No, the classic image of the $l_1$ and $l_2$ balls is not a good explanation...

1

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

2

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

3

It's bad...

4

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.

5

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.

6

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

7

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

8