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Long-Term Expected Credit Spreads and Excess Returns

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We estimate long-term expected credit spreads and excess returns for multiple US corporate bond ratings and maturities and extend the findings of Giesecke et al. (Journal of Financial Economics, 102(2), 233–250, 2011). We develop a risk-neutral valuation model and correct the credit spreads for the well-known “credit spread puzzle”. We calibrate the model on data from 1919 to 2014, which is much longer than used in most other papers analyzing expected credit spreads and excess returns. Our model-implied expected credit spread term structures are in line with the results in the literature.

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  1. 1.

    Helwege and Turner (1999) generated controversy with their findings of an upward-sloping credit spread term structure for low credit quality issuers. These findings have, however, been contradicted by Bohn (1999).

  2. 2.

    The assumption of fractional recovery of face value assumption is supported by empirical evidence; see Bakshi et al. (2001).

  3. 3.

    There exists considerable evidence of a short-term liquidity premium in the US sovereign debt market. See, for example, Nagel (2016) and the references therein.

  4. 4.

    Note that Tn ≡ T with T equal to the bond maturity.

  5. 5.

    The historical interest rates obtained from GFD before April 1953 are based on Homer and Sylla (1996).

  6. 6.

    The yields of the composite of long-term government bonds index of Merrill Lynch are almost identical to the ones from the FED.

  7. 7.

    In our case, this is the 20-year cumulative default probability of the CCC rating.

  8. 8.

    Note that the price of risk parameter has no unit as it is a multiplication factor between the physical and risk-neutral hazard rates. For example, if the price of risk parameter is 4 then this means the risk-neutral investors perceive the risk-neutral default probabilities 4 times larger than the physical default probabilities.

  9. 9.

    Hull et al. (2005) find expected annualized excess returns of 0.81%, 0.86%, 1.12%, 1.58%, 2.03%, 1.36%, and 3.07% for the AAA, AA, A, BBB, BB, B, and CCC ratings, respectively. The authors define these excess returns over the swap rate.

  10. 10.

    Giesecke et al. (2011) report an expected annualized excess return of about 0.8%, which is based on a recovery assumption of 50%, an average credit spread of 1.53%, and average default loss rate of 1.5% measured over the period 1866–2008. However, the authors find that the annual default loss rate decreases by half to roughly 0.75% for the 1900–2008 period, which is a period that better corresponds to our 1919–2014 sample. Taking their finding of an average credit spread of 1.53% and default losses of 0.75% and our recovery assumption of 35% gives an expected excess return of 1.04%.


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I thank Alex Boer, Bert Kramer, and Martin van der Schans for very helpful comments and suggestions. Any remaining errors are my own.

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Table 8.1 The estimated long-term expected credit spreads and excess returns
Table 8.2 The R2 of the marginal and cumulative default probabilities of the original Moody’s data and the estimated model values from optimization of Eq. 8.8
Table 8.3 The Nelson–Siegel fitted average of the US government bond yields of particular maturities for multiple samples
Table 8.4 Descriptive statistics of the individual IG 10Y+ and HY all-maturity (all) rating benchmark for two sample periods
Table 8.5 The findings of three papers that have quantified the liquidity premium in % of ten-year corporate bonds for different ratings
Table 8.6 The assumptions for the par yield \( {c}_i^f(T) \) of the defaultable corporate bond with annual, f = 1, coupon payments, rating i, and maturity T
Table 8.7 The long-term expected par credit spreads \( {s}_i^1(T) \) of Eq. 8.7 for maturities T 1–10 years (panel A) and 11–20 years (panel B), and rating i
Table 8.8 The expected credit excess returns over government bonds based on Eq. 8.11 for maturities T 1–10 years (panel A) and 11–20 years (panel B)

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Hennink, E. (2018). Long-Term Expected Credit Spreads and Excess Returns. In: Bulusu, N., Coche, J., Reveiz, A., Rivadeneyra, F., Sahakyan, V., Yanou, G. (eds) Advances in the Practice of Public Investment Management. Palgrave Macmillan, Cham.

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