Notes 1–3 lived in the Q-world: pricing derivatives consistently with today's market. This note crosses to the P-world of the buy side: forecasting returns and building portfolios that monetise the forecasts. The intellectual core is small and beautiful — mean–variance optimisation and its closed forms, the information coefficient as the unit of forecasting skill, and the Fundamental Law tying them together — but the practical content is in the frictions: real portfolios are constrained (long-only, sector limits), real signals decay (turnover, information horizon), and real trades cost money (spread, market impact). Each friction has a precise, derivable effect on performance, and those derivations are this note's exam material.
By the end of this note you should be able to:
- describe the quant investment pipeline (alpha model → risk model → optimiser → implementation → attribution) and contrast quant with fundamental investing;
- derive all the closed-form mean–variance solutions (unconstrained, minimum-variance, characteristic, with-cash, fully-invested, active) via Lagrange multipliers;
- define IC and IR, decompose realised alpha into its five components, and derive the Fundamental Law with its caveats;
- describe the major factor families (value, quality, momentum) with construction formulas and worked numbers, and explain smart beta;
- build a multifactor alpha model: composite IC, optimal weights , and the factor-vs-IC-correlation constraint;
- derive the turnover formula and explain the information horizon;
- quantify what long-only and sector constraints do to the IR (transfer coefficient);
- solve the optimal-trading problems with quadratic and linear transaction costs (the no-trade zone).
In this lesson
- Contents
- The big picture
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