FRM Exam 1
What are the headline challenges of implementing ERM?
- Measurement - Aggregation - Cultural - Timescale
What departments are involved in ERM?
- Strategic planning - Finance/Treasury - Risk departments (credit, market & operational) - Internal audit
Roles of risk management
-Asses firm risks -Communicate risks -Manage and monitor risks
CAPM (formula)
-Capital Asset Pricing Model Ri = Rf + beta*(Rm - Rf)
Market imperfections that can create value
-Capital structure (financial distress) -Taxes -Agency and information asymmetries
Sovereign risk
-Country specific -Foreign exchange controls that prohibit counterparty's obligations
Shape of portfolio possibilities curve
-Curve must be concave -Straight line connecting any two points must be under the curve
Derivative contract
-Derives value from an underlying asset, rate, or index -Derives value from a security
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
Basis
-Difference between forward price and spot price -Should approach zero as the contract approaches maturity
Capital market line (CML)
-Efficient frontier with inclusion of risk free rate -Straight line with formula Rc = Rf + ((Ra - Rf)/std dev(a))*std dev(c) -c is the total portfolio, a is the risky asset
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
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)
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
Risk types addressed by ERM
-Hazard -Financial -Operational -Strategic
Differences in financial risk management for financial companies vs industrial companies
-Managing risks is a core activity at financial companies -Industrial companies hedge financial risks
Four major types of risk
-Market risk -Liquidity risk -Credit risk -Operational risk
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
3 main types of operational risk
-People risk = fraud, etc. -Model risk = flawed valuation models -Legal risk = exposure to fines and lawsuits
Prices of risk vs sensitivity
-Prices of risk are common factors and do not change -Sensitivities can change
Recovery rate
-Proportion of loss that is recovered -Also referred to as "cents on the dollar"
Parametric VaR
-Quantile of a statistical distribution
Nonparametric VaR
-Quantile of an empirical distribution
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)
Security (primary vs secondary)
-Security is a financial claim issued to raise capital -Primary securities are backed by real assets -Secondary securities are backed by primary securities
Tracking error
-Std dev between portfolio return and benchmark return TE = std dev * (Rp-Rb) -Benchmark funds
Risks excluded from operational risk
-Strategic risk -Business risk -Reputational risk
Debt overhang
-Too much debt -Causes shareholders to seek projects that create short term capital but long term losses
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
Basis risk
-Unanticipated movements in relative prices of assets in a hedged position -All hedges imply some basis risk
Risk
-Volatility of expected outcomes -Outcomes are random but distribution is known or approximated
Ways risk can be mismeasured
-Wrong distribution -Historical sample may not apply
Nonmarketable asset impact on CAPM
-ex. Human capital -Equilibrium return can be higher or lower than it is under standard CAPM
Ten assumptions underlying CAPM
-no transaction costs -assets infinitely divisible -no personal tax -perfect competition -investors only care about mean and variance -short-selling allowed -unlimited lending and borrowing -homogeneity: single period -homogeneity: same mean, variance and error -all assets are marketable
Financial Risk
: refers to the uncertainty off loss because of adverse changes in commodity prices, interest rates, foreign exchange rates, and the value of money.
Who is responsible for ERM?
Board and senior managers
Funding-liquidity risk
Inability to make payment obligations (ex. Margin calls)
What is Enterprise Risk Management also known as.
Integrated Risk Management or Firm Wide risk management
What does ICAAP stand for?
Internal Capital Adequacy Assessment Process
Asset transformers
Liquidity and maturity transformation
Effect of non-price-taking behavior on CAPM
Simple form of CAPM, but market price of risk is lower than if all investors were price takers
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
Standard deviation of two assets (sqrt of variance)
Sqrt((Xa^2)(variance of a) + (1-Xa)^2(variance of b) + 2(Xa)(1-Xa)(covariance))
Carry-backs and carry-forwards
When negative taxable income is moved to a different year to offset future or past taxable income
Settlement risk
When two payments are exchanged the same day and one party may default after payment is made
Solve for minimum variance portfolio
Xmvp = ((variance of b) - covariance)/((variance of a) + (variance of b) - 2 * covariance)
Speculative risk
a situation in which either profit or loss is possible (gambling)
Pure Risks
a situation in which there are only the possibilities of loss or no loss (earthquake)
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
Diversifiable Risk
affects only individuals or small groups. It is also called nonsystematic risk.
Nondiversifiable Risk
affects the entire economy or large numbers of persons or groups within the economy (hurricane). It is also called systematic risk or fundamental risk. Standardized measure of systematic risk is called beta
Retention
an individual or business firm retains part of all of the losses that can result from a given risk.
Loss Exposure
any situation or circumstance in which a loss of possible, regardless of whether a loss occurs.
Enterprise risk management
combines into a single unified treatment program all major risks faced by the firm -- pure risk, speculative risk, strategic risk, operational risk, financial risk.
What risks are typically captured by ERM?
credit, market, investment, liquidity operational risks
Enterprise Risk
encompass all major risks faced by a business firm, which include; pure risk, speculative risk, strategic risk, operational risk, and financial risk.
Self-Insurance
is a special form of planned retention by which part or all of a given loss exposure is retained by the firm
Passive retention
means risks may be unknowingly retained because of ignorance, indifference, or laziness
Active retention
means that an individual is aware of the risk and deliberately plans to retain all or part of it
Methods for paying retained losses
net income (losses are current expenses), unfunded reserve (losses are deducted from bookkeeping account), funded reserve (losses are deducted from liquid fund), credit line (funds are borrowed to pay losses as they occur).
Retention is effectively used when
no other method of treatment is available, the worst possible loss is not serious, or losses are highly predictable.
Chance of Loss
the probability that an event that causes loss will occur.
Objective Risk
the relative variation of actual loss from expected loss.
Noninsurance Transfer
transfers risk to another party through a contract or by hedging (buying and selling futures contracts on organized exchange.
Subjective Risk
uncertainty based on a person's mental condition or state of mind.
Risk
uncertainty concerning the occurrence of a loss.
Strategic Risk
uncertainty regarding the firm's financial goals and objectives.
What does ICAAP require a firm to do?
• Define and quantify the overall risk exposure across all risk types. • Stress and scenario test this exposure. • Compare the results to the available capital.
Uncertainty
Probability distribution is unknown (ex. A terrorist attack)
What is the main aim of ERM?
Protecting Shareholder Value is the main aim to ERM.
Brokers
Reduces transaction and information costs between households and corporations
Multibeta CAPM
Ri - Rf = (market beta)(Rm - Rf) + (sensitivity to inflation risk)(price of inflation risk)...
Zero-beta CAPM (two factor model)
Ri = Rz + (Rm - Rz)*beta -Rz = return on zero-beta portfolio
Business risks
Risks that are assumed willingly, to gain a competitive edge or add shareholder value
Expected return of two assets
Rp = XaRa + XbRb where X is proportion of portfolio
Formula for covariance
Covariance = correlation coefficient * std dev(a) * std dev(b)
Information ratio
IR = (E(Rp) - E(Rb))/(std dev(Rp-Rb)) -Evaluate manager of a benchmark fund
CAPM assumption for EMH
CAPM requires the strong form of the Efficient Market Hypothesis = private information
Asset-liquidity risk
Cannot exit position in market due to size of the position
Efficient frontier
Concave function that extends from minimum variance portfolio to maximum return portfolio
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
CAPM with taxes included (equation)
E(Ri) = Rf + beta[(E(Rm)-Rf)-(tax factor)(dividend yield for market - Rf)] + (tax factor)(dividend yield for stock - Rf)
What is Enterprise Risk Management
ERP is the development of systems and processes allowing an understanding of the totality of the risk faced by the firm, and how such areas of risk interact with one another.
Effect of heterogeneous expectations on CAPM
Equilibrium can still be expressed in returns, covariance, and variance, but they become complex weighted averages
Financial risks
Losses due to market activities ex. Interest rate changes or defaults
Models used in ERM framework
Modeling approach is typically between statistical analytic models and structural simulation models
Where is much of the focus currently in ERM?
Much of the effort involved in ERM at present is in understanding the inter-relationship between the different risk types that face a business. ERM attempts to improve the way various risk specialists work with each other in forming the overall risk picture.
Importance of communication for risk managers
Need to assess risk and tell management so they can determine which risks to take on
Exposure
Potential amount that can be lost
Correlation coefficient effect on diversification
The lower (closer to -1), the higher the payoff from diversification
Tax shield
The uses of debt to fall into a lower tax rate
Loss frequency
refers to the probable number of losses that may occur during some time period
Pooling of Losses
spreading losses incurred by the few over the entire group
Risk Financing
techniques that provide for payment of losses after they occur -- retention, non-insurance transfers, and commercial insurance.
Law of Numbers
the greater the number of exposures, the more closely will the actual results approach the probable results that are expected from an infinite number of exposures.
Objective Probability
the long-run relative frequency of an event based on the assumptions of an infinite number of observations and of no change in the underlying conditions.
Reasons for forming a captive
the parent firm may have difficulty obtaining insurance, to take advantage of favorable regulatory environment, costs may lower than purchasing commercial insurance, a captive insurer has easier access to a reinsurer, a captive insurer can become a source of profit.
