We should buy Bond 1 because the difference between its Z-spread and OAS is the largest.
We prefer Bond 1 to Bond 3 because Bond 1 has a greater Z-spread.
I am not clear here- especially why observation 1 and 2 are not correct- what do they even mean?
When comparing bonds of similar credit quality, you want to compare their OASs, not their Z-spreads. The OAS eliminates the value of any embedded options, so you’re comparing an option-free bond to an option-free bond. The Z-spread does not eliminate the value of any embedded options, so you might be trying to compare bonds with very different characteristics.
Observation 1 simply says that the value of the embedded call option in Bond 1 is greater than the value of the embedded options (if any) in Bond 2 and Bond 3. So what? That’s not a reason to buy a bond.
Observation 3 is trying to compare what are likely incomparable callable bonds. Maybe the call prices are different, or one is callable in one year while the other is callable in 5 years. You want to compare OASs, not Z-spreads.
Thank you for clarifying that.