Default Risk and the Effective Duration of Bonds

Abstract

Basis risk is the risk attribUtabIle to uncertain movements interest rate risk, heightens the anxiety of traders and in the spread hetwveen vields associated with a particular arbitrageurs who are hedging their investments, and finalnclial instrumnenit or class of instriuments, and a compounds the financial institution's problem of reterence interest rate over time. There are seven tvpes matching assets and liabilities. of basis risk: Yields on Much attention has been paid to the first type of basis * Long-term versus short-terimi financial instruments.risk. In recent years, attention has turned toward * Domestic currency versLus foreigin currencies.understanding the relation between credit risk and * ILiqujid versus illiqtuid investillenits, duration. Babbel, Merrill, and Panning focus on that, * BoDnds wvith higher or lower sensitivitv to changes in emphasizing the importance of taking credit risk into interest rate volatility.account when computing measures of duration. * Taxable versuIs tax-free instruments.The consensuis of all work in this area is that credit risk * Spot VersuIs fILtures contracts. shiortens the effective duration of corporate bonds. The * Defatir-free versus non-default-free securities. authors estimate how much durations shorten because of Default Risk and the Effective Duration of Bonds

The Term Structure of Reserve Durations and the Duration of Aggregate Reserves

“…As the review of Bierwag and Fooladi (2006) shows, the duration measure has been refined substantially with the considerations for stochastic interest rate processes, interest-rate-dependent cash flows, and default risk since the original work of Macaulay (1938). The durations of various asset classes, in addition to those of bonds, have also been explored substantially (e.g., Bierwag, Kaufman, and Toevs, 1983;Bierwag, 1987;Leibowitz et al, 1989;Bierwag, Corrado, and Kaufman, 1992;Babbel, Merrill, and Panning, 1997;Hayre and Chang, 1997;Hevert, McLaughlin, and Taggart, 1998;Cornell, 2000;Hamelink et al, 2002;Reilly, Wright, and Johnson, 2007) during the last quarter century.…”

“…It is similar to Morgan (1986) and Kalotay, Williams, and Fabozzi (1993) in considering the interest rate dependence of cash flows. Our treatment of mortality risk is similar to the adjustment for default risk done by Babbel, Merrill, and Panning (1997), Skinner (1997), andJacoby (2003). In short, we applied some analyses of the aforementioned papers done on assets to the most important liabilities of life insurers, the policy reserves.…”

Bond durations: Corporates vs. Treasuries

“…Fooladi et al (1997) define and study a duration-style measure in a specific pricing model different from the mainstream models applied today for the pricing of defaultable claims. Babbel et al (1997) set up a pricing model with the default-free short rate and the value of the issuing firm as state variables. They calibrate the model to data and derive an estimated relation between corporate bond prices and default-free interest rates.…”

Interest risk and default risk: A conditional volatility study

“…The conclusions that can be extracted of the carried out analysis are (t) the relationship between interest rates and prices in the markets of fixed income is not the significant thing that it would be necessary to wait, such and like they show tile values obtained by the coefficients of determination; (2) the value of the coefficient is between the values 0 and -1, which means that the duration of the titles of risky fixed income is lower to the risk free fixed income assets (this result does not coincide completely with those obtained in most of the investigations cited for the American market in that the sensitivity of the risky fixed income is significantly smaller, as those of Fons [1990], Chance [1990], Leland [1994], Leland and Toft [1996], Longstaff and Schwartz [1995], Nawalkha [1996], and Babbel, Merrill, and Panning [1997]); and (3) the use of the models GARCH(1,1) and EGARCH(1,1) implies an improvement in the risky yields models, since gives way the traditional hypothesis of constant variance that is applied in most of the fixed income valuation models, and it introduces the non-linearity existence in the variance of the risky assets. Finally, the normal behavior of the series, as well as the coefficients of asymmetry and skewness, improve regarding those found when the original pattern returns by OLS.…”