spread and interest rate

CFA Level III
#1

Could anyone explain why

spread tightens, interest rate will go up?

spread widens, interest rate will go down?

#2

are u sure those statements are correct?

spread = (x - y)

x = rate on bond, y=rate on treasury of same maturity.

if y is constant - that means rate on bond went down. (so spread would tighten). it also meant that the bond price went up.

#3

if y is constant, spread tighten, means bond yield decreased, and bond price went up, so interest rate go down?

#4

isn’t that what I wrote …

#5

thanks a lot