A friend of mine has a knack of homing in on financial folly like a dowsing rod waved above the Atlantic finds water.

This week he proudly informed me that hed bought a short ETF .

He hasnt done so because hes got too much money and thought the financial services industry deserved a donation, via yet another poorly understood product.

No, he believed that holding a short ETF would help protect his portfolio if we are hit by a new bear market.

The reality is rather different.

If my friend holds the short ETF the way he planned to, he could lose money even if the market does fall.

Insurance that costs you money when you expect it to pay out is surely even worse than having no insurance!

In this post Ill explain why my friend was wrong to buy a short ETF to try to insulate his portfolio from a prolonged downturn in the stock market. (Next week well consider what he might have done instead).

What is a short ETF?

A short ETF (also called an inverse ETF) is an Exchange Traded Fund that delivers the opposite of the daily return from its underlying benchmark – often an existing, conventional ETF.

For example, the db X-Tracker FTSE 100 Short Daily ETF from Deutsche Bank (factsheet ) delivers the opposite of the return youd get from the banks normal FTSE 100 ETF tracker.

• If the FTSE 100 falls 1% in a day, the short ETF will rise 1%

• If the FTSE 100 rises 1% in a day, the short ETF will fall 1%

You can also get leveraged short ETFs. which usually have 2x or 3x in the title. As the name implies, these ETFs return two or three times the opposite of the daily return of their benchmark.

Short ETFs are synthetic ETFs with the usual risks youd expect from such securities, such as counterparty risk.

But theres a more fundamental problem with short ETFs – at least in the way many uninformed buyers aim to use them.

The snag: The only way is not up

The problem arises due to the way that the mathematics of compounding works.

Maths will probably not be on your side with a short ETF should you hold it for more than a day or two.

Over one day, short ETFs do what they say theyll do on the tin (not that every buyer reads the label). They deliver the opposite of the benchmarks return.

The trouble comes if you hold a short ETF for more than one day, let alone the weeks or months my friend had planned in order to try to offset any losses from a falling stock market.

Because of the impact of compounding, longer-term returns will be more or less than youd expect from simply summing the inverse of the daily returns.

The impact is especially noticeable in volatile market conditions. Which is to say most market conditions – shares rarely go up or down in a straight line for long.

Examples of how short ETFs work in practice

This is all pretty counter-intuitive, so lets illustrate it with a couple of examples.

Lets say were bearish about the FTSE 100, because its just broken through the 10,000 level and we think thats quite enough for now.

We decide to buy £10,000 worth of a short ETF that delivers the inverse of the FTSE 100.

In other words, if the FTSE 100 falls 1% in a day, well gain 1% on our £10,000, and vice versa.

In addition, my friend – lets call him Harry – decides to go one better, buying a 2x short ETF with his £10,000.

If the market falls 1% in a day, for example, Harry expects to gain 2%.

Example 1: A declining market

We buy our ETFs on Monday. Lets say were even luckier than we deserve given were punting on a single days return from the FTSE. The market falls 2%.

Here are the returns 1 :