# How Leveraged ETFs Can Return Less Than the Market Index

### A Primer on Exotic ETFs

With the popularisation of passive investing via ETFs, it has led some individuals to speculate in the market through exotic ETFs - including leveraged and inverse ETFs.

If there is something to take away from this edition, it is that you should not hold exotic ETFs long-term as its risk profile is likely different than first expected.

**What is an ETF?**

An ETF, or an exchange traded fund, is a basket of securities that aims to track an underlying market index such as the S&P500. A market index is a metric that tracks the performance of assets in a standardised way, with all major financial hubs having an index - e.g. America’s S&P500, Australia’s ASX200, and Japan’s Nikkei225.

It should be noted that ETFs may not track the index price perfectly, due to a variety of factors such as trading or rebalancing costs, timing differences, and expense ratios.

For general passive investments into broad-market ETFs, you are looking for low expense ratios such as VOO with 0.03%. This is paralleled by actively managed funds like ARKK with a 0.75% expense ratio. Currency-hedged ETFs such as VGAD also sees a greater expense ratio than its unhedged counterparts due to added hedging costs.

**A Primer on Leveraged ETFs**

A leveraged ETF aims to generate daily returns that are some multiple (usually 2 or 3 times) of the * daily performance* of the underlying index.

For example, if the S&P500 is up 1% for the day, a 3X S&P500 ETF will be up 3%. Similarly, if the S&P500 is down 2% for the day, a 2X S&P500 ETF fund will be down 4% for the day. Note that fees and borrowing costs associated with leveraged ETFs has been ignored for simplicity.

Based on this description, you might be inclined to think that if the S&P500 is up 15% for the year, then the 3X S&P500 ETF will be up 45%!

However this is not the case, a trap that many naive investors fall victim to. In certain cases, it might be even possible for leveraged ETF to return * less* than the index.

**Arithmetic vs Geometric Means**

To understand this unintuitive result, we must think of returns as a geometric mean, as opposed to an arithmetic mean.

The arithmetic mean is what we intuitively think about when we hear the term ‘average’. It is simply defined as:

This is paralleled by the geometric mean, which is the n-th root of the product of n numbers. For those that have studied finance before, this is the exact mechanism in how we calculate compound interest formulas. We can also easily express the geometric mean in terms of log returns, which is why many of our important financial formulas such as Black Scholes formula include a logarithmic term.

*Essentially as a good rule of thumb, whenever compounding is involved, you should use the geometric mean.*

**The Intuition Behind Geometric Means for Returns**

In order to understand how geometric means interact with leveraged ETF returns, let us consider the following scenario. The index returns 10% in the first period, and -10% in the second period. We have two ETFs that track the index, a standard unleveraged ETF and a 2X leveraged ETF.

If an investor placed $1000 into each of these ETFs respectively, then the returns will be:

**Unleveraged ETF**= $1000 x (1 + 0.10) x (1 - 0.10) = 990**2X ETF**= $1000 x (1 + 0.20) x (1- 0.20) = 960

We can see that in the above example that although the * arithmetic mean return for both investments is 0%*, the actual final value is different as it is dependent on the geometric mean, and the volatility of the prices. Here, the leveraged ETF manages to return less than the index.

**The World of (Other) Exotic ETFs**

There are other exotic ETFs such as inverses, where if the index increases by 1%, the inverse will decrease by 1% for the day. These incur the same issues as leveraged ETFs, but with generally higher expense ratios due to borrowed costs associated with shorting stocks in order to produce the inverse nature. There are also gurus out there advocating shorting inverse ETFs, as overtime, the price gets slammed into oblivion (see the example below). This is also a terrible idea due to the high borrow costs associated with inverse ETFs, due to it being non-liquid.

Commodity or VIX ETFs are even more dangerous given the presence of contango in futures, a scenario where the future price is higher than the spot price. This causes a constant drag in the price of the ETF, making it unsuitable to hold for long-term investments. Commodity ETFs that are not affected by contango are assets such as gold, where the ETF explicitly tracks physical gold as its underlying, as opposed to future contracts.

Moral of the story, don’t touch exotic ETFs unless you * really* know what you are doing. These instruments are intended for trading, rather than for holding in your investment portfolio.

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*In my past life, I was a derivatives trader at a large proprietary-trading firm on Wall Street. Every Sunday, I publish something I learnt there about investing, trading, and decision making. This article was originally published on my personal website christopherjgan.com.*

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