Investors generally would not want pick the least risky portfolio without regard to the rate of return. Investors generally will be considering a tradeoff between risk and rate of return. But regardless of an investor's attitude toward risk it would be very foolish to choose a portfolio made up entirely of B. This is because there is another portfolio, represented by the point on the red line directly above B, which has the same risk as B but a higher expected rate of return. In fact, there are many portfolios which have a lower risk and a higher expected rate of return. Harry Markowitz described portfolios like all B as inefficient. They are inefficient because there are other portfolios with a lower risk and a higher rate of return. The portfolios which are efficient are the ones on the red line above where it turns backwards toward the point for stock B.

If there are more than two stocks the situation is more complex. The graph below shows part of the picture. The red line represents portfolios made up entirely of stocks A and B. The green line represents portfolios entirely composed of stocks A and C. And, the blue line is for portfolios including only stocks C and B. In this graph the situation for portfolios that include A, B and C are not shown. That is the subject of the next graph.

The efficient portfolios are the ones which give the maximum rate of return for a given level of risk. The inefficent portfolios are the ones such that another portfolio exists that has the same risk but a higher expected rate of return.

When there exitst a risk-free security the picture changes in a qualitative way. In the graph below the the risk and return combinations achieved by combining each portfolio of common stock with the risk-free security are shown as magenta lines.

A point on a line extended beyond the combination for a portfolio made up entirely of common stock represents a portfolio in which funds have been borrowed and invested in common stock. These are shown in the following graph as orange lines. Such portfolios achieve a higher expected rate of return at the cost of incurring higher risk. In the construction of the orange lines it is assumed that the portfolio investor can borrow at the risk-free rate.

The efficient portfolios are the ones on the upper edge of this sheaf of magenta-orange lines. The upper edge is a line which is tangent to the set of risks and rates of return for the portfolios of common stock. The portfolio of common stock at the point of tangency is called the optimal portfolio.

The analysis indicates that any investor who buys common stock buys it in the porportions given by the optimal portfolio. Investors concerned about risk will choose a portfolio made up mostly of the risk-free security and containing little of common stock. An investor who is unconcerned about risk will borrow as much as possible and invest it, along with any unborrowed funds, in the optimal portfolio. This proposition that all investors, to the extent that they buy common stock at all, buy it in the composition of the optimal portfolio is called the Separation Theorem. This concept was discovered and publicized by James Tobin of Yale University, the head of the Council of Economic Advisors under Presidents John Kennedy and Lyndon Johnson.

The tanget line of efficient portfolios is called the Market Line and it represents the tradeoff between risk and return in the market. It shows how much of an increased rate of return investors require for accepting an increased risk.

(to be continued)