The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee Copyright © 2004 by Thomas Ho and Sang Bin Lee. All rights reserved.

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Risk Measurement -Value at Risk (VaR) Definition: a measure of potential loss at a level (99% or 95% confidence level) over a time horizon

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Market Risk Market risk is the losses that arise from the mark to market of the trading securities “Prices” for tradable securities of a portfolio are marked to market that are often derived from the fair values of the valuation models

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management VaR for single securities Definition : is called the critical value which determines the one-tail confidence level of standard normal distribution. Time factor is defined as where t is the time horizon in measuring the VaR. Volatility is the standard deviation of the stock measured in $ over one year.

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management VaR for single securities - portfolio return distribution - the price of the bond - the critical value for a particular interval of a normal distribution

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management 6 - the VaR of the bond - the bond price uncertain value is a multivariate normal distribution 15.3 VaR for single securities

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Delta Normal Methodology (2) VaR for a Portfolio (I) - The portfolio value - The portfolio uncertain value - The VaR of the portfolio

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Portfolio VaR VaR for a Portfolio (II) - Component VaR

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Three Stocks Case A Numerical Example - Calculating the VaR of a portfolio of three different stocks (GM, WMT, and IBM) - Calculating the daily rates of return and the variance-covariance matrix

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Correlations of the Stock Returns Calculating the daily rates of return and the variance- covariance matrix

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management VaR Derivations The detailed derivation of the individual VaR as well as the portfolio VaR is given as follows. Where,

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management VaR Derivation

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Component VaR

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management VaR Calculation VaR calculation output by Delta-Normal Method

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Historical Simulation Methodology The Historical Simulation methodology

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Historical Returns Historical Return data set

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management VaR Calculation 5-day VaRGMWMTIBMTotal Weight1/3 1 Individual stock VaR Portfolio VaR Beta Beta*Weight Component VaR Portfolio Effects VaR calculation output by Historical Simulation Method

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Monte Carlo Simulation Methodology Random numbers generated from Multi Normal Distribution

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Simulations based on the Correlation Matrix The variance-covariance matrix of stock returns generated by Monte Carlo simulation

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management VaR Calculation VaR calculation output by Monte Carlo Simulation Method

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Extreme Value Theory multiply historical returns by – 1 to convert them into positive values. choose a threshold (): a parametric distribution of the tail beyond the threshold. The ratio: count how many observations are beyond the threshold in the actual data and divide it by the total observation. Parameters () estimation VaR calculation

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Extreme Value Theory - Historical return data vs. Standard Normal Distribution - cumulative distribution functions

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management calculate the VaR by the extreme value theory - The formula to calculate the VaR based on the Extreme Value Theory - probability density function

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Credit Risk Definition the loss of principal or interest or any promised payments from the borrow for bonds or loans of any securities

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Credit Risk and Market Risk Model VaR of a Bond - Firm value process (Merton) Integrating Credit Risk and Market Risk in a Portfolio Context (I) - Firm value process (Merton, Longstaff and Schwarzt) - interest rate model (Hull and White)

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Portfolio Credit and Market Risk Integrating Credit Risk and Market Risk in a Portfolio Context - The stock risk

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Portfolio Credit Risk Specify a set of macro-economic factors that would affect the credit risk of the firms. Define the default index by measuring default rate. The macro economic factors are used as the independent variables to explain the default rate. Measure the rating migrations against the speculative default rates: change of the speculative default rate determines the change in the rating migrations. The simulations can then be used to simulate the change in value of a bond portfolio.

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Credit VaR - a Numerical Example by CreditMetrics Initial ratin g Rating at year-end (%) AAAAAABBBBBBCCCDefault AAA AA A BBB BB B CCC One-year Transition Matrix

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management 29 Category1234 AAA AA A BBB BB B CCC Bond numberCredit GradeFace valueMaturityCoupon Rate Recovery Rate 1A1005zero0.60 2BBB BB Bond Data set 15.7 cont.. - Example one -year forward zero curves by crediting rating category

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management 30 GradeAAAAAABBBBBBCCCDefault Price Profit/Loss Probability Cumulative Probab ility cont.. - 1year forward bond Price, Profit/Loss and Probability for the BB-grade bond

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management cont.. - Cumulative Probability of BB-Grade Bond’s Profit/Loss

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management 32 - Estimate the correlation matrix or variance-covariance matrix among the bond returns 15.7 cont.. - Z-threshold

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management cont.. - Bond Portfolio Default Risk Distribution

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Risk Reporting Aggregation of Risks to Equity ($mil.) (the VaR Table)

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Risk Monitoring Back testing

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Risk Measurement Strategic Risk Management –Smith and Smithson (1998) determines the economic factors affecting the equity value of a firm –Hedging against these economic factors is strategic risk management Business Process –Build a model of the firm as a system of processes –Manage the processes by monitoring and controlling the risks in each phase

The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management Risk Measurement (2) Investment Cycle