Thread: Calculating portfolio weight with a certain expected return

You are considering investing $1000 in a complete portfolio. The complete portfolio is compose of t-bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities X and Y. The weight of X and Y in P are 60% and 40% respectively. X has an E[r] of 14% and Y has an E[r] of 10%. To form a complete portfolio with an E[r] of 11%, how much of your complete portfolio should be invested in t-bills?

I'm sort of stumped and don't know where to begin. I want to find the variance I think, but to do so, that means I have to know actual returns, right? Which is not given.

I did start by finding the return on the risky portfolio by doing: (Wx * rx) + (Wy * ry) = (.6 * .14) + (.4 * .1) = 12.4% I'm not entirely sure what to do with this.

Past problems that I have done similar to this have had the std dev given, and I really don't know where to start. Some help would be appreciated.

At all times:

First Moment = = Expected Return = M

Second Moment = = N

Can you find the variance given those two items?

Invest $R t-bills and ($1,000 - $R) in the risky portfolio and see how far you get.