Reading 14, Blue Box number 11b- pls help with the calculation

can someone pls help me to understand what’s going on with question 11 from the BB reading 14 specifically 11.b

they said the index OAS widens, but i don’t understand where the calculation is coming from

It’s a horrible explanation.

Note the sentence from the previous page: “As noted earlier, spread changes for lower-rated bonds tend to be consistent on a proportional percentage rather than absolute basis . . . .”

Therefore, if the index OAS changes 10 bps (out of 125 bps) – an 8% (relative) change – then the A-rated bond’s OAS should change by about 8% of 100 bps or 8 bps, and the BB-rated bond’s OAS should change by about 8% of 300 bps or 24 bps. The change in the portfolio value should be about:

\left(0.5 × 8\ bps × 3.0\right) + \left(0.5 × 24\ bps × 4.0\right) = 60\ bps

Algebraically, this works out to be what they showed, but, as I say, their explanation is awful.

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