<!– The average American is involved in approximately 420 auctions a day (Source: I made it up). Jokes aside, every time you load LinkedIn, Facebook/Instagram, or run a search, you trigger an auction. Yes, hundreds of advertisers are submitting bids competing for your attention every time you go into these sites. This market is huge. Hundreds of millions of dollars are spent every day through…
I was recently asked “Why does the Lasso induce sparsity?” My reflex was to proceed to describe the image we have all seen in our stats/ML classes:
In this post we study how to trap a set of points in high dimensions inside an ellipsoid with minimal volume (John, 1948). This problem has applications in statistics and outlier detection, but my motivation for studying this problem is to be able to represent “uncertainty sets” for doing Robust Optimization. Please see this post if the terms “uncertainty sets” and Robust Optimization are new to…
Stable Diffusion XL: A Portfolio In The Style Of Rene Magritte In a previous post we explored what happens when we try to build Mean Variance (also known as Markowitz) Portfolios using a finite number of samples from the distribution of returns. The results were discouraging, unless you have a prohibitively large number of samples, the resulting portfolios will be very far from the optimal one. In…
In this post we explore what happens when we try to create a Mean Variance Portfolio (MVP) using a finite number of samples from the true distribution of returns. This post is inspired by Chapter 6 of (Paleologo, 2021) Recall that the MVP is the solution to the following optimization problem: \begin{align} \max_{w} \thinspace & \mu^\top w - \lambda w^\top \Sigma w \cr s. t.\thinspace &1^\top w =…
DALL-E: A dull knife, resting, minimalist style, soft colors, more dull.
Stable Diffusion XL: Ceci n'est pas un portfolio A Brief Review of Modern Portfolio Theory A short summary of Modern Portfolio Theory (Markowitz, 1952) is the following. The “risk” of a portfolio is measured by its variance and its “reward” is measured by the expected value of the portfolio itself. Now fix the value of variance, it is possible there are many portfolios with variance equal to the…
Stable Diffusion XL: Coin flipping through the air, in motion, in the style of Dali's The Persistence of Memory
High Dimensional Watermelon, Oil Painting, Cyberpunk