Credit risk assessment of fixed income portfolios: an analytical approach (*) Bernardo PAGNONCELLI Business School Universidad Adolfo Ibanez Santiago, CHILE Arturo CIFUENTES CREM/ FEN University of CHILE Santiago, CHILE Primera Jornada de Regulación y Estabilidad Macrofinanciera January 2014 (*) Based on Credit Risk Assessment of Fixed Income Portfolios Using Explicit Expressions, Finance Research Letters, forthcoming.
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Credit risk assessment of fixed income portfolios: an analytical approach (*)
Credit risk assessment of fixed income portfolios: an analytical approach (*). Bernardo PAGNONCELLI Business School Universidad Adolfo Ibanez Santiago, CHILE. Arturo CIFUENTES CREM/ FEN University of CHILE Santiago, CHILE. Primera Jornada de Regulación y Estabilidad Macrofinanciera - PowerPoint PPT Presentation
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Credit risk assessment of fixed income portfolios:
an analytical approach (*)Bernardo PAGNONCELLIBusiness SchoolUniversidad Adolfo IbanezSantiago, CHILE
ArturoCIFUENTESCREM/ FENUniversity of CHILESantiago, CHILE
Primera Jornada de Regulación y Estabilidad Macrofinanciera
January 2014(*) Based on Credit Risk Assessment of Fixed Income Portfolios Using Explicit Expressions, Finance Research Letters, forthcoming.
• A Brief History of an Interesting Problem
• Regulatory Implications
Portfolio of Risky Assets
N assets
Default Probability, p
Correlation, ρ
Issues:• How risky is this
pool?
• How much can I lose in a bad scenario?
• How much should I put aside to cover potential losses?
• Can it bring the company down?
• Systemic risk?
N = 50
p = 27%
ρ = 18.36%
Example
How risky is this portfolio ?
Assume that the total notional amount is $ 100
each default results in a loss of$ 100/ 40 = $ 2.5
$ 10
0
The naïve approach(assume no correlation) Yi (i=1, …, N) is 1 or 0 (1 = default; 0 = no default)
The number of defaults X is given by
X=Y1 + …+ YN.
X follows a binomial distribution with
E(X)= Np and Var(X)= N p (1-p).
The discrete probability density function is given by
Corre (Yi, Yj) = 0 For all i, j
Number of Defaults
Probability
E(X) = Np = 13.5 defaults Var(X) = N p (1-p) = 9.85
Other approaches (1)
N = 50
p = 27%
ρ = 18.36%
Still assume that ρ = 0 increase the value of p (more or less by pulling a number out of …), say by 20%and then hope that this trick will result in “conservative” results…
E(X) = Np = 16.2 defaults Var(X) = N p (1-p) = 10.89
Other approaches (2)
N = 50
p = 27%
ρ = 18.36%
Replace the original portfolio with a portfolio that has zero correlation but a lower number of bonds (5 instead of 50 in this case)