I am considering investment in security A and B (Portfolio Management). Pl help me to decide what proportion?

I am considering to invest in security A which has an offered historical average return of 18% with a standard deviation of 22% and security B which has offered average returns and standard deviation of 12% and 10% respectively.

(a) If the correlation between A and B is 0.60, what is the least risky combination of these two assets?

(b) If the investor decides to invest in a risk free security that is offering annual return of 5%, what would be the least risk combination of these two assets and the risk free security to give 12% return?

Argh. Sounds like a test question from one of my finance classes.

I would have to look it up in one of my books, but let's see if my intuition and vague recollection can work up a good guess before I actually research the answer.

(a) The answer is likely weighted, but not too strongly for B, i.e. the majority for stock B with some 1/3 or so in A.

(b) My gut says that roughly a roughly even split between the three, but slightly weighted for security A. (say about 37% A, 33% B, 31% risk-free)

Answer to A is -.1 A and 1.1 B. I will let you do the calculus behind this, it is not hard. B should be simple once you have A.