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# Bond portfolio optimization with long-range dependent credits

• *Corresponding author: Hoi Ying Wong

We thank the handling editor and the anonymous referee for their careful reading and constructive comments. HY Wong acknowledges the financial support from the Research Grants Council of Hong Kong with project codes: RMG8601495 and GRF14308422

• Consider the optimal allocation between money market account and corporate bond fund. While the money market account is free of credit risk, corporate bonds are defaultable and exhibit long-range dependence (LRD) in credit risk. We propose a Volterra default intensity model to capture the LRD in credit risk. Using utility maximization, we derive the novel optimal investment strategy for a corporate bond fund. As empirical study shows that the COVID-19 pandemic has lowered the level of LRD in credit risk, we conduct sensitivity analysis and empirically investigate the changes in demand for corporate bonds before and during the pandemic period.

Mathematics Subject Classification: Primary: 49N90, 93C95; Secondary: 60H30.

 Citation:

• Figure 1.  $\pi_t^*$ under different $H$

Figure 2.  Deutsche Bank corporate bond (zero coupon, maturity: 04/22/26) before COVID-19

Figure 3.  Deutsche Bank corporate bond (zero coupon, maturity: 04/22/26) under COVID-19

Figure 4.  $\pi_t^*$ under different loss rate $\delta$ and $H$

Table 1.  Comparison of the demand between before COVID-19 and during COVID-19 for Deutsche Bank corporate bond by indicators. Difference denotes disparity of trading volume on rising and declining days, and ratio is the relative value

 Before COVID-19 During COVID-19 Difference -1747000 -2025000 Ratio 0.8347 0.7746

Table 2.  Calibrated parameters for the default intensity $\lambda_t$ with fixed interest rate

 $\delta=0.4$ $\delta=0.5$ Parameters Before COVID-19 During COVID-19 Before COVID-19 During COVID-19 $\hat{\kappa}$ 0.1565 0.0405 0.1714 0.2383 $\hat{\sigma}$ 0.5945 0.6179 0.5060 0.7089 $\hat{\theta}$ 0.2652 0.6673 0.3463 0.4717 $\hat{H}$ 0.5970 0.4888 0.5994 0.4070 $\delta=0.7$ $\delta=0.8$ Parameters Before COVID-19 During COVID-19 Before COVID-19 During COVID-19 $\hat{\kappa}$ 0.1627 0.1713 0.1334 0.0356 $\hat{\sigma}$ 0.3328 0.4098 0.3087 0.3253 $\hat{\theta}$ 0.2269 0.2677 0.4380 0.7664 $\hat{H}$ 0.6471 0.4803 0.6324 0.4766
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