Second, in blue we find that the finance sector's selection effect is positive (0.212%) although the portfolio underperformed the index (7.47% vs. 7.79%). The model expects the effect to be negative in this case. And why? Because the manager underperformed the index, so the selection effect should be negative to reflect poor selection decisions.
And so, what's the problem?
Well, if you duplicate these numbers you'll see that the sector effects were arrived at by adding the effects of the underlying sub-sectors. This isn't the way it's done. We need to apply the attribution effect formulas to the sector levels. And when we do that, we get:
By calculating the sector effects using the same formulas as we use at the subsector level, our numbers make sense. The technology sector's allocation effect (-0.011%), as well as the finance sector's selection effect (-0.105%), are now both negative, as we'd expect.
Conclusion: sometimes the numbers don't add up ... because they're not supposed to!