Risk Assessment Methods

1
Risk Assessment Methods

• Michael Gapen and Dale Gray
• Foundations of Macro-Financial Surveillance
• November 10-14, 2008

2
Risk Management

• Risk Management
• Process by which risk is identified, measured and
  managed
• Process of adjusting both the risk of large
  losses and the firms vulnerability to them
• Objective
• Determine the level of acceptable risk

3
The Risk Management Process
Identify Risk Exposures
Measure and Estimate Risk Exposures
Find Ways to Shift or Trade Risk
Assess Effects of Exposures
Assess Costs and Benefits of Trading Risk

• Form Risk Mitigation Strategy
• Avoid, Transfer, Mitigate, Keep

Evaluate Performance
4
The IMF and Risk Identification

• Pre-Asia sole focus on flows and prices
• Post-Asia focus on flows and balance sheets
• Characteristics of capital account crises derive
  from portfolio adjustments to shocks
• Balance sheet weakness can drive vulnerability
• Drop in demand for assets of any one sector may
  spill over into other sectors, including public
  sector
• Adjustment in stocks drives flows
• Adjustment in flows reflected in exchange rates,
  interest rates, inflation, growth, current
  account
• Re-affirmed in the sub-prime crisis

5
The IMF and Risk Identification

• What risk are we assessing?
• Financial Risk - losses due to movements in
  financial markets, interest rates, exchange
  rates, default
• Components of financial risk
• Market Risk
• Credit Risk
• Liquidity Risk
• Operational Risk

6
The IMF and Risk Identification

• The IMF is concerned with systemic risk
• When a crisis causes creditors to lose confidence
  in
• a countrys ability to earn foreign exchange to
  service external debt,
• the governments ability to service its debt,
• the banking systems ability to meet deposits
• corporations ability to repay bank loans and
  other debt

7
The IMF and Risk Identification

• Systemic risk means possible
• Widespread corporate defaults
• A joint breakdown of the financial system
• A sovereign default
• An aggregate measure of risk
• Intimately related to default risk
• Expected losses
• Risk transfer across balance sheets
• Question
• Are we measuring this risk?

8
What Have We Been Missing?

• Study of financial fragility has not been well
  served by macroeconomic theory. Financial
  fragility is intimately related to probability of
  default. Default is hard to handle analytically
  being a discontinuous, nonlinear event so most
  macro models abstract from default and financial
  intermediaries such as banks.
• Charles Goodhart
• 2005 Joint INS/MCM Conference

9
Outline Modern Contingent Claims Analysis

• Single Entity Risk
• Corporates, Banks, Sovereign
• Macrofinancial Risk
• Interlinked, aggregated balance sheets
• Workshop
• Fannie-Freddie Case Study
• Sub-prime crisis

10
Contingent Claims Analysis Single Entity Credit
Risk

• Risk Assessment at the Micro Level

11

• Thinking About Default Risk

12
Thinking About Default Risk

• Three main elements determine default
  probability
• Market value of assets
• Uncertainty and risk in future asset value
• Leverage the extent of contractual liabilities
• Note emphasis on a marked-to-market balance
  sheet, where market value of assets is weighed
  against obligated payments

13
Thinking About Default Risk
Asset Value
Exp. asset
Distribution of Asset value
value path
Distress Barrier from Debt
V
0
T
Time
14
Thinking About Default Risk

• Problem asset value and asset risk unobservable
• Solution used an implied measure
• We cant observe A and s directly, but they
  influence the value of something we can
  observethe value of the firms equity
• Our understanding of options and capital
  structure will help us make the connection

15

• Corporate Default Risk The Merton Model

16
Contingent Claims Analysis Corporates, The
Merton Model, and MKMV

• Debt holders have senior claim on firm assets
• Paid first, limited upside, control assets if
  default
• Payoff Min (DB, VA(T))
• Equity has a junior claim on firm assets
• Junior claim, paid after bonds, but unlimited
  upside
• Payoff Max (0, VA(T) - DB)
• Return on equity looks like a call option
• The underlying firms assets
• Strike price value of liabilities (DB)

17
Payoff to Debt and Equity
Payoff
Junior equity
VA-DB
Senior debt
0
VAAsset Value
DB
18
Contingent Claims Analysis

• Equity as a call option on firm assets
• Also use the following relationship
• Solve the two equations for VA and sA

19
Contingent Claims Analysis

• Uses a limited number of inputs
• Market value and volatility of traded equity
• Distress barrier (DB) from existing debt
• DB ST debt ½ LT debt interest
• Discount rate
• Time horizon (usually 1 year)

20
Contingent Claims Analysis
Asset Value
Exp. asset
Distribution of Asset value
value path
Distance to Distress
Distress Barrier from Debt
V
0
Probability of Default
T
Time
21
Contingent Claims Analysis

• Distance to Distress
• Number of standard deviations asset value is from
  distress barrier
• Probability of Default
• Cumulative normal distribution N(-d2)

22
Contingent Claims Analysis

• Improved predictive power
• MKMV analysis shows CCA to be more effective at
  default prediction
• Power comes from nonlinear option pricing
• Option price sensitivities the Greeks
• Delta change in option price from small change
  in the underlying asset
• Gamma change in delta from a change in the
  underlying asset
• Vega change in option price from a small change
  in underlying asset volatility

23
Option Price Sensitivities

• Value of option is most sensitive to changes in
  the underlying around the distress
  barrier...which is why it captures default risk
  so well and is good for simulations

24
Additional CCA Risk Indicators

• Risk-neutral spreads
• Insert call option formula to get VSL
• Which can be rearranged as

25
Contingent Claims Analysis

• Expected loss on senior debt
• Value of debt has two components
• Pure default-free value
• If no default, receive stated payments
• Default risk
• Shareholders put assets to the debt holders in
  the event of default
• Expected loss promised payments market value
  of assets
• Amount of expected loss is an implicit put option
  on firm assets with debt as the strike price

26
Contingent Claims Analysis

• Expected loss on senior debt and loans?
• Risky Debt Default free value Expected loss
• Expected losses across the loan portfolio yields
  a value for credit risk
• One input for risk-weighted capital

27

• From Risk-Neutral to Implied Actual

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From Risk-Neutral to Actual

• Risk-Neutral Pricing
• Results from B-S-M and riskless hedge port.
• Advantage option value doesnt depend on
  investor risk preferences
• Disadvantage real world risk indicators are
  based on investor risk aversion
• Market practicioners often adjust RN risk
  indicators into implied actual risk indicators

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Implied Actual Default Probability

• RN distance-to-distress has asset drift of rf,
  and a RN default probability of N(d2)
• Actual distance-to-default has asset drift of
  µA and default probability of N(d2, µ)
• These are related by the market price of risk, ?,
  
• The market price of risk is estimated by,
• where SR is the market Sharpe Ratio, ?A,M is the
  correlation of the asset return with the market,
  and sA is the standard deviation of asset return

30
Risk-Neutral Versus Actual Default Probability
31
Estimated Implied CDS spreads

• The protection buyer in a CDS contract pays a
  premium over the term or until a credit even
  occurs
• The protection seller is obligated to make a
  contingent payment of par minus recovery
  following a credit event
• RN default probability (RNDP) can be used with
  expected loss given default (LGD)
• Estimated implied CDS spreads (EICDS) should
  correspond closely with actual market observed
  CDS data

32
Multiple Layers of Liabilities Payoff to Senior
Debt, Subordinated Debt and Equity
Payoff
Value of Junior equity
Default Put Option on Senior Debt
VA-DB2
Value of Senior debt
DB1
Value of Subordinated debt
SUB
0
DB1
VAAsset Value
DB2
Expected Loss on Subordinated Debt
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Contingent Claims Analysis Final Thoughts

• Advantages
• It is based on market data
• A structural approach
• Requires less data input
• Incorporates nonlinearities
• Issues
• Normal distribution of VA
• From Risk-neutral to implied actual
• Yet this route isnt needed for valuing expected
  losses
• Harder to use for private firms

34

• Contingent Claim Analysis for Banks

35
Contingent Claims Analysis Banks

• Does it work for banks?
• Yes, but may think about adjustments
• Distance to Default
• Distance to Corrective Action

Equity
Bank Assets
Deposits and senior debt
PCAR Prompt corrective action ratio, or when
capital gets low and the regulator reacts
36
Contingent Claims Analysis Banks
37
Valuing the Implicit Guarantee

• Any government guarantee against bank default
  would need to offset expected loss on senior
  liabilities
• Risky Debt Default free value Expected loss
• Risky debt default-free debt implicit
  guarantee

38
Valuing the Implicit Guarantee Thailand 2002
End-2000
Value of the financial sector guarantee 1997
Crisis
End-1999
Gapen and others, IMF Working Paper No. 04/121
39

• Sovereign Contingent Claims Analysis

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Sovereign Contingent Claims Analysis

• Can it be applied to the sovereign?
• Gapen and others, IMF Staff Papers (2008)
• IMF WP 07/233 for application to Turkey
• Step 1- Begin with the segregated, but linked,
  balance sheets of the government and monetary
  authorities
• Step 2 Define Priority of Liabilities
• Step 3 - Consolidate into one balance sheet, in a
  common currency

41
Sovereign Contingent Claims Analysis
Implicit call option on assets
Default-free value minus expected loss (implicit
put option on assets)

• Key points
• Book value of domestic currency liabilities acts
  like equity shares
• Exchange rate acts like an equity price

42
Sovereign Contingent Claims Analysis
ASSETS LIABILITIES
Modeled as Implicit Call Options on Assets
Domestic Currency Liabilities
Foreign Reserves plus Other Assets
Default-Free Value of Foreign Currency Debt minus
Implicit Put Option on Assets
Value of Risky Foreign Currency Denominated Debt
Question Who is responsible for this expected
loss given default?
43
Sovereign Contingent Claims Analysis

• Contingent Claim Analysis on the following
  sovereigns
• Brazil, Bulgaria, Colombia, Korea, Malaysia,
  Mexico, Philippines, Poland, Russia, South
  Africa, Turkey, and Venezuela
• Credit risk indicators for each distance to
  distress, probability of default, credit spreads,
  etc.
• Robustness checks no database of sovereign
  defaults, but tested empirically against observed
  market data (cds and EMBI spread data)
• Scenario and simulation analysis

44
Two examples, D2D and CDS
45
Two examples, RNS and EMBI
46
Robustness Checks
47
Robustness of Sovereign CCA
Data Brazil, Turkey, Venezuela, Russia, S.
Africa, Poland, Malaysia, Korea,
Philippines, Mexico, and Colombia, 889 data
points from 2002-2004
48
Poor Correlation of Debt-to-GDP with Spreads
Panel Data for 19 EM countries, 1996-2002
49
Aggregated CCA Simulation and Risk Analysis
50
Macrofinancial Risk

• Aggregated Contingent Claims Analysis

51
Aggregated Contingent Claims

• Create an aggregated corporate sector, banking
  sector, and sovereign balance sheet
• Can create sub-sectors as well
• Or combinations of single-entity and bundled
  corporates an financial institutions
• Could also do household sector
• Apply CCA framework
• Calibrate marked-to-market balance sheet
• Compute risk indicators for each sector
• Sectors are linked through the expected losses on
  risky debt

52
Aggregated Contingent Claims Interlinked Balance
Sheets
Equity
Corporate Sector Assets
Default-free Debt Value implicit put option
Equity
Financial Sector Assets
Deposits and Debt Value implicit put option
Money Local Currency Debt
Sovereign Assets
Def-free Debt Value implicit put option
implicit put option value of the guarantee!
Contingent Liab
53
Aggregated Contingent Claims Interlinked Balance
Sheets
Examples of Risk Transmission via Implicit Put
Options in Risky Debt or Implicit Government
Guarantees
1
Negative Shock to Corporate Sector
Corporate Sector
Banks / Financial Institutions
Sovereign
Asia
2
Banking Sector Crisis or Deposit Run
Banks / Financial Institutions
Sovereign
Uruguay
3
Capital Outflow / Exchange Rate Shock affecting
Sovereign
Sovereign
Debt Holders ( Foreign and Local )
Banks / Financials Corporates
Brazil
54
The Aggregated CCA in Practice Brazil 2002
55
The Aggregated CCA in Practice Brazil 2002
Distance to distress in March 2002 before the
crisis
56
The Aggregated CCA in Practice Brazil 2002
Distance to distress in Sept of 2002 the
peak of the crisis
57
The Aggregated CCA in Practice
58
In Conclusion

• Finally, when is this guy going to break for
  lunch?

59
Macrofinancial Risk

• Macro models and risk
• Geared to forecast the mean (first moment)
• Transversality conditions preclude default
• Early warning models are not structural, do not
  have links, high noise to signal content
• Finance models and risk
• Capture mean and higher moments
• Structural linkage of balance sheets to assess
  likelihood and depth of risk transmission
• Measurement of (non-linear) risk transmission is
  not possible using macroeconomic flow or
  accounting frameworks

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Three Necessary Types of Accounts
FIRM or BANK
ECONOMY

• Income Statement
• Balance Sheet (mark-to-market)
• Risk Accounts (e.g. expected
  loss, value at risk, etc.)

• Flow-of-Funds
• Balance Sheets (economic value balance sheets
  of sectors)
• Risk Accounts for Economy

Macrofinance framework gives these two missing
accounts
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Aggregated CCA Output The Risk Accounts for Each
Sector

• Market Value of Assets
• Market Value of Debt
• Default Barrier
• Implicit Put Option
• MV Junior Claim/Equity
• Volatility of Asset (Implied)
• Volatility of Junior Claim
• Distance to Distress
• Asset minus Default Barrier
• Probability of Default (Est. Actual)
• Spread (Est. actual and other)
• Probability of Default (RN)
• Recovery Rate (1-LGD)

• Banking Sector Guarantee (Put Option)
• Non-Banking Sector Guarantee
• Risk exposures and measures from option
  sensitivities (e.g., delta, gamma, vega)
• Debt (Put Option Embedded in Debt)
• Equity/Junior Claim
• Guarantee to Banks
• Guarantee to Non-Banks

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A View from the Desk

• The IMF and Risk Identification
• Systemic risk default triggered, risk
  transmission across balance sheets
• Risk Measurement
• CCA links balance sheets through implicit put
  options
• Quantifiable measures of systemic risk
• Easy to simulate
• Risk Management
• Can direct policy to reducing risk
• Can estimate the size of Fund program needs

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A View from the Desk

• Put market movements in perspective
• Relate to capital account flows
• Might they amplify systemic risk? (GFSR Oct 07)
• Understand the risk management tools
• What the models tell us, where pitfalls lie
• Improve discussions with FSA, banks, and market
  participants
• What do the risk accounts say?
• Monitoring the monitor

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Frequently Asked Questions

• Why cant I just use bond spreads, prices, or CDS
  spreads as risk measures?
• Answer Two reasons
• These short-cuts do not provide a measure of
  expected loss, which is essential for risk
  management. In fact, deriving probability of
  default from these market prices involves making
  an assumption about recovery rates, which means
  you are assuming the risk measure you are trying
  to quantify.
• These short-cut measures are not part of a
  structural model, which allows for interaction
  between balance sheets and for simulation. An
  options-based approach includes the sensitivity
  measures so critical in assessing risk transfer.

65
Frequently Asked Questions

• Why cant I use traditional debt-to-GDP measures?
• Answer Debt-to-GDP has proven to have a low
  correlation with market data such as bond prices
  and spreads (see figure next page). Debt-to-GDP
  ratio identifies an element of sovereign risk,
  but is not part of a structural framework that
  measurably relates debt payments with the
  capacity to pay. Nor is it released with enough
  frequency to enable its use during periods of
  stress where vulnerabilities may build or subside
  rapidly. Finally, debt-to-GDP does not reveal
  probability of default or measures for expected
  loss, the latter of which is essential for risk
  management.

66
Frequently Asked Questions

• How does the sovereign CCA handle fixed and
  floating exchange rates?
• Answer If the exchange rate is floating the
  volatility comes largely from the exchange rate.
  If the exchange rate is managed or fixed
  there is little or no volatility in the exchange
  rate but, to keep the exchange rate stable, more
  money and local-currency debt must be issued and
  bought back (via sterilization operations).
  There is thus higher volatility in the quantities
  of local-currency liabilities from the issue and
  repurchase operations as the counterpart to less
  volatility in the exchange rate. (An Analogy A
  firm that tries to fix its stock price must issue
  and repurchase shares with the result that the
  market cap, shares times stock price, still has
  volatility.)

67
Frequently Asked Questions

• What about off balance sheet liabilities?
• Answer The ability of the model to handle off
  balance sheet liabilities depends on the ability
  of analysts to understand firm operations and
  price equity accordingly. As such, the model may
  or may not fully capture off balance sheet
  liabilities, but tests against actual defaults
  suggests it performs much better than alternative
  approaches (which also do not incorporate off
  balance sheet items).

68
Frequently Asked Questions

• Is the model applicable across countries?
• Answer Moodys KMV has shown that the model
  applies very well across markets at the corporate
  and financial levels, and IMF WP 05/155 shows it
  applies to sovereigns. The distance-to-default
  measure incorporates many of the idiosyncrasies
  of different countries and industries. For
  example, the business risk, as measured by the
  asset volatility, varies for a given industry
  across countries. The different economic
  prospects for countries are obviously captured by
  the individual equity, exchange rate, and asset
  valuations. As a result, we believe that the
  distance-to-distress captures most of the
  relevant inter-country differences in default
  risk and risk transmission.

69
Frequently Asked Questions

• Can the model be applied to non-traded firms and
  financial institutions?
• Answer Yes, by using proxies. Moodys KMV has
  show that the model works well even for thinly
  traded or OTC firms with market caps as little as
  US20mn. The best way to incorporate non-traded
  entities is to find publicly traded entities with
  similar characteristics. If none are available,
  it may also be possible to use the aggregate
  characteristics of traded companies in that
  sector or sub-sector as a proxy. Using proxies
  obviously entails model risk and the output
  should be treated appropriately.
• Moodys commercially available RiskCalc product
  is actually designed to address non-traded
  institutions.

70
Frequently Asked Questions

• Does the model assume equity and exchange rate
  markets are efficient?
• Answer No. The efficiency of a market usually
  refers to the degree to which the current price
  reflects all the relevant information about a
  firms value or countrys prospects. The market
  reflects a summary of many investors forecasts
  and it is unusual if any one individuals, or
  committees, forecast is better. Consequently, we
  believe that the best source of information
  regarding the equity or exchange rate value is
  the market. The market, though, can be caught by
  surprise, usually in cases of fraud such as
  Enron.