM: .12%
Operation .Risk .Capital: .Advanced .Measurement .Approach .- .ANS✓✓-Banks .can
.use .their .own .models .if .they .show:
1. .Can .capture .fat .tail .losses .(99.9th .percentile .over .1-year .horizon)
2. .Include .internal .loss .data, .external .loss .data, .scenario .analysis .and .business
.environment .control .factors
3. .Allocate .capital .in .a .way .that .incentivizes .good .behavior
Basel .1: .Capital .Requirements .- .ANS✓✓-1. .Total .Assets .to .Capital .< .20
2. .Total .Capital .to .RWA .< .8%
3. .Equity .Capital .> .2% .RWA
4. .Tier .1 .capital .> .4% .RWA
Basel .1996 .Amendment .- .ANS✓✓-Requires .banks .to .measure .market .risks
.associated .with .trading .activities .and .have .capital .to .back .them.
1. .Standardized .Measurement .Approach .- .assigns .a .capital .charge .to .each
.element .in .trading .book .separately. .Ignores .correlations.
2. .Internal .Models .Approach .- .max(Var[10], .m_c*Var[60]) .+ .SRC
SRC .is .a .specific .risk .charge .that .captures .company .risks
Basel .2: .3 .Pillers .- .ANS✓✓-1. .Minimum .Capital .- .0.8 .* .(credit .RWA .+ .market
.RWA .+ .operation .RWA)
2. .Supervisory .Review
3. .Market .Discipline .- .More .disclosure .of .risks .taken .and .capital .to .cover .those
.risks
Solvency .I .and .II .- .ANS✓✓-Establishes .capital .requirements .for .insurance
.companies.
Solvency .capital .ratio .(less .severe .consequences) .- .firm .must .submit .plan .to
.restore .capital
