The Problem of Volatility Drag

False Symmetry Although it took me a while to realize it, Wednesday's column showed the effect of volatility drag.

That article reviewed the bull-market case for putting the riskiest portion of a portfolio--house money, if you like--into an S&P 500 fund bought with leverage. The highest-return assets available to retail investors, such as emerging-growth companies or frontier markets, haven't delivered on their expectations. So why not follow the advice of the capital asset pricing model (CAPM) and leverage the market portfolio?

To my surprise, I found that even when selecting a time period that would reward leverage, the long bull market from 1985-2017, I couldn't recommend the strategy. Yes, a portfolio that was leveraged by 30% (rebalanced monthly), so as to provide 130% stock market exposure, beat

(Over the next 17 years, the S&P 500 would gain but 2% annually, with margin-account interest rates consistently in double digits. Borrowing at 14% to own more of something paying 2%, for almost two decades, would not have been pleasurable.)

Consider a case where the stock market drops 10% in a month, then rebounds by 11.11% the following month. The values of a $1,000 unleveraged portfolio at the end of each month would be:

Month 1--$900 Month 2--$1,000

Back to the start.

In contrast, the values of a $1,000 portfolio placed in the 130% leveraged portfolio would become:

Sept. 30--$870 Oct. 31--$995.54

The discrepancy between the $1,000 in the first case and the $995.54 in the second owes to among the simplest concepts in investing. Declining by 5% and then rising by 5% is not the same as doing so by 10%, or by any other number. They all lead to different outcomes. The order matters not--the loss could come first, or the gain--but the magnitude does. Most dramatically, an investment that drops 100% is finished. It ceases to exist.

Memory Lapse Of course, I already knew that. Indeed, I wrote about volatility drag (although in different words) in a previous column, which discussed the problems of leveraged exchange-traded funds that are rebalanced daily. However, when establishing expectations for my leveraged versus unleveraged portfolio I defaulted to the lazy heuristic: In a bull market, the portfolio that had 30% more equity would make 30% more money, with the effect compounding.

Not so. The leveraged portfolio did outperform, but not by the full 30% because of volatility drag. (At least I was correct that the advantage would compound over time; I didn't reason, "Oh, the S&P 500 gained 3,471% during that stretch, so the leveraged portfolio would be up 30% more than that, say about 4,600% or so." Small consolation, I know.)

Volatility drag is another way of stating the discrepancy between arithmetic and geometric returns. Arithmetic returns, calculated by summing the monthly (or daily, or whatever) totals, find the pairs of a) -5 and +5 and b) -50 and +50 to be the same things. They each sum to zero, after all. Geometric returns, in contrast, comprehend that the two situations are highly unlike. The first turns a $1,000 portfolio into $975, while the second leads to $750.

Thus, a portfolio that is leveraged by X amount will have an arithmetic return that equals (1 + X) times the return on the unleveraged version of the portfolio, but its geometric return will be lower, as by definition the geometric return always trails the arithmetic return. That is, unless the investment has unvarying results--Bernie Madoff!--in which case the two numbers match. How much the geometric return lags depends upon the amount of leverage, the volatility of the underlying portfolio, and the rebalancing decision.

Further Details For a single period, there is no difference between the two calculations. Which begs a question: Does volatility drag contravene the CAPM's recommendation that aggressive investors leverage the market portfolio? After all, the CAPM assumes a single time period, while volatility drag only occurs for multiple time periods. I have not (yet) sorted out the answer to that question, but I do know that the primary difficulty with academic finance models lies not with their reasoning, but rather with their assumptions. So, perhaps.

If an investor is to use leverage, over the long term, my study's assumption of monthly rebalancing is overkill. There's no need for the everyday investor, without strict hedging requirements, to keep such a consistent leverage ratio. If the stock market rises, thereby raising the equity/loan ratio so that the portfolio becomes less leveraged, let it ride, at least for a while. The same holds true when stocks fall, unless the broker forces the action by issuing a margin call.

Also, when readjusting the leverage ratio after a downturn, by repaying part of the loan, it is best to do so by spending cash, rather than through selling shares. That advice, of course, is easier said that followed; would you wish to pony up more cash for your leveraged portfolio in January 2009, after it had fallen by 50%? But otherwise, the leveraged strategy becomes procyclical, in that it sells stocks after they decline, while holding them after they rise. That is no way to invest.

Final Words Volatility drag illustrates the appeal of absolute return investment strategies. If an absolute return fund could post reasonably high gains, its lack of volatility drag could enable it to outpace riskier competitors, which would make it a win-win proposition. Unfortunately, although absolute return funds usually manage to remain in the black, they struggle to achieve "reasonably high gains." Steadiness alone is insufficient.

However, there comes a point when the unsteadiness becomes too severe. The investment's volatility causes more than merely psychological damage; it actively harms profits. Such is the case for leveraged stock-index portfolios.

Note: Three years ago, the CFA Institute published the intriguingly titled "The Myth of Volatility Drag (Part 1)." For me, that article did not fulfill its promise, and there appears to have been no successors. But I include it for those who wish to read a counterargument.

Half Measures Two weeks back, I wrote about my personal-investment dilemma. I had two energy-pipeline funds, bought in the spring of 2016 when oil stocks slumped, that had rebounded. I wished to take profits, but was wary of the taxman with those being held in taxable accounts. What to do?

I made the coward's decision; I split the difference. Out went Alerian MLP ETF AMLP at a good price, by chance the sale occurred just as the stock market began its brief sell-off). I retain the somewhat more-aggressive ClearBridge Energy MLP Opportunity EMO, which is a closed-end fund.

The only explanation I can offer for selling one fund while retaining the other is that it will minimize regret, as now whichever direction those funds take, I can celebrate a success (while forgetting about the failure). There surely is no logical defense.

John Rekenthaler has been researching the fund industry since 1988. He is now a columnist for Morningstar.com and a member of Morningstar's investment research department. John is quick to point out that while Morningstar typically agrees with the views of the Rekenthaler Report, his views are his own.