*Why* Does The Lasso Induce Sparsity?

No, the classic image of the l1l_1 and l2l_2 balls is not a good explanation...

How to Optimally Trap Points in High-Dimensional Spaces Inside Ellipsoids

We review how to describe ellipsoids and formulate an optimization problem to enclose sets of points inside an ellipsoid with minimal volume.

Searching for Robust Markowitz Portfolios: Part I

We explore whether the framework of Robust Optimization can help us create good portfolios when we are uncertain about future returns.

The Sample Efficiency of Markowitz Portfolios

It's bad...

The Sharpe Ratio: It Ain't That Sharp

We review the definition of Sharpe ratio, a widely used metric to measure portfolio performance. We show, when it works, how to create portfolios that optimize for it, and its potentially fatal drawbacks.

Portfolio Construction: Kelly vs Markowitz

We briefly review a common approach to portfolio construction based on balancing mean and variance. Then we establish a connection with what Kelly taught us about optimal gambling. Finally, with simulations, I show how one can get wrecked using these tools under the presence of fat tails.

The Art of Optimal Betting

We derive and discuss the Kelly Criterion, a formula for betting optimally and achieving exponential wealth growth.

Why You Should Never Buy High Dimensional Watermelons

We explore the distribution of the volume of high dimensional spheres.