Diversification

Exam items lean on the math of two-asset portfolio variance: a plug-and-chug where lowering the correlation coefficient (ρ) shrinks portfolio standard deviation. The classic “tell” is ρ = +1, the only case with zero diversification benefit — portfolio risk is exactly the weighted average of the two SDs, so the two assets plot as a straight line on a risk–return graph. Any ρ < +1 bows that line leftward toward the y-axis; ρ = –1 lets you weight the assets to build a (theoretically) risk-free combination with zero standard deviation. A favorite trap: at ρ = +1 it is standard deviation, not variance, that equals the weighted average — don’t average the variances.

Distinguish diversification from its neighbors. Asset allocation sets the asset-class weights and explains roughly 90% of return variability over time; diversification is the risk-reduction mechanism inside that choice. The efficient frontier curves precisely because correlations sit below +1 — diversification is the cause, the frontier the picture. Memory hook: “correlation kills, not count” — a herd of co-moving stocks barely diversifies.