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As mentioned previously, the value of the risk aversion has an intuitive interpretation. The expected excess rate of return on the optimal portfolio (E[R_P] − R_f) divided by its variance, σ²P, is equal to the degree of risk aversion, λ:

(1.9)

The value of the parameter of risk aversion, λ, is chosen in close consultation with the plan sponsor. There are qualitative methods that can help the portfolio manager select the appropriate value of the risk aversion. The portfolio manager may select a range of values for the parameters and present asset owners with resulting portfolios so that they can see how their level of risk aversion affects the risk-return characteristics of the portfolio under current market conditions.

EXHIBIT 1.3 Hypothetical Risk Returns for Two Portfolios

Example: Consider the information for two well-diversified portfolios shown in Exhibit 1.3. The riskless rate is 2 % per year.

Assuming that these are optimal portfolios for two asset owners, what are their degrees of risk aversion?

We know from Equation 1.9 that the expected excess return on each portfolio divided by its variance will be equal to the degree of the risk aversion of the investor who finds that portfolio optimal.

Aggressive investor: (15 % − 2 %)/(16%²) = 5.1

Moderate investor: (9 % − 2 %)/(8%²) = 10.9

As expected, the aggressive portfolio represents the optimal portfolio for a more risk-tolerant investor, while the moderate portfolio represents the optimal portfolio for a more risk-averse investor.

APPLICATION 1.5.8

Suppose that an investor's optimal portfolio has an expected return of 10 %, which is 8 % higher than the riskless rate. If the variance of the portfolio is 0.04, what is the investor's degree of risk aversion, λ?

Using Equation 1.9, λ can be expressed as: