FRM Exam 1
Shortcomings of risk metrics
-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
Need to assess risk and tell management so they can determine which risks to take
on
Ways firms can fail to account for risks
-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
-Wrong distribution
-Historical sample may not apply
Roles of risk management
-Asses firm risks
-Communicate risks
-Manage and monitor risks
Practical considerations related to ERM implementation
-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
Modeling approach is typically between statistical analytic models and structural
simulation models
Risk types addressed by ERM
-Hazard
-Financial
-Operational
-Strategic
Traits of ERM
-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)
-Relationship drawn from CML
-RAP = [(market std dev)/(portfolio std dev)]*(Portfolio return - risk free rate) + risk
, free rate
-annualized
VaR-based analysis (formula)
-Risk replaced with VaR
(Portfolio return - risk free rate)/(portfolio VaR/initial value of portfolio)
Sortino ratio
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
IR = (E(Rp) - E(Rb))/(std dev(Rp-Rb))
-Evaluate manager of a benchmark fund
Tracking error
-Std dev between portfolio return and benchmark return
TE = std dev * (Rp-Rb)
-Benchmark funds
Treynor measure
-Excess return divided by portfolio beta
Tp = (E(Rp) - Rf)/portfolio beta
-Better for well diversified portfolios
Sharpe measure
-Excess return divided by portfolio volatility (std dev)
Sp = (E(Rp) - Rf)/(std dev of Rp)
-Better for non-diversified portfolios
Jensen's alpha
-Excess return equated to alpha plus expected systematic return
alpha_p=
E(Rp) - Rf = alpha + beta(E(Rm) - Rf)
Arbitrage Pricing Theory
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
-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)
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
-Prices of risk are common factors and do not change
-Sensitivities can change
Shortcomings of risk metrics
-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
Need to assess risk and tell management so they can determine which risks to take
on
Ways firms can fail to account for risks
-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
-Wrong distribution
-Historical sample may not apply
Roles of risk management
-Asses firm risks
-Communicate risks
-Manage and monitor risks
Practical considerations related to ERM implementation
-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
Modeling approach is typically between statistical analytic models and structural
simulation models
Risk types addressed by ERM
-Hazard
-Financial
-Operational
-Strategic
Traits of ERM
-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)
-Relationship drawn from CML
-RAP = [(market std dev)/(portfolio std dev)]*(Portfolio return - risk free rate) + risk
, free rate
-annualized
VaR-based analysis (formula)
-Risk replaced with VaR
(Portfolio return - risk free rate)/(portfolio VaR/initial value of portfolio)
Sortino ratio
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
IR = (E(Rp) - E(Rb))/(std dev(Rp-Rb))
-Evaluate manager of a benchmark fund
Tracking error
-Std dev between portfolio return and benchmark return
TE = std dev * (Rp-Rb)
-Benchmark funds
Treynor measure
-Excess return divided by portfolio beta
Tp = (E(Rp) - Rf)/portfolio beta
-Better for well diversified portfolios
Sharpe measure
-Excess return divided by portfolio volatility (std dev)
Sp = (E(Rp) - Rf)/(std dev of Rp)
-Better for non-diversified portfolios
Jensen's alpha
-Excess return equated to alpha plus expected systematic return
alpha_p=
E(Rp) - Rf = alpha + beta(E(Rm) - Rf)
Arbitrage Pricing Theory
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
-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)
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
-Prices of risk are common factors and do not change
-Sensitivities can change
