AI in Portfolio Management - A Primer

On overview of classical portfolio theory, and of its modern incarnation using deep learning.

Transcript

1. Camilo Thorne — Frankfurt, July 2026 A Primer AI in Portfolio Management
3. ?
4. How c a n I best invest my money? ?
5. Markowitz Theory [Markowitz & Sharpe 1952] • M a them a tic a l theory of a sset investment • Core ide a s: Invest in groups (“portfolios”) of (un)correl a ted ssets M a ximize returns by optimizing investment a lloc tion • Comp a re perform a nce by Sh a rpe r a tio a nd b a ck-testing • Relies on st a tistics a nd optimiz a tion theory
6. R1 w1 Rn wn ⋮ Rw = ∑ i wi Ri Asset Returns Alloc a tions w = w1 , …, wp μw σw = w⊤Σw Portfolio Portfolio return Portfolio v a ri a nce Portfolio expected return
8. μw − σw Optimize w⊤1 = 0 Subject to Gener a l Form (Derives optim a l ) w*
9. σw μw
10. σw μw w0 σw (μw ) = Aμ2 w − 2Bμw + C AC − B2 A = 1⊤Σ−11 B = 1⊤Σ−1μ C = μ⊤Σ−1μ
11. σw μw w0 Rf SR = μw − Rf σw μw (σw ) = μw − Rf σw + Rf
12. μw − σw Optimize w⊤1 = 0 Subject to Gener a l Form (Derives optim a l ) w*
13. σ2 w = wTΣw Minimize w⊤1 = 0 Subject to Minimum V a ri a nce (Derives optim a l ) w*
14. wTσw wTΣw M a ximize w⊤1 = 0 Subject to M a ximum Diversi f ic a tion (Derives optim a l ) w*
15. DL Strategies [Zohran & Zhang 2020] • Cl a ssic a l M a rkowitz theory returns st a tic portfolios • In re a lity, we w a nt to a djust investments to m a rket swings • Core hypothesis: Return / price series cont a in su ff icient inform a tion (e.g. price momentum) We c a n le a rn from d a t a a dyn a mic str a tegy th a t self- djusts through time C a n be c a ptured by a DL model & loss functions
16. wt = f(R[t − k, t]; θ) L(θ) = 1 T ∑ t μw,t σw,t
18. Good!
20. Other Quantitative Strategies • P a irs Tr a ding • Me a n reversion • Currency sw a ps • Options tr a ding (Bl a ck Scholes / Browni a n motion) • Long only (W a rren Bu ff ett) • …
21. References • Bodie, Zvi a nd K a ne, Alex a nd M a rcus, Al a n J. Investments. McGr w-Hill, 2009 • Zh a ng, Zih a o a nd Zohren, Stef a n. Elements in Qu ntit tive Fin nce. C mbridge University Press, 2025. • P a lom a r, D a niel P. Portfolio Optimiz a tion: Theory nd Applic tion. C mbridge University Press, 2025. • M a rkowitz, H a rry. Portfolio selection. The Journ l of Fin nce, 7:1 (77-91), 1952. • Sh a rpe, Willi a m F. A simpli f ied model for portfolio n lysis. M n gement science, 9:2 (277-293), 1963.
22. Th a nk you!