“The magic of compounding returns” is one of those phrases that has been coming up in conversations about investing since, literally, the tulip derivatives bubble of the 1600s.

It is no surprise then that when talking about minimum volatility portfolios (or min vol) compounding repeatedly comes up as one of the explanations for why low-beta portfolios may do better than the market in term of their returns per unit of risk. The notion behind these discussions is that “downside protection” compounds over time, which suggests there is some sort of engineering involved in the process.

Accounting for the effects of compounding is, of course, an important aspect of long-term investing. Compounding, however, is not the source of the better risk-adjusted returns of a min vol portfolio. Lower risk does not automatically deliver better returns per unit of risk simply due to compounding. [Dividend and Low-Volatility ETFs]

Let me explain. Say you’re starting with a $100 investment in the market. You sell $30 and keep the proceeds in cash. The total portfolio — $70 invested in the market and $30 in cash — will have a beta of 0.7. This will offer lower risk than the market as well as “downside protection” in the sense that when the market goes down by, say, 10%, this portfolio will only go down by 7%. No matter how much compounding you do, however, this portfolio will have the same ratio of return per unit of risk as the market itself. Lower beta or lower risk will not automatically result in better returns per unit of risk than those of the market simply because of compounding.

So, what are the mechanics behind a min vol portfolio? In an earlier post, I computed the returns of a portfolio of low-beta securities to help explain what drives the min vol effect. Let’s look at those returns a bit more closely. In particular, imagine trying to explain the returns of that low-beta portfolio in terms of its exposure to the market, plus additional returns that arise from the fact that we have overweighted low-beta securities. (Low-beta securities, as I have argued in previous posts, have tended to offer better risk-adjusted returns due to behavioral biases and institutional constraints in the marketplace.

From 1959 until 2011, analysis shows that the performance of the low-beta portfolio can be explained, on average, as an exposure of 0.62 to the market plus an additional return of 2.75% per year[1]. This last return would generally be called “alpha” in an active manager’s jargon because the 2.75% comes on top of the exposure to the market. It is the result of the market not properly pricing the differences in beta across stocks, as I have argued in some of my previous posts.