Does the term “portfolio optimization” sound intimidating? Does the arithmetical or computational aspect bring back the terror of high school math class? Rest easy, this article will explain it at a high level by focusing on the concepts and using intuition instead of math.

Portfolio optimization is a standard technique in finance. Its goal is to find the best possible portfolio, subject to constraints. For example, we may want to track a target portfolio (the goal, called the ‘objective function’) but hold at least 30% in equities and at most five percent in cash (the constraints).

Things get more interesting when there are multiple—and often competing—goals. For instance, selling an appreciated concentrated position may improve tracking (good) but realize tax (bad).

Let’s step back and think of a more intuitive scenario.

When you choose your lunch, you look at multiple factors jointly, such as taste, cost, healthiness, calories, convenience, how filling it is. Let’s try to encode some rules on how you would do it, assuming that:

- You only care about it being cheap and having low calories. This is for simplicity, and also because these two are easily quantifiable. Equivalently, assume that all foods have the same taste, healthiness, etc., and only vary in cost and calories.
- You must buy and eat exactly one meal, not 0, ½, 2, etc.

A reasonable rule is to choose any meal under $15 (avoids the filet mignon) and under 700 calories (avoids deep dish pizza). However, this has two problems.

First, behavior is intuitively wrong around the cutoffs. For example, a $14.99 meal with 699 calories would be chosen over a $1 meal with 701 calories.

Second, how do you choose between two meals that both pass the cutoffs? It’s easy to cover the simple cases: for the same calorie count, prefer the cheaper one, and for the same price, prefer the lower-calorie one.

Likewise, cheaper AND lower-calorie foods will always be preferred over expensive, high-calorie meals. That’s easy. Things only get complicated when one meal has lower cost but the other has lower calories.

The main concept in optimization, when there are multiple competing goals, is *quantifying those tradeoffs*. Using our lunch example, what if we could convert calories into dollars, and add that to the cost? That is, determine how much extra money we are willing to pay to eat 1 less calorie—or, equivalently, how many more calories we are willing to consume to save $1. This ‘cost’ is a general concept; it does not have to be a true dollar cost. The main point is to find common units of measurement for each goal, so we can compare them. In a way, this transforms an apples-to-oranges comparison into a “cost of apples vs. cost of oranges” comparison.

When you choose the $1, 701-calorie meal over the $14.99, 699-calorie one: you are deciding that two calories are not worth the extra $13.99. You are effectively performing an optimization in your head.

Let’s move back to portfolio land now. A good portfolio is a combination of several goals, including:

**Matching some target**: e.g. 60% equities, 40% fixed income.**Complementing remaining holdings:**e.g., all else being equal,- A homeowner needs less inflation protection than a renter.
- A Google executive with stock grants should hold fewer “Google-like” investments.

**Low taxes**: postpone taxes, when possible.**Low trading fees**.**Low holding costs**(such as ETF expense ratios).

Using the rules approach is easier, but wrong. If we avoid any fund that charges over 20 basis points, we could miss out on a fund that charges 21 bps but otherwise looks great on #1 and #2.

A trade-off approach avoids this. It does take some initial thought to find some common ‘portfolio quality’ metric to convert each goal into. For example, you could say that 10 bps of extra expense ratio is “just as bad” as paying a 2% fee upfront. My math was to capitalize the expense ratio using a 5% discount rate, but you any sensible approach would do, possibly even a subjective one: you could say “a client would be equally annoyed between paying an extra 10 bps in perpetuity vs. paying 2% upfront”. The point is that, once you establish those “exchange ratios” between the goals and the shared ‘portfolio quality’ metric, portfolio optimization can take over from there, and find the best balance between all the different goals.

There are many tradeoffs involved in choosing a portfolio. An approach that evaluates these tradeoffs intelligently will result in a better portfolio than using rules with hard cutoffs, such as ‘if an asset class is more than 5% off its target, rebalance”. Although it is not the only approach for handling those tradeoffs, portfolio optimization is the most rigorous and well-established one.

*Iraklis Kourtidis is the founder and CEO of Rowboat Advisors, which builds investing software for separately managed accounts with a focus on tax efficiency and direct indexing. He also built the first fully automated version of direct indexing in 2013 for automated investment service Wealthfront.*