## A Baseball Analogy

Imagine you’re the general manager of a Major League ball club. Your primary job is to construct (and maintain) a team of players that will win lots of games, while keeping the total player payroll as low as possible. When considering a hypothetical roster a baseball GM has two primary objectives in mind:

- Total annual payroll (plus any associated “luxury tax”)
- Expected season wins (and post-season wins)

These objectives can also be called *heuristics* — rules of thumb to help find solutions to complex problems. These heuristics can be turned into numbers (quantified) by creating *cost functions* or *utility functions*. Please don’t let all of this jargon disembolden you; we are merely talking a little baseball here.

The cost function function for payroll is just that… the total annual salaries for a proposed roster. It is called a *cost* function because cost is something we are trying to **minimize**. Expected wins is called a *utility* function, because utility is good, and we want to **maximize** it.

Now, accurately predicting number of wins for a hypothetical (or real) roster of players is a real challenge. Every scout and adviser is going to have his or her own ideas or heuristics. Just watch Moneyball to see what I mean. To turn any given roster into a utility score a GM could write a proposed roster on a whiteboard and point-blank ask each advisory “How many wins will this team produce?” The GM could average these predictions and, boom!, that’s an utility function. The GM could also hire a computer scientist and statistician to code up a utility function for any proposed roster relying on a chosen set of stats.

Either way, now the GM has can evaluate any proposed roster based on two metrics: cost and wins. These data can be plotted, and quickly patterns will emerge. Some proposed rosters will be both more expensive and less “winning” than others. These rosters are said to be *dominated*, and they can be removed from consideration. Once all the dominated rosters are eliminated, what remains is a series of dots that form a curve. As one moves up that curve, one finds more winning, but more expensive rosters. Moving the other way, the payroll cost is less, but the expected wins decrease. This curve resembles what financial folks call an *efficient frontier* — the expected risk/reward tradeoff for an optimized portfolio selected from a basket of securities.

## Back to Portfolio Optimization Software

The baseball analogy above tries to explain mathematical concepts without resorting to math. OK, I did use a few math words, but no equations!

There are several differences between a baseball roster and an investment portfolio. Key differences from an investment portfolio are: 1) You can own multiple shares of a stock or ETF (but have only 1 of any player), 2) You can trade stocks/ETFs virtually whenever you want.

Nonetheless, the baseball analogy is useful in illustrating what Sigma1 Software will be able to do for fund managers and investors. Instead of building a baseball roster, you are building an investment portfolio. In the classic “CAPM” investing model, the cost function is* standard deviation* (risk), and the utility function is *expected return*. **Historical** standard deviation is easy to compute, but expected return is much harder to accurately compute.

Now, if you are an active fund manager, you probably have in-house analysts paid to help you pick stocks (just like GM’s have scouts). But scouting reports from analysts do not a portfolio make… even if your analysts are giving you positive-alpha stock picks. A robust asset allocation strategy is necessary to build a robust portfolio out of your chosen list of securities.

## The Vision for Sigma1 Portfolio Software

#### A Vision for Financial Professionals

It started with the desire to create software that would allow me to build a better portfolio for my proprietary trading fund — Software that could optimize portfolios using heuristics, cost functions, and utility functions of my own choosing. I wanted to create portfolio software for investment managers that:

- Allows them to select their own list of securities (or chosen dynamically from all investable securities)
- Takes advantage of one or more “seed portfolios” if desired
- Allows proprietary heuristics, cost functions, market models, etc. to plug seamlessly into the optimization engine
- Isn’t limited to linear or Gaussian risk-analysis measures
- Runs in minutes or hours, not days
- Is capable of efficiently utilizing distributed and parallel computing resources — Scalability

#### A Vision for “Retail” Investors

For retail investors, the general investing public, I envision scaled-down versions of the professional portfolio optimization software. The retail investor software will run as an application on a web server. A free version will provide portfolio optimization for a small basket of user-chosen securities, perhaps limiting portfolio size to 10. A paid-subscription plan will offer more features and allow retail users to build larger portfolios.

To keep the software easy to use, a variety of ready-to-use heuristics will be available. These are likely to include:

- Standard deviation
- Historic best-year and worst-year analysis
- Beta (versus common indices)
- Diversification measures (e.g. sector, market-cap)
- Price-to-earnings
- Proprietary expected-return predictors