Explaining technical investment concepts in a non-technical way is critical to having a meaningful dialog with individual investors. Most individual investors (also called “retail investors”, or “small investors”) do not have the time nor the desire to learn the jargon and concepts behind building a solid investment portfolio. This is generally true for most individual investors regardless of the size of their investment portfolios. Individual investors expect investment professionals (also called “institutional investors”) to help manage their portfolios and explain the major investment decisions behind the management of their individual portfolios.

In the same way that a good doctor helps her patient make informed medical decisions, a good investment adviser helps her clients make informed investment decisions.

I get routinely asked how the HALO Portfolio Optimizer works. Every time I answer that question, I face two risks: 1) that I don’t provide enough information to convince the investment profession or their clients that HALO optimization provides significant value and risk-mitigation capability and 2) I risk sharing key intellectual property (IP) unique to the Sigma1 Financial HALO optimizer.

This post is my best effort to provide both investment advisers and their clients with enough information to evaluate and understand HALO optimization, while avoiding sharing key Sigma1 trade secrets and intelectual property. I would very much appreciate feedback, both positive and negative, as to whether I have achieved these goals.

### First Principle of Portfolio Optimization Software

Once when J.P. Morgan was asked what the market would do, he answered “It will fluctuate.” While some might find this answer rather flippant, I find it extremely insightful. It turns out that so-called modern portfolio theory (MPT) is based understanding (or quantifying) market fluctuations. MPT labels these fluctuations as “risk” and identifies “return” as the reward that a rational investor is willing to accept for a given amount of risk. MPT assumes that a rational investor, or his/her investment adviser will diversify away most or all “diversifiable risk” by creating a suitable investment portfolio tailored to the investor’s current “risk tolerance.”

In other words, the primary job of the investment adviser (in a “fiduciary” role), is to maximize investment portfolio return for a client’s acceptable risk. Said yet another way, the job is to maximize the risk/reward ratio for the client, without incurring excess risk.

Now for the first principle: **past asset “risk” tends to indicate future asset “risk”.** In general an asset that has been previously more volatile will tend to remain more volatile, and and asset that has been less volatile will tend to remain less volatile. Commonly, both academia and professional investors have equated volatility with risk.

### Second Principle of Portfolio Optimization Software

The Second Principle is closely related to the first. The idea is that the **past portfolio volatility tends to indicate future portfolio volatility**. This thesis is so prevalent that it is almost inherently assumed. This is evidenced by search results that reaches beyond volatility and looks at the hysteresis of return-versus-volatility ratios, papers such at this.

**Past Performance is Not Necessarily Indicative of Future Results.**

### Third Principle of Portfolio Optimization Software

The benefits of diversification are manifest in risk mitigation. If two assets are imperfectly correlated, then their combined volatility (risk) will be** less than the weighted averages** of their individual volatilities. An in-depth mathematical description two-asset portfolio volatilities can be found on William Sharpe’s web page. Two-asset mean-variance optimization is relatively simple, and can be performed with relatively few floating-point operations on a computer. This process creates the two-asset efficient frontier*. As more assets are added to the mix, the computational demand to find the optimal efficient frontier grows geometrically, if you don’t immediately see why look at page 8 of this paper.

A much simpler explanation of the the third principle is as follows. If asset A has annual standard deviation of 10%, and asset B an annual standard deviation of 20%, and A and B are not perfectly correlated, then the portfolio of one half invested in A and the other half invested in B will have a annual standard deviation of less than 15%. (Non-perfectly correlated means a correlation of less than 1.0). Some example correlations of assets can be found here.

In so-called plain English, the Third Principle of Portfolio Optimization can be stated: “For a given level of expected return, portfolio optimization software can reduce portfolio risk by utilizing the fact that different assets move somewhat independently from each other.”

### Forth Principle of Portfolio Optimization Software

The Forth Principle of Portfolio Optimization establishes a relationship between risk and return. The classic assumption of modern portfolio theory (MPT) is that so-called systematic risk is rewarded (over a long-enough time horizon) with increased returns. Portfolio-optimization software * seeks to reduce or eliminate unsystematic risk* when creating an optimized set of portfolios. The portfolio manager can thus select one of these optimized portfolios from the “best-in-breed” list created by the optimization software that is best suited to his/her client’s needs.

### Fifth Principle of Portfolio Optimization Software

The 5th Principle is that the **portfolio manager and his team adds value to the portfolio composition process** by 1) selecting a robust mix of assets, 2) applying constraints to the weights of said assets and asset-groups, and 3) assigning expected returns to each asset. The 5th Principle focuses on the assignment of expected returns. This process can be grouped under the category of investment analysis or investment research. Investment firms pay good money for either in-house or contracted investment analysis of selected securities.

### Applying the Portfolio Optimization Principles Together

Sigma1 Financial HALO Software applies these five principles together to help portfolio managers improve or fine-tune their proprietary-trading and/or client investment portfolios. HALO Portfolio Optimization software utilizes the assets, constraints, and expected returns from the 5th Principal as a starting point. It then uses the 4th Principal by optimizing away systematic risk from a set of portfolios by taking maximum advantage of varying degrees of non-correlation of the portfolio assets. The 3rd Principle alludes to the computational difficulty of solving the multi-asset optimization problem. Principles 1 and 2 form the bedrock of the concepts behind the use of historical correlation data to predict and estimate future correlations.

### The Fine Print

Past asset volatility of most assets and most portfolios is historically well correlated with future volatility. However, not only are assets increasingly correlated, there is some evidence that asset correlations tend to increase during times of financial crisis. Even if assets are more correlated, there remains significant value in exploiting partial-discorrelation.

(*) The two-asset model can be represented as two parametric functions of a single variable, “t”, ER(t), and var(t). t simply represents the investment proportion invested in asset 0 (aka asset A). For three variables, expected return becomes ER(t0,t1) as does var(t0,t1). And so on for increasing numbers of assets. The computational effort required to compute ER(t0…tn) scales linearly with number of assets, but var(t0…tn) scales geometrically.

Optimizing efficiently within this complex space benefits from creative algorithms and heuristics.