Romeo and Juliette are sitting on their front patio, sipping on their martini glasses and discussing their retirement funds.

Romeo: Sweet heart, I saw our wealth manager, Jack, today. He is very unhappy that our entire retirement fund is invested in T-bills that just pay us 5% return. He has introduced me to two uncorrelated (zero correlation) funds, love 1 and love 2. They each have 10% standard deviation. The firs fund, love 1, offers 15% expected return while the second fund love 2 offers an expected return of 20%. Jack suggests we should allocate some fund to each of these funds.

Juliette: Perhaps we should do that.

Romeo: But, as I told Jack, these funds have exactly identical risk but love 2 offers higher return. Even if we decide to take some risk, investing in love 2 would be enough. Why should we invest in love 1 that has exactly the same risk but lower return?

Juliette: I recently participated in an investment workshop and learned diversification helps reducing risk. So, if we decide to take some risk, we should invest in both funds.

Romeo: But diversification pays off when funds have different risks and different returns. The funds that are available here have the same risk. So if we want to take that risk, the choice is clear, we should pick the one that offers higher return. Besides, there is no way I agree to subject our $1,000,000 investment money to 10% risk.

Juliette: How much risk will you tolerate to take?

Romeo: At most 5%.

Juliette: Well, tonight is too nice to be spoiled with discussion about our investment fund. Let us enjoy the evening and just agree that we need to take some risk to enhance the potential performance. We can worry about the details of our investment tomorrow.

They both are in agreement on that.

1. If Romeo and Juliette decide to allocate some or all of their $1 million fund in a risky investment, should they invest in one or both of these funds? If you believe they should invest in just one of the funds, identify the fund (love 1 or Love 2) and explain why. If you believe they should split all or some of their $1 million between the two funds, explain why and how, and Show your work in detail.
2. Assuming they agree to take 5% risk (measured by standard deviation), how would you advise them to break their $1,000,000 fund between T-bills (at 5% return) and one or both of these funds to achieve target risk? Show your work.
3. What is the expected return of the portfolio you design in Part (b) above? Show your work.