EDS Tool Overview

Stochastic Gradient Descent

What Is It?

Often referred to as SGD
- This method is an iterative approach to optimization
- This approach can be traced back to at least 1951
Two parts:
- Stochastic = random starting position
- Gradient Descent = the approach used to optimize
This method is so popular it is a default tool in Microsoft Excel

Basic Gradient Descent

Assumes All Trade-Offs Are Smooth

A seeker finds the most benefit per unit of uncertainty
It does this by 'rolling' along the line

Yup, found the best

Stochastic Gradient Descent

Why Does this Matter? Part I: Rough Trade-offs

The real world isn't like theory, it's messier
SGD sends several 'seekers' to find the best option given the complexities of the real world

I'm The Best!

Only This is Truly The Best

Stochastic Gradient Descent

Why Does this Matter? Part II: Many Different Risks & Goals

Risk, uncertainty, and opportunities come in many different forms
A technique like SGD is needed to consider all of these simultaneously

Does It Work?

Proof Is In The Pudding

Forgetting about all of these details the important question is:
- Does it work?
EDS has now conduct 30+ projects
- In 100% of cases, improvements have been made after the analysis
How?
- In essence, the ability to consider more factors and information leads to more informed decisions
- Simply, more informed decision making leads to better outcomes

Why Doesn't Everyone Do It?

A Natural Question is to Ask Why Haven't You Seen This Before

The simple answer is many have tried
- Using SGD means it is difficult to be 'sure' the solution is best
- Past solutions haven't been able to solve this issue
In short, it is easy to do poorly
Only the EDS technology can provide consistent and confident results
- Our distributed approach coordinates a single problem across a cluster of computers

What Is So Special About EDS?

Distributed, Coordinated, & Informed

A real world problem usually includes:
- 100s of important factors
  - Qualitative & Quantitative
- 1000s of potential investments
EDS's technology has three key pillars for success:
1. Distributed: Only distributed systems can handle problems of this size
2. Coordinated: Working with a distributed system means that all of the distributed workers must be coordinated
3. Informed: Keeping a memory of what solutions work best means EDS can solve these problems faster

On The Shoulders Of Giants

\small Utility = \underbrace{\small \mu}_{\text{\tiny Return}} - \underbrace{\small \lambda \tiny 1 \small \cdot \sigma}_{\text{\tiny Variance}} - \underbrace{\small \lambda \tiny 2 \small \cdot TEV}_{\text{\tiny Tracking Error}} - \underbrace{\small \lambda \tiny 3 \small \cdot TFS}_{\text{\tiny Factor Sensitivity}} ...

Building on current methods adds interpretability and transparency
Extendable frameworks allow inclusions from other models and insights
- Tail-Risk, Diversification Ratio, Black-Litterman, etc.

1950s

1980s

2010s

An Extendable

Framework

EDS's mathematical insights extend current best practices

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