Figure 1.

Basic concepts of portfolio selection. (A) Any asset can be mapped on the E(r)–σ(r), or yield–risk, space. Combining A and B creates a possible space of yield and risk depending on the mixture and covariance of the two assets against fluctuation. Maximum risk reduction is achieved when the prices of the two assets change in opposite directions because this offsets fluctuation. Increasing the number of assets involved generally reduces risk. The efficient frontier is achieved by optimally combining all available assets. Availability of a larger number of assets with different yield–risk characteristics improves the overall portfolio, analogous to an increase in the degree of design of freedom in highly optimized tolerance (Carlson and Doyle, 1999; Reynolds et al, 2002). In actual investment planning, investment with a fixed return asset is considered to form a capital market line, but this is not considered in biological applications because there is no zero-risk-fixed-yield genotype. (B) The probability distribution of expected return is shown for each asset and portfolio in (A) to visually illustrate their relationships.