*This blog post is available as a PDF download here.*

**Summary**

- We believe that capital efficiency should remain a paramount objective for investors.
- The prudent use of leverage can help investors employ more risk efficient portfolios without necessarily sacrificing potential returns.
- Many investors, however, do not have access to leverage (be it via borrowing or derivatives). They may, however, have access to leverage via Levered ETFs.
- Levered ETFs are often dismissed as trading vehicles, not suited for buy-and-hold investors due to the so-called “volatility drag.” We show that the volatility drag is a component of all compounding returns, whether they are levered or not.
- We explore the impact that the reset period can have on Levered ETFs and demonstrate how these ETFs may be used in the context of a portfolio to introduce diversifying, alternative exposures.

Early last month, we published a piece titled *Portable Beta: Making the Most of the Returns You’re Already Getting*, in which we outlined an argument whereby investors should focus on capital efficiency. We laid out four ways in which we believe that investors can achieve greater efficiency:

- Reduce fees to take home more of what you earn.
- Express active views more purely so that we are not caught paying active management prices for closet beta.
- Focus on risk management by “diversifying your diversifiers” with strategies like trend following that can help increase exposure to higher return asset classes without necessarily increasing the overall portfolio risk profile.
- Utilize modest leverage so that investors can create more risk-efficient portfolios without necessarily sacrificing potential return.

Unfortunately, for many investors, access to true leverage – either through borrowing or the use of derivatives – may be beyond their means. Fortunately, there are a number of ETFs available today that allow investors to access leverage in a packaged manner.

**Wait, Aren’t Levered ETFs Dangerous?**

Levered ETFs have quite a reputation, and not a good one at that. A quick search will result in numerous articles that tell you why they are a dangerous, bad idea. They are pejoratively dismissed as “trading vehicles,” unsuitable for “buy and hold.”

Most often, the negative publicity hinges on the concept of *volatility decay *(or, sometimes “volatility drag”)*.* To illuminate this concept, let’s assume there is a stock that can only go up either +X% or down –X%. Thus, in any two-day period, we have the following growth in our wealth:

Up | Down | |

Up | (1 + X%)(1 + X%) | (1 - X%)(1 + X%) |

Down | (1 + X%)(1 – X%) | (1 – X%)(1 – X%) |

If we expand out the returns, we are left with:

Up | Down | |

Up | 1 + 2X% + X%^{2} | 1 - X%^{2} |

Down | 1 - X%^{2} | 1 - 2X% + X%^{2} |

Note that in the case where the stock went up +X% and then down -X% (or down –X% and then up +X%), we did not end up back at our starting wealth. Rather, we ended up with a loss of -X%^{2}.

On the other hand, we can see that when the stock goes the same direction, we actually outperform twice the daily return by +X%^{2}.

What’s going on here?

It is nothing more than the math of compound returns. The returns of the second day *compound *the returns of the first.

The effect earns the moniker *volatility decay* because in return environments that are mean-reversionary (e.g. positive returns follow negative returns, and vice versa), our capital decays due to the -X%^{2} term.

Note, however, that we haven’t even introduced leverage into the scenario yet. This drag is not unique to levered ETFs: it is just the math of compounding returns. Why it gets brought up so frequently with respect to levered ETFs is because the leverage can accentuate it. Consider what happens if we introduce a daily leverage factor of L:

Up | Down | |

Up | 1 + 2LX% + L^{2}X%^{2} | 1 - L^{2}X%^{2} |

Down | 1 - L^{2}X%^{2} | 1 – 2LX% + L^{2}X%^{2} |

When L=1, we have a standard long-only investment. When L=2, we have our 2X daily levered ETFs. What we see is that when L=1, our drag is simply –X%^{2}. When L=2, however, our drag is 4X%^{2}. When L=3, the drag skyrockets to 9X%^{2}. Of course, the so-called drag turns into a benefit in trending markets (whether positive or negative).

So why do we not see this same effect when we use traditional leverage? After all, are these ETFs not using leverage under the hood to achieve their returns?

The answer lies in the *daily reset*. Note that these ETFs aim to give you a multiple of returns *every day.* The same is not true if we simply lever our notional exposure and never reset it. By “reset,” we mean pay back what we owe and re-borrow capital in order to maintain our leverage ratio.

To achieve 2X daily returns, the levered ETFs basically borrow their NAV, invest in the asset class, and then pay back what they borrowed. Hence, every day they reset how much they borrow.

If we never reset, however, the proportion of our capital that is levered varies over time. Consider, for example, investing $10,000 of our own capital in the SPDR S&P 500 ETF and borrowing another $10,000 to invest alongside (for convenience, we’re going to assume zero borrowing cost). As the market has gone up over time, the initial $10,000 borrowed becomes a smaller and smaller proportion of our capital.

*Source: CSI. Calculations by Newfound Research. Assumes portfolio applies 100% notional leverage applied to SPDR S&P 500 ETF (“SPY”) at inception of ETF. Assumes zero cost of leverage. *

This happens because while we owe the initial $10,000 back, the returns made on that $10,000 are ours to keep. In the beginning, our portfolio will behave very much like a 2X daily levered ETF. As the market trends upward over time, however, we not only compound our own capital, but compound our gains on the levered capital. This causes our actual leverage to decline over time. As a result, our daily returns will gradually converge towards that of the market.

In practice, of course, there would be a cost associated with borrowing the $10,000. However, the same fact pattern applies so long as the growth of the portfolio exceeds the cost of leverage.

Resetting, therefore, is a necessary component of maintaining leverage. On the one hand, we have daily resets, which keeps our leverage proportion constant. On the other hand, we have “never reset,” which will decay the leverage proportion over time (assuming the portfolio grows faster than the cost of leverage). There are, of course, shades of gray as well. Consider a 1-year reset:

*Source: CSI. Calculations by Newfound Research. Assumes portfolio applies 100% notional leverage applied to SPDR S&P 500 ETF (“SPY”) at inception of ETF and reset every 252-days thereafter. Assumes zero cost of leverage. *

Note that in 2008, the debt proportion of our balance sheet spiked up to nearly 90% of our capital. What happened? This is *reset timing risk*. On 4/2008, the portfolio reset, borrowing $92,574 against our equity of $92,574. Over the next year, the market fell approximately 39%. Our total assets tumbled from $185,148 to $114,753 and we still owed the initial $92,574 we borrowed. Thus, our actual *equity* over this period fell an astounding -76.7%.

(It is worth pointing out that if we had considered a “never reset” portfolio that started on 4/2008, we’d have the same result.)

*Frequent readers of our commentary may be wondering, “can this reset timing risk be controlled with overlapping portfolios just like other timing risks?” Yes … ish. On the one hand, there is not a whole lot we can do about the drawdown itself: 100% notional leverage plus a 37% drawdown means you’re going to have a bad time. Where overlapping portfolios can help is in ensuring that resets do not necessarily occur at the worst possible point (e.g. the bottom of the drawdown) and lock in losses.*

As a general rule, we probably don’t want to apply N-times exposure over a time frame an asset class can experience a return of -1/N%. For example, if we want 2x equity exposure, we want to make sure we reset our leverage exposure well before equities have a chance to lose 50% (1/2). Similarly, if we want 3x exposure, we need to reset well before we can lose 33.3% (1/3).

**So, Are They Evil or What?**

We would argue that volatility decay takes the blame when it is not actually the culprit. Volatility decay is nothing more than the math of compounding returns: it happens whether you are levered or not.

The danger of most levered ETFs is more easily explained. If I told you I was going to take your investment, use it as collateral to gain 100% notional exposure to equities, and then *invest* that collateral in equities as well – an asset class than can *easily *lose 50% –what would you say? When put that way, it sounds a little nuts. It really isn’t much more complicated than that.

The reset effect really just introduces a few more nuanced wrinkles. The more frequently we reset, the less risk we run of going bust, as we take risk off the table as our debt-to-equity ratio climbs. That’s how we can avoid complete ruin with 100% leverage in an asset class that falls more than 50%.

On the other hand, the more frequently we reset, the closer we keep the portfolio to the target volatility level, increasing the drag from short-term mean reversion.

We’ve said it before and we’ll say it again: risk cannot be destroyed, only transformed.

But, these things might have their use yet…

**Levered ETFs in a Portfolio**

Held as 100% of our wealth, a 2X daily reset equity ETF may not be too prudent. In the context of a portfolio, however, things change.

Consider, for example, using 50% of our capital to invest in a 2x equity exposure and the remaining 50% to invest in bonds. In effect, we have created 150% exposure to a 67/33 stock/bond mixture. For example, we could hold 50% of our capital in the ProShares Ultra S&P 500 ETF (“SSO”) and 50% in the iShares Core U.S. Bond ETF (“AGG”).

To understand the portfolio exposure, we have to look under the hood. What we really have, in aggregate, is: 100% equity exposure and 50% bond exposure. To get to 150% total notional exposure, we have to borrow an amount equal to 50% of our starting capital. Indeed, at the portfolio level, we cannot differentiate whether we are using that 50% borrowing to lever up stocks, bonds, or the entire mixture!

In this context, levered ETFs become a lot more interesting.

The risk, of course, is in the resets. To really do this, we’d have to rebalance our portfolio back to a 50/50 mix of the 2x levered equity exposure and bonds on a daily basis. If we could achieve that, we’d have built a daily reset 1.5x 66/33 portfolio.

More realistically, investors may be able to rebalance their portfolio quarterly. How far does that deviate from the daily rebalance? We plot the two below.

*Source: CSI. Calculations by Newfound Research. Returns for the Daily Rebalance and Quarterly Rebalance portfolios are backtested and hypothetical. Returns are gross of all fees except underlying ETF expense ratios. Returns assume the reinvestment of all distributions. Cost of leverage is assumed to be equal to the return of a 1-3 Year U.S. Treasury ETF (“SHY”). Past performance is not indicative of future results. The Daily Rebalance portfolio assumes 50% exposure to a hypothetical index providing 2x daily exposure of the SPDR S&P 500 ETF (“SPY”) and 50% exposure to the iShares US Core Bond ETF (“AGG”) and is rebalanced daily. The Quarterly Rebalance portfolio assumes the same exposure, but rebalances quarterly. *

Indeed, for aggressive investors, a levered equity ETF mixed with bond exposure may not be such a bad idea after all. However – and to steal a line from our friends at Toroso Asset Management – levered ETFs are likely “buy-and-adjust” vehicles, not buy-and-hold. The frequency of adjusting, and the cost of doing so, will play an important role in results.

**A Particular Application with Alternatives**

Where levered ETFs may be particularly interesting is in the context of liquid alternatives.

In the past, we have said that many liquid alternatives, especially those offered as ETFs, have a volatility problem. Namely, they just don’t have enough volatility to be interesting.

Traditionally, allocating to a liquid alternative requires us removing capital from one investment to “make room” in our portfolio, which creates an implicit hurdle rate. If, for example, we sell a 5% allocation of our equity portfolio to make room for a merger arbitrage strategy, not only do we have to expect that the strategy can create alpha beyond its fees, but it also has to be able to deliver a long-term return that is at least in the same neighborhood of the equity risk premium. Otherwise, we should be prepared to sacrifice return for the benefit of diversification.

One solution to this problem with lower volatility alternatives is to fund their allocation by selling bonds instead of stocks. Bonds, however, are often our stable ballast in the portfolio. Regardless of how poorly we expect core fixed income to perform over the next decade, we have a high degree of certainty in their return. Asking us to sell bonds to buy alternatives is often asking us to throw certainty out the window.

By way of example, consider the Reality Shares DIVS ETF (“DIVY”). We wrote about this ETF back in August 2016 and think it is a particularly compelling story. The ETF buys the floating leg of dividend swaps, which in theory captures a premium from investors who want to insure their dividend growth exposure in the S&P 500.

For example, if the swap is priced such that the expected growth rate of S&P 500 dividends is 5% over the next year, but the realized growth is 6%, then the floating leg keeps the extra 1%. The “insurance” aspect comes in during years where realized growth is below the expected rate, and the floating leg has to cover the difference. To provide this insurance, the floating leg demands a premium.

A dividend swap of infinite length should, in theory, converge to the equity risk premium. Short-term dividend swaps (e.g. 1-year), however, seem to exhibit a potentially unique risk premium, making them an interesting diversifier within a portfolio.

While DIVY has performed well since inception, finding a place for it in a portfolio can be difficult. With low volatility, we have two problems. First, for the fund to make a meaningful difference, we need to make sure that our allocation is large enough. Second, we likely have to slot DIVY in for a low volatility asset – like core fixed income – so that we make sure that we are not creating an unreasonable hurdle rate for the fund.

Levered ETFs may allow us to have our cake and eat it too.

For example, ProShares offers an Ultra 7-10 Year Treasury ETF (“UST”), which provides investors with 2x daily return exposure to a 7-10 year U.S. Treasury portfolio. For investors who hold a large portfolio of intermediate-term U.S. Treasuries, they could potentially sell some exposure and replace it with 50% UST and 50% DIVY.

As before, the question of “when to reset” arises: but even with a quarterly [rebalance, we think it is a compelling concept.

*Source: CSI. Calculations by Newfound Research. Returns for the S&P 500 Dividend Swaps Index and 50% 2x Daily 7-10 Year US Treasuries / 50% Dividend Swap Index portfolios are hypothetical and backtested. Returns are gross of all fees except underlying ETF expense ratios. Returns assume the reinvestment of all distributions. Cost of leverage is assumed to be equal to the return of a 1-3 Year U.S. Treasury ETF (“SHY”). Past performance is not indicative of future results. The 50% 2x Daily 7-10 Year US Treasuries / 50% Dividend Swap Index assumes a quarterly rebalance.*

**Conclusion**

Leverage is a tool. When used prudently, it can help investors potentially achieve much more risk-efficient returns. When used without care, it can lead to complete ruin.

For many investors who do not have access to traditional means of leverage, levered ETFs represent one potential opportunity. While branded as a “trading vehicle” instead of a buy-and-hold exposure, we believe that if prudently monitored, levered ETFs can be used to help free up capital within a portfolio to introduce diversifying exposures.

Beyond the leverage itself, the daily reset process can introduce risk. While it helps maintain the leverage ratio – reducing risk after losses – it also re-ups our risk after gains and generally will increase long-term volatility drag from mean reversion.

This daily reset means that when used in a portfolio context, we should, ideally, be resetting our entire portfolio daily. In practice, this is impossible (and likely imprudent, once costs are introduced) for many investors. Thus, we introduce some tracking error within the portfolio.

We should note that there are monthly-reset leverage products that may partially alleviate this problem. For example, PowerShares and ETRACS offer monthly reset products and iPath offers “no reset” leverage ETNs that simply apply a leverage level at inception and never reset until the ETN matures.

Perhaps the most glaring absence in this commentary has been a discussion of fees. Levered ETP fees vary wildly, ranging from as low as 0.35% to as high as 0.95%. When considering using a levered ETP in a portfolio context, this fee must be added to our hurdle rate. For example, if our choice is between just holding the iShares 7-10 Year U.S. Treasury ETF (“IEF”) at 0.15%, or 50% in the ProShares Ultra 7-10 Year Treasury ETF (“UST”) and 50% in the Reality Shares DIVS ETF (“DIVY”) for a combined cost of 0.93%, the extra 0.78% fee needs to be added to our hurdle rate calculation.

Nevertheless, as fee compression marches on, we would expect fees in levered ETFs to come down over time as well, potentially making these products interesting for more than just expressing short-term trading views.

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