Risk Management

• CreditMetrics was proposed by J.P. Morgan in 1997, spun-off and acquired by MSCI in 2010

• Model bases on the rating transition matrix

• Ratings can be the internal ratings of the bank or public agency ratings

• Other than Vasicek and CreditRisk+ that only assess losses arising from defaults, CreditMetrics takes downgrades and defaults into account

• With a Monte Carlo Simulation the probability distribution of total credit losses (default and downgrade) is determined which allows a calculation of the credit VaR of the portfolio

  • If counterparty defaults before end-of-year the credit loss is EAD x LGD

  • If counterparty does not default before end-of-year the credit loss is calculated by valuing all

    transactions with the counterparty at end-of-year point

CreditMetrics is a bottom up approach

1. Using credit ratings and the likelihood of a rating migration to calculate standard deviation of the value of a credit product (individual product)

2. Building a portfolio value taking into consideration

• correlation and 
• exposure

Typical process to calculate the value of a credit product

1. One-year transition matrix

2. Specify the horizon

3. Specify forward-pricing model

4. Specify forward distribution of a bond change

Merton’s model regards the equity of a company as a call option on the assets of the firm

In a simple situation the equity value is max (A- DT, 0)

where A is the value of the firm (asset value) and DT is the debt repayment required.

At maturity of the debt, the owners of the company will

• −  pay back the debt (and acquire the assets) if the value of the assets is greater than the value of debt.

• −  leave the company to the lender and “walk away” if the value of the assets is less than the value of debt.

• Merton and Black-Scholes research provided the basic concepts, to use the share price of a company to derive its default probability

• When the market value of a firm’s assets drop below a certain level, it will default

•  KMV (now Moody’s Analytics) developed a user-friendly product called EDFTM– Expected

  Default Frequency – which was dominant in the early 90s.

• The main advantage is that the default probability is calculated regularly, monthly in the past, and now daily

• Using Black-Sholes option pricing formula, Moody’s Analytics deducts the market value of assets and its volatility for a given time horizon

• According to the Moody’s Analytics EDFTM model, a firm defaults when the market value of its assets falls below its liabilities

− The main advantage of Moody's Analytics EDFTM is that it creates a link between the equity and credit markets. It provides daily default probabilities, taking into account latest news.

− However:

• Somewhat of a black box

• Can lead to volatile results if equity price is volatile

• The model uses the book value of liabilities, which is not updated regularly, especially in most

  European and Asian countries

− EDFsTM became less relevant for the largest corporates with the development of CDS and price discoverability.

• CreditRisk+ was proposed by Credit Suisse Financial Products in 1997 as a methodology for calculating VaR

• Actuarian Model, using analytical approximation well established in the insurance industry – roots in mortality models

• CreditRisk+ makes tWo important assumptions

  • The probability of default for a loan in a given period is the same in any other period

  • For a large number of obligors, the PD by any particular obligor is small, and the number of

    defaults in a given period is independent of the number of defaults in another period

=> Under these assumptions the probability distribution for the number of defaults is well

represented by a Poisson distribution

• Obligors are divided into bands (sub-portfolios) whereas all obligors in a band have approx. the same exposure

• The distribution of defaults over all bands is consolidated from the distribution of defaults of the different bands

Advantages

• Relatively easy to implement

• An explicit function can be derived for the probability of portfolio bond or loan losses

• Marginal risk contribution by an obligor can be computed

• Focusing on defaults means it only needs relatively few estimates and inputs (PD and LGD statistics for every instrument are sufficient)

  Disadvantages

• Not sensitive to potential future changes of the credit quality (main difference to CreditMetrics)

• Credit exposure in the portfolio are taken to be constant and independent of any other factors (ref linkage of credit exposure to default probabilities)

• Kamakura Risk Information Services (KRIS) is based on a reduced-form model

  • Reduced-form models produce explicit formulas for the value of risky debt and credit

    derivative products

  • Depend principally on credit market spreads

  • Other used input factors can be equity prices or balance sheet information

• KRIS can be applied to the construction of default models for all types of borrowers: retail, small businesses, large unlisted, municipal, sovereign

• Logistical regression formula that predicts the default hazard rate – i.e., the probability of default for a given time, provided the firm has survived until then

• The reduced-form approach has been better able to predict U.S. corporate defaults than other approaches

• Creditdefaultswapsarethemostcommonformofcreditderivatives

• It is a legal contract which transfers the credit risk of a reference entity from one party

  (protection buyer) to another party (protection seller)

• The reference entity can be a corporate, a country, sovereign, or an asset-backed security

• The market has exploded since its creation in the mid 90’s

• A Credit Linked Note (CLN) is a structured security combining a regular bond and a credit derivative

• A CLN is also called a synthetic corporate bond

• In a CLN the protection buyer transfers credit risk to an investor via an intermediary

  bond-issuing entity

• This issuer can be the protection buyer itself or an SPV

• Other than with a CDS the notional amount is already paid in at issuance of the CLN and invested in risk free securities

• The CLN is paid back to the investor at maturity in case of no credit event

• In case of a credit event the CLN is exercised: Investor receives the notional amount

  after subtraction of compensation payment

Definition Market Risk (Basel Committee for Banking Supervision, 2006) „Market risk can be defined as the risk of losses in on and off- balance sheet positions arising from adverse movements in market prices.“¨

From a regulatory perspective, market risk stems from all the positions included in banks' trading book as well as from commodity and foreign exchange risk positions in the whole balance sheet.

Market Risk can be regarded as systematic risk or non-diversifiable risk as opposed to specific risk, i.e. the idiosyncratic risk of a single asset (see also: CAPM)

• Decision on the desired risk profile

• Allocation (delegation) of responsibilites

• Complete, timely and precise identification of positions (!)

• Correct Valuation and Profit/Loss Determination (P+L) (!)

• Speed and number of Transactions

• Complexity of Positions (!)

• Netting (!)

• Leverage (!)

• Risk vs. Uncertainty

• Method vs. «common sense»; Science or Art?

• Cultural Challenge («Trader Culture»?)

• Reaction to Risk Signals: Corrective action

• Practicability of intended action: Market Liquidity

Estimation of that value (Value at risk) with
a) Historical Simulation („non-parametric procedures“)
b) Monte-Carlo Simulation ((semi-)parametric procedure)
c) Parametric Procedures (simplestcase:Delta-Normal-Method)

Note: The VaR is a widely used risk measure, but neither the only one nor the one best rooted in theory.

The expected shortfall (ES) measures the loss one has to expect (> risk capital) in case losses exceed the loss level defined by the confidence level. ES is a „Coherent Risk Measure“.

The Expected Shortfall (ES) is equal to the expected value of the losses > risk capital. Technically speaking, the residual distribution is assumed to represent 100% of such losses (i.e. the area below the curve (starting from risk capital) = 1).

Expected shortfall (ES) measures the “average” loss of all the losses exceeding the risk capital threshold (determined by the confidence level).

Risk capital is equal to the potential loss during a defined time period that is not exceeded with a defined probability.*