direction is northwest, because in this direction we simultaneously increase the expected return and de- crease the variance of the rate of return. This means that any portfolio that lies northwest of P is superior to P. What can be said about portfolios in the quadrants II and III? Their desirability, com- pared with P, depends on the exact nature of the investors risk aversion. Suppose an in- vestor identifies all portfolios that are equally attractive as portfolio P. Starting at P, an increase in standard deviation lowers utility; it must be compensated for by an increase in expected return. Thus point Q in Figure 6.2 is equally desirable to this investor as P. In- vestors will be equally attracted to portfolios with high risk and high expected returns com- pared with other portfolios with lower risk but lower expected returns. These equally preferred portfolios will lie in the mean-standard deviation plane on a curve that connects all portfolio points with the same utility value (Figure 6.2), called the indifference curve. To determine some of the points that appear on the indifference curve, examine the util- ity values of several possible portfolios for an investor with A 4, presented in Table 6.1.     Figure 6.2 The indifference curve.   E (r )     Indifference curve   Q   E (rP ) P                P II. Portfolio Theory 6. Risk and Risk Aversion The McGraw−Hill Companies, 2001           162 PART II Portfolio Theory