This formula shows that the variance of returns “drains” the arithmetic average returns to produce the smaller, realized, compound returns (Source: Decker, Robert: The Variance Drain and Jensen’s Inequality).

Why does this matter for investors?

It ties back to our previous posts on compounding returns and minimizing losses.

In order to optimally take advantage of the power of compounding, investors must avoid large losses and recoveries requiring exponential growth. In addition, investors must also avoid the negative power of compounding by seeking to lower volatility and variance drain as best as possible.

The table below shows different scenarios with the same arithmetic annual return (i.e. 10%) but coupled with different levels of volatility.

Generally speaking, there are two rules of thumb to remember when it comes to volatility drag.

  1. The higher the level of volatility, the more detrimental the impact of volatility drag, as evidenced in the table above.
  2. The longer the time period, the bigger the negative impact will be.

This situation is also explored in a post on volatility we recently wrote for In addition, the greater the volatility, the more unlikely it is that an investor will be able to “stay the course” and stick with an investment or strategy.

We can see how these factors all tie together in their mathematical application within an investor’s portfolio: compounding, avoiding large losses, and now volatility. Compounding, whether negative or positive, is the common thread throughout all of them. As a recap, the four key mathematical principles outlined in “Math Matters” are:

  1. The importance and power of compounding
  2. The value of avoiding large losses to returns
  3. The importance of variance drain
  4. The value of a non-normal distribution of returns

Marc Odo is the Director of Investment Solutions at Swan Global Investments, a participant in the ETF Strategist Channel.