Yes, this headline looks silly. Almost nine years into a powerful rally, and with the Dow suddenly caving, I bring up the subject of leverage. Talk about a columnist high on the fumes of a bull market!

But never mind the timing. This subject is evergreen. Consider this a "clip-and-save" article; it would have been equally relevant had it been published in March 2009. (Although appearing even more ridiculous.)

More than half a century ago, William Sharpe advanced the capital asset pricing model, for which he was later awarded a Nobel Prize. That model states that although volatile stocks tend to deliver higher returns, the best policy for aggressive investors is not to overweight such companies but instead to hold more of the overall stock market. Determine one's risk tolerance, then leverage the portfolio by the required amount.

Which, of course, almost nobody does. Adventurous investors buy initial public offerings and venture-capital funds and pink-sheet companies, but they rarely borrow in the manner that Professor Sharpe suggested. The most celebrated stock market model ever created … is ignored.

Once a day

The most popular leveraging approach is daily rebalancing, practiced by most leveraged exchange-traded funds. When the trading day concludes, the fund adjusts the borrowing amount so that the targeted leverage ratio is achieved. That is, if the goal is 100 per cent leverage, such that one dollar will command two dollars' worth of assets, then the borrowing is managed so that the portfolio enters each new trading day repositioned at its original leverage ratio.

Don't try this strategy at home. For one, daily rebalancing is enormously fussy; who would want such complexity? For another, the approach's benefit is wasted on long-term owners. Those who use ETFs as short-term instruments prefer their funds to match their stated leverage ratio. Daily rebalancing aids their enterprise. It does no favours for the rest of us.

In fact, it frequently causes damage. In a ground-breaking 2009 article, Morningstar's Paul Justice discussed why leveraged funds drift from their expected return targets. (Based in part on Paul's argument, the SEC seven months later issued an alert that warned of the "extra risks" of leveraged ETFs.) Over any time span longer than a single day, a daily rebalanced fund might not (and likely won't) match its back-of-the-envelope expectation.

Compound fractures

The culprit is the effect of compounding. Paul gives a straightforward, incontrovertible example--an "aha" moment, if you will.

The S&P 500 gains 10 per cent one day, then loses 10 per cent the next day. The index's cumulative return is negative 1 per cent. That math is straightforward. A US$100 investment grew by $10 on the first day, to become $110. The investment then dropped by $11 the next day--10 per cent of the $110 starting amount--so that the final balance became $99. Down 1 per cent. (That a 10 per cent gain followed by a 10 per cent loss doesn't equal zero is another "aha" moment for investor education, albeit at a less-advanced level.)

Now, let's consider a fund that is a 100 per cent leveraged version of the S&P 500, rebalanced daily. That fund has $200 invested in stocks as Day 1 opens. That $200 initial stake becomes $220 at the day's end, which means that the fund is worth $120. The fund adjusts its leverage ratio, so that it commands $240 worth of assets as Day 2 opens (twice its value of $120). The fund then drops $24 because stocks fall by 10 per cent, which means that it is now worth $96. Down 4 per cent.

Have you guessed why the two numbers don't match? The reason is not immediately intuitive (at least not to me, and Paul reports that it's not to most investment professionals, either). It is because the fund borrows more after Day 1. To be sure, that 10 per cent gain was pleasant--but it requires that the fund go further into hock to maintain its 100 per cent leverage ratio.

Thus, when market falls on Day 2, the fund has more borrowed money at work than when the market rose the previous day. (The leverage ratio remains the same, but the assets at risk have increased.)

Aha!

This, of course, was a dramatic example. The stock market generally is not so volatile. In addition, the effect of compounding can cut the other way, and help daily rebalanced funds. Nevertheless, because of its complexity, tax problems (for those with taxable accounts), and long-term tracking error, daily rebalancing is not a sound approach for the patient investor.

Just once

The second path is the opposite of the first. It is to leverage initially, and then never again. The investor with $100,000 who wishes for a 100 per cent leveraged position (to keep the comparison consistent with the daily rebalanced version) will borrow $100,000 at the time of purchase. The investor then lets the $200,000 investment ride, repaying the $100,000 loan at her convenience.

This tactic, it will be noted, can also be thought of as the opposite of another common investment technique: dollar-cost averaging. The previous paragraph's buyer had $200,000 with which to purchase equities--the $100,000 that she immediately put into stocks, and then the $100,000 loan that she eventually repaid. We can compare her results to that of the dollar-cost investor who also has $200,000. She, of course, will take her time in putting that money to work.

The stock market's early results will determine the winner. If stocks surge out of the gate, the dollar-cost-averaging investor's opportunity cost will outweigh the leveraged buyer's interest cost, so the leveraged portfolio will triumph. If, on the other hand, stocks are mostly flat or negative in their early years, then the dollar-cost average portfolio will win. The relative success of the leveraged strategy depends upon when equities do well.

In other words, borrowing for the initial purchase of securities, but never again, is not true leverage. Assuming that the purchaser invests the same amount of money in either scenario--because without such an assumption, we are not analysing the effects of leverage, but are instead analysing the trivial case of larger investments versus smaller stakes--the outcome is determined by timing. Leveraging initially, but only the once, turns dollar-cost averaging on its head.

Goldilocks?

Which leads to the third possible path: rebalancing the leverage ratio somewhere between our first case of daily and our second of never. Monthly is a possibility, as is annual.

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John Rekenthaler is vice president of research for Morningstar, based in the US. He is a columnist for Morningstar.com and a member of Morningstar's investment research department. This is a financial news article to be used for non-commercial purposes and is not intended to provide financial advice of any kind. Opinions expressed herein are subject to change without notice and may differ or be contrary to the opinions or recommendations of Morningstar as a result of using different assumptions and criteria.

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