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# Re: Mental Models-Orthogonality & Portfolio Diversification.

### I relate the mathematical concept of Orthogonality to Portfolio Diversification.

Everyone in finance understands the broad concept of **Portfolio Diversification**. Whether you’re talking about a portfolio of stocks or a portfolio of managers or even a portfolio of asset classes, the general idea is that picking assets with low (or even negative) correlations with *each other* can lower the volatility of the overall portfolio without sacrificing overall returns.

I tweeted last year about this concept as it pertains to a simple two-asset portfolio:

If your eyes glaze over with algebraic equations, I’d like to introduce you to another, more visual Mental Model to explain this concept: **Orthogonality**.

First, let’s understand the concept of orthogonality from the standpoint of vector mathematics. Wikipedia offers this definition:

“Orthogonality is a system design property which guarantees that modifying the technical effect produced by a component of a system neither creates nor propagates side effects to other components of the system.”

The easiest way to visualize what this means is to see what *perpendicularity *means in a simple two-dimensional system:

In a flat plane, two lines are *perpendicular* to one another if they are at right angles to one another. In this case, to be perpendicular *is* to be orthogonal to one another.

Orthogonality in the context of mathematics in two dimensions refers to the concept that two lines or variables are independent of each other; changes in one variable do not affect the other. In the context of portfolio diversification, this means that the returns of one asset in a portfolio are not influenced by the returns of another asset.

Perpendicularity is basically the two-dimensional subset of orthogonality. Because we live in three dimensions, it’s also very easy to visualize orthogonality in three dimensions, where x, y, and z vectors are all orthogonal to each other and independent of one another:

The utility of thinking in orthogonal terms is that the concept can be extended to any number of dimensions, even if it becomes a bit harder for us to visualize this idea:

Portfolios of assets seldom come in three dimensions or less, so it becomes visually difficult to imagine orthogonality across *n *dimensions, but the concept as a guiding principle in looking for diversification is useful regardless of whether you’re thinking in terms of an n-stock portfolio or an n-asset portfolio.

From my own asset allocation perspective, I constantly think about orthogonality of returns when I consider a new investment, be it a stock, a fund, a piece of real estate, or some other asset.

The first step is to establish a comparison baseline against which orthogonality should be measured. As a retired hedge fund professional, I recognize that I have a certain skill set that gives me easy access to public stocks and futures markets, so I will consider my comparison baseline to be “liquid stock/futures exposures.” Therefore, in my search for assets that have orthogonal qualities to those baselines, I am generally looking for funds or assets that are driven by completely different factors and/or accessible by managers with completely different skill sets than mine.

Because my personal balance sheet also has high concentrations of residential real estate assets and energy private equity already, over the last four years I have allocated to areas that I think have a high degree of orthogonality to my existing exposures: direct loans, direct startups, venture capital funds, opportunistic real estate funds across multiple sectors and geographies, distressed/activist RMBS strategies, structured equity and secured lending financing platforms, multi-sleeve funds investing in everything from rural car washes to private equity to busted oil & gas financings, etc.

The idea isn’t so much to be mathematically precise about the exact asset class cross-correlations (which is often difficult/impossible to determine for new vehicles and/or less liquid funds and assets) as it is to really think about big picture, underlying *drivers* of asset returns and how they might be orthogonal to my comparison baselines. I never want to give myself the illusion of precision when no such thing exists. As I always like to say, “I’d much rather be generally accurate than precisely wrong.”

The current confusing macroeconomic backdrop is one that I describe as a messy “macroeconomic pond,” criss-crossed by a myriad of ripples and counter-ripples that make it difficult to establish concentrated bets with high conviction:

The silver lining is that for the first time in decades, TINA (“There Is No Alternative”) has been replaced by her more attractive sister TIA (“There IS an Alternative”):

T-Bills are really not a bad place to park liquidity while hunting for the next Orthogonal Asset to your overall portfolio — especially when T-Bills themselves can be thought of as an orthogonal vector to most comparison baselines.

## Re: Mental Models-Orthogonality & Portfolio Diversification.

Personally, been laddering 1 to 4m subject to

1. expectations of final hike month

2. no maturity during July-Sept (until get more info on debt ceiling). Perhaps in June will do 6m (well outside uncertainty of receiving principal of Tbill)

3. maturity date near

a) econ stats to Fed mtg date

b) new corporate bond issues' expected date of issue ... USD corp bonds short-term in EM/FM of 8.5%+ (double-digit% on private corp credit and even higher on real estate development)

4. commissions ... unfortunately % of investment related , so it's a larger % of total asset, the shorter the term ...thus been doing 2 to 4.5m maturities

Stats, algebra, stochastic calculus , yes know orthogonalization and risk diversification, though in a real local economy (vs public market) where activity observable, sometimes over-concentrate

Michael: great thinking all the time - thank you for sharing :)

One question - why would you lock in 6 mo T-Bills here vs stay even shorter duration to take advantage of the FFR continuing to increase? Why not be 2/3 mo T-Bills and keep laddering up vs lock into a 6 mo Bill?