Let’s start with the idea that CAPM (Capital Asset Pricing Model) is incomplete. Let me prove it in a few sentences. Everyone knows that, for investors, “risk-free” rates are always less than borrowing (margin) rates. Thus the concept of CAL (the capital asset line) is incomplete. If I had a sketch-pad I’d supply a drawing showing that there are really three parts of the “CAL” curve…

- The traditional CAL that extends from Rf to the tangent intercept with the efficient-frontier curve.
- CAC (capital-asset curve)
- CAML (capital-asset margin line, pronounced “camel”)

Why? Because the CAML has it’s own tangent point based on the borrower’s marginal rate. Because the efficient frontier is monotonically-increasing the CAL and CAML points will be separated by a section of the EF curve I call the CAC.

All of this is so obvious, it almost goes without saying. It is strange, then, that I haven’t seen it pointed out in graduate finance textbooks, or online. [If you know of a reference, please comment on this post!] In reality, the CAL only works for an unleveraged portfolio.

### CAPM is Incomplete; Warren Buffett Shows How

Higher risk, higher return, right? Maybe not… at least on a risk-adjusted basis. Empirical data suggests that high-beta stock and portfolios do not receive commensurate return. Quite to the contrary, low-beta stocks and portfolios have received greater returns than CAPM predicts. In other words, low-beta portfolios (value portfolios in many cases) have had higher historical alphas. Add leverage, and folks like Warren Buffett have produced high long-term returns.

### Black Swans and Grey Swans

On the fringe of modern-portfolio theory (MPT) and post-modern portfolio theory (PMPT), live black swans. Black swans are essentially the most potent of unknown unknowns, also known as “fat tails”.

At the heart of PMPT is what I call “grey swans.” This is also called “breakdown of covariance estimates” or, in some contexts, financial contagion. Grey-swan events are much more common, and somewhat more predictable… That is if one is NOT fixated on variance.

Variance is close, semivariance is closer. I put forth the idea that PMPT overstates its own potential. Black swans exists, are underestimated, and essentially impossible to predict. “Grey swans” are, however, within the realm of PMPT. They can be measured in retrospect and anticipated in part.

### Assets are Incorrectly Priced

CAPM showed a better way to price assets and allocate capital. The principles of semivariance, commingled with CAPM form a better model for asset valuation. Simply replacing variance with semivariance changes fifty years of stagnant theory.

Mean-return variance is positively correlated with semivariance (mean semi-variance of asset return), but the correlation is far less than 1. Further, mean variance is most correlated when it matters most; when asset prices drop. The primary function of diversification and of hedging is to efficiently reduce variance. Investors and pragmatists note that this principle matters more when assets crash together — when declines are correlated.

The first step in breaking this mold of contagion is examining what matter more: semivariance. Simply put, investors care much less about compressed upward variance than they do about compressed downward variance. They care more about semivariance. And, eventually, they vote with their remaining assets.

A factor in retaining and growing an AUM base is content clients. The old rules say that the correct answer the a key Wall Street interview question is win big or lose all (of the client’s money). The new rules say that clients demand a value-add from their adviser/broker/hybrid. This value add can be supplied, in part, via using the best parts of PMPT. Namely semivariance.

That is the the end result of the of the success of semivariance. The invisible hand of Sigma1, and other forward-looking investment companies, is to guide investors to invest money in the way that best meets their needs. The eventual result is more efficient allocation of capital. In the beginning these investors win. In the end, both investors and the economy wins. This win/win situation is the end goal of Sigma1.