“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 terms 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.
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. 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.
This decomposition explains why the min vol portfolio does better, on average than the market in terms of returns per unit of risk. If the market is up, say, 10% then the low beta portfolio will be up 6.2% just from its exposure to the market - plus 2.75% of additional return. That results in a total return of 8.95% for an “upside capture” of 89%. On the other hand, if the market is down 10% then the low-beta portfolio will be down 6.2% from its exposure to the market - plus 2.75% of additional return. That results in a total return of 3.45%, and a “downside capture” of 34%. On average, there is better upside capture than downside capture.
The key point is that these asymmetric “capture ratios” arise not because of compounding but simply because the min vol portfolio provides additional return on top of exposure to the market. This is the same thing that happens with any active fund that is successful in delivering alpha on top of its benchmark.
Take the case of a hypothetical manager who is benchmarked to the S&P 500 and delivers 2% alpha on top the S&P 500 returns. If the S&P 500 is up 10% then such a manager would have a return of 12%. If the market is down 10% the manager would be down 8%, thus providing 120% upside capture and 80% downside capture - the same asymmetric capture ratios as a min vol portfolio.
In the end, investors who are considering minimum volatility as part of their portfolio need to be comfortable not with the capture ratios or the impact of compounding, but with the origin of that additional return and its explanations, both behavioral as well as induced by arbitrage constraints in the marketplace.
 This is a straightforward computation. I have taken the monthly returns of the low-beta portfolio introduced as a simple experiment in my previous post and looked at how closely they can be matched by a combination of the market returns and a constant additional return. This the same computation used to get the beta of an individual stock in the traditional CAPM setup. The CAPM or capital asset pricing model posits that the performance of an asset or portfolio can be explained by a linear combination of the performance of the market (i.e. its exposure or “beta”) and an additional component that is specific to each asset. Standard theory is that the additional component specific to each asset should be, on average, zero. Assets or portfolios that have, over time, returns in addition to their exposure to the market that are larger than zero are generally described as having “alpha."