## A Primer for Risk Measurement of Bonded Debt from the Perspective of a Sovereign Debt ManagerThis paper presents some conventional and new measures of market, credit, and liquidity risks for government bonds. These measures are analyzed from the perspective of a sovereign's debt manager. In particular, it examines duration, convexity, M-square, skewness, kurtosis, and VaR statistics as measures of interest rate exposure; a VaR statistic as the prominent measure of exchange rate exposure; the balance sheet approach (or contingent claims approach), and its consequent probability of default as the most promising measure of credit risk exposure; and an elasticity approach and a VaR statistic to measure liquidity risk. Along with the formulas for the various statistics proposed, we provide simple examples of their application to some common risk valuation cases. Finally, we present an integrated approach for the simultaneous estimation of a portfolio's interest rate and exchange rate risk using the VaR methodology. The integrated approach is then extended to also include N risk factors. This approach allows us to measure the total risk of a portfolio, provided that the volatilities and correlations among the risk factors can be estimated. |

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### Contents

Introduction | 3 |

Measurement of Credit Risk | 19 |

Measurement of Liquidity Risk | 26 |

2 other sections not shown

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### Common terms and phrases

99 percent approximation assessing asset value model assume bond debt bond portfolio bond prices bond's calculated cash flows change in FX change in value changes in interest Cholesky compounding correction factor correlation counterparty covariance matrix credit ratings credit risk debt stock decrease default probability defined discount duration and convexity eigenvalue decomposition entity's equation estimate exchange rate exposure exchange rate risk Financial fixed income formula government bond historical immunized integrated approach interest rate changes interest rate exposure interest rate risk investors Jorion kurtosis linear liquidity gap liquidity premium liquidity risk M-square Macaulay duration market risk market value maximize convexity Monte Carlo simulation multiplied parallel shifts parametric present value price changes probability distribution probability of default random numbers recovery rate risk exposure risk factors risk management Risk Measurement scenarios sensitivity skewness standard deviation term structure U.S. dollar variance vector volatility yield curve yield to maturity zero coupon bond