This concept leverages the portfolio deviation calculation by computing it with and without the asset of interest. This result can then be presented relative to the asset of interest’s size or exposure. In this way two important dimensions of an asset’s contribution to portfolio risk; namely its volatility and exposure. 52
Fundamentals of Financial Risk ManagementMarginal Standard DeviationThe marginal standard deviation computed in CreditMetrics is defined as:where is the standard deviation of the portfolio including asset i, is the dollar size of asset i and is the standard deviation of the portfolio without asset i. 53MSDPiPiPiP
Fundamentals of Financial Risk ManagementMSD Calculations 54
Fundamentals of Financial Risk ManagementPortfolio Risk and Limits 55Exposure ($M)MSD (%)020040060080010001200140016000.02.04.06.08.010.012.014.016.0Outside MSD & Exposure LimitsExposure Limit ExceededMSD Limit ExceededInside LimitsP+I- P= R31251098764
Fundamentals of Financial Risk ManagementCredit Simulation and Pricing 56
Fundamentals of Financial Risk ManagementPortfolio Valuation Using Simulation Techniques To gain a better understanding of the mechanics of determining a fair value for embedded credit loss in a portfolio, consider a simple 5 loan portfolio as shown 57
Fundamentals of Financial Risk ManagementLoan Amortization Example58
Fundamentals of Financial Risk ManagementTime Profile of Default Credit default models need to take into account the timing of defaults which can be done by leveraging survival analysis used extensively in medical research and other fields. At a fundamental level, survival analysis combines the estimation of an event of interest such as a default or prepayment with the timing of the event. Not all loans default 2 years after origination, for example, but rather occur at intervals over the life of the loan depending on their characteristics. Given a cumulative distribution function for a variable T (denoting time), the function can be defined as F(t) = P(T<=t). From this a survivor function S(t) describing the probability that a loan survives past time t is defined as: S(t) = P(T>t) = 1-F(t)59
Fundamentals of Financial Risk ManagementSurvival Analysis By definition, S(0) must equal 1, or 100% of the loans are in existence at time t=0. A more interesting function for default or prepayment events is one related to the survivor function called the hazard function. It describes the probability that an event will occur between some time interval t and t+ . The hazard function h(t) is thus defined in continuous form as the following:60h(t)limP(tTt t Tt)t
Fundamentals of Financial Risk ManagementSurvival Analysis The relationship between the h(t) and S(t) can be expressed as: The default rate PD(t) can then be defined as 1- where represents the survival rate for the default analysis.
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- Normal Distribution, Modern portfolio theory