Cognitive Bias: Syllogism

Diversified portfolios have lower risk. Some low-risk portfolios are constituted of Treasury Securities. Therefore, some diversified portfolios are constituted of Treasury Securities.

Is this correct?

Taken independently, the sentences are correct. 

Yet, the logic in between them is not correct. 

If we read it rapidly, we tend to skip this point and agree with the statement. 

This is a syllogism fallacy. The most famous example of syllogism fallacy used in the academic literature is the following: 

All roses are flowers. Some flowers fade quickly. Therefore some roses fade quickly. 

Again, all these sentences are correct independently but the logics in-between is false.

Reference:
Frederick, S. (2005). Cognitive reflection and decision making. The Journal of Economic Perspectives, 19(4), 25-42.