What is the correlation between the two bonds’ returns?

Consider a portfolio of two equally weighted credit bonds from two different issuers in the same sector. Assume that interest rate risk is modeled by a single variable ΔR, the change of interest rates, and that credit risk in that sector is modeled by another factor ΔS/S, the percentage change of average credit spreads in the sector. Remember this is the DTS factor referred to in the chapter. The loading to this factor is the DTS of the bond. The first bond has interest rate duration D₁ = 4yr, spread duration of SD₁ = 4.5yr and spread of S₁ = 400 bps. The second one has interest rate duration D₂ = 6yr, spread duration of SD₂ = 6.5yr and spread of S₂ = 100 bps. The volatility of the interest rate factor is σ_ΔR = 30 bps/month, the volatility of the spread factor is σ_ΔS/S = 10%/month, and their correlation is ρ = – 30%. The idiosyncratic risk of the securities in this sector is proportional to a parameter. Similar to the systematic spread risk, that parameter measures the average percentage change of idiosyncratic spreads in the sector. The volatility of that parameter is σ^idio_ΔSIS= 14% / month. The proportionality factor used to calculate idiosyncratic risk is given by the DTS level of the bond.