since spread change tends to be proportional to the size of the spread for low rated bonds, why is formula E [ExcessSpread] ≈ Spread0 − (EffSpreadDur × ΔSpread) − (POD × LGD) also used to assess investment grade bonds like A and Baa? I’m reading Fixed-Income Active Management: Credit Strategies page 119 example 30.

This is an adjustment for equation 5 on P81, which is a formula to calculate the %ΔPV(spread), not the ExcessSpread.

thank you, so basically these two formulas are interchangeable in this reading?

equation 5 of page 81: %Δ PV Spread ≈ − (EffSpreadDur × ΔSpread) + (½ × EffSpreadCon × ( Δ Spread ) 2 )

equation 10 of page 82: E [ExcessSpread] ≈ Spread0 − (EffSpreadDur × ΔSpread) − (POD × LGD)

No they are not interchangable.

E [ExcessSpread] ≈ Spread0 − (EffSpreadDur × ΔSpread) − (POD × LGD)

tells you the return over **a period of time** you will get due to the spread.

Spread(0) - the initial spread

− (EffSpreadDur × ΔSpread) the effect due to the chnage in spread

− (POD × LGD) the effect due to decling credit quality.

It is expressed in years but we coud expand it

E [ExcessSpread] ≈ Spread0 x (d/360) − (EffSpreadDur × ΔSpread) − (POD × LGD) x (d/360)

where d- number of days.

So we want to examine an **instanteous ** mover

E [ExcessSpread] ≈ Spread0 x (0/360) − (EffSpreadDur × ΔSpread) − (POD × LGD) x (0/360)

E [ExcessSpread] ≈ − (EffSpreadDur × ΔSpread)

Which is a simplifcation of the other equation ignoring the convexity effect

%Δ PV Spread ≈ − (EffSpreadDur × ΔSpread) + (½ × EffSpreadCon × ( Δ Spread ) 2 )

The above equation tells about the change in price expected if spread changes.

Whereas

E [ExcessSpread] ≈ Spread0 − (EffSpreadDur × ΔSpread) − (POD × LGD)

estimates the return will we get, over a period of time, due spread

No, these are two separate formulas.

Equation 10 is to calculate the expected excess return.

Equation 5 is to calculate the change in bond price (for a given yield spread change).

As for the credit spread change for the lower-rated bonds, we don’t have to consider this unless there’re specific words like empirical evidence or DTS. I think the book just want us to know this empirical observation not to calculate it as part of Equation 5 or 10. Actually I didn’t seen an example in the book that calculated the credit spread change of investment-grade and low rated bonds separately.