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

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

2

It's bad...

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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.

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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.

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

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

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