An estimated line of expected return against market sensitivity that sits entirely above the theoretical one is not a market on sale, because pricing errors scatter above and below instead of lifting everything by the same amount. In a two-factor world where every asset carries the same 0.75 exposure to the second risk, the fitted single-factor line comes out exactly parallel to the theoretical one and exactly 3 percentage points above it, with residuals of zero, while a mispricing world engineered to have the same average lift leaves errors of both signs as large as 6.5 points. Let the second exposure grow with sensitivity and the slope moves too, at which point the two lines can cross inside an ordinary sample.
Two stocks with equal expected returns, variances 0.10 and 0.40, and correlation 0.5: the reflex differentiates the portfolio variance and reports an interior weight. The minimum sits at 100% in the calmer stock, and the usual explanation for that, which blames the no-shorting rule, is wrong. The vertex of the variance parabola lands exactly on w = 1, so the constraint does no work at all and the answer survives dropping it.
Six sevenths in the quieter share beats holding it alone, because what the jumpy share adds at the margin is its correlation times its own swing, fifteen against twenty. The derivative of the variance at a full allocation is exactly +1/50, so the informal test and the first-order condition are one statement. The article carries the exact optimum sqrt(27/700), the convexity making it a minimum, and the correlation threshold of two thirds above which the dip disappears entirely.