Investor's Risk Preference
Rational investors invest in efficient portfolios. The choice of an optimal portfolio from efficient portfolios depends on the risk-return trade-off for the investor, A risk-averse investor seeks risk-free opportunities or considers risk) opportunities with positive risk premium (compensation for additional risk). Other things being equal, a highly risk-averse investor holds a portfolio on the lower end of the efficient.frontier. ,0\5 the aversion to risk weakens, one moves up along the efficient frontier. In Example 3, an investor who prefers portfolio C is more risk-averse than one who prefers portfolio E, Between these two points, the risk premium is 5 per cent (= 18% - 13%) for additional risk of 10 per cent (22% - 12%),
Is the risk-return trade-off available and implicit in the slope of the efficient frontier (CML) adequate? Are all investors satisfied by it? Determination of the risk premium that the investor on expect in well functioning capital markets is one of the prime concerns of financial theory, However, the risk premium sought by an investor depends on his risk preference/tolerance,
Utility functions, or indifference curves, are normally used to portray an investor's attitude towards risk. Portrays the indifference map for a hypothetical investor. All portfolios along an indifference curve are equally satisfactory to the concerned investor. The higher is the curve, the higher is the satisfaction. Many systems have been developed to measure the satisfaction or utility score of a portfolio. The investor is administered risk questionnaires containing questions on the investing experience of the person, financial security and tendency to make risky or conservative choices. The scores obtained are convened into a risk aversion index. The approach followed by the Association of Investment Management and Research (AMR) combines the investor's risk aversion with the expected return and variance of returns to assign a utility score, The utility score (U) for a portfolio is defined as:8
U = E(r) - 0,005..Acs
Where E(r) = Expected return
A = Index of the investor's risk aversion
o2 = Variance of returns
o.oo5 = Scaling factor that allows expected return and standard deviation in the equation as percentages.
Table 3.6 presents expected return, standard deviation of returns and utility scores for some portfolios that yield the same satisfaction to an investor, given his risk aversion index; this value is assumed as equal to 2. All portfolios lie along the same indifference curve with a utility score of 4. It is obvious that utility scores vary directly .with expected return and inversely with variance (risk). The higher the utility score, the more attractive is the profile of a portfolio.