# How to calculate yield spread?

I came across this multiple choice question on yield spread and I can't understand why the reasoning for the selected answer is correct.Can you confirm or clarify ?

( emphasis in the text is mine) The bond's market price of 103.73 can be computed by discounting its cash flows continuously at 4.0% per annum, which is represented by the flat yellow line. Specifically:

$3.00e^{-.04*0.5} + 3.00e^{-.04*1.0} + 3.00e^{-.04*1.5} + > 103.00e^{-.04*2} > = 103.73$.

The bond's same market price of \$104.73 can also be derived by discounting the same cash flows according to the continuous discount rates given by the the steep blue line. The lower steep line, which shows a rate of 0.40% at six months, is actually two nearby curves: a swap rate curve and nearby spot rate curve.

Both start at 0.40% but, as the spot rate curve is slightly steeper, by year 2.0, the spot rate is 1.61% while the swap rate is 1.60%. For this purpose, we assume both the spot and are risk-free curves; e.g., US Treasury.

a) The bond's yield-to-maturity is 4.0%

b) The yield spread, represented by the solid red vertical arrow, is the difference between 4.0% (yellow line) and 0.40% (spot rate at six months)

c) If the price of the bond decreased due solely to perceived credit risk of bond (without any change in market risk), the upper curves (yellow and blue) would shift up

d) The z-spread, represented by the dashed red vertical arrow, is the difference between the (upper steep) blue line and the (lower steep) spot rate; e.g., 2.42% = 4.03% - 1.61%