Efficient Frontier and Capital Market Line
The frontier
Plot every possible portfolio in risk-return space. The upper-left boundary is the efficient frontier: the best return available at each level of risk.
Anything below it is dominated, since another portfolio offers more return for the same risk. Rational investors hold frontier portfolios and choose a point on it according to risk tolerance.
The frontier is a hyperbola, and its curvature comes entirely from imperfect correlation. Were all assets perfectly correlated, it would be a straight line and diversification would achieve nothing.
Drag the correlation to +1 and watch the curve straighten onto the line between the two assets. Every bit of the bow, and every point safer than the safer asset alone, comes from that one number.
Adding a risk-free asset
Now allow lending and borrowing at . Combining the risk-free asset with any risky portfolio traces a straight line from through that portfolio.
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