What a factor is, and why it explains more than a sector label

A sector label is a statement about what a company does. A factor is a statement about what its share price responds to. The two agree often enough to be confused and disagree often enough to matter.

Lesson 14 used one common driver with a sensitivity of 1. A factor is that generalised: a driver with its own volatility, and a separate sensitivity — a loading — for each holding. Track 1 lesson 11 introduced beta, which is the loading on one particular factor, the broad market. A factor model keeps the arithmetic and allows several drivers, so two holdings can share one exposure while differing on others.

Two holdings classified in different industries. Their loadings on one shared factor are 1.15 and 0.92, that factor's volatility is 4.1 percent a month, and their residual volatilities are 6.8 and 5.9 percent. The shared covariance is 1.15 times 0.92 times 4.1 squared = 17.785. The first holding's variance is 1.15 times 4.1, squared, plus 6.8 squared = 22.231 plus 46.24 = 68.471, so its volatility is 8.27 percent. The second's is 14.228 plus 34.81 = 49.038, so 7.00 percent. The correlation is 17.785 divided by 57.9456 = 0.3069.

The factor supplies 32.47 percent of the first holding's variance and 29.01 percent of the second's, and that partial sharing produces a correlation of 0.31 between two holdings no industry classification would group. Double the factor's volatility to 8.2 percent and the correlation goes to 0.6389 with every loading and residual unchanged.

For collateral this is the difference between two kinds of grouping rule. A rule built on industry labels cannot see this pair; a rule built on factor loadings can, which is why Track 7 lesson 11's list included look-through and factor groupings alongside issuer and industry. Those four rules catch different pairs, and a portfolio can pass three and fail the fourth.