KIS 채권평가 - Beyond Pricing

Risk Types

Market Risk

Any risk associated with market movement(Market Price, Market Interest, FX) against current position

Market Risk Management

Portfolio , Rate of Return, Risk analysis to mange against Market Risk

Credit Risk

• The risk of default on a debt that may arise from a borrower failing to make required payments.
• Measurement
  • Probability of Default(PD): Probability of Default with in period( usually within a year)
  • Exposure At Default(EAD): the gross exposure under a facility upon default of an obligor
  • Expected Loss: Loss expected within the exposure. Credit Risk is Zero, if the all the loss can be collected after the default
• Measuring Method

• inform of Method, Model

  Method	Model
  Financial Statement Data Method	Altman Z-score regression analysis, Logit, Probit model
  Option Model Method	KMV model, Black-Scholes model
  Economic Indicator Method	Use of GNP changes, equity Index and etc to calculated Probability of default
  Decision Tree Method	Analyze individual companies by categorizing the entire set into similar groups
  Neutral network Method	Estimation of default probability using linear, nonlinear, and neural networks
  Mathematical Method	Linear Programming, NON-Linear Programming

Risk Factor Management

Manage Risk Factor by rate of return and volatility of the market

Risk Management

Market Risk Management Process

Market risk management consists of processes: data acquisition, data analysis, result data and screen display

Market Risk Management

Risk associated with Portfolio management and Return is managed though Risk analysis and Pricing

VaR

The maximum amount of loss that can occur over a period of time with a given confidence level under normal market conditions

• For example, if the VaR for a target period of 1 year and a confidence level of 95% is KRW 1 billion, It means 95% chance that the maximum loss can be less than KRW 1 billion with in a year
• The market risk can be controlled, if there were KRW 1 billion.
• The higher the confidence level, the larger the VaR..

By implementing VaR,

• It is possible to objectively quantify the risk instead of based on experience
• Benefits of managing the risks that occur across various sectors as whole, since financial institutions can calculate the risks that occur in various markets(Bonds Equites and others)
• Effective allocation of resources using VaR

Portfolio VaR

• Portfolios risk can be calculated by looking into individual risk elements in the portfolio
• By disassemble the portfolio, portfolio returns consist of a linear combination of individual asset returns.
• The weight of individual asset returns given based on the amount of initial investment amount
• Therefore, VaR in a portfolio can be measured by combining the risks of individual assets with in the portfolio

The portfolio returns from time t to time t + 1 are as follows

The weights (Wi,t) are given at the beginning of the period and sum to 1. The expected returns of the portfolio are as follows.

The variance of the portfolio includes not only the risk of individual assets (securities)(σ12) but also the covariance(σij) between assets.

If the correlation is low or the number of assets increases, the risk of the portfolio decreases, but the VaR of the portfolio that does not consider the dispersion effect is the sum of the individual VaRs.

Types of VaR

Incremental VaR

• The incremental VaR of a stock i represents the change in total VaR when the stock is excluded from the current portfolio.
• To obtain the incremental VaR, we set the holding position of i to 0, calculate VaR of the portfolio again, and subtract it from the VaR of the portfolio that includes the position of i.
• Incremental VaR equation
• 
• Incremental VaR can be used to minimize VaR for investments when the amount of investment is limited or when the amount of investment must be reduced.
• If we reduce the amount of investment by KRW 500,000 and reduce VaR to the maximum, we can reduce the amount of investment in the stocks that have the largest incremental VaR
• In order to obtain the incremental VaR for individual items, it takes some time to calculate the matrix as above

Marginal VaR

• Marginal VaR represents the changes in total VaR when the value i in one of item in the current portfolio changes.
• Expressing this in a formula Marginal VaR
• 
• Marginal VaR of i item is proportional to the correlation coefficient between the return of i item and the return of the portfolio
• The smaller the correlation with the portfolio, the smaller the change in portfolio VaR given the same amount is added, when there is negative correlation the portfolio VaR will decrease.
• Marginal VaR is defined as movement of the VaR related with movement of the one unit of investment. Therefore, to obtain an accurate marginal VaR, comparison between two different portfolio VaR is required
• To obtain the Marginal VaR, increase one unit of investment amount in the current portfolio and calculate differences between the previous and the existing portfolio.

Component VaR

• Component VaR is the contribution of a specific item to the entire portfolio’s VaR
• Component VaR is useful for analyzing how much the VaR value of a portfolio can be reduced when a specific items or asset group is removed from the current portfolio.
• However, if the constituent items of the portfolio are changed, the VaR value changes due to the correlation between the constituent items changes
• Therefore, Component VaR is the ratio of the VaR value of the current portfolio, it is an approximated value.
• Incremental VaR is when items is removed from the portfolio. Component VaR is an approximation of Incremental VaR.
• Therefore, in general, the value of Incremental VaR or Component VaR is similar.
• Jorion defines the Component VaR as follows.
• 

VaR Analysis

Back-Testing

The back test for verifying the model is to verify the conformity through comparison of the P/L generated under the confidence level, and to extract the P/L data, back test, documentation and report to the supervisory authority.

VaR Model Analysis

• Back Test through P/L calculation
• By comparing calculated the VaR with the actual rate of return on the portfolio on the next day
• Back Test should be done on a regular basis
• Modification of the VaR model or analysis of the cause due to an exception events

VaR Model Analysis(Regular)

KIS-VaR

Market Risk Analysis Screen

By basic input information for VaR calculation, the market VaR screen is able to provide position information, market risk information and VaR information by risk factor.

Market Risk Analysis Summery Screen

Market risk analysis summary screen provides position information, market risk information, and VaR information by risk factor through basic input information required for VaR calculation.