FRM Exam 1 Questions and answers 2025
Shortcomings .of .risk .metrics .- .ANS✓✓--May .not .scale .over .time
-Historical .data .may .be .meaningless
-Not .designed .to .account .for .catastrophes
-VaR .says .nothing .about .losses .in .excess .of .VaR
-May .not .handle .sudden .illiquidity
Importance .of .communication .for .risk .managers .- .ANS✓✓-Need .to .assess .risk
.and .tell .management .so .they .can .determine .which .risks .to .take .on
Ways .firms .can .fail .to .account .for .risks .- .ANS✓✓--Firm .may .ignore .known .risk
-Somebody .in .firm .may .know .about .risk, .but .it's .not .captured .by .models
-Realization .of .a .truly .unknown .risk
Ways .risk .can .be .mismeasured .- .ANS✓✓--Wrong .distribution
-Historical .sample .may .not .apply
Roles .of .risk .management .- .ANS✓✓--Asses .firm .risks
-Communicate .risks
-Manage .and .monitor .risks
Practical .considerations .related .to .ERM .implementation .- .ANS✓✓--Designate
.ERM .champion .- .usually .CRO
-Make .ERM .part .of .firm .culture
-Determining .all .possible .risks
-Quantifying .operational .and .strategic .risks
-Integrating .risks .(dependencies)
-Lack .of .risk .transfer .mechanisms
-Monitoring
Models .used .in .ERM .framework .- .ANS✓✓-Modeling .approach .is .typically
.between .statistical .analytic .models .and .structural .simulation .models
Risk .types .addressed .by .ERM .- .ANS✓✓--Hazard
-Financial
-Operational
-Strategic
,Traits .of .ERM .- .ANS✓✓--Enterprise .Risk .Management
-ERM .is .a .discipline .- .culture .of .enterprise
-ERM .applies .to .all .industries
-ERM .is .not .just .defensive, .adds .value
-ERM .encompasses .all .risks
-ERM .addresses .all .stakeholders
Risk-adjusted .performance .measure .(RAP) .- .ANS✓✓--Relationship .drawn .from
.CML
-RAP .= .[(market .std .dev)/(portfolio .std .dev)]*(Portfolio .return .- .risk .free .rate) .+
.risk .free .rate
-annualized
VaR-based .analysis .(formula) .- .ANS✓✓--Risk .replaced .with .VaR
(Portfolio .return .- .risk .free .rate)/(portfolio .VaR/initial .value .of .portfolio)
Sortino .ratio .- .ANS✓✓-Sortino .ratio .= .(E(Rp) .-R_min)/sqrt(MSD_min)
MSD_min=summation(R_pt-R_min)^2/N
where .R_pt .is .return .of .the .portfolio .at .time .t
-MAR .- .minimum .acceptable .return .also .denoted .as .R_min .is .the .diff .between
.Sortino .and .Sharpe
Information .ratio .- .ANS✓✓-IR .= .(E(Rp) .- .E(Rb))/(std .dev(Rp-Rb)) .
-Evaluate .manager .of .a .benchmark .fund
Tracking .error .- .ANS✓✓--Std .dev .between .portfolio .return .and .benchmark
.return
TE .= .std .dev .* .(Rp-Rb)
-Benchmark .funds
Treynor .measure .- .ANS✓✓--Excess .return .divided .by .portfolio .beta
Tp .= .(E(Rp) .- .Rf)/portfolio .beta
-Better .for .well .diversified .portfolios
Sharpe .measure .- .ANS✓✓--Excess .return .divided .by .portfolio .volatility .(std
.dev)
Sp .= .(E(Rp) .- .Rf)/(std .dev .of .Rp)
-Better .for .non-diversified .portfolios
Jensen's .alpha .- .ANS✓✓--Excess .return .equated .to .alpha .plus .expected
.systematic .return
alpha_p=
E(Rp) .- .Rf .= .alpha .+ .beta(E(Rm) .- .Rf)
Arbitrage .Pricing .Theory .- .ANS✓✓-a .theory .of .risk-return .relationships .derived
.from .no-arbitrage .considerations .in .large .capital .markets
1. .Create .factor .portfolio .
2.Derive .returns .for .each .factor .portfolio .
, 3. .Calculate .risk .premiums .for .each .factor .portfolio
APT .for .passive .portfolio .management .- .ANS✓✓--Track .an .index .with .a
.portfolio .that .excludes .certain .stocks
-Track .an .index .that .must .include .certain .stocks
-To .closely .track .an .index .while .tailoring .the .risk .exposure
APT .(equation .and .assumptions) .- .ANS✓✓-
E(R_i)=R_f+B_i1RP1+B_i2RP2+...+B_ikRPk
-Returns .on .any .stock .are .linearly .related .to .a .set .of .indexes
-Law .of .one .price
-Returns .follow .k-factor .process
-Well .diversified .portfolios .can .be .formed
-No .arbitrage .opp .exists
Prices .of .risk .vs .sensitivity .- .ANS✓✓--Prices .of .risk .are .common .factors .and
.do .not .change
-Sensitivities .can .change
Multibeta .CAPM .- .ANS✓✓-Ri .- .Rf .= .(market .beta)(Rm .- .Rf) .+ .(sensitivity .to
.inflation .risk)(price .of .inflation .risk)...
Effect .of .non-price-taking .behavior .on .CAPM .- .ANS✓✓-Simple .form .of .CAPM,
.but .market .price .of .risk .is .lower .than .if .all .investors .were .price .takers
Effect .of .heterogeneous .expectations .on .CAPM .- .ANS✓✓-Equilibrium .can .still
.be .expressed .in .returns, .covariance, .and .variance, .but .they .become .complex
.weighted .averages
Nonmarketable .asset .impact .on .CAPM .- .ANS✓✓--ex. .Human .capital
-Equilibrium .return .can .be .higher .or .lower .than .it .is .under .standard .CAPM
Risk .- .ANS✓✓--Volatility .of .expected .outcomes
-Outcomes .are .random .but .distribution .is .known .or .approximated
Derivative .contract .- .ANS✓✓--Derives .value .from .an .underlying .asset, .rate, .or
.index
-Derives .value .from .a .security
Nonparametric .VaR .- .ANS✓✓--Quantile .of .an .empirical .distribution
Parametric .VaR .- .ANS✓✓--Quantile .of .a .statistical .distribution
Four .major .types .of .risk .- .ANS✓✓--Market .risk
-Liquidity .risk
-Credit .risk
-Operational .risk
Shortcomings .of .risk .metrics .- .ANS✓✓--May .not .scale .over .time
-Historical .data .may .be .meaningless
-Not .designed .to .account .for .catastrophes
-VaR .says .nothing .about .losses .in .excess .of .VaR
-May .not .handle .sudden .illiquidity
Importance .of .communication .for .risk .managers .- .ANS✓✓-Need .to .assess .risk
.and .tell .management .so .they .can .determine .which .risks .to .take .on
Ways .firms .can .fail .to .account .for .risks .- .ANS✓✓--Firm .may .ignore .known .risk
-Somebody .in .firm .may .know .about .risk, .but .it's .not .captured .by .models
-Realization .of .a .truly .unknown .risk
Ways .risk .can .be .mismeasured .- .ANS✓✓--Wrong .distribution
-Historical .sample .may .not .apply
Roles .of .risk .management .- .ANS✓✓--Asses .firm .risks
-Communicate .risks
-Manage .and .monitor .risks
Practical .considerations .related .to .ERM .implementation .- .ANS✓✓--Designate
.ERM .champion .- .usually .CRO
-Make .ERM .part .of .firm .culture
-Determining .all .possible .risks
-Quantifying .operational .and .strategic .risks
-Integrating .risks .(dependencies)
-Lack .of .risk .transfer .mechanisms
-Monitoring
Models .used .in .ERM .framework .- .ANS✓✓-Modeling .approach .is .typically
.between .statistical .analytic .models .and .structural .simulation .models
Risk .types .addressed .by .ERM .- .ANS✓✓--Hazard
-Financial
-Operational
-Strategic
,Traits .of .ERM .- .ANS✓✓--Enterprise .Risk .Management
-ERM .is .a .discipline .- .culture .of .enterprise
-ERM .applies .to .all .industries
-ERM .is .not .just .defensive, .adds .value
-ERM .encompasses .all .risks
-ERM .addresses .all .stakeholders
Risk-adjusted .performance .measure .(RAP) .- .ANS✓✓--Relationship .drawn .from
.CML
-RAP .= .[(market .std .dev)/(portfolio .std .dev)]*(Portfolio .return .- .risk .free .rate) .+
.risk .free .rate
-annualized
VaR-based .analysis .(formula) .- .ANS✓✓--Risk .replaced .with .VaR
(Portfolio .return .- .risk .free .rate)/(portfolio .VaR/initial .value .of .portfolio)
Sortino .ratio .- .ANS✓✓-Sortino .ratio .= .(E(Rp) .-R_min)/sqrt(MSD_min)
MSD_min=summation(R_pt-R_min)^2/N
where .R_pt .is .return .of .the .portfolio .at .time .t
-MAR .- .minimum .acceptable .return .also .denoted .as .R_min .is .the .diff .between
.Sortino .and .Sharpe
Information .ratio .- .ANS✓✓-IR .= .(E(Rp) .- .E(Rb))/(std .dev(Rp-Rb)) .
-Evaluate .manager .of .a .benchmark .fund
Tracking .error .- .ANS✓✓--Std .dev .between .portfolio .return .and .benchmark
.return
TE .= .std .dev .* .(Rp-Rb)
-Benchmark .funds
Treynor .measure .- .ANS✓✓--Excess .return .divided .by .portfolio .beta
Tp .= .(E(Rp) .- .Rf)/portfolio .beta
-Better .for .well .diversified .portfolios
Sharpe .measure .- .ANS✓✓--Excess .return .divided .by .portfolio .volatility .(std
.dev)
Sp .= .(E(Rp) .- .Rf)/(std .dev .of .Rp)
-Better .for .non-diversified .portfolios
Jensen's .alpha .- .ANS✓✓--Excess .return .equated .to .alpha .plus .expected
.systematic .return
alpha_p=
E(Rp) .- .Rf .= .alpha .+ .beta(E(Rm) .- .Rf)
Arbitrage .Pricing .Theory .- .ANS✓✓-a .theory .of .risk-return .relationships .derived
.from .no-arbitrage .considerations .in .large .capital .markets
1. .Create .factor .portfolio .
2.Derive .returns .for .each .factor .portfolio .
, 3. .Calculate .risk .premiums .for .each .factor .portfolio
APT .for .passive .portfolio .management .- .ANS✓✓--Track .an .index .with .a
.portfolio .that .excludes .certain .stocks
-Track .an .index .that .must .include .certain .stocks
-To .closely .track .an .index .while .tailoring .the .risk .exposure
APT .(equation .and .assumptions) .- .ANS✓✓-
E(R_i)=R_f+B_i1RP1+B_i2RP2+...+B_ikRPk
-Returns .on .any .stock .are .linearly .related .to .a .set .of .indexes
-Law .of .one .price
-Returns .follow .k-factor .process
-Well .diversified .portfolios .can .be .formed
-No .arbitrage .opp .exists
Prices .of .risk .vs .sensitivity .- .ANS✓✓--Prices .of .risk .are .common .factors .and
.do .not .change
-Sensitivities .can .change
Multibeta .CAPM .- .ANS✓✓-Ri .- .Rf .= .(market .beta)(Rm .- .Rf) .+ .(sensitivity .to
.inflation .risk)(price .of .inflation .risk)...
Effect .of .non-price-taking .behavior .on .CAPM .- .ANS✓✓-Simple .form .of .CAPM,
.but .market .price .of .risk .is .lower .than .if .all .investors .were .price .takers
Effect .of .heterogeneous .expectations .on .CAPM .- .ANS✓✓-Equilibrium .can .still
.be .expressed .in .returns, .covariance, .and .variance, .but .they .become .complex
.weighted .averages
Nonmarketable .asset .impact .on .CAPM .- .ANS✓✓--ex. .Human .capital
-Equilibrium .return .can .be .higher .or .lower .than .it .is .under .standard .CAPM
Risk .- .ANS✓✓--Volatility .of .expected .outcomes
-Outcomes .are .random .but .distribution .is .known .or .approximated
Derivative .contract .- .ANS✓✓--Derives .value .from .an .underlying .asset, .rate, .or
.index
-Derives .value .from .a .security
Nonparametric .VaR .- .ANS✓✓--Quantile .of .an .empirical .distribution
Parametric .VaR .- .ANS✓✓--Quantile .of .a .statistical .distribution
Four .major .types .of .risk .- .ANS✓✓--Market .risk
-Liquidity .risk
-Credit .risk
-Operational .risk
