Elements

The Elements of quant.

Built like Euclid’s Elements: a few definitions, then one proposition per page, each proved with a formula or a chart and closed with ∎.

Def.Definitions

1.Origin: $O = (0,\,0)$ The point every quantity is measured from. Every curve on this site starts there.
2.Edge α: $\alpha = \mathbb{E}[\,r_t - b_t\,]$ The expected return of a strategy in excess of its benchmark.
3.Noise: $\varepsilon_t,\ \ \mathbb{E}[\varepsilon_t] = 0$ Variation with no expected value. It can look like an edge for a long time.
4.Null hypothesis: $H_0:\ \alpha = 0$ The assumption that there is no edge, held until the data rejects it.
5.Half-life: $t_{1/2} = \frac{\ln 2}{\lambda}$ The time it takes an edge that decays at rate λ to lose half its strength.
6.Drawdown: $DD_t = 1 - \frac{V_t}{\max_{s \le t} V_s}$ How far a portfolio’s value stands below its last peak.

I–VIPropositions

And the laws of risk