# Leveraged and inverse ETFs – the exotic side of exchange-traded funds

**Julian Oakland**

Exchange-traded funds (ETFs) are supposed to be simple and straightforward, and for the most part they are, but one group punches well above its weight when it comes to market impact. In this post, I show that leveraged and inverse (L&I) ETFs generate rebalancing flows that: (1) are always in the same direction of the underlying market move; (2) grow significantly with both increasing and inverse leverage; and (3) must be transacted towards the end of the trading day. These features give rebalancing flows the potential to amplify market moves when markets are at their most vulnerable. L&I ETFs do not currently pose a risk to UK financial stability, but this could change if they grow in popularity.

**What are ETFs?**

ETFs are baskets of securities that can be traded continually on public exchanges at market prices, just like shares, and typically track an index, a sector, a commodity, or other assets. The first ETF launched in 1993 tracking the S&P 500 index, and since then, ETFs have grown in number, size, and popularity, enabling investors to gain passive exposure to all sorts of markets without significant management fees. However, as time passed, the ETF universe grew to include actively managed products, including rule-based trading strategies like L&I ETFs.

Turning to the topic of this post, Leveraged ETFs are designed to deliver a **multiple** of the return on a basket **over a one-day period**, typically the underlying basket 2* or 3*, while **Inverse ETFs** are designed to deliver the **opposite** of the return on a basket (basket return -1*). Leveraged inverse ETFs combine the two models and are designed to deliver a **multiple** of the **opposite** return on a basket (typically -2* or -3*). These numbers are the ETF leverage factor and can be found in the ETF name or within its prospectus.

**What do L&I ETFs hold?**

L&I ETFs use derivatives to achieve their aims, and if positively leveraged invest in the underlying assets in addition to entering into long swaps and futures positions to deliver the desired return. These funds also hold cash and money-market instruments to cover losses and margin calls on swaps and futures, and to provide a return to help fund the swaps and futures. The inverse and inverse leveraged funds similarly enter into short swap and futures positions, hold cash and money-market instruments, but hold none of the underlying assets.

**A worked example**:

**Consider a -3* ETF on an index priced at 100 with starting net asset value (NAV) of 100**.

At the start of the day, through a portfolio of cash-like instruments and short futures and swaps, the ETF has an Index exposure of **-300** (ETF leverage factor * NAV)*.*

To illustrate exposure, calculate the profit/loss to a 1% move up in the index: if you are long 100 units worth £1 each, you make: 1%*100*£1 = £1. If you are short 300 units worth £1 each, you make 1%*(-300)*£1 = -£3. **And so for every £1 that the index earns, a -300 exposure to that index earns -£3**.

Depending on the moves in the index during the day, the NAV and exposure of this ETF will change.

**If the index decreases by 5% to 95**, the new NAV = starting NAV + ETF return = 100 + 3*(100 – 95) = 115.

And the exposure is now: -3*(100 – 5) = -285.

**If the Index increases by 5% to 105**, the new NAV = 100 – 3*(105 – 100) = 85.

And the exposure is now: -3*(100 + 5) = -315.

**At the end of each day the ETF return is added to starting NAV to get the NAV for the next day and the portfolio is rebalanced to ensure the leverage is -3* new NAV.**

With NAV = 115 and exposure -285, we need -60 more exposure to maintain -3* leverage, and so need to sell futures/swaps to get to an exposure of -345.

With NAV = 85 and exposure -315, we need +60 exposure to maintain -3* leverage, and so need to buy futures/swaps to get to an exposure of -255.

Table A illustrates rebalancing for common L&I ETF leverage factors, including for a vanilla ETF (leverage = 1), and shows that rebalancing is formulaic, given starting NAV, the leverage factor, and the market move.

**Table A: Calculations for different ETF Leverage, L, with starting NAV N = 100 and index move on the Day D = -5%**

ETF leverage |
Exposure (ETF leverage * NAV) |
ETF return |
New NAV (starting NAV + ETF return) |
New exposure (starting exposure + ETF return) |
Exposure needed (ETF leverage * new NAV) |
Rebalancing (exposure needed – new exposure) |

1 | 100 |
-5 | 95 | 95 | 95 | 0 |

-1 | -100 |
5 | 105 | -95 | -105 | -10 |

2 | 200 |
-10 | 90 | 190 | 180 | -10 |

-2 | -200 |
10 | 110 | -190 | -220 | -30 |

3 | 300 |
-15 | 85 | 285 | 255 | -30 |

-3 | -300 |
15 | 115 | -285 | -345 | -60 |

Formula |
L*N |
L*N*D |
N + L*N*D |
L*N + L*N*D |
L*N + L^{2}*N*D |
N*D*(L^{2} – L) |

I’ll pause here to look at non-intuitive features of L&I ETFs:

**(1) L&I ETFs generate procyclical rebalancing flows: they are always in the same direction as the underlying market move.**

(L^{2} – L) > 0 for all L > 1 and L < 0; therefore, rebalancing flows for these leverage factors always have the same sign as D, and so are always in the same direction as the market move, for both positive or inverse leverage factor: if the underlying index has sold off, all L&I ETFs must sell, and if the index has risen, all L&I ETFs must buy.

**(2) The higher the leverage, and the more negative the leverage, the higher the percentage of starting NAV that needs to be traded to rebalance.**

Using the rebalancing formula, Chart 1 illustrates rebalancing flows to show the power of increasing the leverage and of making it inverse.

**Chart 1: Rebalancing flows for differently leveraged ETFs**

**(3) Rebalancing flows occur towards the end of the trading day, with leverage reset to the closing price of the underlying index.**

Leverage is dynamic, so rebalancing too early in the day risks having to unwind trades at a loss if underlying moves are reversed – the closing price is key here.

**What does this mean in the real world?**

On 13 September 2022, equity markets had their largest sell-off since 2020, with the Nasdaq 100 down 5.2% and the S&P 500 down 4.3%. Using ETF fund data from etfdb.com and equity market data from www.cboe.com, I calculated rebalancing flows for all US equity L&I ETFs on this day to be just over US$20 billion of equities sold, representing around 3.8% of the total value of all S&P 500 shares traded (or the equivalent of just over 100,000 E-mini S&P 500 futures – as an old futures and options trader, these numbers made me gulp!).

Nomura Holdings Inc. estimate L&I ETF rebalancing flows to be US$15.5 billion on the day, and although our precise estimates of the flows differ (it would be great to mark each other’s homework!), we agree that these flows are likely to have amplified the sell-off.

Selling flows hitting a market towards the end of a down day risk a sudden and severe drop in prices and liquidity, and significant losses can occur – a flash crash. If such conditions persist into the market close and beyond, effects can transmit to other jurisdictions (eg in the 1987 crash, portfolio insurance amplified equity market sell-offs).

In the past 50 years there have been two days of equity market declines greater than 10%: the most recent is a down 12% day on 16 March 2020 during the ‘dash for cash’, and the other is the 1987 crash. Based on fund data and own calculations, I estimate this move led to rebalancing flows equal to around 9.4% of the total value of all S&P 500 shares traded, or around 246,000 S&P E-mini futures contracts (8.5% of daily volume). US equity markets closed on their lows that day, with Covid news dominating, but it is possible that L&I ETF rebalancing flows amplified these moves.

**Conclusions**

Rebalancing must happen towards the end of the day to set L&I ETFs up with the correct leverage for the next day, and this can add pressure to weak markets when liquidity is already impaired, amplifying market moves.

These products are currently a tiny part of the UK financial system, with products focusing on UK markets representing <0.2% of the total. As such, financial stability risks to the UK appear limited but could arise through contagion from other markets; so it may be wise to monitor these products.

The L&I ETF segment continues to grow and innovate along with the broader ETF market and any acceleration in growth, or concentration on specific themes, means risks could materialise in the future.

Guarding against complacency, I quote Warren Buffet: ‘…derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal’.

**This post was written while Julian Oakland was working in the Bank’s Capital Markets Division.**

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