Question

Aimee is considering investing in two risky portfolios ABC and XYZ.  She wants to choose one risky portfolio (either ABC or XYZ) for investment purposes.

If she decides to construct a complete portfolio by choosing one risky portfolio and a risk -free asset, what will determine the risky portfolio choice for Aimee’s investment?

1. Reward-to-variability ratio (Sharpe Ratio)
2. Correlation between ABC and XYZ.
3. Risk tolerance level of investors

Once she has selected the risky portfolio, what factor / characteristic will explain her allocation of wealth between the risky portfolio and risk-free asset in the complete portfolio?  Why? [Hint: Use a graph to reflect on what you will explain in words]

Answer 1

a. Reward-to-variability ratio (Sharpe Ratio)

The risky portfolio is common for all the investors irrespective of the risk-return profile of the investor. Here, the risky portfolio is chosen by adjusting the weights of the risky assets such that the Sharpe ratio is maximized.

Once the risky portfolio is decided, Aimee's individual risk-return profile is to be considered in calculating how much proportion of her assets is invested in the risk-free portfolio and what proportion is to be invested into risky asset portfolio. In short, Aimee's risk profile is characterized by her capital allocation line.

Here, the Capital allocation line (CAL) slope is determined by the risk-return preferences of Aimee and the efficient frontier is constructed using the risky-assets. The point M, where the CAL meets the efficient frontier, is how the allocation of her wealth would be decided between the risk-free and the risky assets.