**Certification:**PRM Exam I

**Chapter:**Portfolio Mathematics

**LOS:**Describe tolerances and preferences for Risk vs. Return

We earlier learned that investors can diversify their risk by allocating their investments into various assets. How different investors choose investments depends on their tastes and preferences. For any investor the investment decision can be broken down into two separate decisions:

1. The choice of the optimal proportions (w) of the risky assets held to achieve an optimal portfolio.

This choice depends on the investor’s views and the objective market variables, that is, mean, standard deviation, and correlations. The optimal portfolio weights can be determined using the portfolio theory.

2. The second choice is about how much the investor is willing to borrow to add to his own initial capital invested, in risky assets.

This will depend on the risk profile of the investor.

A very risk-averse investor, will most likely invest most of this wealth in risk-free assets and will invest very little amount in the risky assets. The amount invested in the risky assets will still be invested in the optimal proportions (w) decided in the first choice.

A high risk-taking investor on the other hand, will borrow at the risk free rate and invest the proceeds in the risky assets in tghe optimal proportion w.

Note that the optimal proportion (w) in the risky assets will be the same for both types of investors.

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